RainbowStats Command Reference

TextField Area

The text field is where your program begins. Data is sourced from the St. Louis Federal Reserve (FRED). Enter commands here or select from the list.

OIL=DCOILWTICO

Add Button

Submit the current command to your workspace. Pressing Enter performs the same action. Submitted commands appear below the toolbar.

Edit Button

Review and modify your script or scenario. After making changes, re-run the scenario.

Save Scenario

Save your scenario locally (browser storage). It will be available when you return. The server does not store this data.

Load Scenario

Load a previously saved scenario.

Copy Link

Generate a shareable link that reproduces your current scenario.

Import

Import a scenario into your workspace.

Focus

Expand or contract the viewing panel.

POP

Display the raw server response for detailed inspection.

Chat GPT

Analyze the current table or HTML output using ChatGPT.

Clipboard

Copy the current viewing panel to the clipboard.

Clip Compact

Copy a compact version of the viewing panel.

Commands

Open the command reference panel.

Studies

Ability to Save Scripts to your file

Save Study

Save a Study - will prompt for a name

Delete Study

Delete a Current Study

CLEAR

Clear the current tool equation map.

CFTC_FTT_SEARCH

Search for CFTC data

CFTC_TFF_SEARCH("yen")

CFTC_FTT

Get CFTC data

YenPosition=CFTC_TFF("097741","LEV_MONEY_NET","FUTURES_ONLY")

ALIGN_FIPS

Align lists by county FIPS identifiers.

ALIGN_STATES

Align lists by U.S. state identifiers.

BLS_GENDER

Build the server’s occupational earnings comparison by sex.

G=BLS_GENDER(2024,50)
EXTRACT(G,"comparison")

ECB_FAVORITES

Return the installed ECB favorites catalog.

Aliases: ECBFAVORITES

ESTAT_FAVORITES

Return the installed ESTAT favorites catalog.

Aliases: ESTATFAVORITES

EXTRACT_LIST

Collect extractable result objects.

FRED_QD_SERIES

Load a series through the FRED-QD integration.

LIST

Construct a series list.

LIST_BETWEEN

Select a date interval from a series list.

LIST_SINCE

Select observations from a date onward.

Aliases: SERIES_SINCE, SINCE

LOOP_BLS_OCCUPATIONS

Run the server’s BLS occupation loop.

LOOP_BLS_OCCUPATIONS(2024,50)

READ_JSON_SERIES

Read a named time series from a supported JSON file.

Aliases: JSON_SERIES, READJSON, READJSONSERIES

REMOVE

Remove a series from a list.

SAME_DATE_RANGE

SAME_DATE_RANGE(seriesOrList,...) flattens individual series and DataLists in argument order and returns a DataList through DataSeriesList.getSameDateRange(). It can change frequency and date labels, not merely trim endpoints: monthly INDPRO with quarterly GDP produced quarterly output; monthly EIA month-end and FRED month-start inputs were relabeled and could lose extra boundary months. Align full histories before clipping, then inspect frequency, dates, counts and list size. No specific aggregation, interpolation or internal-missing-value policy is promised by this dispatcher; choose explicit frequency conversion/aggregation when it matters. Non-series inputs are ignored rather than rejected. Aliases: SAME_RANGE, COMMON_RANGE.

Aliases: COMMON_RANGE, SAME_RANGE

Aligned=SAME_DATE_RANGE(INDPRO,PAYEMS)
Aligned

SOCRATA

Load a column through the generic Socrata integration.

SOCRATA_DAILY

Load a daily series from a Socrata dataset.

SOCRATA_META

Inspect Socrata dataset metadata.

SOCRATA_SEARCH

Search Socrata datasets.

ADD_ANNOTATION

Add policy annotations or a single chart annotation.

Aliases: ANNOTATE

ADD_ANNOTATION(LINE_CHART(UNRATE),20200301,"March 2020")

ADD_DATE_ANNOTATION

Annotate an explicit date and y value.

Aliases: DATE_ANNOTATE

ADD_DATE_ANNOTATION(LINE_CHART(UNRATE),20200401,14.8,"April 2020")

ADD_NUMERIC_XMARKER

Add an explicitly numeric x-axis marker.

ADD_NUMERIC_XMARKER(SCATTER_PLOT(UNRATE,JTSJOR),4,"Vacancy rate")

ADD_XMARKER

Add an x-axis marker.

Aliases: XMARKER

ADD_XMARKER(LINE_CHART(UNRATE),20200301,"March 2020")

ADD_YMARKER

Add a horizontal y-axis marker.

Aliases: YMARKER

ADD_YMARKER(LINE_CHART(UNRATE),5,"Five percent")

ARG

Construct a named argument.

ARG_LIST

Collect named arguments.

BULLET_SLIDE

Build a bullet slide.

Aliases: BULLETSLIDE

REMOVE_ANNOTATIONS

Remove annotations from a supported chart.

Aliases: CLEAR_ANNOTATIONS

REMOVE_ANNOTATIONS(LINE_CHART(UNRATE))

STR

Return raw argument text as a string.

TEXT

Create a D3 HTML paragraph.

TEXT_SLIDE

Build a text slide.

Aliases: TEXTSLIDE

SANKEY_CHART

Render a Sankey group as a chart.

SANKEY_CHART(CREATE_SANKEY_GROUP(LIST(PAYEMS,INDPRO)))

SANKEY_GROUP

Combine Sankey paths and nested groups.

SANKEY_GROUP(SANKEY_PATH(SANKEY_LINK("A"),SANKEY_LINK("B"),INDPRO))

SANKEY_LINK

Create a Sankey endpoint or link identifier.

SANKEY_LINK("Supply","Demand")

SANKEY_PATH

Create a time-varying Sankey path.

SANKEY_PATH(SANKEY_LINK("Supply"),SANKEY_LINK("Demand"),INDPRO)

ABS

Replace each value with its nonnegative magnitude.

x = DIFF(SERIES_SINCE(INDPRO,20010101))
LINE_CHART(ABS(x))

BEG_DATE

Return the beginning observation date.

BEG_VALUE

Return the first series value.

CURRENT_DATE

Return today as numeric YYYYMMDD.

Aliases: CURRENTDATE

END_DATE

Return the ending observation date.

END_VALUE

Return the last series value.

Aliases: LAST_VALUE

EXP

Raise e to each input value.

x = SERIES_SINCE(INDPRO,20010101)
LINE_CHART(EXP(LOG(x)))

INTERPOLATE_VALUE

Interpolate a series value at a date.

LAG

Apply the existing observation lag.

MAX

Return the maximum series value.

MAX_DATE

Return the date of the maximum value.

MIN

Return the minimum series value.

MIN_DATE

Return the date of the minimum value.

QUANTILE

Return a series quantile.

SIZE

Count series observations.

SYM

Parse a symbolic expression.

TO_ARRAY

Create a numeric array.

TO_NORMAL

Normalize series through the existing normalize method.

Aliases: NORMALIZE, TONORMAL

Animated Line_Chart

Animated Graph a series

Animated_Line_chart(UNRate)

ADD_SERIES_LINE

Add a two-point line to a chart.

ADD_SERIES_LINE(LINE_CHART(UNRATE),20200101,5,20251201,5,"Reference")

ADD_SUBTITLE

Append a subtitle to a line chart.

Aliases: SUBTITLE

ADD_SUBTITLE(LINE_CHART(UNRATE),"Monthly observations")

ANIMATED_BAR_CHART

Animate a rolling bar chart.

ANIMATED_BAR_CHART(LIST(UNRATE,U6RATE))

ANIMATE_SCATTER_PLOT

Animate a rolling scatter plot.

ANIMATE_SCATTER_PLOT(UNRATE,JTSJOR,30)

AREA_LINE_CHART

Shade the area between two series and overlay a third line.

AREA_LINE_CHART(U6RATE,UNRATE,UNRATE)

BAR_CHART

Draw bars for a series or a rolling bar view for a list.

Aliases: BARCHART, BAR_GRAPH

BAR_CHART(SERIES_SINCE(UNRATE,20200101))

BAR_CHARTD3

Compare series using the period bar chart.

Aliases: LATEST_BAR, PERIOD_BAR

BAR_CHARTD3(LIST(UNRATE,U6RATE))

BINARY_SPLIT

Display the existing split-regression chart.

Aliases: BINARYSPLIT, SPLIT_REGRESSION

BINARY_SPLIT(UNRATE,JTSJOR)

COMBINE

Collect operators in the existing combined panel.

COMBINED3

Collect supported objects into a D3 combo.

DISCRIMINANT

Build the existing two-series discriminant chart.

DUAL_LINE_CHART

Draw two series on separate left and right y axes.

Aliases: DUAL_CHART

DUAL_LINE_CHART(UNRATE,U6RATE)

GARCH

Construct the existing GARCH volatility analysis.

GRAPH

Choose the existing recommended chart for a series.

GRAPH(INDPRO)

HIST

Display the distribution of a series as a histogram.

HIST(LOGDIFF(INDPRO))

LINE_CHART

Plot observed values for one or more time series. For a compact view of long histories, see EPICYCLE_LINE_CHART.

Aliases: LINECHART, LINE_GRAPH

LINE_CHART(SERIES_SINCE(INDPRO,20000101))

LINE_GRAPH_WITH_MEAN

Draw a series with its mean line.

Aliases: LINE_CHART_WITH_MEAN, MEAN_CHART, MEAN_LINE_CHART

LINE_GRAPH_WITH_MEAN(UNRATE)

LOGISTIC_CURVE

Return a fitted logistic series.

LINE_CHART(LOGISTIC_CURVE(INDPRO))

LOGISTIC_GRAPH

Display a logistic fit with residuals.

Aliases: LOGISTIC_CHART, LOGISTIC_FIT, LOGISTIC_PLOT

LOGISTIC_GRAPH(INDPRO)

LOGISTIC_GRAPH_BOUND

Display a logistic fit with lower and upper bounds.

LOGISTIC_GRAPH_BOUND(INDPRO,1,200)

LOGISTIC_GRAPH_LOWER

Display a logistic fit constrained by a lower bound.

LOGISTIC_GRAPH_LOWER(INDPRO,1)

LOGISTIC_GRAPH_UPPER

Display a logistic fit constrained by an upper bound.

LOGISTIC_GRAPH_UPPER(INDPRO,200)

MERGE_CHARTS

Merge D3 line or scatter charts.

MERGE_CHARTS("Combined",LINE_CHART(UNRATE),LINE_CHART(U6RATE))

POISSON_CHART

Display the existing shock-probability chart.

POISSON_CHART(INDPRO,5)

POLY_FIT

Build the existing polynomial-fit chart.

POLY_SCATTER

Plot a polynomial relationship with fitted bands.

POLY_SCATTER(UNRATE,JTSJOR,3)

POLY_SPLINE

Evaluate the existing polynomial-spline chart operator.

POLY_SPLINE(LIST(UNRATE,JTSJOR),2,3)

PUBLICATION_CHART

Create the existing publication chart presentation.

Aliases: PUBLISH

PUBLICATION_CHART(LINE_CHART(UNRATE))

ROLL_BETA

Compute a rolling regression slope.

ROLL_CORR

Compute a rolling correlation.

ROLL_QUADRATIC

Display the existing rolling quadratic relationship.

ROLL_QUADRATIC(UNRATE,JTSJOR,36)

ROLL_STD

Compute a rolling standard deviation.

SCATTER_PLOT

Plot two series with the existing fitted confidence band.

Aliases: SCATTERPLOT

SCATTER_PLOT(UNRATE,JTSJOR)

SET_TITLE

Set the title of a supported chart.

SET_TITLE(LINE_CHART(UNRATE),"Unemployment")

SET_TITLE_SUBTITLE

Set a title and append subtitles.

Aliases: SETTITLESUBTITLE, TITLE, TITLE_SUBTITLE

SET_TITLE_SUBTITLE(LINE_CHART(UNRATE),"Unemployment","Monthly observations")

SPLIT_POLY_FIT

Fit polynomial segments around supplied split dates.

SPLIT_POLY_FIT(LIST(UNRATE,JTSJOR),2,20200301)

STACKED_BAR_CHART

Display multiple series as stacked bars.

Aliases: STACKEDBAR, STACKEDBARCHART

STACKED_BAR_CHART(LIST(UNRATE,U6RATE))

TERM_CHART

Compare relative series paths.

Aliases: RELATIVE_COMPARISON, TERM_GRAPH

TERM_CHART(INDPRO,PAYEMS)

VOL_STUDY

Construct the existing volatility-study analysis.

AGGREGATE_TO_PERIOD

Aggregate a series with an explicit period and method.

Aliases: AGGREGATE, AGGREGATETOPERIOD, RESAMPLE

AQS

Load an EPA AQS daily air-quality series.

BOE

Load data through the Bank of England integration.

BOE_SEARCH

Search the BOE data catalog.

CDC

Load data through the Centers for Disease Control and Prevention integration.

CDC_SEARCH

Search the CDC data catalog.

CHINA

Load data through the China data source integration.

CHINA_SEARCH

Search the installed China data integration.

CLIP

Clip series values using numeric bounds.

COMEXT

Load data through the Eurostat Comext integration.

COMEXT_NETWORK

Build a trade network through the server Comext integration.

COMPOUND_SUM

Compute the existing compounded cumulative series.

Aliases: COMPOUNDSUM

COMTRADE

Load data through the UN Comtrade integration.

CUM_SUM

Compute cumulative sums.

Aliases: CUMSUM

DART

Load DART adult fish passage or river-environment data.

DIFF

Calculate changes between consecutive observations.

x = SERIES_SINCE(UNRATE,20010101)
LINE_CHART(DIFF(x))

ECB

Load data through the ECB integration.

ECB_SEARCH

Search ECB data with an optional topic selector.

Aliases: ECBSEARCH, SEARCH_ECB

EIA

Load a U.S. Energy Information Administration series using the exact code returned by EIA_SEARCH(source,topic), for example S=EIA(PET.MCRSTUS1.M). Pass the provider code as raw text; punctuation, underscores and case are part of the code, not arithmetic. Monthly, weekly and annual codes are different series. Inspect EXTRACT(S,"summary") and the source definition for units, coverage, geography and inventory inclusion of the Strategic Petroleum Reserve. EIA does not automatically deflate prices, seasonally adjust observations or construct the paper-specific global inventory series. Do not assume an empty search means no data or substitute US measures for global data without labeling the substitution.

S=EIA(PET.MCRSTUS1.M)
EXTRACT(S,"summary")

EIA_BEST

Select EIA matches through the server integration.

EIA_SEARCH

Search EIA bulk-series metadata within one source and return a table of up to 50 matches; it does not return the observation series. Sources: PET, NG, ELEC, COAL, INTL, EMISS, TOTAL, STEO. Bare tokens or outer quotes are accepted. Use short keywords, geography or distinctive code fragments, for example EIA_SEARCH(INTL,World), EIA_SEARCH(PET,MCRSTUS1), EIA_SEARCH(PET,F000000). Search matching/ranking is provider-specific: do not assume natural-language, Boolean or all-word matching. Empty results do not establish unavailable data; try a shorter term or another source. Copy a returned full code into EIA(code), then verify actual coverage and units. Aliases: EIASEARCH, SEARCH_EIA.

Aliases: EIASEARCH, SEARCH_EIA

EIA_SEARCH(INTL,World)

EQUICENT

Apply the existing equicent transformation to a series or list.

EQUICENT(INDPRO)

ESTAT

Load data through the Japan e-Stat integration.

ESTAT_LOOP

Load Japan e-Stat search results through the server loop hook.

Aliases: ESTATLOOP

ESTAT_SEARCH

Search the ESTAT data catalog.

Aliases: ESTATSEARCH, SEARCH_ESTAT

EUKLEMS_SEARCH

Search the EUKLEMS data catalog.

EUROSTAT

Load data through the Eurostat integration.

EXTRACT

Extract an output from a supported result object.

Aliases: EX

KURTOSIS

Summarize tail behavior using excess kurtosis.

x = LOGDIFF(SERIES_SINCE(INDPRO,20010101))
KURTOSIS(x)

LAST

Return the last requested observations.

Aliases: TAIL

LOG

Take the natural logarithm of positive values.

x = SERIES_SINCE(INDPRO,20010101)
LINE_CHART(LOG(x))

LOGDIFF

RainbowStats LOGDIFF and LOG_DIFF: fractional log changes, explicit lags, series-list transformations, percentage scaling and EXTRACT support.

Aliases: LOG_DIFF

LOGDIFF(US_ZERO(DGS10,10))

MEAN

Calculate the arithmetic average of the supplied observations.

Aliases: AVG

x = SERIES_SINCE(UNRATE,20010101)
MEAN(x)

NYFED

Load data through the Federal Reserve Bank of New York integration.

NYFED_SEARCH

Search the NYFED data catalog.

POSITIVE_PART

Compute the existing positive part transformation.

Aliases: POSITIVE

SEARCH

Search FRED and load up to 20 matching series.

Aliases: FRED_SEARCH, SEARCH_FRED

SEARCH_RID

Load FRED series associated with a numeric release ID.

SERIES_BETWEEN

SERIES_BETWEEN(seriesOrList,start,end) selects a date window from a series or separately from every series in a DataList, returning the corresponding type. Dates are numeric YYYYMMDD, not quoted strings. Both endpoints are inclusive in verified monthly FRED and EIA checks. Selection uses observation timestamps: a month-start endpoint can exclude a month-end-labeled observation in that month. For January 1975 through December 2019 use 19750101,20191231 and inspect the output. This is date selection, not alignment, resampling or missing-value filling. Apply LOGDIFF, DIFF or required lags before clipping when the first desired result needs earlier history. Alias: BETWEEN.

Aliases: BETWEEN

Growth=LOGDIFF(INDPRO)
Sample=SERIES_BETWEEN(Growth,19750101,20191231)
EXTRACT(Sample,"summary")

SERIES_STATS

Return descriptive statistics in a table.

SKEW

Summarize the asymmetry of the supplied observations.

x = LOGDIFF(SERIES_SINCE(INDPRO,20010101))
SKEW(x)

STDDEV

Measure dispersion around the mean.

x = LOGDIFF(SERIES_SINCE(INDPRO,20010101))
STDDEV(x)

TO_ANNUAL

Convert series frequency using toAnnual.

Aliases: TOANNUAL

TO_INDEX

Apply the existing base-increase transformation.

TO_MONTHLY

Convert series frequency using toMonthly.

Aliases: TOMONTHLY

TO_QUARTERLY

Convert series frequency using toQuarterly.

Aliases: TOQUARTERLY

TO_WEEKLY

Convert series frequency using toWeekly.

Aliases: TOWEEKLY

TREASURY

Load data through the U.S. Treasury integration.

TREASURY_SEARCH

Search the TREASURY data catalog.

Aliases: SEARCH_TREASURY, TREASURYSEARCH

UPDOWN_SERIES

Compute the existing up/down count transformation.

USBR

Load a Bureau of Reclamation RISE daily series.

USDA

Load data through the U.S. Department of Agriculture integration.

USDA_SEARCH

Search the USDA data catalog.

USGS

Load a USGS daily observation series.

VOL_DRAG_INDEX

Apply the existing volatility-drag index transformation.

VOL_DRAG_INDEX(INDPRO,2)

CHOLESKY

Create Cholesky Matrix from a list of series.

CholMatrix=CHOLESKY(covvar(LogDiff(List(DGS10,DEXJPUS,DGS30)))))

COL_COUNT

Count matrix columns.

CORR

Compute a correlation matrix or pairwise correlation.

Aliases: CORRELATION

COVVAR

Compute a covariance matrix or pairwise covariance.

DATA

Convert series observations to a data matrix.

INVERT

Compute a matrix inverse.

ROW_COUNT

Count matrix rows.

TRANSPOSE

Transpose a numeric matrix.

ACF_CHART

Display autocorrelation and partial-autocorrelation analysis.

Aliases: ACFCHART, ACF_GRAPH

ACF_CHART(LOGDIFF(INDPRO),24)

ARIMA

Build the existing automatic ARIMA analysis.

EPICYCLES

Display the existing epicycle reconstruction.

EPICYCLES(SERIES_SINCE(INDPRO,20000101),8)

MVTRANSFER_FUNCTION

Build the existing multivariable transfer-function analysis.

PDL_REGRESSION

Fit the existing polynomial distributed-lag model.

Aliases: PDL

p=PDL_REGRESSION(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS)),12,2)
EXTRACT(p,"periodbarchart")

SPECTRUM

Display the power spectrum of a series.

SPECTRUM(LOGDIFF(INDPRO))

TRANSFER_FUNCTION

Build the existing two-series transfer-function analysis.

VAR_MODEL

VAR_MODEL(alignedList,lags) estimates a reduced-form VAR in the supplied series, without automatic differencing, lag selection, unit-root testing or structural shock identification. Align inputs first with SAME_DATE_RANGE and inspect the resulting frequency and dates. For a growth VAR, use LOGDIFF on positive levels and clip after transformation. lags counts lagged observations of every supplied variable. EXTRACT keys: model; chart:n (zero-based equation index); shockdiff:target:shockSeries:shockSize (zero-based indices in list order, 24-step conditional shock-minus-baseline path); dsge (installed VAR(1) conversion only). A shock size uses the supplied variable units: 0.01 in raw LOGDIFF is approximately one percent. Responses in growth units are not cumulative level effects or identified structural elasticities. Unrecognized extract keys fall back to the model table.

Growth=SERIES_BETWEEN(SAME_DATE_RANGE(LOGDIFF(INDPRO),LOGDIFF(PAYEMS)),19750101,20191231)
V=VAR_MODEL(Growth,12)
EXTRACT(V,"chart:0")

VAR_MODEL_FIT

Chart a fitted VAR equation.

ADD_DUMMY_SERIES

Add event or monthly dummy variables using the existing paths.

ADD_DUMMY_SERIES(LIST(INDPRO,PAYEMS),1)

ADD_MONTHLY_DUMMY_SERIES

Append monthly dummy series to a list.

REGRESSION(ADD_MONTHLY_DUMMY_SERIES(LIST(INDPRO,PAYEMS)))

BEST_BIC_REGRESSION

Search candidate regressors and return the selected regression.

r=BEST_BIC_REGRESSION(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS),LOGDIFF(CPIAUCSL)),1)
EXTRACT(r,"model")

BEST_COVID_REGRESSION

Select predictors and fit a COVID-adjusted regression. IMPORTANT: Use only when the estimation sample spans March 2020, preferably with observations before and after COVID onset. Do not apply to pre-COVID-only or post-onset-only samples; use ordinary regression instead.

r=BEST_COVID_REGRESSION(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS),LOGDIFF(CPIAUCSL)),1)
EXTRACT(r,"model")

BEST_REGRESSION

Search candidate regressors and return the selected regression.

r=BEST_REGRESSION(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS),LOGDIFF(CPIAUCSL)),1)
EXTRACT(r,"model")

BOOTSTRAP

Construct the existing bootstrap analysis.

CLINICAL_TRIALS

Load matching clinical-trial records.

Aliases: CT_SEARCH

CONSTRAINED_OLS

Fit constrained ordinary least squares.

Aliases: CONSTRAINED

r=CONSTRAINED_OLS(LIST(INDPRO,PAYEMS),1)
EXTRACT(r,"r2chart")

CPS_WAGE_BANDS

Group CPS wages using supplied numeric boundaries.

DIFFERENCE_IN_DIFFERENCES

Estimate the existing difference-in-differences event analysis.

Aliases: DID, DIFF_IN_DIFF

m=DID(treated,controls,20200301)
EXTRACT(m,"summary")

DISCOVER_MODEL

Run the existing genetic-search, forest and OLS pipeline.

m=DISCOVER_MODEL(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS),LOGDIFF(CPIAUCSL)))
EXTRACT(m,"slideshow")

FIXED_THRESHOLD_REGRESSION

Estimate two regimes at a fixed threshold.

t=FIXED_THRESHOLD_REGRESSION(LIST(UNRATE,JTSJOR),1,4)
EXTRACT(t,"model")

GENETIC_MODEL

Search lagged predictors using the existing genetic model.

m=GENETIC_MODEL(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS),LOGDIFF(CPIAUCSL)))
EXTRACT(m,"slideshow")

GLS

Apply the existing rolling GLS calculation.

r=REGRESSION(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS)))
g=GLS(r,12)
EXTRACT(g,"model")

GROUPED_CROSS_SECTION

Analyze a county cross section grouped by state.

HUBER_REGRESSION

Fit the existing Huber robust-regression selection.

HUBER_REGRESSION(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS)))

INSTRUMENT_HACKING

Demonstrate selection effects from searching over instruments.

m=INSTRUMENT_HACKING(200)
EXTRACT(m,"summary")

IV_REGRESSION

Estimate instrumental-variables regression.

iv=IV_REGRESSION(LIST(Y,X),LIST(Z1,Z2))
EXTRACT(iv,"first_stage_f")
EXTRACT(iv,"beta:1")

LOOP

Expand a wildcard function into a combined presentation.

LOOP(LINE_CHART($$),DGS10,DGS2)

LOOP_ECB

Load a geographic series list after wildcard substitution.

Aliases: ECB_LOOP

LOOP_ECB(EXR.A.$$.EUR.SP00.A,"$$ exchange rate")

LOOP_EURO_ECB

Load a geographic series list after wildcard substitution.

LOOP_EURO_ECB(ICP.M.$$.N.000000.4.ANR,"$$ inflation")

LOOP_OBJECTS

Expand a wildcard function while retaining its result objects.

MODELS=LOOP_OBJECTS(REGRESSION(LIST(LOGDIFF(INDPRO),LOGDIFF($$))),PAYEMS,CPIAUCSL)

LOOP_STATE2

Load a list across the installed U.S. state set.

LOOP_STATE2($$UR)

LOOP_STATE_ANSICODE

Load a list across the installed U.S. state set.

LOOP_STATE_ANSICODE(ATNHPIUS$$A)

LOOP_US_COUNTY

Load a geographic series list after wildcard substitution.

LOOP_US_COUNTY(PCPI$$,"WA")

MATCHED_COMPARISON

Compare matched observations across groups.

m=MATCHED_COMPARISON(LIST(UNRATE,JTSJOR,CPIAUCSL),1,4)
EXTRACT(m,"balance")

PC_ANALYSIS

Build the existing principal-component analysis object.

PRINC_COMPONENTS

Return principal-component series.

QCEW

Load BLS Quarterly Census of Employment and Wages data.

QUANTILE_RANDOM_FOREST

Fit quantile random-forest regression.

m=QUANTILE_RANDOM_FOREST(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS),LOGDIFF(CPIAUCSL)))
EXTRACT(m,"slideshow")

RANDOM_FOREST

Fit a random-forest regression.

m=RANDOM_FOREST(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS),LOGDIFF(CPIAUCSL)))
EXTRACT(m,"slideshow")

REGRESSION

Fit ordinary least squares.

Aliases: REG

r=REGRESSION(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS)))
EXTRACT(r,"slideshow")

REGRESSION_COVID

Fit regression with a COVID-onset adjustment. IMPORTANT: Use only when the estimation sample spans March 2020, preferably with observations before and after COVID onset. Do not apply to pre-COVID-only or post-onset-only samples; use ordinary regression instead.

r=REGRESSION_COVID(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS)))
EXTRACT(r,"model")

RIDGE_REGRESSION

Compare ridge regressions over the existing lambda grid.

Aliases: RIDGE

RIDGE_REGRESSION(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS)))

SIMU_REGRESSION

Collect regression equations into a system.

s=SIMU_REGRESSION(REGRESSION(UNRATE,U6RATE),REGRESSION(INDPRO,PAYEMS))
EXTRACT(s,"residual_covariance")

SPECTRAL_KL

Build the existing spectral Kullback-Leibler analysis.

SPECTRAL_KL(LIST(INDPRO,PAYEMS),LIST(INDPRO,PAYEMS))

STAGGERED_SYNTHETIC_CONTROL

Estimate the existing staggered synthetic-control analysis.

Aliases: SSC

m=SSC(outcomes,20120101,20150101,0)
EXTRACT(m,"event_att")

STATE_FIXED_EFFECTS

Append state fixed-effect variables to a cross section.

STATE_FIXED_EFFECTS(crossSection,"largest")

SUR_REGRESSION

Estimate seemingly unrelated regressions from a regression system.

Aliases: SUR

system=SIMU_REGRESSION(REGRESSION(UNRATE,U6RATE),REGRESSION(INDPRO,PAYEMS))
sur=SUR_REGRESSION(system)
EXTRACT(sur,"summary")

THREE_STAGE_REGRESSION

Build the existing instrumental-variables system estimator.

system=SIMU_REGRESSION(REGRESSION(UNRATE,U6RATE),REGRESSION(INDPRO,PAYEMS))
THREE_STAGE_REGRESSION(system,LIST(CPIAUCSL))

THRESHOLD_REGRESSION

Search for a two-regime regression threshold.

t=THRESHOLD_REGRESSION(LIST(UNRATE,JTSJOR),1,24)
EXTRACT(t,"slideshow")

TRANSITION_MATRIX

Build the existing series transition analysis.

BINOMIAL_DIST

Construct a binomial distribution.

Aliases: BINOMIAL

CAUCHY_DIST

Construct a Cauchy distribution.

DISTRIBUTION_MAP

Build the existing distribution-map presentation.

DISTRIBUTION_MAP(LIST(UNRATE,U6RATE))

EXPONENTIAL_DIST

Construct the existing exponential distribution.

FIT_DIST

Fit a distribution and display its chart.

Aliases: HIST_FIT

FIT_DIST(LOGDIFF(INDPRO))

GAMMA_DIST

Construct the existing gamma distribution.

NORMAL_DIST

Construct a normal distribution.

Aliases: NORMAL

RANDOM

Sample a distribution into a numeric array.

UNIFORM_DIST

Construct the existing uniform distribution.

Option Pricer

Pricing of Simple European/American Options

Option_Pricer

Model Comparison using Characteristic Functions

Pricing of European Options Using Different Models

Option_Modeler

US Government Bond Pricer

Pricing of U.S. Government Bonds

US_GOVT_BOND_PRICER

US Corporate Bond Pricer

Pricing of U.S. Corporate Bonds

US_CORPORATE_BOND_PRICER

US Convertible Bond Pricer

Pricing of U.S. Simple Convertible Corporate Bonds

US_CONVERTIBLE_BOND_PRICER

Structured Product Developer

In Development, a Tool for Evaluating Structured Products

Structured_Product_Developer

Cash Flow Defeasance -- In Progress

Defeasance of a Monthly Series of Cash Flows

Defeasance_model

Spectral Barriers

Calculation of Barrier Options using Eigenfunctions

Spectral_Barriers

ADD_LP_EQUATION

Add a linear constraint to an LP or LP regression.

Aliases: LP_ADD_EQUATION

ADD_LP_EQUATION(P,"X+Y<=4")

DSGE_MODEL

Create an empty linear or affine DSGE model, not a fitted model. Build and retain it with M=DSGE_MODEL(); M=ADD_DSGE_SHOCK(M,"EPS"); M=ADD_DSGE_EQUATION(M,"X=0.5*LAG(X,1)+EPS"); M=COMPILE_DSGE(M); M=SOLVE_DSGE(M). Always assign returned model updates back to M. Set period-zero values with M=SET_DSGE_INITIAL(M,"X",2), then display FORECAST_DSGE(M,12). This is a user-specified linear system, not automatic Bayesian estimation, nonlinear solution or structural identification.

M=DSGE_MODEL()
M=ADD_DSGE_SHOCK(M,"EPS")
M=ADD_DSGE_EQUATION(M,"X=0.5*LAG(X,1)+EPS")
M=COMPILE_DSGE(M)
M=SOLVE_DSGE(M)
M=SET_DSGE_INITIAL(M,"X",2)
FORECAST_DSGE(M,12)

DUALMODEL_LP

Display the existing LP dual table.

DUALMODEL_LP(P)

LINEAR_LP

Create an ordinary linear-programming model.

P=LINEAR_LP(Production)

LP_ADD_PERIOD_EQUATION

Add period-specific constraints to an LP regression.

R=LP_ADD_PERIOD_EQUATION(LIST(Y,X),"Intercept>=0",20200101,20201231)
EXTRACT(R,"model")

LP_REGRESSION

Create a linear-programming regression.

Aliases: LP_OLS

r=LP_REGRESSION(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS)))
EXTRACT(r,"model")

MAX_LP

Maximize an LP objective.

MAX_LP(P)

MIN_LP

Minimize an LP objective.

MIN_LP(P)

MODEL_LP

Return an ordinary LP model.

MODEL_LP(P)

SET_LP_OBJECTIVE

Set the objective of an ordinary LP.

SET_LP_OBJECTIVE(P,3*X+2*Y)

SET_PARAMETER

Set an object parameter.

Aliases: SET

COMPARE_PRESIDENT

Chart the existing presidential-period comparison.

COMPARE_SELECTED_PRESIDENTS

Compare relative paths over selected presidential terms.

Aliases: COMPAREPRESIDENTS

COMPARE_SELECTED_PRESIDENTS(UNRATE,OBAMA,TRUMP)

PARTY_REGRESSION

Fit the existing party-dummy regression.

r=PARTY_REGRESSION(UNRATE)
EXTRACT(r,"model")

PARTY_SERIES

Create the existing Democratic or Republican party-period series.

POLITICAL_ANALYSIS

Build the existing political-period analysis.

PRESIDENT_REGRESSION

Fit regression with presidential-term dummy variables.

r=PRESIDENT_REGRESSION(UNRATE)
EXTRACT(r,"model")

SPECTRAL_TRANSFER_FUNCTION_WELCH

Display Welch spectral transfer-function analysis.

SPECTRAL_TRANSFER_FUNCTION_WELCH(LOGDIFF(INDPRO),LOGDIFF(PAYEMS))

SPECTRAL_TRANSFER_MATRIX

Display a selected spectral transfer-matrix result.

SPECTRAL_TRANSFER_MATRIX(LIST(INDPRO,PAYEMS),PEAK)

INTEREST_RATES

Open the existing interest rates model.

INTEREST_RATES()

MARKETPAGE

Open the existing marketpage model.

MARKETPAGE()

MERTON_DEBT_GDP

Open the existing merton debt gdp model.

MERTON_DEBT_GDP()

Series Analysis

Quick View of a Time Series

series_analysis

Bid Analyzer

Competitive Bidding with Asymmetric Information - Wilson

Bid_Analyzer

Dual Series Analysis

Analysis of Two Time Series, ScatterPlot,Regression etc

dual_series_analysis

Multivariate Series Analysis

Analysis of Mutivariate Time Series,Correlations,Regression etc

multi_series_analysis

Sankey Charts

Chart of various economic flows

Sankey_Charts

PROBIT

Estimate a binary-response probit regression using maximum likelihood and the standard normal cumulative distribution. Use PROBIT(outcome,LIST(X1,X2,...)) to model the probability of an event, such as a recession, default, or economic contraction, from explanatory variables. Returns a ProbitCombo with fitted probabilities, coefficient statistics, classification diagnostics, and D3 visualizations. Use EXTRACT(model,fitted) to obtain fitted probabilities and EXTRACT(model,series) for the original outcome.

PROBIT(outcome,LIST(X1,X2))

RECESSION_PROBIT

Create recession-probability analysis from predictors.

RECESSION_PROBIT(LIST(T10Y3M,LOGDIFF(INDPRO)))

SLIDESHOW

Build an animated slideshow.

Aliases: SLIDE, SLIDES

Series Simulator

Historical Time Series Simulation

series_simulator

Normal Test

Testing the concept of user created simulations

Normal_Test

AFFINE_RATES

Open the existing affine rates model.

AFFINE_RATES()

MORT_DURATION

Transform yield observations using the existing mort duration calculation.

MORT_DURATION(DGS10,10)

MORT_PAYMENT

Transform yield observations using the existing mort payment calculation.

MORT_PAYMENT(DGS10,10)

US_BOND_DURATION

Transform yield observations using the existing us bond duration calculation.

US_BOND_DURATION(DGS10,10)

US_ZERO

Transform yield observations using the existing us zero calculation.

US_ZERO(DGS10,10)

ZCB_CIR_CURVE

Build a model term structure.

ZCB_CIR_CURVE(R0,0.03,TMIN,1,TMAX,10,N,10)

ADD_DSGE_EQUATION

Append a quoted linear or affine equation and return the updated DSGE model. Use M=ADD_DSGE_EQUATION(M,"X=0.5*LAG(X,1)+EPS"); always reassign M. Supports +, -, *, /, parentheses, registered scalar parameters, LAG(variable,1) and LEAD(variable,1); products or division involving endogenous variables must remain linear. Register shocks before compilation. Adding equations invalidates compilation and solution; compile and solve again. Does not automatically linearize nonlinear equations.

Aliases: ADD_EQUATION

M=DSGE_MODEL()
M=ADD_DSGE_SHOCK(M,"EPS")
M=ADD_DSGE_EQUATION(M,"X=0.5*LAG(X,1)+EPS")
M=COMPILE_DSGE(M)
M=SOLVE_DSGE(M)
M=SET_DSGE_INITIAL(M,"X",2)
FORECAST_DSGE(M,12)

ADD_DSGE_SHOCK

Register a named exogenous innovation in a DSGE model. Use M=ADD_DSGE_SHOCK(M,"EPS") and retain the returned model. Register the name before compiling equations that use it. Duplicate shock names are rejected; adding a shock invalidates compiled and solved results, so compile and solve again. Registering a shock does not apply it: FORECAST_DSGE sets future innovations to zero.

Aliases: ADD_SHOCK

M=DSGE_MODEL()
M=ADD_DSGE_SHOCK(M,"EPS")
M=ADD_DSGE_EQUATION(M,"X=0.5*LAG(X,1)+EPS")
M=COMPILE_DSGE(M)
M=SOLVE_DSGE(M)
M=SET_DSGE_INITIAL(M,"X",2)
FORECAST_DSGE(M,12)

COMPILE_DSGE

Compile a defined linear or affine DSGE system into coefficient matrices; return the compiled model. Use M=COMPILE_DSGE(M), then M=SOLVE_DSGE(M). Compilation alone does not create a solved policy rule and clears stale solution results. Retain every model update by reassignment. Inspect compiled matrices with EXTRACT(M,"current_matrix"), EXTRACT(M,"lag_matrix") or other documented matrix keys.

M=DSGE_MODEL()
M=ADD_DSGE_SHOCK(M,"EPS")
M=ADD_DSGE_EQUATION(M,"X=0.5*LAG(X,1)+EPS")
M=COMPILE_DSGE(M)
M=SOLVE_DSGE(M)
M=SET_DSGE_INITIAL(M,"X",2)
FORECAST_DSGE(M,12)

FORECAST_DSGE

Display a deterministic path from a solved DSGE model: F=FORECAST_DSGE(M,12). Requires M=SOLVE_DSGE(M) first; set initial values with M=SET_DSGE_INITIAL(M,"X",2). Horizon is a positive integer number of model periods, not inferred calendar months or quarters. Includes period zero and periods 1 through horizon, with future shocks zero and the solved intercept included. Returns an initial-conditions/line-chart slideshow, not a model: keep F separate from M. Generic deviation-axis wording may need explanation for level equations; SET_TITLE on the slideshow does not retitle its inner chart.

M=DSGE_MODEL()
M=ADD_DSGE_SHOCK(M,"EPS")
M=ADD_DSGE_EQUATION(M,"X=0.5*LAG(X,1)+EPS")
M=COMPILE_DSGE(M)
M=SOLVE_DSGE(M)
M=SET_DSGE_INITIAL(M,"X",2)
FORECAST_DSGE(M,12)

SET_DSGE_INITIAL

Set a finite period-zero endogenous-variable value for a deterministic DSGE forecast and return the model. Use M=SET_DSGE_INITIAL(M,"X",2), retaining M. Endogenous variables without explicit initial values start at zero. Setting initial values preserves an existing solved rule; unknown variable names are checked when forecasting. Units follow the equations: a log deviation of 0.01 can mean approximately 1 percent, while 1 can mean one unit in a level equation. This does not inject a future shock.

M=DSGE_MODEL()
M=ADD_DSGE_SHOCK(M,"EPS")
M=ADD_DSGE_EQUATION(M,"X=0.5*LAG(X,1)+EPS")
M=COMPILE_DSGE(M)
M=SOLVE_DSGE(M)
M=SET_DSGE_INITIAL(M,"X",2)
FORECAST_DSGE(M,12)

SOLVE_DSGE

Solve a user-specified linear or affine DSGE system and return the solved model. Use M=SOLVE_DSGE(M); keep the returned M for initial conditions, extraction and forecasting. Compiles if needed. Requires a nonempty valid system; success depends on equation consistency, rank and solver solution conditions. Inspect EXTRACT(M,"solver_summary"), EXTRACT(M,"stability") and EXTRACT(M,"policy_residual"). Does not estimate parameters or establish causal identification.

M=DSGE_MODEL()
M=ADD_DSGE_SHOCK(M,"EPS")
M=ADD_DSGE_EQUATION(M,"X=0.5*LAG(X,1)+EPS")
M=COMPILE_DSGE(M)
M=SOLVE_DSGE(M)
M=SET_DSGE_INITIAL(M,"X",2)
FORECAST_DSGE(M,12)

ADD_ITEM

Add series to a stored data list.

APPEND

Join values into text.

GET_SERIES

Select one series from a list.

INDEX_100

Apply the existing index-100 transformation.

INTERPOLATE

INTERPOLATE(Y,X) returns a numeric dated series by interpolating Y onto the dates supplied by X. Argument order matters: Y supplies the values and units; X supplies the target observation calendar, not explanatory values. Calls the existing Y.getInterpolatedDates(X) method even when the two inputs have the same frequency. Use INTERPOLATE(radiation,water) to align solar radiation with observed buoy water-temperature dates before regression or transfer-function analysis. Returns a SeriesOperator suitable for REGRESSION, LIST and MVTRANSFER_FUNCTION. Both arguments must be nonempty numeric dated series. Uses linear interpolation in elapsed milliseconds, keeps exact source values at matching timestamps, omits target dates outside Y's span and omits interpolated NaN values. Preserves Y's name, code, units and source and sets the output frequency from X. No extrapolation. It does not create a complete daily calendar unless X supplies one, and does not by itself establish calendar-day lag semantics. Interpolated values are estimates. For SOLAR, direct calculation on X's dates is preferable when available: EXTRACT(SOLAR(X,location),RADIATION).

water=NDBC("42040","WTMP",2000,2025)
location=GEO_LOCATION(29.207,-88.237)
solar=SOLAR(water,location)
radiation=EXTRACT(solar,"RADIATION")
alignedSolar=INTERPOLATE(radiation,water)
reg=REGRESSION(water,alignedSolar)
EXTRACT(reg,"slideshow")

LIST_SUMMARY

Return a summary table for a series list.

MAKE_SIMILAR_SERIES

Create a series using new values and existing dates.

NEGATIVE_PART

Compute the existing negative part transformation.

Aliases: NEGATIVE

ROLL_COV

Compute a rolling covariance.

ROLL_MEAN

Compute a rolling mean.

ROLL_OLS

Compute a rolling OLS fitted value.

SET_FIRST

Move a selected series to the first position.

SET_NAME

Copy a series and give it a new name.

Aliases: NAME

SET_UNITS

Set units on a series copy or Sankey chart.

VELOCITY

Divide one operator value by another.

ZSCORE

Compute the existing z-score transformation.

ADD_LP_EQUATION_RANGE

Add a date-bounded constraint to an existing LP regression.

Aliases: LP_ADD_RANGE

ADD_LP_EQUATION_RANGE(R,"Intercept>=0",20200101,20201231)

ADD_TEXT

Add a text-block paragraph to a D3 HTML panel.

AI_PANEL

Create the existing AI graph analysis panel.

HTML_SLIDE

HTML_SLIDE(html) returns a D3HtmlOperator that renders an HTML fragment and is directly accepted by SLIDE/SLIDESHOW and COMBINED3. Pass one quoted HTML literal or an expression evaluating to StringOperator. Use it for explanatory text, headings, tables, source links and supported inline SVG. Example: intro=HTML_SLIDE("<h1>Seasonal response</h1><p>Source and interpretation.</p>"); slide(intro,EXTRACT(model,"actualvsfitted")). Markup is preserved, not escaped as visible text. Text-only slides should use TEXT_SLIDE. Unlike MAKE_HTML, this returns a D3 panel rather than HTMLObject. Use trusted presentation content. This command does not sanitize HTML, execute JavaScript, fetch images, grant network permissions or export a file. Viewer sanitization and CSP still apply. External images may be blocked; prefer approved RainbowStats-hosted assets with caption/source links. Use simple fragments and inline styles, not complete HTML documents, scripts, iframes or event handlers. Maximum 32000 HTML characters; the MCP script/request/result limits apply separately. Avoid base64 images and oversized tables. One equation per line; put slide(...) last. If HTML_SLIDE is unavailable, refresh command discovery after deploying and registering the core command.

intro=HTML_SLIDE("<h1>Seasonal response</h1><p>Read the diagnostics before interpreting a fit.</p>")
notes=HTML_SLIDE("<h2>Sources</h2><p><a href='https://rainbowstats.com/commandDesc/index.html'>Command reference</a></p>")
slide(intro,notes)

MAKE_HTML

Wrap evaluated string content as HTMLObject.

RECIPES

Build the existing economic recipes slideshow.

ANIMATED_LINE_CHART

Animate a time-series line.

ANIMATED_LINE_CHART(SERIES_SINCE(INDPRO,20200101))

ANIMATE_SANKEY_CHART

ANIMATE_SANKEY_CHART(group) animates dated flows in a SankeyGroup, showing how links change across observations. Build the group using SANKEY_PATH(fromLink,toLink,series) and SANKEY_GROUP(path,...); each path must use a numeric time series. The animation viewer includes a 'Download animated SVG' button. Tell the user that they can download the complete animation as a standalone .svg for embedding in a blog or webpage; the exported SVG does not require the RainbowStats JavaScript renderer. Use consistent source/target identifiers for the same transition throughout the animation. This command returns a scriptable animation, not an ordinary SLIDE/SLIDESHOW panel. Do not interpret aggregate flows as individual-level transitions unless the input data actually measure those transitions.

BOLLINGER

Display Bollinger bands for a series.

BOLLINGER(INDPRO,12,2)

CREATE_SANKEY_GROUP

Create a Sankey group from a series list.

CREATE_SANKEY_GROUP(LIST(PAYEMS,INDPRO))

EXPONENTIAL_GRAPH

Display the existing exponential-fit chart.

EXPONENTIAL_GRAPH(INDPRO)

GAAP_HISTO

Open the existing GAAP histogram-building interface.

GAAP_HISTO()

GEOMETRIC_JS

GEOMETRIC_JS(pList,qList[,ridge]) measures how much two economic regimes differ in their entire fitted multivariate Gaussian distributions—not just their averages or regression coefficients. P and Q are DataLists containing the same variables in the same column order; rows are observations, and the samples may have different dates or sizes. The operator fits each regime's mean vector and covariance matrix, uses shared pooled standardization and optional covariance ridge (default 1e-8), constructs the normalized geometric Gaussian midpoint G proportional to sqrt(P*Q), and returns [KL(P||G)+KL(Q||G)]/2 in nats. The measure is symmetric, nonnegative, and not generally bounded by ln(2). Zero means identical fitted regularized Gaussians; a larger value indicates more distributional separation. It is NOT a p-value, causal estimate, or automatically a structural-break test. Serial dependence and non-Gaussian data require caution. The default four-slide educational presentation explains the statistic, Gaussian geometric midpoint, variable-level mean/variance changes, regularization, and econometric interpretation. EXTRACT(model,"divergence"), EXTRACT(model,"kl_p"), EXTRACT(model,"kl_q"), EXTRACT(model,"means"), EXTRACT(model,"covariance_p"), EXTRACT(model,"covariance_q"), EXTRACT(model,"covariance_g"), EXTRACT(model,"summary"), and EXTRACT(model,"slideshow") are supported. For macroeconomic regime comparisons, use matching transforms (e.g. inflation and rate changes), split each variable into two date windows, build LISTs, then GEOMETRIC_JS(before,after). This is a finite-dimensional Gaussian implementation, not the full infinite-dimensional Hilbert-space theorem.

P=LIST(SERIES_BETWEEN(UNRATE,20000101,20071231),SERIES_BETWEEN(FEDFUNDS,20000101,20071231))
Q=LIST(SERIES_BETWEEN(UNRATE,20100101,20191231),SERIES_BETWEEN(FEDFUNDS,20100101,20191231))
M=GEOMETRIC_JS(P,Q)
SLIDE(M)
EXTRACT(M,"divergence")

PLOT_MATRIX

Plot matrix columns as lines.

PLOT_MATRIX(CURVE,0,1)

SANKEY_CHARTS

Open the existing Sankey chart-building interface.

SANKEY_CHARTS()

SCATTER_LAST

Report the existing SCATTER_LAST placeholder status.

SCATTER_LAST(LIST(UNRATE),LIST(U6RATE),12)

SET_XAXIS

Set the x-axis label.

SET_XAXIS(LINE_CHART(UNRATE),"Date")

SET_YAXIS

Set the y-axis label.

SET_YAXIS(LINE_CHART(UNRATE),"Percent")

SIMU_GRAPH

Display one column of a simulation summary.

SIMU_GRAPH(summary,0)

SPECTRAL_TRANSFER_FUNCTION

Display spectral transfer-function analysis.

SPECTRAL_TRANSFER_FUNCTION(LOGDIFF(INDPRO),LOGDIFF(PAYEMS))

WEIGHT_CHART

Display official CPI or PPI component weights.

Aliases: WEIGHTCHART

WEIGHT_CHART(CPIAUCSL,0.9)

YX_SCATTER

Build the existing y-versus-x scatter view.

YX_SCATTER(LIST(UNRATE,JTSJOR))

AQS_CLASSES

List EPA AQS parameter classes.

AQS_COUNTIES

List EPA AQS counties in a state.

AQS_MONITORS

List EPA AQS monitors for a parameter and date range.

AQS_PARAMETERS

List EPA AQS parameters in a class.

AQS_SEARCH

Search EPA AQS sites.

AQS_SITES

List EPA AQS sites in a county.

AQS_STATES

List EPA AQS states.

AQS_VARIANTS

Inspect available EPA AQS observation variants.

BOND_LIST

Collect parsed bond offerings for tranche-level analysis.

BOND_LIST(IBMNotes,AppleNotes)

CFTC_TFF

Load a CFTC financial-futures position series.

CFTC_TFF_SEARCH

Find CFTC Traders in Financial Futures contracts.

CLINICAL_TRIAL

Load a specific clinical-trial study.

Aliases: CT_STUDY

DART_SEARCH

Search DART station, species and variable information.

DMO

Load data through the UK Debt Management Office integration.

DMO_SEARCH

Search the DMO data catalog.

EDGAR_BOND_TERMS

Read one recent FWP by ticker or CIK and dashed accession. Returns an extractable BondOperator with one row per supported fixed-rate USD tranche with primary-market pricing and Treasury spread in basis points.

EDGAR_BOND_TERMS(AAPL,"0001140361-25-017410")

EDGAR_SEARCH

Search recent SEC filings by ticker or numeric CIK. Optional exact form and row limit (default 25, maximum 200). Earlier SEC history files are outside this search.

EDGAR_SEARCH(IBM)

EUKLEMS

Load data through the EU KLEMS integration.

FRED_QD

Load a FRED-QD series using the existing public spelling.

GET_FRED_DATES

Return the existing FRED release-date table.

GET_FRED_RELEASES

Return the existing FRED release table.

OECD

OECD("agency,dataset,version","selection") loads one OECD Data Explorer time series through the server's cached OECD provider. Pass two literal text arguments: the flow contains agency, dataset ID and an explicit structural version, and selection contains one explicit code for every dimension in the dataset's own dimension order, separated by dots. Quote the flow to protect its commas. Use the OECD catalogue search and the selected dataset's structure/codelists or Developer API query builder to obtain real codes; there is no universal dimension order. Returns an ordinary SeriesOperator. Existing cached data may be served while background refresh runs; a first uncached request may return an empty series while retrieval is queued. Provider values use base units after UNIT_MULT scaling; missing observations remain NaN. Dataset-specific rights and third-party restrictions still apply; retain the source attribution.

OECD("<agency>,<dataset>,<version>","<complete-single-series-dimension-key>")

OECD_SEARCH

OECD_SEARCH("search words"[,limit]) searches the cached OECD dataset catalogue and returns a D3HtmlOperator table. Alternatively, OECD_SEARCH("agency,dataset,version"[,limit]) lists actual series in that dataset, including complete ready-to-run OECD(flow,selection) commands. Append filter words after the flow inside the same quoted string, such as OECD_SEARCH("agency,dataset,version United States",100), to narrow the series list. Series discovery downloads a bounded dataset once and caches distinct observed keys and labels for seven days; keys are not guessed from codelist combinations. Default limit 25; integer literal 1 through 200. Case-insensitive search requires all whitespace-separated words to occur in the agency, dataset ID, name or description. Results include dataset name, description, flow (agency,dataset,version), a list-series command, and optional OECD/structure links. Dataset keyword search identifies datasets; flow search identifies their actual series. Copy the complete command from the series-list table, or inspect OECD Data Explorer for more detail, then use OECD("agency,dataset,version","complete-single-series-dimension-key"). Do not invent selection codes. The catalogue is cached for seven days; first retrieval can require a network request. Network/rate-limit failure without a catalogue produces an explanatory HTML result; stale cached results are identified. Reuse restrictions depend on the dataset.

OECD_SEARCH("income inequality",25)

QCEW_SEARCH

Search the existing industry-code registry.

USBR_LOCATION_META

Inspect Bureau of Reclamation RISE metadata.

USBR_META

Inspect Bureau of Reclamation RISE metadata.

USBR_SANKEY

Chart the existing Elephant Butte annual reservoir budget.

USBR_SEARCH

Find Bureau of Reclamation RISE catalog items.

USGS_META

Inspect USGS station and parameter metadata.

USGS_SEARCH

Search USGS monitoring sites.

WORLD_BANK_CROSS_SECTION

Load a World Bank cross section for a year and indicators.

WORLD_BANK_SEARCH

Search World Bank indicator information.

ARDL

Estimate an Autoregressive Distributed Lag ARDL(p,q) model by OLS: ARDL(y,LIST(x1,x2,...),p,q). Uses p lags of dependent variable y and lags 0 through q of every explanatory variable, after aligning dates. Returns an educational D3 slideshow with labeled coefficients, classical standard errors, actual-vs-fitted levels, residuals, conditional long-run multipliers, error-correction adjustment and equilibrium-error chart. Use slide(model) or EXTRACT(model,slideshow); EXTRACT supports summary, coefficients, long_run, adjustment, fitted, residuals and equilibrium_errors. ARDL does not automatically test cointegration: no bounds test or automatic lag selection is included. Check integration orders (not I(2)), autocorrelation, structural breaks, and endogeneity before long-run or causal interpretation.

Consumption=PCEC96
Income=DSPIC96
Model=ARDL(Consumption,LIST(Income),2,2)
slide(Model)
EXTRACT(Model,"long_run")

ARMA

Fit the existing explicit ARMA specification.

GMM

Estimate two-step linear instrumental-variable GMM with Newey-West HAC moment covariance and robust standard errors. Syntax GMM(y,LIST(x1,x2),LIST(z1,z2)[,hacLags]); optional nonnegative hacLags chooses Bartlett-kernel bandwidth; omitting it selects automatic floor(4*(n/100)^(2/9)); zero means heteroskedasticity-only. Dependent variable and all instruments/regressors are aligned by date, intercepts are included automatically. Returns an educational D3 slideshow via slide(model) and EXTRACT(model,slideshow). Extracts: summary, coefficients, diagnostics, j_test, fitted, residuals. For overidentified models, reports a HAC Hansen J statistic with chi-square p-value. Instrument relevance and exogeneity remain assumptions; HAC does not fix weak or invalid instruments. This is linear IV-GMM, not dynamic-panel or nonlinear GMM.

Y=UNRATE
X=FEDFUNDS
Z1=GS10
Z2=T10Y3M
Model=GMM(Y,LIST(X),LIST(Z1,Z2),12)
slide(Model)
EXTRACT(Model,"j_test")

MONTE_CARLO

Construct the existing multivariate Monte Carlo operator.

SARIMA

Fit the existing explicit seasonal ARIMA specification.

SIMU_FORWARD

Accumulate simulated increments into level paths.

SIMU_MEAN

Return a simulation-summary mean path matrix.

SIMU_STD

Return a simulation-summary standard-deviation path matrix.

SIMU_SUMMARY

Run the existing simulation-summary engine.

STL

STL(series,period[,seasonalWindow[,trendWindow[,robust]]]) performs additive Seasonal-Trend decomposition using LOESS. Returns an extractable STLOperator with a slideshow of observed, trend, seasonal and remainder components, plus settings and diagnostics. Use period 12 for monthly annual seasonality, 4 for quarterly annual seasonality or 7 for complete daily weekly seasonality. Period counts observations, not elapsed years. Default seasonalWindow=7, automatic odd trend window and robust=0. Robust=1 reduces outlier influence. All observations must be finite, strictly date-ordered and regularly spaced; more than two complete cycles are required. No missing dates or values are silently dropped or interpolated. Extract trend, seasonal, remainder, adjusted, fitted and weights as ordinary dated series; also extracts seasonal_strength, trend_strength, reconstruction_error, summary and slideshow. Suitable for employment, production, temperature, river flow and ecological seasonal analysis. Use non-seasonally-adjusted inputs to study seasonality. For proportional seasonality, consider STL(LOG(positiveSeries),period). This is a descriptive single-season smoother, not MSTL or a forecast; historical components can revise.

Employment=SERIES_SINCE(PAYNSA,20000101)
D=STL(Employment,12,7,23,1)
D

TWFE

Estimate static binary-treatment two-way fixed effects (TWFE) for panel policy evaluation: TWFE(outcomes,date1,date2,...,ARG(START_DATE,yyyymmdd),ARG(END_DATE,yyyymmdd)). outcomes is a DataList/LIST with the SAME outcome for different units (states, countries, firms); it is NOT a LIST of Y and explanatory X variables. Supply exactly one absorbing adoption date in YYYYMMDD per unit, in LIST order; use 0 for never treated. Sample-window ARG options are optional. The first observed date on or after adoption has D=1 permanently. Dates are intersected exactly without interpolation; nonfinite outcomes remove entire dates. Units must have matching frequency and outcome units. Fits Y_it=intercept+unitFE_i+dateFE_t+beta*D_it+error_it on the retained balanced panel, with equal cell weights. Reports unit-clustered CR1 SE, t(G-1) confidence interval/p-value, within R-squared, adoption status, residualized-treatment information concentration, and NEGATIVE treated-cell weight diagnostics. CR1 uses full dummy rank K=G+T. Returns an Extractable TWFEOperator whose default display/JSON is an educational D3 slideshow. Use slide(model), EXTRACT(model,slideshow), or individual extracts. Scalar extracts: effect/beta, se, p_value, within_r_squared, nobs, cluster_count, negative_weight_mass (absolute negative sum), negative_weight_share (negative/total absolute mass, fraction 0-1), negative_weight_fraction (negative/all treated cell count, fraction 0-1). Matrix extracts: ci [lower,upper]; coefficient_data [beta,se,t,p,lower,upper]; panel_data [unit_index_1based,date,outcome,D,fitted,residual,D_tilde,treatment_weight]. DataList extracts in input-unit order: actual, fitted, residuals, treatment, weights (D*D_tilde/sum(D_tilde²)), linear_weights (D_tilde/sum(D_tilde²) on all cells), residualized_treatment, residualized_outcome. HTML extracts: summary, coefficients, diagnostics, adoption, weight_summary, cohort_weights, unit_effects. Editable D3 charts: outcome_chart (raw cohort means), weight_chart (positive/negative/net treatment weights by calendar date), fit_chart (actual/fitted for first unit). time_effects returns centered date-FE series; json returns structured JSON text with labeled panel columns. TWFE() or TWFE(HETEROGENEOUS_DEMO) generates a reproducible synthetic panel where all effects are positive but beta is negative; TWFE(CONSTANT_DEMO) recovers +2 with the same design/weights. No network data required for demos. Negative weights can make beta differ in sign from every treatment effect; they do not by themselves prove bias. Causal interpretation requires parallel untreated trends, no anticipation and no spillovers. Unit clustering assumes independent units; few clusters or concentrated treatment information weaken inference. Static TWFE is NOT modern cohort-time ATT, imputation DiD, event-study leads/lags, generic covariate panel regression, or synthetic control. Use DID for a common-date two-group contrast; SSC is a distinct staggered synthetic-control alternative. No analytic/population weights, additional regressors, unbalanced-panel estimation, two-way clustering or wild-cluster bootstrap are implemented.

Aliases: TWO_WAY_FIXED_EFFECTS

Model=TWFE()
slide(Model)

VAR_MODEL_DIFF

Chart the VAR shock-path difference.

VAR_MODEL_SHOCK

Chart the existing shocked VAR path.

VECM_MODEL

VECM_MODEL(levelsList,varLags,rank) estimates a Johansen reduced-rank VECM with unrestricted intercepts in change equations and no deterministic trend. Supply aligned levels or log levels, not pre-differenced inputs. varLags is the levels-VAR order: 12 means 11 lagged differences; 13 means 12. rank remains user supplied, from 1 through number of variables minus 1. Native diagnostics now include rank_test (Johansen trace/max-eigenvalue tests and 90/95/99% critical values for up to 12 variables), unit_root (ADF in input levels with constant and constant+trend, and first differences with constant; AIC lag selection, MacKinnon p-values), lag_selection (unrestricted levels-VAR AIC/BIC/HQIC/FPE on a common sample), autocorrelation (adjusted multivariate portmanteau) and stability (companion roots, allowing the expected k-r unit roots). These checks do not silently replace the fitted rank or lag. Scalar extracts trace_rank_5pct, maxeig_rank_5pct, aic_lag, bic_lag, whiteness_p, largest_transient_root, expected_unit_roots and observed_unit_roots allow programmatic inspection; selected ranks can be zero or full rank and must not be blindly fed back into this supplied-rank command. EXTRACT also supports slideshow, cointegration, adjustment, short_run, fitted, residuals, equilibrium_errors, eigenvalues and diagnostics. Optional extract keys unit_root:24, lag_selection:24 and autocorrelation:36 request diagnostic horizons; use colon-separated integer literals. Fitted values are first differences, not levels or forecasts. A successful fit does not establish cointegration, causal identification or structural stability.

Levels=SERIES_BETWEEN(SAME_DATE_RANGE(LOG(INDPRO),LOG(PAYEMS)),19750101,20191231)
EC=VECM_MODEL(Levels,13,1)
EXTRACT(EC,"slideshow")

BERNOULLI

Construct a one-trial binomial distribution.

CREATE_RANDOM

Sample a distribution into a matrix.

LOGNORMAL_DIST

Construct a lognormal distribution.

PARETO_DIST

Construct the existing Pareto distribution.

POISSON_DIST

Construct the existing Poisson distribution.

STUDENT_T_DIST

Construct the existing Student-t distribution.

BEST_BIC_COVID_REGRESSION

Search candidate regressors and return the selected regression.

r=BEST_BIC_COVID_REGRESSION(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS),LOGDIFF(CPIAUCSL)),1)
EXTRACT(r,"model")

LASSO_REGRESSION

LASSO_REGRESSION(LIST(Y,X1,...)[,lambda[,maxIterations[,tolerance]]]) fits Gaussian lasso by coordinate descent. Y is first; require >=1 predictor and >=3 common finite observations. Omit lambda for automatic expanding-window validation (minimum 30 observations); explicit lambda must be finite and >=0. Objective SSE/(2*n)+lambda*sum(abs(theta)); X is centered and scaled using sqrt(sum((X-mean)^2)/n); Y is centered but NOT scaled; intercept is unpenalized. Reported beta uses original units. Lambda is an absolute penalty in response units, not a percentage, p-value or number of selected variables. Default maxIterations=10000 (1..1000000), tolerance=1e-8 (0<tolerance<=0.01). Stop when maximum KKT violation <= tolerance*max(1,lambdaMax); fail clearly on nonconvergence. LambdaMax=max(abs(Z'*(Y-mean(Y))))/n is reported in summary; lambda>=lambdaMax gives zero slopes. Automatic mode: 5 expanding windows starting at half the sample; 30 log-spaced fractions of each training lambdaMax from 1 to .001 plus zero. Select lowest pooled validation MSE (exact ties prefer larger fraction), then apply winning fraction to full-sample lambdaMax and refit. All fold scaling uses training rows only. Validation uses observed predictors; no automatic forecast lags. Selection score is not an independent test score. Extract validation for the curve and validationtable for all grid scores. Explicit mode runs no search. Align once using getSameDateRange (may convert frequency); reject remaining nonfinite or nonmatching dates. Constant predictors get zero slopes. Collinear/p>=n lasso fits are allowed, but coefficient solutions may be nonunique. Default output is an educational D3 slideshow. EXTRACT keys: model (HTML coefficients, no OLS p-values), summary (training metrics, lambdaMax, convergence), beta (intercept then original-order slopes), standardizedbeta (predictor theta only, no intercept), selected (retained coefficient HTML), data, selecteddata (Y first, may be Y alone), fitted, residuals, actual_vs_fitted, autocorrelation, slideshow, regression (optional full baseline OLS), refit (optional post-selection OLS). OLS extracts may return an error if singular or no predictors remain. Refit is NOT lasso; its inference ignores selection, including HAC. Lasso does not correct serial correlation, establish causality or test significance. Sine/cosine are penalized individually, not as groups.

housing=LOGDIFF(HOUSTNSA)
permits=LOGDIFF(PERMITNSA)
fit=LASSO_REGRESSION(LIST(housing,permits))
fit

LOCAL_PROJECTION

LOCAL_PROJECTION(LIST(Y,shock[,controls...])[,horizon[,lags]]) estimates horizon-wise responses to one unit of a supplied shock. Defaults: horizon 12, lags 1. All list members enter as lag controls. Output is an impulse chart with pointwise 95% Bartlett HAC bands. Extract impulse, model, response, se, lower, upper or slideshow.

housing=LOGDIFF(HOUSTNSA)
permits=LOGDIFF(PERMITNSA)
lp=LOCAL_PROJECTION(LIST(housing,permits),24,2)
lp

LOGIT

Estimate a binary logistic regression for a 0/1 outcome and predictor series using maximum likelihood. Return a D3 presentation with estimated coefficients, standard errors, classification accuracy, and fitted event probabilities. Use LOGIT for recession indicators, defaults, policy events, and other binary outcomes; use PROBIT when a standard-normal latent-response link is preferred. Syntax: LOGIT(outcome,LIST(X1,X2)). Extract fitted probabilities with EXTRACT(model,fitted) and the observed outcome with EXTRACT(model,series).

model=LOGIT(outcome,LIST(X1,X2))
probabilities=EXTRACT(model,fitted)

SEASONAL_REGRESSION

SEASONAL_REGRESSION(LIST(Y,X1,...)[,period[,harmonics]]) compares baseline OLS with OLS augmented by dated sine/cosine pairs, using the same aligned sample. Returns an educational comparison slideshow by default. First series is Y. Default annual period: monthly 12, quarterly 4, weekly 365.2425/7, daily or unknown 365.2425 days. Annual data require an explicit multiyear period. Harmonics default 1, range 1..20; period > 2*harmonics. Alignment uses getSameDateRange and may change frequency; period units follow aligned Y. EXTRACT keys: regression (baseline RegressionOperator), seasonalregression (augmented RegressionOperator), comparison or summarytable (HTML beta comparison), summary (fit metrics and interpretation), harmonicAnalysis:N (fixed-period OLS and each harmonic count through N), slideshow, data (baseline list), seasonaldata (augmented list). Extract a regression first to access its model, hac, fitted, residuals or autocorrelation. Beta differences are descriptive, not tests. Higher R-squared is expected for nested OLS; compare adjusted R-squared, AIC/BIC and residual diagnostics. DW movement is descriptive, not a test that seasonal terms caused autocorrelation. No causal claim or automatic model selection. Spectrum mode: SEASONAL_REGRESSION(list,"spectrum"[,maxCycles=4]); compares K=0..4 by residual Welch peaks, full-fit DW/ACF and expanding-window RMSE with observed X. Requires at least 64 regular observations. Extract summary, coefficients, validation, periods, model:K or acf:K.

Housing=SERIES_BETWEEN(LIST(HOUSTNSA,PERMITNSA),20000101,20241231)
Fit=SEASONAL_REGRESSION(Housing,"spectrum",4)

TVP_REGRESSION

TVP_REGRESSION(LIST(Y,X1,...,X8)[,focusIndex=1]) fits a joint Bayesian regression with random-walk coefficients. One response, 1 to 8 predictors. Focus 1 refers to X1. Compares varying vs constant focus slope by conditional log Bayes factor over four prior scales; the intercept and other slopes may vary under both hypotheses. Discrete variance-ratio priors are summed directly. X is standardized on the initial max(20,3*(predictors+1)) training rows. Require at least 10 additional rows and at most 4000 total. Align via getSameDateRange; require matching increasing dates and finite values. One transition per observation, including across calendar gaps. Default slideshow. EXTRACT beta returns all original-unit smoothed coefficient series. beta:J, chart:J, lower:J, upper:J select a coefficient (0=intercept, 1=X1,...). Other keys: evidence, summary, actual_vs_fitted, fitted, residuals, data, slideshow. Pointwise 90% credible limits condition on the varying model at prior mean 0.01. Smoothed fits use future observations.

Data=SERIES_BETWEEN(LIST(LOGDIFF(INDPRO),LOGDIFF(PAYEMS),UNRATE),20000101,20241231)
Fit=TVP_REGRESSION(Data,2)
Evidence=EXTRACT(Fit,"evidence")

BETA

Return the existing beta matrix for a series list.

FORWARD_FROM_DENSITY

Compute forward/mean from a density grid.

KDE

KDE(series[,bandwidth]) estimates an unweighted Gaussian kernel density from finite observations without choosing a Normal, Gamma or Exponential family. Use for exploratory distributions, skew, multimodality, tail probabilities and simulated draws. Returns an extractable KDEOperator with a default three-slide presentation: normalized histogram with KDE and Normal comparison, KDE CDF, and settings/diagnostics. Optional bandwidth is a positive number in the input's units; omitted bandwidth uses a robust Silverman rule. Extract pdf:x, cdf:x, quantile:p or samples:n:seed for numerical evaluation and reproducible Gaussian-mixture sampling. Also extracts bandwidth, n, dropped, mean, stddev, sample_stddev, median, density, cdf, matrix, summary and slideshow. Nonfinite observations are dropped and counted. Unlike FIT_DIST(series,"CURVE"), this estimates a nonparametric density. Gaussian kernels have unbounded support, no boundary correction, and ignore date ordering. This is a descriptive marginal distribution, not an FFT risk-neutral model or an automatically valid forecast.

Changes=LOGDIFF(SERIES_SINCE(DEXJPUS,20200101))
D=KDE(Changes)
D

KURTOSIS_FROM_DENSITY

Compute kurtosis from a density grid.

MEAN_FROM_DENSITY

Compute mean from a density grid.

MEDIAN

Return the series median.

NORMAL_TEST

Open the existing normal-distribution test object.

SKEW_FROM_DENSITY

Compute skewness from a density grid.

SPECTRAL_ARIMA

Discover an ARIMA/SARIMA or sequential harmonic-plus-ARIMA model using spectral peaks, a differencing screen, ACF/PACF proposals, conditional CSS-AICc and held-out level forecast RMSE. SPECTRAL_ARIMA(series[,period[,maxModels[,horizon]]]); period=0 detects a period, maxModels defaults to 24 (range 4..64), horizon defaults to 12. Uses existing FFTWrapper-backed SpectralAnalysis with a dedicated shared-parameter segmented CSS fitter. Sequential 60-second discovery budget checked during objective evaluation; final refit is additional. Dates are checked: retain all finite observations in explicit contiguous blocks; reset AR/MA and differencing at each gap. Report per-block initialization losses; never compress time or interpolate measurements. Long periods use calendar Fourier terms (K=1 or 2) plus short ARIMA errors. Short periods also test seasonal AR, MA and seasonal differencing. AICc is approximate CSS screening and compared only within identical differencing/seasonality/harmonic families; family winners use a common validation interval. Extract spectrum, candidates, search/coverage, education/notes, model, actual/data, fitted, residuals, forecast (numeric points), forecast_chart (previous 12 observations plus shaded ±1 forecast-error SD), forecast_sd, forecast_lower, forecast_upper, actualvsfitted, autocorrelation and slideshow. Residual lag pairs never cross gaps; pooled portmanteau/PACF diagnostics are explicitly approximate. Educational reference: Box-Jenkins, Time Series Analysis: Forecasting and Control; explains identification, estimation and diagnostic checking. A spectral peak does not uniquely identify ARIMA orders or justify differencing. Residual diagnostics and out-of-sample review remain necessary; no speedup guarantee, no causal interpretation.

water=NDBC("42040","WTMP",2000,2025)
model=SPECTRAL_ARIMA(water)
EXTRACT(model,"slideshow")

STD_FROM_DENSITY

Compute standard deviation from a density grid.

VARIANCE_FROM_DENSITY

Compute variance from a density grid.

BID_ANALYZER

Open the existing bid analyzer model.

BID_ANALYZER()

CAPITAL_STOCK

Calculate the existing capital-stock series.

CAPITAL_STOCK(INDPRO,0.06)

CORP_BOND_DURATION

Transform yield observations using the existing corp bond duration calculation.

CORP_BOND_DURATION(DGS10,10)

CORP_ZERO

Transform yield observations using the existing corp zero calculation.

CORP_ZERO(DGS10,10)

DEFEASANCE_MODEL

Open the existing defeasance model model.

DEFEASANCE_MODEL()

EUROPEAN_FFT

Price European options using the existing characteristic-function FFT model.

CF=SYM(EXP(i*U*((R-0.5*SIG^2)*T)-0.5*SIG^2*U^2*T))
F=EUROPEAN_FFT(CF,S0,100,R,0.03,T,1,ALPHA,1.5,N,4096,ETA,0.25,SIG,0.2,CF_RETURN,1)
EXTRACT(F,"diagnostics")
SLIDE(F)

FORWARD_SERIES

Calculate a historical series of outright forward prices for a fixed maturity from spot prices, annual financing rates and income yields using simple net carry: F(t,T) = S(t) * (1 + (r(t) - y(t)) * days(t,T)/365.25). Each rate independently accepts a constant decimal or a time series; percent-marked series are converted automatically. Supports forward-pricing, cost-of-carry and financing-versus-income scenario analysis. Returns a price series, not forward points, a forecast or a term structure. Syntax: FORWARD_SERIES(spotSeries,startDate,maturityDate,financingRate,yieldRate).

Aliases: FORW_SERIES

FORWARD_SERIES(DEXJPUS,20050101,20050315,IR3TIB01JPM156N,IR3TIB01USM156N)

FWD_FROM_CURVE

Calculate a continuously compounded forward rate from a saved curve matrix.

C=ZCB_VASICEK_CURVE(R0,0.03,TMIN,1,TMAX,10,N,10)
EVAL(FWD_FROM_CURVE(C,T1,2,T2,5))

KKT_PORTFOLIO

Construct the editable constrained-portfolio model.

KKT_PORTFOLIO(LIST(US_ZERO(DGS10,10),US_ZERO(DGS2,2)))

MERTON_IMPLIED_VOL

Infer annualized firm asset, equity and debt return volatility from leverage and a bond spread.

MERTON_IMPLIED_VOL(0.50,10,4.428,80)

OPTION_DELTA_SERIES

OPTION_DELTA_SERIES(Series,start,end,strike,vol,rate,yield,type): Calculate a historical European option delta series, the sensitivity of option premium to a unit change in underlying price. Strike and expiry end are fixed; remaining time decreases at each underlying observation. Volatility, interest rate and yield each accept a decimal number or independently percent-scaled series. Returns a normal series for charts, differences, hedging analysis and multi-leg strategy arithmetic. Type is CALL or PUT. Supports zero volatility and expiry. European exercise only; values are theoretical, per unit of underlying.

OPTION_DELTA_SERIES(DEXJPUS,20050101,20050315,105,0.10,IR3TIB01JPM156N,IR3TIB01USM156N,"CALL")

OPTION_MODELER

Open the existing option modeler model.

OPTION_MODELER()

OPTION_PRICER

Open the existing option pricer model.

OPTION_PRICER()

OPTION_SERIES

OPTION_SERIES(Series,start,end,strike,vol,rate,yield,type): Calculate a historical European call or put premium series using Black-Scholes with continuous yield (Garman-Kohlhagen for currency options). Strike and expiry end are fixed; remaining time decreases at each underlying observation. Volatility, interest rate and yield each accept a decimal number or independently percent-scaled series. Returns a normal series for charts, differences, hedging analysis and multi-leg strategy arithmetic. Type is CALL or PUT. Supports zero volatility and expiry. European exercise only; values are theoretical, per unit of underlying.

OPTION_SERIES(DEXJPUS,20050101,20050315,105,0.10,IR3TIB01JPM156N,IR3TIB01USM156N,"CALL")

REAL_RATES_DEBT_GDP

Compare general-government gross debt/GDP with inflation-adjusted ten-year sovereign yields for thirteen countries, including the United States. Returns a slideshow with linear and quadratic regressions including and excluding Japan, nominal-yield comparisons, data coverage, and a separate ECB headline-HICP sensitivity check. Default snapshot: 2023. Real rates are trailing-headline-inflation yield proxies, not real policy rates, inflation-linked bond yields, or expected ten-year real yields. Syntax: REAL_RATES_DEBT_GDP().

REAL_RATES_DEBT_GDP()

SOLVE_STRIKE

SOLVE_STRIKE(fftModel,longStrike,longQuantity,shortQuantity,targetPremium,type) requires a pricing model built by EUROPEAN_FFT; first consult DESCRIBE_COMMAND("EUROPEAN_FFT") for its construction and supported models. Selects a European option short-leg strike from that FFT pricing grid so longQuantity*price(longStrike)-shortQuantity*price(shortStrike)=targetPremium. Use target 0 for an even-premium or zero-upfront-premium ratio spread, a positive target for a debit or a negative target for a credit. CALL and PUT are supported; both legs have the same type, expiry and pricing model. Optional minStrike,maxStrike restrict the search. Returns a trade result displayed as a compact three-slide slideshow: trade/premiums, expiry P/L chart, premium verification. Use EXTRACT(result,"strike") to obtain the numeric short strike for OPTION_SERIES or OPTION_DELTA_SERIES. Uses linear strike-grid interpolation, verifies the achieved premium, and rejects extrapolation, invalid grids and nonunique targets. Supports strike selection for put/call ratio spreads and same-type verticals; does not price mixed-type collars or solve multiple butterfly wings. COMPLETE MODEL CONSTRUCTION FOR MCP: create CF=SYM(EXP(i*U*(R-Q-0.5*SIG^2)*T-0.5*SIG^2*U^2*T)), then F=EUROPEAN_FFT(CF,S0,100,R,0.03,Q,0.01,T,1,ALPHA,1.5,N,16384,ETA,0.25,SIG,0.20,CF_RETURN,1). Pass F as fftModel, for example SOLVE_STRIKE(F,100*EXP(0.02),1,2,0,"PUT"). S0 is spot, R the quote-currency rate, Q the income yield or FX base-currency rate, T remaining years, SIG annualized volatility; rates and volatility are decimals. N must be a power of two; CF_RETURN=1 means log-return CF. For other distributions, construct the appropriate symbolic CF and parameters through EUROPEAN_FFT, then pass its original result to this solver.

CF=SYM(EXP(i*U*(R-Q-0.5*SIG^2)*T-0.5*SIG^2*U^2*T))
F=EUROPEAN_FFT(CF,S0,156.72,R,0.011199964516129033,Q,0.03630967741935484,T,152/365.25,ALPHA,1.5,N,16384,ETA,0.25,SIG,0.10,CF_RETURN,1)
S=SOLVE_STRIKE(F,155.09088241574716,1,2,0,"PUT")
S

SPECTRAL_BARRIERS

Open the existing spectral barriers model.

SPECTRAL_BARRIERS()

STRUCTURED_PRODUCT_DEVELOPER

Open the existing structured product developer model.

STRUCTURED_PRODUCT_DEVELOPER()

US_CONVERTIBLE_BOND_PRICER

Open the existing us convertible bond pricer model.

US_CONVERTIBLE_BOND_PRICER()

US_CORPORATE_BOND_PRICER

Open the existing us corporate bond pricer model.

US_CORPORATE_BOND_PRICER()

US_GOVT_BOND_PRICER

Open the existing us govt bond pricer model.

US_GOVT_BOND_PRICER()

ZCB_CIR

Calculate a model zero-coupon discount factor.

ZCB_CIR(R0,0.03,KAPPA,0.5,THETA,0.04,SIG,0.01,T,5)

ZCB_VASICEK

Calculate a model zero-coupon discount factor.

ZCB_VASICEK(R0,0.03,KAPPA,0.5,THETA,0.04,SIG,0.01,T,5)

ZCB_VASICEK_CURVE

Build a model term structure.

ZCB_VASICEK_CURVE(R0,0.03,TMIN,1,TMAX,10,N,10)

CHOLESKEY

Compute the existing Cholesky factorization.

COMBINE_MATRIX

Merge numeric matrices by columns.

CREATEMATRIX

Create an editable numeric matrix.

CUM_COL

Compute cumulative sums down a selected column.

GET_COL

Extract one matrix column.

GET_ROW

Extract one matrix row.

INTERP_COL

Interpolate one matrix column onto another matrix’s x values.

SET_COL_NAMES

Return a copy with column names.

UPDATEMATRIX

Update a matrix through EditableUpdater.

UPDATE_OBJECT_MATRIX

Update an object matrix through ObjectMatrixUpdater.

CONFIGURE

Configure a supported object.

Aliases: CONFIG

DESCRIBE_COMMAND

Look up the current syntax, examples, extracts and documentation of a registered RainbowStats command, including aliases.

DESCRIBE_COMMAND("SPECTRUM")

MCP_VERSION

Check the live RainbowStats MCP server version, discovery instructions, tool metadata, UI resource and local command registration.

MCP_VERSION()

OPERATOR

OPERATOR() returns a styled HTML reference in a D3HtmlOperator for RainbowStats arithmetic, series transformations, statistics and EXTRACT capabilities. Consult this reference before writing ratios, percentages, spreads, scaling or arithmetic involving a DataList. Use native expressions directly; there is no need to find a separate arithmetic command for each calculation. Series A supports A+B, A-B, A*B, A/B and A%B with either a series or a numeric scalar B on the right. These operations return a Series. % means percent of, not remainder/modulo or percentage change: numerator % denominator expresses the numerator as a percentage of the denominator. / is division. RainbowStats handles series units/scaling internally; do not add guessed unit multipliers. Use % for a percentage rather than automatically multiplying a ratio by 100. For DataList L, put L FIRST (on the LEFT): L+n, L-n, L*n, L/n, L%n and L+S, L-S, L*S, L/S, L%S apply the operation separately to every member series, returning a DataList. A right-hand series is applied to every member. Do not reverse these to n+L, n*L, S+L or S*L even for commutative arithmetic; SeriesOperator does not implement a DataList right operand. Series-first scalar arithmetic is also the form verified by this reference. L/R supports two equally sized DataLists: member i of L is divided by member i of R, in LIST ORDER, not matched by country, code or name. Check order first. DataList+DataList, DataList-DataList, DataList*DataList and DataList%DataList are not implemented by the supplied DataListOperator. For pairwise percentages of two lists, first verify matching order and size, then use (L/R)*100, taking account of the units of the resulting ratios. Do not infer unsupported types. Series and DataList also implement log, exp, diff, logdiff, lag, last N, sin, cos, tanh, base increase, mean, standard deviation, skewness, excess kurtosis and covariance. Series additionally implements abs, numeric power, sqrt and correlation. Series statistics return numbers; DataList mean/stddev/skewness/ kurtosis return one-column matrices, one row per member. DataList covariance returns its own covariance matrix. Discover the registered transformation command names/signatures before invoking them; Java method names are not DSL syntax. EXTRACT(A,"summary"|"arima"|"cumulative"|"logdiff"|"diff"|"logistic"|"epicycle") accesses a Series. The | notation lists alternatives; pass ONE quoted key. EXTRACT(L,"summary"|"linechart"|"barchart"|"animatedbarchart"|"lastbarchart"| "daily"|"weekly"|"monthly"|"quarterly"|"annual"|"percent") accesses a DataList. Frequency extraction FILTERS members by frequency; it does not resample them. The percent extraction filters percentage-unit series; it does not calculate shares. Other DataList keys: "series:0" (zero-based), "removeseries:0", "setfirst:0", "units:text" (or "unit:text"), "namecontains:text", "endswith:text", "binary_split:y:x" (zero-based y and x indices), or a member series code. Do not use the advertised but unimplemented fredcode key. The supplied DataList slideshow extraction falls through to barchart; use explicit chart keys. Example expressions, where A and B are series and L and R are DataLists: Spread=A-B; Ratio=A/B; Share=A%B; Scaled=A/1000; Adjusted=L-A; Shares=L%A; PairwiseRatios=L/R; EXTRACT(Shares,"lastbarchart"). Use parentheses to make compound formulas explicit. For economic interpretation, check compatible units, frequencies and observation dates; arithmetic is not a substitute for deliberate frequency conversion or missing-data alignment.

SEARCH_COMMAND

Find registered RainbowStats commands by task, keyword, capability, example, or extract key.

Aliases: SEARCH_COMMANDS

SEARCH_COMMAND("spectral seasonality")

ANCOVA

Compare adjusted group means and test equality of slopes on complete CSV rows. X and Y must be numeric.

Aliases: ANCOA

Cats=CROSS_SECTION("https://cran.r-universe.dev/MASS/data/cats/csv")
Fit=ANCOVA(Cats,"Hwt","Bwt","Sex")

CROSS_SECTION

Build a cross section from dated series or a quoted HTTPS CSV URL.

CROSS_SECTION_STUDY_LIST

CS_STUDIES([source]) lists dataset slideshows, analyses and research credits by collection. Filter by collection name or CSV host.

Aliases: CROSS_SECTION_STURY_LIST, CS_STUDIES

DUAL_SERIES_ANALYSIS

Construct the existing two-series analysis object.

EPICYCLE_LINE_CHART

Draw a DataList as approximate Fourier lines, retaining up to 128 components per series by default.

INSPECT

Open the inspector for a named object that supports inspection.

INSPECT(C)

MANN_KENDALL

Tie-corrected Mann–Kendall trend test and exact Sen slope per calendar year. Uses 3 to 3000 unique dated observations.

Trend=MANN_KENDALL(UNRATE)

MULTI_SERIES_ANALYSIS

Construct the existing multiseries analysis object.

SERIES_ANALYSIS

Construct the existing single-series analysis object.

SERIES_SIMULATOR

Construct the existing series-simulation object.

STATE_PCA_EFFECTS

Append state PCA loading coordinates to a county cross section.

DERIV

Differentiate a symbolic expression.

EVAL

Evaluate a symbolic expression with real values.

EVALC

Evaluate a symbolic expression with complex values.

INTEGRAL

Compute a definite integral using Simpson integration.

INTEGRATE

Find a symbolic antiderivative.

SYM_LATEX

Return symbolic mathematics as display LaTeX.

COS

Apply cosine to a number in radians, or to standardized values of a series or each series in a list. Series results are bounded from -1 to 1 and labeled Index.

COS(1)
x = DIFF(SERIES_SINCE(UNRATE,20010101))
LINE_CHART(COS(x))
LINE_CHART(COS(LIST(x,DIFF(SERIES_SINCE(U6RATE,20010101)))))

GAMMA

Evaluate the mathematical gamma function for a supported input.

GAMMA(5)

POW

Raise a supported operator value to a power.

SIN

Apply sine to a number in radians, or to standardized values of a series or each series in a list. Series results are bounded from -1 to 1 and labeled Index.

SIN(1)
x = DIFF(SERIES_SINCE(UNRATE,20010101))
LINE_CHART(SIN(x))
LINE_CHART(SIN(LIST(x,DIFF(SERIES_SINCE(U6RATE,20010101)))))

SQRT

Calculate the square root of each value.

x = SERIES_SINCE(INDPRO,20010101)
LINE_CHART(SQRT(x))

TANH

Apply hyperbolic tangent directly to a number, or to standardized observations of a series or each series in a list. Creates bounded nonlinear features, compresses extremes, and preserves ordering. Series results use Index units.

TANH(1)
x = DIFF(SERIES_SINCE(UNRATE,20010101))
LINE_CHART(TANH(x))
LINE_CHART(TANH(LIST(x,DIFF(SERIES_SINCE(U6RATE,20010101)))))

LIST_SCENARIOS

List stored scenario files.

VIEW_SCENARIO

Read a stored scenario.

GEO_LOCATION

Create a reusable geographic location object from latitude and longitude, optionally elevation in meters and an IANA time zone. Use it with SOLAR to derive daylight duration, sunrise, sunset, solar noon, solar declination, solar elevation and extraterrestrial radiation for the dates of an existing economic, environmental or ecological time series. Useful in photoperiod, salmon migration, hydrology, agriculture, climate and solar-energy research.

location = GEO_LOCATION(47.6062,-122.3321,50,"America/Los_Angeles")

SOLAR

Compute date-aligned astronomical solar variables at any geographic location using the observation dates of an existing time series. Extract DAYLIGHT, SUNRISE, SUNSET, SOLAR_NOON, DECLINATION, MAX_ELEVATION and RADIATION. Supports research on photoperiod and salmon migration, water temperature, seasonal biology, agriculture, hydrology, climate, evaporation and solar-energy potential. No external API or weather station is needed. RADIATION is extraterrestrial solar energy, not measured surface sunlight.

salmon = DART("BON","CHINOOK")
location = GEO_LOCATION(45.64436,-121.94075,24,"America/Los_Angeles")
solar = SOLAR(salmon,location)
daylight = EXTRACT(solar,"DAYLIGHT")
radiation = EXTRACT(solar,"RADIATION")

FIT_SOLAR_ELLIPSE

FIT_SOLAR_ELLIPSE(response,location[,bootstrap]) or FIT_SOLAR_ELLIPSE(response,solarSeries[,bootstrap]) returns an Extractable SolarEllipseObject in ecostats. Fits each coordinate against an intercept and annual calendar cosine/sine (365.2425 elapsed days), producing a time-ordered seasonal ellipse rather than an OLS line or covariance confidence ellipse. location is a GeoLocationOperator: calculate extraterrestrial radiation on response dates. An explicit solarSeries is matched by exact timestamps with no interpolation or frequency conversion; UTC calendar is used. FIT_SOLAR_ELLIPSE(response) attempts EXTRACT(response,geolocation), suitable for native NDBC series when preserved by the dispatcher. Reports means, amplitudes, signed wrapped phase delay in days (positive=response follows solar), amplitude ratio, in-sample R-squared/RMSE, standardized axes, rotation, eccentricity, foci, area and direction. Geometry is centered on fitted means and scaled by observed paired-sample standard deviations; axes/foci depend on this metric and are not physical orbit parameters. Default bootstrap=199, range 0..499; approximate whole-calendar-year cluster percentile intervals require at least five well-covered years. Assumes exchangeable years; no causal inference or forecast validation. Minimum 60 finite pairs, 1.5 years of span and ten represented months; strictly increasing dates, at most one observation per calendar day; maximum 100000 input observations and 10 million pair-replicates. Extract model/summary, scatter/scatterfit (native D3 observed points with fitted loop in original units), ellipse/chart, geometry/foci, animation, svg, yearly, intervals, diagnostics/coverage, education/notes, actual/data, solar, fitted, solar_fitted, residuals, actualvsfitted, delay_days, amplitude_ratio, response_amplitude, solar_amplitude, slideshow. Animation is a self-contained SVG annual fitted trajectory with month readouts and an animated SVG download link; daylight is shown when location is supplied. Location-only extracts daylight (hours), daylight_change (signed minutes/day from a centred one-day finite difference), declination and max_elevation (degrees) reuse SolarOperator.calculate; negative daylight_change means losing daylight. Residuals are dated response minus its harmonic fit, suitable for SPECTRAL_ARIMA. Additional harmonics, trend and changing response are not fitted. Solar radiation here is potential extraterrestrial energy, not measured surface sunlight.

water=NDBC("42040","WTMP",2000,2025)
location=EXTRACT(NDBC_META("42040"),"geolocation")
loop=FIT_SOLAR_ELLIPSE(water,location)
EXTRACT(loop,"slideshow")

NDBC

NDBC means NOAA National Data Buoy Center. Retrieve marine buoy and coastal station observations as a native daily numeric time series. NDBC(station,variable[,startYear,endYear[,minSamples]]) supports water temperature WTMP, air temperature ATMP, wind speed WSPD, wind direction WDIR, gust GST, significant wave height WVHT, wave periods DPD/APD, mean wave direction MWD, pressure PRES, dew point DEWP, visibility VIS, pressure tendency PTDY and water level TIDE when reported. EXTRACT(result,GEOLOCATION) returns a GeoLocationOperator for SOLAR(result,location), using catalogue coordinates with UTC and zero-meter defaults. Use NDBC_SEARCH to find station IDs and NDBC_META for station details. Historical files are saved by requested station and year and stitched into long series. Dates are UTC; daily means are sample-weighted; directions use circular means; missing values and days are omitted. Default years: 2000 through today. Use EXTRACT(result,coverage) to inspect missing days, archive availability, warnings and sources before modeling; EXTRACT(result,data) gives daily values and sample counts; raw gives original timestamps. Ecological uses include seasonal ocean warming, thermal exposure, storm cooling, coastal habitat conditions and lagged relationships with fish returns. Buoy measurements do not directly establish harmful blooms, oxygen depletion or ecological causation. Remove seasonality before interpreting unusual warmth as a marine heatwave. Alias NOAA_BUOY.

Aliases: NOAA_BUOY

water=NDBC("42040","WTMP",2000,2025)
water

NDBC_META

Describe a NOAA National Data Buoy Center (NDBC) station by ID: station name, coordinates/location, owner, platform type and operational notes, with a link to NOAA's station history. NDBC_META(station) uses the station catalogue; it does not infer sensor depths, exact available variables, period of record or continuous coverage. Check NOAA history and EXTRACT(NDBC(...),coverage) for those questions. Useful before ecological temperature, storm and fisheries analysis. Results implement Extractable. EXTRACT(result,geolocation:n) returns a GeoLocationOperator for zero-based displayed row n, usable by SOLAR. EXTRACT(result,station_id:n) returns a station ID usable by NDBC. Other row extracts: name, latitude, longitude, owner, type, hull, payload, timezone, notes, location_text, history_url and station_url, with :n appended. Unindexed row keys require exactly one match; no silent first-match selection. count returns row count; table returns the display. geolocations and station_ids return ordered extractable collections; EXTRACT(collection,0) retrieves the first item. Collections are not numeric DataLists. Catalogue coordinates are not historical positions. Geolocation defaults elevation to zero and timezone to UTC; timezone extract preserves the original NOAA code. Missing coordinates raise a descriptive error without dropping rows.

Aliases: NOAA_BUOY_META

NDBC_META("42040")

NDBC_SEARCH

Search NOAA National Data Buoy Center (NDBC) station catalogue by station ID, name, location, owner, type or notes. NDBC_SEARCH(query) returns an Extractable station-results operator with a readable station table, history links and example NDBC calls. Case-insensitive; all query words must match. Use location names or state abbreviations such as Cape Elizabeth, WA, or Dauphin Island; state names are not automatically translated to abbreviations. Search downloads only the small station catalogue, not observation data for the network. Inactive and historical stations may appear. A match does not guarantee current operation, temperature observations, or complete history. Use NDBC_META and NDBC, then inspect EXTRACT(result,coverage). Results implement Extractable. EXTRACT(result,geolocation:n) returns a GeoLocationOperator for zero-based displayed row n, usable by SOLAR. EXTRACT(result,station_id:n) returns a station ID usable by NDBC. Other row extracts: name, latitude, longitude, owner, type, hull, payload, timezone, notes, location_text, history_url and station_url, with :n appended. Unindexed row keys require exactly one match; no silent first-match selection. count returns row count; table returns the display. geolocations and station_ids return ordered extractable collections; EXTRACT(collection,0) retrieves the first item. Collections are not numeric DataLists. Catalogue coordinates are not historical positions. Geolocation defaults elevation to zero and timezone to UTC; timezone extract preserves the original NOAA code. Missing coordinates raise a descriptive error without dropping rows.

Aliases: NOAA_BUOY_SEARCH

NDBC_SEARCH("Cape Elizabeth")

WORLD_GDP

WORLD_GDP(indicator,year[,fit,xScale,yScale]) returns one country scatter chart comparing a World Bank WDI outcome with GDP per capita, PPP (constant 2021 international dollars). Arguments resolve through the command tool: quoted strings, numeric expressions and assigned variables are supported. Defaults: fit=log, xScale=log, yScale=linear. Fits: log means Y=a+b*ln(GDP); linear means Y=a+b*GDP; loglog means ln(Y)=a+b*ln(GDP); none omits the fit. X and Y display scales independently accept log or linear; changing display scale does not change the model. Exact-year ISO3 country alignment, no aggregates, interpolation or carry-forward. Missing/nonfinite pairs and nonpositive GDP are excluded; logarithmic outcomes also exclude nonpositive Y. Chart includes regression equation, R squared, sample size, country hover values and World Bank attribution. Unweighted OLS is descriptive, not causal. For loglog, R squared/residuals are in log-outcome units. EXTRACT keys: chart, regression, model, summary, data, residuals, outliers, source, sources, metadata, license. Use WORLD_BANK_SEARCH to find outcome codes. Suitable for markets JSON command fields; no time-window placeholder is needed.

Aliases: WORLD_BANK_CHART_GDP

WORLD_GDP("SP.DYN.LE00.IN",2023)