SIN — Sine transformation

Syntax

SIN(number)
SIN(series)
SIN(seriesList)

Inputs and results

A NumberOperator returns Math.sin(number), with the input interpreted in radians. A SeriesOperator applies Math.sin(z) to every observation, where z = (value - mean) / standardDeviation. A DataListOperator applies the series transformation separately to each member, using that member's own mean and standard deviation.

Series results preserve observation dates and frequency, use the label Index, and range from -1 to 1.

Examples

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

Notes and interpretation

Series inputs are standardized automatically; number inputs are used directly. One standard deviation from a series mean corresponds to one radian. The periodic transformation is nonlinear and many-to-one: different input values can produce the same output. It can be explored as a bounded nonlinear feature in stationary-series analysis, but does not by itself identify seasonality or make a series stationary.

Standardization requires a finite, positive standard deviation. Constant series cannot be standardized. Sample mean and standard deviation are calculated over the supplied input series; restrict the input period first when needed. For forecasting or backtesting, computing these statistics over the full sample can introduce future information.