RainbowStats ยท Time-series commands

ARDL

Autoregressive Distributed Lag regression with interpretable short-run and conditional long-run effects.

Syntax

ARDL(y,LIST(x1,x2,...),p,q)

p is the number of lags of y (at least 1). q is the maximum lag of each predictor (0 or greater); current X values are included. The same q applies to all X series.

Example

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

Output

Returns an ARDLOperator whose default JSON serializes the D3 slideshow. Extracts: slideshow, summary, coefficients, long_run, adjustment, fitted, residuals, equilibrium_errors.

Interpretation

ARDL estimates one dependent variable using its own lagged levels and current/lagged explanatory levels. The implied long-run multiplier for predictor X is the sum of its lag coefficients divided by one minus the sum of the dependent-variable lag coefficients. The adjustment coefficient is the sum of the dependent-variable lag coefficients minus one. The error-correction representation is an algebraic reparameterization, not a cointegration test.

Use levels when studying long-run relationships. Check that none of the variables is I(2), choose lag orders carefully, inspect residual autocorrelation and stability, and conduct a valid bounds test before claiming cointegration. The implementation uses classical OLS standard errors, not HAC.

Available extracts

Save the command result in a variable, then use EXTRACT(result, "key"). Availability can depend on the input form and fitted model.

In indexed patterns such as beta:n, replace n with the required index.