TS_FCAST

The TS_FCAST function computes future or past values of a stationary time-series using a P ^th order autoregressive model. The result is an Nvalues -element vector whose type is identical to X .

A P ^th order autoregressive model relates a forecasted value x _t of the time series X = [ x ₀ , x ₁ , x ₂ , ... , x _t-1 ], as a linear combination of P past values.

The coefficients f ₁ , f ₂ , ... , f _P are calculated such that they minimize the uncorrelated random error terms, wt .

This routine is written in the IDL language. Its source code can be found in the file


ts_fcast.pro

in the

lib

subdirectory of the IDL distribution.

Arguments

X

An n -element single- or double-precision floating-point vector containing time-series samples.

P

An integer or long integer scalar that specifies the number of actual time-series values to be used in the forecast. In general, a larger number of values results in a more accurate forecast.

Nvalues

An integer or long integer scalar that specifies the number of future or past values to be computed.

Keywords

BACKCAST

Set this keyword to produce past values (backward forecasts or "backcasts")

DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

Example

Define an n -element vector of time-series samples:

X = [6.63, 6.59, 6.46, 6.49, 6.45, 6.41, 6.38, 6.26, 6.09, 5.99, $

5.92, 5.93, 5.83, 5.82, 5.95, 5.91, 5.81, 5.64, 5.51, 5.31, $

5.36, 5.17, 5.07, 4.97, 5.00, 5.01, 4.85, 4.79, 4.73, 4.76]

PRINT, TS_FCAST(X, 10, 5) ; Compute and print five future values of the time-series using ten time-series values.

IDL prints:

4.65870 4.58380 4.50030 4.48828 4.46971

PRINT, TS_FCAST(X, 10, 5, /BACKCAST) ; Compute five past values of the time-series using ten time-series values.