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### TS_FCAST

TS_FCAST

The TS_FCAST function computes future or past values of a stationary time-series using a P-th order autoregressive model.

A P-th order autoregressive model relates a forecasted value xt of the time series X = [x0, x1, x2, ... , xt-1], as a linear combination of P past values. The coefficients φ1, φ2, ... , φP 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.

## Examples

`; 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]; Compute and print five future values of the time-series using ten ; time-series values:PRINT, TS_FCAST(X, 10, 5); Compute five past values of the time-series using ten time-series ;values:PRINT, TS_FCAST(X, 10, 5, /BACKCAST)`

IDL prints:

`4.65870      4.58380      4.50030      4.48828      4.46971`
`6.94862      6.91103      6.86297      6.77826      6.70282`

## Syntax

Result = TS_FCAST( X, P, Nvalues [, /BACKCAST] [, /DOUBLE] )

## Return Value

The result is an Nvalues-element vector whose type is identical to X.

## 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.

## Version History

 4 Introduced