## 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 f1, f2, ... , fP 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.

### 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.

### 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
```

Introduced: 4.0