## 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.

### Calling Sequence

Result = TS_FCAST( X, P, Nvalues )

### 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.

IDL prints:

6.94862      6.91103      6.86297      6.77826      6.70282