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### TS_SMOOTH

TS_SMOOTH

The TS_SMOOTH function computes central, backward, or forward moving averages of an n-element time-series. Autoregressive forecasting and backcasting are used to extrapolate the time-series and compute a moving average for each point.

Note: Central moving averages require Nvalues/2 forecasts and Nvalues/2 backcasts. Backward moving averages require Nvalues-1 backcasts. Forward moving averages require Nvalues-1 forecasts.

This routine is written in the IDL language. Its source code can be found in the file ts_smooth.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 the 11-point central-moving-averages of the time-series: PRINT, TS_SMOOTH(X, 11)`

IDL prints:

`6.65761 6.60592 6.54673 6.47646 6.40480 6.33364`
`6.27000 6.20091 6.14273 6.09364 6.04455 5.99000`
`5.92273 5.85455 5.78364 5.72636 5.65818 5.58000`
`5.50182 5.42727 5.34182 5.24545 5.15273 5.07000`
`5.00182 4.94261 4.87205 4.81116 4.75828 4.71280`

## Syntax

Result = TS_SMOOTH( X, Nvalues [, /BACKWARD] [, /DOUBLE] [, /FORWARD] [, ORDER=value] )

## Return Value

The result is an n-element vector of the same data type as the input vector.

## Arguments

### X

An n-element single- or double-precision floating-point vector containing time-series samples. Note that n must be greater than or equal to 11.

### Nvalues

A scalar of type integer or long integer that specifies the number of time-series values used to compute each moving-average. If central-moving averages are computed (the default), this parameter must be an odd integer greater than or equal to three.

## Keywords

### BACKWARD

Set this keyword to compute backward-moving averages. If BACKWARD is set, the Nvalues argument must be an integer greater than one.

### DOUBLE

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

### FORWARD

Set this keyword to compute forward-moving averages. If FORWARD is set, the Nvalues argument must be an integer greater than one.

### ORDER

An integer or long-integer scalar that specifies the order of the autoregressive model used to compute the forecasts and backcasts of the time-series. By default, a time-series with a length between 11 and 219 elements will use an autoregressive model with an order of 10. A time-series with a length greater than 219 will use an autoregressive model with an order equal to 5% of its length. The ORDER keyword is used to override this default.

## Version History

 5 Introduced