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

Note that 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.

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.

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_SMOOTH(X, 11) ; Compute the 11-point central-moving-averages of the time-series.

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