PREWHITEN procedure

Filters a time series before spectral analysis (A.W.A. Murray).

Option

Parameters

Description

PREWHITEN provides filtering of time series data prior to spectral analysis. Parameters SERIES and FILTERED specify the input and output series, respectively. The filtered series y is given by

y_t = x_t - φ × x_t-1

where x is the input series. (Thus φ = 1 would give first differencing.) The value of φ is specified by the PHI option; the default value of φ=0.99 is often suitable. Alternatively, an empirical approach is to use the value

φ = (1 - 1/L)

where L is the lag at which inspection suggests that the autocorrelation in the series becomes negligible.

   To "recolour" the spectrum of the series after estimation, you can multiply by

1/((1 + φ²) - (2×φ×cos(2π×f)))

where f is the frequency at which the spectrum is estimated.

Option: PHI. Parameters: SERIES, FILTERED.

Method

The procedure uses the FILTER directive with two TSMs defined as follows:

TSM filter; ORDER=!(1,0,0); PARAM=!(1,0,0,PHI)

TSM arima; ORDER=!(0,1,0); PARAM=!(1,0,0)

FILTER SERIES; NEWSERIES=FILTERED; FILTER=filter; ARIMA=arima

The procedure is based on ideas from Granville Tunnicliffe Wilson, University of Lancaster.

Action with RESTRICT

The behaviour is as for the FILTER directive.