Software for decomposing a time-series into frequency components

Given a time-series X it is often convenient to decompose X into a number of frequency components. For example, if X represents a year of daily pollutant measurements, one might consider breaking X into a long-term series, representing pollutant fluctuations greater than 2 months, and a short-term series, representing pollutant fluctuations less than or equal to 2 months. Such a decomposition could be used to determine the long-term and short-term effects of the pollutant.

The software below is based on the fast Fourier transform and comes in three flavors -- SAS, Splus, and, R (the R and Splus functions are not identical). Each is accompanied by html documentation.

To download the function of macro use the right mouse button on the download links below.

SAS

View macro
Download
Documentation

Splus

View function
Download
Documentation

	

Example Decomposition


        The plot below shows the decomposition of a series.  The top
	curve represents the original series (365 data points in length).
	Here the series has been decomposed into for components -- one
	representing the long-term fluctuations in the series (those
	with cycles greater than 2 months), two mid-term components,
	one representing cycles between	2 months and 1 month and another
	representing cycles between 1 month and 1 week.  Finally there
	is a component representing cycles less	than one month.
	

	The original series is the sum of the four component series.