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.
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.