Spectral analysis and the application of filters in the examination of business cycles

Abstract

The spectral analysis enables division of a given time series into
components characterised by a different frequency of fluctuations. Therefore,
it is possible to use it for the extraction of the cyclical component from
macroeconomic data. The most popular method of analysing components
with a specific frequency is the use of Hodrick-Prescott, Baxter-King and
Christiano-Fitzgerald filters, which are the subject of this paper. Empirical
applications showed very little difference in the operation of the filters. In
particular, they indicate that the results obtained for the BK and the CF
filters do not differ significantly from each other and are similar regardless
of whether they are used for data containing the seasonal component or not.
Although the BK and the CF filters should efficiently separate the cyclical
component from the seasonal one, they work better when filtered data is
seasonally adjusted. In the case of not adjusted data, they mix the cyclical
component with the seasonal one.