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Filtering of Multivariate Time Series in the Principal Component Space

Ludwik Liszka

Swedish Institute of Space Physics

Sörfors 634

S-905 88 Umeå

Sweden

### Abstract

Observing a non-stationary physical phenomenon, a time series
of a variable is measured. Usually, there are several variables
which must be measured in order to get complete information about
the process. The experiment results in a set of univariate time
series. The question is whether the conventional method of
handling time series (each one separately), reveals all the
properties of the process.

An alternative method to approach the problem is to treat all
the observed time series as a single multivariate time series.
The principal component method is one of possibilities to
transform the multivariate time series into a different space,
usually of less dimensions. The principal component method offers
an interesting possibility to search for periodical or
quasi-periodical phenomena in the data through filtering of
multivariate data in the principal component space.

The present report shows examples of filtering of multivariate
data in the principal component space: enhancement of waves in
multisensor temperature measurements and removal of instrumental
effects in a sequence of frequency spectra.

The filtering in the principal component space together with
decomposition techniques improves our possibilities to study
complex processes.

IRF Scientific Report 238

January 1997.

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