Statistical Methods in Medical Research 4ed

454 Further regression models
Spells commencing per week
40
30
20
10
New Year
0 0 10
August Bank Holiday Christmas week
20 30 40 50
Week no.
Fig. 12.11 The estimated seasonal trend in weekly spells of sickness absence (1960±64) (reproduced
from Pocock, 1974, with permission from the author and publishers).
is a single sinusoidal curve with a period of 1 year. A comparison of the two curves shows
that the seasonal trend is nearly sinusoidal, but that there are clear departures from the
simple curve, particularly at annual holiday periods.
Spectral analysis
Here the time series is effectively decomposed into an infinite number of periodic
components, each of infinitesimal amplitude, so the purpose of the analysis is to
estimate the contributions of components in certain ranges of frequency. A
spectral analysis may show that contributions to the fluctuations in the time
series come from a continuous range of frequencies, and the pattern of spectral
densities may suggest a particular time-domain representation. Or the spectral
analysis may suggest one or two dominant frequencies, leading to a subsequent
harmonic analysis. A further possibility is that the spectrum may be a mixture of
discrete and continuous components, as, for example, in a time series in which a
harmonic term is combined with an autoregressive error term.
Various features of a spectral decomposition may provide useful summary
statistics for a time series. Gevins (1980), for instance, reviews a considerable
body of work in which spectral analyses of series of human brain electrical
potentials have been used to discriminate between different clinical states or as
a basis for various forms of pattern recognition and cluster analysis.