Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

314 12. PCA for Time Series and Other Non-Independent DataFigure 12.8. Propagation of waves in space and time in Hilbert EOF1, HilbertEOF2, and the sum of these two Hilbert EOFs.distinction between MTM-SVD and standard frequency domain PCA isthat the former provides a local frequency domain decomposition of thedifferent spectral estimates given by the multitapers, whereas the latterproduces a global frequency domain decomposition over the spectral estimates.Mann and Park (1999) describe tests for the statistical significanceof the oscillations found by MTM-SVD using a bootstrap approach, which,it is claimed, is effective for a general, smoothly varying, coloured noisebackground, and is not restricted to red noise as in Allen and Smith (1996)and Allen and Robertson (1996).12.2.5 Cyclo-Stationary and Periodically Extended EOFs(and POPs)The assumption of temporal stationarity is implicit for most of the methodsdescribed in this chapter. In meteorological data there is often a cycle witha fixed period, most commonly the annual cycle but sometimes a diurnalcycle. There may then be stationarity for times at the same point in thecycle but not across different points in the cycle. For example, for monthlydata the probability distribution may be same every April but different in