The genetic analysis of repeated measures. II. The Karhunen-Loève expansion.

A genetic analysis of time series, i.e., long stretches of repeated observations such as typically encountered in psychophysiological research, raises problems that are related to the proper handling of autocorrelat ion. Fo r instance, a standard univariate technique such as A N O V A of repeated measures is based on the assumption of compound symmetry of the autocorrela t ion function. This means that observations at different time points t and t' should always have the same correlat ion irrespective of the lag t' t. Box (1954) indicated that even moderate deviations from compound symmetry in an ANOVA of repeated measures lead to great distort ions in probabili ty levels for comparisons between time points. In general, the autocorrelat ion of a time series will be some decreasing funct ion of the lag t' t (cf. Box and Jenkins, 1976) and consequent ly will lack compound symmetry. Such lag-dependent autocorrelat ions are