Time-series analysis--spectral analysis and the search for cycles

In summary, spectral analysis is one analytic strategy for analyzing time-series data. Specifically, spectral analysis enables researchers to detect cyclicity and determines the variance in the data accounted for by cyclic activity. Results describe cycle frequency, period, and amplitude. Unlike cosinor analysis (Lentz, 1990b), spectral analysis does not directly determine peak time nor directly indicate time-ordered relationships, as does autocorrelation (Taylor, 1990). Cyclic relationships between time-series data can be detected using coherency (Gottman & Ringland, 1981), an extension of spectral analysis which is beyond the scope of this article. A word of caution is in order for the uninitiated researcher. Spectral analysis, as well as autocorrelation and cosinor analysis, entails within-subject analysis of single variables. Currently, means of determining relationships between time series, such as cross-correlation and coherency, are bivariate. The need to analyze the pattern of individual variables within-subject, followed by examination of bivariate relationships between pairs of variables, is wisely balanced by limited numbers of variables and small sample size.