This chapter discusses nonparametric multivariate techniques. Time series analysis, which appears to follow the pattern of other least squares procedures, in fact presents special problems. Demographers attempting to project population shifts have long exploited time-series methods originally developed by economists for the analysis of long-term trend and periodic (cyclic and seasonal) fluctuations in economic indicators. Increasingly, social scientists interested in such questions as changes in voting patterns or religious affiliation, or other attitudinal shifts over time are making use of these techniques. To use this linear model and to apply the least-squares machinery, it is necessary to make three assumptions concerning the error terms: (1) the error term has mean zero, (2) the error term has constant variance independent of overall observations, and (3) the error terms corresponding to different points in time are not correlated. If a study requires precise decomposition of time series and examination of periodicities, one may wish to take advantage of spectral analysis. Its strength lies in its potential for providing better forecasts and its avoidance of the inaccuracies that arise from autocorrelation. However, the methods are untested in that relatively few studies exist to examine interpretations.
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