This chapter proposes that the major goal of any functionalist inquiry is to clarify the nature, determinants, and consequences of a given timeseries process. It begins by arguing that, although social scientists tend to state generalizations in linear form, it is likely that the most important time-series processes are nonlinear. Therefore we must develop a taxonomy of time series: We must be able to classify a given variable as having stationarity through time–a constant mean, constant variance, and no autocorrelation–or as departing from stationarity in any of a large number of linear and nonlinear patterns; next, we must examine the structural determinants and consequences of any given pattern, stationary or otherwise. The chapter then provides an extended discussion of Malthus's theory of population in which it is shown that the original version of this theory would have been applicable only to societies in which the basic demographic processes were more or less stationary through time, and that the efforts of recent neo-Malthusians have been directed, appropriately, toward explaining departures from stationarity in these same processes. Throughout this chapter there is an implicit recognition that the form of a time series provides clues as to the sort of theoretical explanation that would be appropriate: In general, stationary series require stability models, and nonstationary series require growth models (cf. Kasarda, 1974).

A major deficiency of social theory is its tendency to neglect relationships that depart from rectilinearity. In Hage's words (1972:92), “… sociology has generally relied upon linear or straight-line operational linkages,” although recent work shows an increasing willingness to search for nonlinear relationships, of which Hage notes several examples.