You must remember this: Dealing with long memory in political analyses

Abstract

Recent research by Box-Steffensmeier and Smith (Box-Steffensmeier, J.M., Smith, R.M., 1996. The dynamics of aggregate partisanship. American Political Science Review 90, 567–580; Box-Steffensmeier, J.M., Smith, R.M., 1998. Investigating political dynamics using fractional integration methods. American Journal of Political Science 42, 661–689) has alerted scholars to the problems involved in the analysis of fractionally integrated time series. This paper pursues this line of inquiry by compiling evidence on the time series properties of a number of common variables used in political research, including macropartisanship, presidential approval, the monthly and quarterly index of consumer sentiment, percentage liberalism in Supreme Court decision making, and others. In applying a variety of formal tests to these series, we fail to reject hypotheses of random walk or fractionally integrated processes while commonly rejecting hypotheses of stationary behavior. Evidence obtained from point estimates of the fractional differencing parameter, d, supports these findings while providing a glimpse into the long-memory characteristics of many political time series. Finally, Monte Carlo studies are performed that demonstrate the likelihood of spurious regressions when researchers fail to account for the fractional dynamics of time series.