Recent developments in the analysis of long-memoried processes provide important leverage for analysing time-series variables of interest to political scientists. This article provides an accessible exposition of these methods and illustrates their utility for addressing protracted controversies regarding the political economy of party support in Britain. Estimates of the fractionally differencing parameter, d, reveal that governing party support, prime ministerial approval and economic evaluations are long-memoried and non-stationary, and that governing party support and prime ministerial approval are fractionally cointegrated. Pace conventional wisdom that party leader images matter little, if at all, analyses of multivariate fractional error correction models show that prime ministerial approval has important short-run and long-run effects on party support. Prospective and retrospective personal economic evaluations are influential but, contrary to a longstanding claim, national economic evaluations are not significant. The article concludes by suggesting that individual-level heterogeneity is a likely source of the observed aggregate-level fractional integration in governing party support and its determinants. Specifying parsimonious models that incorporate theoretically meaningful heterogeneity is a challenging topic for future research.