Explaining cointegration analysis: Part 1

Abstract

`Classical' econometric theory assumes that observed data come from a stationary process, where means and variances are constant over time. Graphs of economic time series, and the historical record of economic forecasting, reveal the invalidity of such an assumption. Consequently, we discuss the importance of stationarity for empirical modeling and inference; describe the effects of incorrectly assuming stationarity; explain the basic concepts of non-stationarity; note some sources of non-stationarity; formulate a class of non-stationary processes (autoregressions with unit roots) that seem empirically relevant for analyzing economic time series; and show when an analysis can be transformed by means of differencing and cointegrating combinations so stationarity becomes a reasonable assumption. We then describe how to test for unit roots and cointegration. Monte Carlo simulations and empirical examples illustrate the analysis.