Modelling Economic Time Series in the Presence of Variance Non-Stationarity: A Practical Approach

Although non-stationarity in the level of a time series is always tested (and there is a variety of tests for this purpose), non-stationarity in the variance is sometimes neglected in applied research. In this work, the consequences of neglecting variance non-stationarity in economic time series, and the conceptual difference between variance non-stationarity and conditional variance are discussed. An ad hoc method for testing and correcting for variance non-stationarity is suggested. It is shown that the presence of variance non-stationarity leads to misspecified univariate ARIMA models and correcting for it, the number of model parameters is vastly reduced. The implications of the tests for the hypothesis of weak form market efficiency (WFME) are discussed. More specifically it is argued that the usual autocorrelation tests are inappropriate when based on the differences of asset prices. Finally, it is shown how the analysis of outliers is affected by the presence of variance non-stationarity.