MODELLING ECONOMIC TIME SERIES IN THE PRESENCE OF VARIANCE NON-STATIONARITY:
A PRACTICAL APPROACH
Alexandros E. Milionis
Bank of Greece, Department of Statistics
ABSTRACT
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.
Keywords: Applied time series analysis, economic time series, Box-Jenkins modelling, variance non-stationarity, conditional variance, outlier analysis, efficient market hypothesis.
JEL classification: C22
The author is grateful to Steven Hall and Heather Gibson for helpful comments. The paper reflects the views of the author and not necessarily the views of the Bank of Greece.
Alexandros E. Milionis,
Department of Statistics,
Bank of Greece, 21 E. Venizelos Av.,
102 50 Athens, Greece,
Tel. + 30 210 3203109
Fax. + 30 210 3236035
Email: amilionis@bankofgreece.gr