The importance of variance stationarity in economic time series modelling. 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 financial 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. Implications for the tests of 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.

[1]  Stephen Taylor,et al.  Forecasting Economic Time Series , 1979 .

[2]  George E. P. Box,et al.  Intervention Analysis with Applications to Economic and Environmental Problems , 1975 .

[3]  A. A. Weiss.  ARMA MODELS WITH ARCH ERRORS , 1984 .

[4]  G. C. Tiao,et al.  Estimation of time series parameters in the presence of outliers , 1988 .

[5]  E. Elton.  Modern portfolio theory and investment analysis , 1981 .

[6]  W. Enders.  Applied Econometric Time Series , 1994 .

[7]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[8]  Alastair R. Hall,et al.  Testing for a Unit Root in Time Series With Pretest Data-Based Model Selection , 1994 .

[9]  W. Fuller,et al.  Distribution of the Estimators for Autoregressive Time Series with a Unit Root , 1979 .

[10]  Daniel B. Nelson.  Stationarity and Persistence in the GARCH(1,1) Model , 1990, Econometric Theory.

[11]  P. Phillips.  Testing for a Unit Root in Time Series Regression , 1988 .

[12]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[13]  K. J. White.  Econometric models & economic forecasts : a computer handbook using SHAZAM for use with Pindyck & Rubinfeld, Econometric models & economic forecasts, third edition , 1991 .

[14]  Clive W. J. Granger,et al.  Experience with using the Box-Cox transformation when forecasting economic time series , 1979 .

[15]  W. Fuller,et al.  LIKELIHOOD RATIO STATISTICS FOR AUTOREGRESSIVE TIME SERIES WITH A UNIT ROOT , 1981 .

[16]  R. Tsay.  Time Series Model Specification in the Presence of Outliers , 1986 .

[17]  Rosenberg,et al.  Estimation of Time , 1922 .

[18]  Lon-Mu Liu,et al.  Joint Estimation of Model Parameters and Outlier Effects in Time Series , 1993 .

[19]  E. Fama.  EFFICIENT CAPITAL MARKETS: A REVIEW OF THEORY AND EMPIRICAL WORK* , 1970 .

[20]  K. J. Cohen,et al.  Implications of Microstructure Theory for Empirical Research on Stock Price Behavior , 1980 .

[21]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[22]  Agustín Maravall,et al.  Unobserved Components in Economic Time Series , 1993 .

[23]  Clive W. J. Granger,et al.  A New Look at Some Old Data: The Beveridge Wheat Price Series , 1971 .

[24]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[25]  H. Akaike.  A new look at the statistical model identification , 1974 .

[26]  Terence C. Mills,et al.  Time series techniques for economists , 1990 .

[27]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .