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

Author

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  • 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.

Suggested Citation

  • Alexandros E. Milionis, 2003. "Modelling Economic Time Series in the Presence of Variance Non-Stationarity: A Practical Approach," Working Papers 07, Bank of Greece.
  • Handle: RePEc:bog:wpaper:07
    as

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    File URL: http://www.bankofgreece.gr/BogEkdoseis/Paper200307.pdf
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    References listed on IDEAS

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    1. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    2. Nelson, Harold Jr. & Granger, C. W. J., 1979. "Experience with using the Box-Cox transformation when forecasting economic time series," Journal of Econometrics, Elsevier, vol. 10(1), pages 57-69, April.
    3. Agustín Maravall, 1996. "Unobserved Components in Economic Time Series," Working Papers 9609, Banco de España;Working Papers Homepage.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    6. James D. Hamilton & Baldev Raj, 2002. "New directions in business cycle research and financial analysis," Empirical Economics, Springer, vol. 27(2), pages 149-162.
    7. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Citations

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    Cited by:

    1. George Hondroyiannis & Sophia Lazaretou, 2007. "Inflation persistence during periods of structural change: an assessment using Greek data," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 34(5), pages 453-475, December.
    2. Eleni Angelopoulou, 2005. "The Comparative Performance of Q-type and Dynamic Models of Firm Investment: Empirical Evidence from the UK," Working Papers 27, Bank of Greece.
    3. Sideris, Dimitrios, 2006. "Testing for long-run PPP in a system context: Evidence for the US, Germany and Japan," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 16(2), pages 143-154, April.
    4. George A. Christodoulakis & Stephen E Satchell, 2006. "Exact Elliptical Distributions for Models of Conditionally Random Financial Volatility," Working Papers 32, Bank of Greece.

    More about this item

    Keywords

    Applied time series analysis; economic time series; Box-Jenkins modelling; variance non-stationarity; conditional variance; outlier analysis; efficient market hypothesis.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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