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A model for long memory conditional heteroscedasticity

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  • Giraitis, Liudas
  • Robinson, Peter M.
  • Surgailis, Donatas

Abstract

For a particular conditionally heteroscedastic nonlinear (ARCH) process for which the conditional variance of the observable sequence rt is the square of an inhomogeneous linear combination of rs, s 2, r' has long memory autocorrelation and normalized partial sums of ri converge to fractional Brownian motion.

Suggested Citation

  • Giraitis, Liudas & Robinson, Peter M. & Surgailis, Donatas, 2000. "A model for long memory conditional heteroscedasticity," LSE Research Online Documents on Economics 299, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:299
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    File URL: http://eprints.lse.ac.uk/299/
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    References listed on IDEAS

    as
    1. Andersen, Torben G & Bollerslev, Tim, 1997. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
    2. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-268, July.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. C. W. J. Granger & Zhuanxin Ding, 1995. "Some Properties of Absolute Return: An Alternative Measure of Risk," Annals of Economics and Statistics, GENES, issue 40, pages 67-91.
    5. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    6. 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.
    7. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    8. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    9. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(1), pages 3-22, February.
    10. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    11. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 280-283, July.
    12. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
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    More about this item

    Keywords

    ARCH processes; long memory; Volterra series; diagrams; central limit theorem; fractional Brownian motion;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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