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LARCH, Leverage and Long Memory

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Author Info
Liudas Giraitis
Remigijus Leipus
Peter M Robinson
Donatas Surgailis

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Abstract

We consider the long memory and leverage properties of a model for the conditional variance of an observable stationary sequence, where the conditional variance is the square of an inhomogeneous linear combination of past values of the observable sequence, with square summable weights. This model, which we call linear ARCH (LARCH), specializes to the asymmetric ARCH model of Engle (1990), and to a version of the quadratic ARCH model of Sentana (1995), these authors having discussed leverage potential in such models. The model which we consider was suggested by Robinson (1991), for use as a possibly long memory conditionally heteroscedastic alternative to i.i.d. behaviour, and further studied by Giraitis, Robinson and Surgailis (2000), who showed that integer powers, of degree at least 2, can have long memory autocorrelation. We establish conditions under which the cross-autovariance function between volatility and levels decays in the manner of moving average weights of long memory processes. We also establish a leverage property and conditions for finiteness of third and higher moments.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2003/460.

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Date of creation: Oct 2003
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Handle: RePEc:cep:stiecm:/2003/460

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Related research
Keywords: Leverage; long memory; linear ARCH; LARCH; finiteness of moments.;

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  3. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241. [Downloadable!] (restricted)
  6. Sentana, Enrique, 1995. "Quadratic ARCH Models," Review of Economic Studies, Blackwell Publishing, vol. 62(4), pages 639-61, October. [Downloadable!] (restricted)
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  7. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-78, December. [Downloadable!] (restricted)
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  8. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March. [Downloadable!] (restricted)
  9. Liudas Giraitis & Peter M Robinson, 2000. "Whittle Estimation of ARCH Models," STICERD - Econometrics Paper Series /2000/406, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  10. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February. [Downloadable!]
  11. 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. [Downloadable!] (restricted)
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  14. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March. [Downloadable!]
  15. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September. [Downloadable!] (restricted)
  16. Antonis Demos, 2002. "Moments and dynamic structure of a time-varying parameter stochastic volatility in mean model," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 345-357, 06. [Downloadable!] (restricted)
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  18. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July. [Downloadable!] (restricted)
  19. 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. [Downloadable!] (restricted)
  20. Giraitis, Liudas & Robinson, Peter M., 2001. "Whittle Estimation Of Arch Models," Econometric Theory, Cambridge University Press, vol. 17(03), pages 608-631, June. [Downloadable!]
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