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A GARCH (1,1) estimator with (almost) no moment conditions on the error term

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  • PREMINGER, Arie
  • STORTI, Giuseppe

Abstract

A least squares estimation approach for the estimation of a GARCH (1,1) modelis developed. The asymptotic properties of the estimator are studied given mild regularity conditions, which require only that the error term has a conditionalmomen t of some order. We establish the consistency, asymptotic normality and the law of iterated logarithm for our estimate. The finite sample properties are assessed by means of an extensive simulation study.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2006068.

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Date of creation: 00 Aug 2006
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Handle: RePEc:cor:louvco:2006068

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Keywords: GARCH (1; 1); least squares estimation; consistency; asymptotic normality; law of the iterated logarithm;

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  1. Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
  2. Storti, G., 2006. "Minimum distance estimation of GARCH(1,1) models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1803-1821, December.
  3. 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.
  4. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
  5. Kristensen, Dennis & Linton, Oliver, 2006. "A Closed-Form Estimator For The Garch(1,1) Model," Econometric Theory, Cambridge University Press, vol. 22(02), pages 323-337, April.
  6. Filippo Altissimo & Valentina Corradi, 2002. "Bounds for inference with nuisance parameters present only under the alternative," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 494-519, 06.
  7. Francq, Christian & Zako an, Jean-Michel, 2000. "Estimating Weak Garch Representations," Econometric Theory, Cambridge University Press, vol. 16(05), pages 692-728, October.
  8. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
  9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  10. Berkes, István & Horváth, Lajos, 2003. "The rate of consistency of the quasi-maximum likelihood estimator," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 133-143, January.
  11. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
  12. 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.
  13. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
  14. Sakata, Shinichi & White, Halbert, 2001. "S-estimation of nonlinear regression models with dependent and heterogeneous observations," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 5-72, July.
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Cited by:
  1. HAFNER, Christian M. & PREMINGER, Arie, 2006. "Asymptotic theory for a factor GARCH model," CORE Discussion Papers 2006071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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