Comptes Rendus
Statistics/Probability Theory
Estimating parameters of a k-factor GIGARCH process
Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 435-440.

Some crucial time series of market data, such as electricity spot prices, exhibit long-memory, in the sense of slowly-decaying correlations combined with heteroskedasticity. To be able to modelize such a behaviour, we consider in this Note the k-factor GIGARCH process and we propose two methods to address the related parameter estimation problem. For each method, we develop the asymptotic theory for the estimation.

Plusieurs données de marché, telles que les prix spot de l'électricité, présentent de la longue mémoire, au sens de la décroissance hyperbolique des autocorrélations combinée avec un phénomène d'hétéroskédasticité. Pour modéliser de tels comportements, nous considérons dans cette Note les processus GIGARCH à k facteurs et nous proposons deux méthodes d'estimation des paramètres de ce modèle. Enfin, nous développons les propriétés asymptotiques de ces estimateurs.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.07.014
Abdou Kâ Diongue 1, 2; Dominique Guégan 1

1 ENS Cachan IDHE-MORA, UMR CNRS 8533, 61, avenue du président Wilson, 94231 Cachan cedex, France
2 EDF R&D, 1, avenue du général de Gaulle, 92141 Clamart cedex, France
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Abdou Kâ Diongue; Dominique Guégan. Estimating parameters of a k-factor GIGARCH process. Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 435-440. doi : 10.1016/j.crma.2004.07.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.014/

[1] I.V. Basawa; P.D. Feign; C.C. Heyde Asymptotic properties of maximum likelihood estimators for stochastic processes, Sankhya Ser. A, Volume 38 (1976), pp. 259-270

[2] C.-F. Chung Estimating a generalized long-memory process, J. Econometrics, Volume 73 (1996), pp. 237-259

[3] C.-F. Chung A generalized fractionally integrated ARMA process, J. Time Series Anal., Volume 17 (1994), pp. 111-140

[4] A.K. Diongue, D. Guégan, B. Vignal, Processus GIGARCH: Estimation et applications aux prix spot de l'électricité, Preprint MORA, 14, 2003

[5] L. Ferrara; D. Guégan Comparison of parameter estimation methods in cyclical long-memory time series (C. Dunis; J. Timmermann, eds.), Development in Forecasts Combination and Portfolio Choice, Wiley, 2001

[6] L. Giraitis; P.M. Robinson Whittle estimation of ARCH models, Econometrics Theory, Volume 17 (2001), pp. 608-631

[7] D. Guégan A new model: The k-factor GIGARCH process, J. Signal Process., Volume 4 (2000), pp. 265-271

[8] D. Guégan A prospective study of the k-factor Gegenbauer process with heteroscedastic errors and an application to inflation rates, Finance India, Volume 17 (2003), pp. 1-20

[9] Y. Hosoya A Limit theory for long-range dependence and statistical inference on related models, Ann. Stat., Volume 25 (1997), pp. 105-137

[10] W.F. Stout Almost Sure Convergence, Academic Press, New York, 1974

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