Statistics/Probability Theory
On the ARCH model with random coefficients
Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 221-224.

In the usual ARCH model, the coefficients have a degenerate distribution, and it is thus constant over realizations. In this Note we introduce the ARCH model, involving coefficients that are independent random variables and may vary over realizations. Conditions for the existence of a stationary solution and conditions ensuring the existence of higher order moments are obtained. The covariance structures of such models are studied.

Contrairement aux modèles ARCH usuels, où les coefficients sont supposés constants, nous considérons dans cette Note, une classe de modèles ARCH à coefficients aléatoires. Les conditions assurant l'existence et l'unicité de solutions stationnaires ainsi que l'existence des moments d'ordre supérieur et la structure de covariance de cette classe de modèles sont étudiées.

Published online:
DOI: 10.1016/j.crma.2007.11.023
Bibi, Abdelouahab 1; Bousseboua, Moussedek 1

1 Département de mathématiques, Université Mentouri Constantine, Algeria
     author = {Bibi, Abdelouahab and Bousseboua, Moussedek},
     title = {On the {ARCH} model with random coefficients},
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Bibi, Abdelouahab; Bousseboua, Moussedek. On the ARCH model with random coefficients. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 221-224. doi : 10.1016/j.crma.2007.11.023.

[1] Bougerol, P.; Picard, N. Stationarity of GARCH processes and of some nonnegative time series, J. Econometrics, Volume 52 (1992), pp. 115-127

[2] Engle, R.F. Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation, Econometrica, Volume 50 (1982), pp. 987-1008

[3] Dick, V.D.; Teräsvirta, T.; Franses, P.H. Smooth transition autoregressive models – A survey of recent developments, Econometric Reviews, Volume 21 (2002) no. 1, pp. 1-47

[4] Furstenberg, H.; Kesten, H. Products of random matrices, Ann. Math. Statist., Volume 31 (1960), pp. 457-469

[5] Liu, J. On the existence of a general multiple bilinear time series, J. Time Ser. Anal., Volume 10 (1989), pp. 341-355

[6] Kazakevičius, V.; Leipus, R.; Viano, M.-C. Stability of random coefficient ARCH models and aggregation schemes, J. Econometrics, Volume 120 (2004), pp. 139-158

[7] Klivečka, A. Random coefficient GARCH(1,1) model with i.i.d. coefficients, Lithuanian Math. J., Volume 44 (2004) no. 4, pp. 374-384

[8] Thavaneswaran, A.; Appadoo, S.S.; Samanta, M. Random coefficient GARCH models, Math. Comput. Modelling, Volume 41 (2005), pp. 723-733

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