On periodic GARCH processes: Stationarity, existence of moments and geometric ergodicity

被引：15

作者：

Bibi A. ^{[1
]}

Aknouche A. ^{[2
]}

机构：

[1] Département de Math., Univ. Mentouri, Constantine

[2] Faculté de Math., U.S.T.H.B., Algiers

来源：

Mathematical Methods of Statistics | 2008年 / 17卷 / 4期

关键词：

geometric ergodicity; higher-order moments; periodic GARCH processes; stationarity;

D O I：

10.3103/S1066530708040029

中图分类号：

学科分类号：

摘要：

This paper examines some probabilistic properties of a class of models featuring periodicity in conditional heteroskedasticity (we refer to it as the periodic GARCH process (PGARCH)). In these models, the parameters are allowed to switch between different regimes. The periodic structure in a GARCH process shares many properties with periodic ARMA process (PARMA). We examine the strict and second order periodic stationarities, the existence of higher-order moments, the covariance structure, the geometric ergodicity and β-mixing of the PGARCH(p, q) process under general and tractable assumptions. Some examples are proposed to illustrate the various concepts. © 2008 Allerton Press, Inc.

引用

页码：305 / 316

页数：11

共 13 条

[1]

Bollerslev T., Ghysels E., Periodic Autoregressive Conditional Heteroskedasticity, J. Of Business and Economic Statistics, 14, pp. 139-151, (1996)

[2]

Bougerol P., Picard N., Stationarity of GARCH Processes and Some Nonnegative Time Series, J. Econometrics, 52, pp. 115-127, (1992)

[3]

Bougerol P., Picard N., Strict Stationarity of Generalized Autoregressive Processes, Ann. Probab., 20, pp. 1714-1730, (1992)

[4]

Carrasco M., Chen X., Mixing and Moment Properties of Various GARCH and Stochastic Volatility Models, Econometric Theory, 18, pp. 17-39, (2002)

[5]

Chen M., An H.Z., A Note on the Stationarity and the Existence of Moments of the GARCH Model, Statistica Sinica, 8, pp. 505-510, (1998)

[6]

Davydov Y., Mixing Conditions for Markov Chains, Theory Probab. And Appl., 18, pp. 313-328, (1973)

[7]

Doukhan P., Mixing, Lecture Notes in Statistics, 85, (1994)

[8]

Franses P.H., Paap R., Modeling Day-of-the-Week Seasonality in the S&P 500 Index, Appl. Financial Economics, 10, pp. 483-488, (2000)

[9]

Franses P.H., Paap R., Random-Coefficient Periodic Autoregression, (2005)

[10]

Gladyshev E.G., Periodically Correlated Random Sequences, Soviet Math., 2, pp. 385-388, (1961)

← 1 2 →