Ergodicity conditions for a double mixed Poisson autoregression

Aknouche, Abdelhakim and Demouche, Nacer (2018): Ergodicity conditions for a double mixed Poisson autoregression.

Abstract

We propose a double mixed Poisson autoregression in which the intensity, scaled by a unit mean independent and identically distributed (iid) mixing process, has different regime specifications according to the state of a finite unobserved iid chain. Under some contraction in mean conditions, we show that the proposed model is strictly stationary and ergodic with a finite mean. Applications to various count time series models are given.

• Item Type: MPRA Paper
• Language: English
• Keywords: Double mixed Poisson autoregression, negative binomial mixture INGARCH model, ergodicity, weak dependence, contraction in mean
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C40 - General; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C46 - Specific Distributions ; Specific Statistics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C50 - General

References

Aknouche, A.; Rabehi, N. (2010). On an independent and identically distributed mixture bilinear time series model. Journal of Time Series Analysis, 31, 113-131.

Aknouche, A., Bentarzi, W.; Demouche, N. (2018). On periodic ergodicity of a general periodic mixed Poisson autoregression. Statistics & Probability Letters, 134, 15-21.

Bauwens, L., Preminger, A.; Rombouts, J. (2010). Theory and inference for a Markov Switching GARCH model. Econometrics Journal, 13, 218-244.

Cox, D.R. (1981). Statistical analysis of time series: some recent developments. Scandinavian Journal of Statistics, 8, 93-115.

Christou, V.; Fokianos, K. (2014). Quasi-likelihood inference for negative binomial time series models. Journal of Time Series Analysis, 35, 55-78.

Davis, R.A.; Liu, H. (2016). Theory and inference for a class of observation-driven models with application to time series of counts. Statistica Sinica, 26, 1673-1707.

Dean, C., Lawless, J.F.; Willmot, G.E. (1989). A mixed Poisson-Inverse-Gaussian regression model. The Canadian Journal of Statistics, 17, 171-181.

Dedecker, J.; Prieur, C. (2004). Coupling for τ-dependent sequences and applications. Journal of Theoretical Probability, 17, 861-885.

Diop, M.L., Diop, A.; Diongue, A.K. (2016). A mixture integer-valued GARCH model. REVSTAT - Statistical Journal, 14, 245-271.

Doukhan, P., Fokianos, K.; Tjøstheim, D. (2012). On weak dependence conditions for Poisson autoregressions. Statistics and Probability Letters, 82, 942-948.

Doukhan, P.; Wintenberger, O. (2008). Weakly dependent chains with infinite memory. Stochastic Processes and their Applications, 118, 1997-2013.

Francq, C.; Zakoian, J.M. (2008). Deriving the autocovariances of powers of Markov-switching GARCH models, with applications to statistical inference. Computational Statistics & Data Analysis, 52, 3027-3046.

Haas, M., Mittnik, S.; Paollela, M.S. (2004). A new approach to Markov-Switching GARCH models. Journal of Financial Econometrics, 4, 493-530.

Hind, J. (1982). Compound Poisson regression models. Proceedings of the International Conference on Generalised Linear Models, pp 109-121.

Zhu, F. (2011). A negative binomial integer-valued GARCH model. Journal of Time Series, 32, 54-67.

Zhu, F., Li, Q.; Wang, D. (2010). A mixture integer-valued ARCH model. Journal of Statistical Planning and Inference, 140, 2025-2036.