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Multivariate Markov-switching ARMA processes with regularly varying noise

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  • Stelzer, Robert

Abstract

The tail behaviour of stationary -valued Markov-switching ARMA (MS-ARMA) processes driven by a regularly varying noise is analysed. It is shown that under appropriate summability conditions the MS-ARMA process is again regularly varying as a sequence. Moreover, it is established that these summability conditions are satisfied if the sum of the norms of the autoregressive parameters is less than one for all possible values of the parameter chain, which leads to feasible sufficient conditions. Our results complement in particular those of Saporta [Tail of the stationary solution of the stochastic equation Yn+1=anYn+bn with Markovian coefficients, Stochastic Process. Appl. 115 (2005) 1954-1978.] where regularly varying tails of one-dimensional MS-AR(1) processes coming from consecutive large values of the parameter chain were studied.

Suggested Citation

  • Stelzer, Robert, 2008. "Multivariate Markov-switching ARMA processes with regularly varying noise," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1177-1190, July.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:6:p:1177-1190
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    References listed on IDEAS

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    1. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    2. de Saporta, BenoI^te, 2005. "Tail of the stationary solution of the stochastic equation Yn+1=anYn+bn with Markovian coefficients," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1954-1978, December.
    3. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
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    3. Hay, Diana & Rastegar, Reza & Roitershtein, Alexander, 2011. "Multivariate linear recursions with Markov-dependent coefficients," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 521-527, March.
    4. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).

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