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Existence of small-order moments for Markov-switching stochastic recurrence equations

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  • Kandji, Baye Matar

Abstract

In this note, we show that the stationary solution of a stochastic recurrence equation, driven by an independent pair of finite-state space Markov chains and an independent and identically distributed process, admits a small-order moment. We use this property to extend, to the entire stationary parameter space, the consistency and asymptotic normality proofs for a recently introduced Hurdle GARCH model.

Suggested Citation

  • Kandji, Baye Matar, 2025. "Existence of small-order moments for Markov-switching stochastic recurrence equations," Statistics & Probability Letters, Elsevier, vol. 226(C).
    • Handle: RePEc:eee:stapro:v:226:y:2025:i:c:s0167715225001282
    DOI: 10.1016/j.spl.2025.110483
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    References listed on IDEAS

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    1. Elton, John H., 1990. "A multiplicative ergodic theorem for lipschitz maps," Stochastic Processes and their Applications, Elsevier, vol. 34(1), pages 39-47, February.
    2. Luc Bauwens & Arie Preminger & Jeroen V. K. Rombouts, 2010. "Theory and inference for a Markov switching GARCH model," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 218-244, July.
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