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Long-memory GARCH via a two-dimensional Markov chain

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  • Kyungsub Lee
  • Kennedy Titus Kayaki

Abstract

This paper proposes a GARCH-type volatility model in which level-and-slope updates of a latent power-law kernel generate state-dependent decay of past shocks within a two-dimensional Markov state. We derive a joint Foster--Lyapunov condition and establish positive Harris recurrence and uniqueness of the invariant distribution. Simulations show substantial low-frequency persistence in log-squared innovations, especially near the diagnostic stability boundary. Empirically, the model captures a substantial portion of observed volatility persistence and delivers competitive out-of-sample forecast accuracy using only a two-dimensional Markov state.

Suggested Citation

  • Kyungsub Lee & Kennedy Titus Kayaki, 2026. "Long-memory GARCH via a two-dimensional Markov chain," Papers 2607.25189, arXiv.org.
    • Handle: RePEc:arx:papers:2607.25189
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    References listed on IDEAS

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    Cited by:

    1. Kennedy Titus Kayaki & Kyungsub Lee, 2026. "Asymmetric Long-Memory GARCH: Sign-Dependent Kernel Injection in a Two-Dimensional Markov Chain," Papers 2609.06422, arXiv.org.

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