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arXiv · 2607.25189

Long-memory GARCH via a two-dimensional Markov chain

Kyungsub Lee·Kennedy Titus Kayaki
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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.

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Kyungsub Lee, Kennedy Titus Kayaki. 2026-07-28. Long-memory GARCH via a two-dimensional Markov chain. https://arxiv.org/abs/2607.25189

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