arXiv subjects

Kennedy Titus Kayaki

Publications and source records attributed to Kennedy Titus Kayaki.

2 recordsLinked to original sources

arXiv2026

Asymmetric Long-Memory GARCH: Sign-Dependent Kernel Injection in a Two-Dimensional Markov Chain

We introduce ALM-GARCH, an asymmetric long-memory GARCH model in which positive and negative innovations enter conditional variance with different injection amplitudes and kernel offsets. These departures define testable level and memory channels relative to a nested symmetric benchmark. Positive Harris recurrence holds for interior configurations under a Foster-Lyapunov condition. Across five equity indices and Bitcoin, joint symmetry is rejected throughout, driven primarily by the level channel. The memory channel is supported for the Nikkei 225, KOSPI, and Bitcoin but is weakly identified when the positive branch is nearly inactive. Out-of-sample performance is broadly comparable to standard benchmarks.

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arXiv2026

Long-memory GARCH via a two-dimensional Markov chain

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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