Long-memory GARCH via a two-dimensional Markov chain

Battle Count: 75

The paper is highly relevant to quantitative trading through its volatility forecasting capabilities. The two-dimensional Markov structure provides computational tractability while capturing long-memory persistence in volatility. Out-of-sample QLIKE performance is competitive with GARCH(1,1) and close to FIGARCH. The model's parsimony (3 parameters) and finite-dimensional state make it practical for real-time implementation. However, it does not outperform HAR-RV for realized variance forecasting, and the lack of asymmetry limits its applicability in equity markets with leverage effects.

The model requires implementing a two-dimensional recursive update (equations 6-7 or 9-10) with Gaussian quasi-MLE estimation. The state space is simple ([0,∞)×[γ,∞)), and the recursion is straightforward. However, the stability verification requires computing the drift envelope S(c) and the log-drift Λ(c) numerically, and the joint stability condition requires finding λ such that sup_c{Λ(c)+λS(c)}<0. The simulation and local Whittle estimation add moderate complexity. Overall, the model is more complex than GARCH(1,1) but far simpler than FIGARCH or infinite-order ARCH models.

The paper provides detailed mathematical derivations, simulation parameters (grid of p, ξ, γ values, sample sizes, bandwidth choices), and estimation procedures. However, no code or repository is explicitly mentioned. The Oxford-Man Institute Realized Library data is publicly available. Fixed random seeds are mentioned for reproducibility of simulations. The model is fully specified with equations (6)-(7) and (9)-(10).