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

Battle Count: 73

The paper is primarily a structural econometric contribution to volatility modeling rather than a direct trading strategy paper. However, the decomposition of volatility asymmetry into level and memory channels is relevant for risk management, option pricing, and volatility-aware trading strategies. The leverage effect quantification and sign-dependent persistence profiles could inform position sizing, hedging, and regime-aware trading. The out-of-sample forecasting results are comparable but not superior to existing benchmarks, limiting direct trading application. The model's main value is diagnostic/structural rather than predictive.

Implementation requires: (1) multi-start optimization of a two-dimensional Markov chain recursion with sign-dependent updates, (2) Gaussian quasi-ML estimation with log-parameterization for positivity constraints, (3) Foster-Lyapunov stability verification via deterministic Gauss-Hermite quadrature on an adaptively refined carrier grid, (4) parametric bootstrap with B=999+ replications for likelihood-ratio test calibration, (5) profile likelihood analysis for the fixed exponent, (6) expanding-window out-of-sample forecasting with re-estimation every 250 days, and (7) Diebold-Mariano tests with Newey-West long-run variance. The theoretical machinery (Harris recurrence proofs, drift envelopes, information geometry) adds significant conceptual complexity.

The paper provides a detailed supplementary appendix with full proofs, parameter estimates, simulation and sensitivity results, optimization diagnostics, and additional figures. Replication materials including per-date forecasts and date checks are mentioned as retained. Data sources (Oxford-Man Institute Realized Library, Bitstamp) are publicly available. However, no explicit GitHub repository URL is provided, and the multi-start estimation procedures and bootstrap designs are described but code availability is not confirmed.