The study of volatility is important in several areas of finance, and GARCH models have been widely used in the literature due to their ability to capture key stylised facts of financial time series. However, in some cases, financial time series exhibit structural changes in volatility dynamics, for which standard GARCH models may be inadequate; in such situations, Markov-switching GARCH models provide a more suitable framework. On the other hand, outliers are often present in empirical data. This paper shows that conventional estimators can be strongly affected by outliers and proposes an estimator that is more robust to their presence. The simulation results and empirical applications indicate that the proposed robust estimator is competitive and useful under contamination, but not uniformly superior to the QML-t estimator.
Jean S. M. Diniz, L. Hotta· Computational statistics (Ze...· 0 citations
Environmental monitoring networks increasingly record pollutant levels as curves observed over time at fixed stations. Yet, exposure and risk assessment often require predicting these curves, with their uncertainty, at unmonitored locations. Conventional smooth-basis methods for such spatially correlated functional data, including spline-based kriging, tend to over-smooth acute, high-frequency episodes such as pollution peaks. We propose a parsimonious wavelet-based Bayesian hierarchical model that anchors a single, shared Mat\'ern correlation matrix at each resolution level, avoiding the parameter inflation of coefficient-specific spatial processes. Adaptive sparsity is enforced through a spatially informed regularized horseshoe prior, allowing the model to borrow strength across neighboring locations. At the same time, a non-centered parameterization ensures stable inference under the No-U-Turn Sampler. In simulation studies across distinct signal-to-noise regimes, incorporating spatial dependence substantially stabilizes reconstruction under severe noise relative to strictly independent models. Applied to PM$_{10}$ concentrations from Mexico City and benchmarked against ordinary kriging for functional data and a hierarchical Bayesian wavelet alternative, the model captures acute pollution events and, beyond improving point prediction, delivers sharper and better-calibrated credible intervals at unobserved locations.
Alvaro Alexander Burbano-Moreno, Alex Rodrigo dos Santos Sousa, L. Hotta· 0 citations
