Time-partitioning Gaussian Process Mixture Model

arXiv:2610.20860v1 Announce Type: cross Abstract: We propose the Time-partitioning Gaussian Process Mixture Model (TPGPMM), a Bayesian nonparametric framework for identifying persistent regimes and modelling nonstationary dependence in time series. The model combines an adaptive Pitman--Yor prior on contiguous segmentations with regime-specific Gaussian processes, without imposing Markovian within-regime dependence. Learning the Pitman--Yor discount parameter allows adaptation to homogeneous and heterogeneous regime lengths. A split--merge Metropolis-within-Gibbs sampler with exact Gibbs boundary updates jointly learns change points and model hyperparameters, quantifying uncertainty over segmentations and within-regime dynamics. With an RBF kernel and a fixed, conservative observation-noise level, TPGPMM favours sparse segmentations that distinguish persistent shifts from transient shocks. Simulations demonstrate recovery of the regime structure. Applications to the CBOE Volatility Index (VIX) and the 10-year United States Treasury yield identify regimes aligned with major market and monetary-policy events. Variants that estimate observation noise improve predictive accuracy relative to the main specification, but can produce less sparse or less event-aligned segmentations. A variant with regime-specific means fits better than a fitted stationary Gaussian process and forecasts about as accurately. These results highlight a trade-off between interpretable regime identification and predictive accuracy.