Time-partitioning Gaussian Process Mixture Model

Guilherme Piantino, Hedibert F. Lopes

Nonstationarity and heterogeneous dynamics are common in financial and macroeconomic time series. Volatility alternates between calm and turbulent regimes, interest rates follow monetary-policy cycles, and major events trigger persistent structural shifts. We propose the Time-partitioning Gaussian Process Mixture Model (TPGPMM), a Bayesian nonparametric framework for regime identification and nonstationary prediction that infers such regimes and their within-regime dependence from data, without Markovian assumptions. It combines (i) an adaptive Pitman-Yor process prior on ordered compositions, mapped to block lengths with contiguity enforced by construction, and (ii) regime-specific Gaussian processes for temporal dependence, yielding a nonstationary predictive distribution. By inferring its discount parameter, the prior adapts to homogeneous and highly heterogeneous regime lengths. Unlike sequential or Markov-switching methods, it flags persistent structural shifts as change points rather than reacting to transient shocks. A split-merge Metropolis-within-Gibbs sampler with exact Gibbs updates of regime boundaries jointly learns change points and hyperparameters in batch,…