Regime switches in time series

Rosario Barone (Assistant Professor of Statistics)

Stefano Peluso  (Full Professor of Statistics)

Department of Statistical Sciences, Università Cattolica del Sacro Cuore

Abstract

Part I - Rosario Barone

We propose an efficient Bayesian framework for inference in continuous-time point processes modulated by latent semi-Markov dynamics. Unlike Markov-modulated Poisson processes, which impose exponential sojourn times and hence memoryless regime durations, the proposed approach accommodates flexible duration dependence while retaining exact likelihood-based inference. The method relies on a path augmentation strategy that combines a semi-Markov forward–filtering backward–sampling recursion on a sparse time grid with a Metropolis–Hastings update based on uniformization to reconstruct continuous-time latent trajectories. We show that, under a Gamma specification for sojourn times, the semi-Markov model nests the Markov case as a limiting scenario, in which the sampler degenerates to an exact Gibbs update. Simulation studies demonstrate accurate recovery of latent paths and parameters with favorable computational performance. An application to extreme volatility events in S&P 100 stocks illustrates the empirical relevance of duration-dependent regime dynamics and highlights the informational gains relative to Markov specifications.

Part II - Stefano Peluso

We study Bayesian inference for structural breaks in vector autoregressive (VAR) models, where both contemporaneous and dynamic interdependencies complicate regime identification. Within this framework, we extend the asymptotic analysis of Shimizu (2022) to multiple dependent series and establish conditions under which the posterior distribution of the change-point location under conjugate priors asymptotically concentrates on the true break. Consistency is further demonstrated for non-conjugate priors, and the results are extended to multiple change-points under controlled overlaps between estimated and true regimes. Simulation studies confirm the accurate recovery of  structural breaks, and empirical applications to U.S. macroeconomics data illustrate the method’s advantages over existing approaches.