Robust Monte Carlo tests for regime-switching models
Bank of Canada researchers developed new Monte Carlo likelihood-ratio tests for Markov switching models. These tests provide finite-sample and asymptotically valid procedures for determining the number of regimes, even with nonstationary processes or non-Gaussian errors.
Novel tests for regime shifts
This paper introduces two novel Monte Carlo likelihood-ratio tests (LMC-LRT and MMC-LRT) for Markov switching models.
These tests enable robust hypothesis testing for M0 regimes against M0 + m regimes, for any M0 ≥ 1 and m ≥ 1. They apply to univariate and multivariate models, including Hidden Markov Models, Markov-switching VARs, and MS-GARCH.
The Maximized Monte Carlo likelihood-ratio test (MMC-LRT) is a key contribution, offering an identification-robust procedure with both finite-sample and asymptotic validity.
The tests avoid assumptions of stationarity, Gaussian errors, or constrained parameter spaces.
This broadens their use to complex settings, including m > 1 regimes, multivariate structures, non-Gaussian errors, or non-stationary processes, where existing methods often fail.
Simulations confirm accurate size control and strong power.
The tests are implemented via the MSTestR package.
Challenges of regime identification
Markov switching models capture nonlinearities from regime shifts.
Determining the number of regimes is a fundamental challenge, as standard hypothesis testing procedures are often inapplicable.
This is due to unidentified parameters under the null and violated regularity conditions for asymptotic results.
Most existing likelihood-ratio (LR) tests are limited to comparing a linear null (M0 = 1) against a two-regime alternative (m = 1).
These tests typically require restrictive assumptions like stationarity, Gaussian errors, and constrained parameter spaces, and focus on univariate settings.
This highlights a significant gap for robust, finite-sample valid inference in more complex scenarios, including multiple regimes, multivariate data, or non-stationary processes.
A robust leap for empirical models
This paper offers a critical methodological advancement for time series analysis, directly addressing long-standing challenges in testing Markov switching models.
The Maximized Monte Carlo likelihood-ratio test (MMC-LRT) provides a robust solution for complex scenarios previously untestable.
This enables researchers to more accurately select models and analyze regime shifts, significantly enhancing the reliability of empirical findings.