Markov Regime-Switching Model (MS-AR / MS-VAR)
Also known as: regime-switching model, Markov-switching autoregression, MS-AR, MS-VAR, hidden Markov regime model, Markov Rejim Değiştirme Modeli (MS-AR / MS-VAR)
The Markov regime-switching model lets the parameters of a time series change probabilistically across hidden regimes governed by a Markov chain. Introduced by Hamilton (1989) and developed further by Kim and Nelson (1999), it automatically detects business-cycle phases such as expansions and contractions.
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When to use it
Use a Markov-switching model for a continuous time series that plausibly alternates between distinct, recurring regimes - for example macroeconomic series with expansion and recession phases, or financial series with calm and volatile periods. You need a reasonably long series (at least about 60 observations) and must decide in advance how many regimes (k) to estimate. It suits forecasting, classification of cycle phases, and explanatory work, but assumes the regime dynamics are well described by a Markov chain.
Strengths & limitations
- Automatically identifies and dates hidden regimes such as business-cycle expansions and contractions without labelling them by hand.
- Allows the intercept, autoregressive dynamics, and error variance to differ across regimes, capturing structural change and asymmetry.
- Provides probabilistic (smoothed) regime inference for every time point rather than a single hard split.
- The number of regimes k must be chosen by the analyst and is not learned automatically.
- Estimation maximises a multimodal likelihood that can be sensitive to starting values and may converge to local optima.
- Requires a fairly long series (about 60 observations or more) so that each regime is visited often enough to be estimated.
Frequently asked
How many regimes should I use?
The number of regimes k is set by the analyst, not learned from the data. Two regimes (for example expansion and contraction) is the classic choice; compare candidate models with information criteria and economic interpretability, and avoid adding regimes that capture only a handful of observations.
What is the hidden Markov chain doing?
It governs which unobserved regime is active at each time point. Movement between regimes follows fixed transition probabilities, so each regime has a degree of persistence, and the model infers the probability of each regime from the observed data.
How is the model estimated when the regimes are unobserved?
By maximum likelihood. The Hamilton filter recursively computes the probability of each regime given past data and marginalises over the hidden states to form the likelihood; Bayesian Gibbs sampling is an alternative. Because the likelihood is multimodal, it helps to try several starting values.
How is this different from a structural-break model?
A structural-break model assumes a one-off, permanent change at an unknown date, whereas a Markov-switching model allows the series to move back and forth between recurring regimes probabilistically, which fits cyclical phenomena like business cycles.
Sources
- Hamilton, J. D. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57(2), 357-384. DOI: 10.2307/1912559 ↗
- Kim, C. J. & Nelson, C. R. (1999). State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications. MIT Press. ISBN: 978-0262112383
How to cite this page
ScholarGate. (2026, June 1). Markov Regime-Switching Model (MS-AR / MS-VAR). ScholarGate. https://scholargate.app/en/econometrics/markov-switching
Which method?
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