Threshold and Smooth-Transition VAR (TVAR / STVAR)
Also known as: TVAR, STVAR, regime-switching VAR, threshold VAR, smooth-transition VAR, Eşik VAR ve Geçiş Değişkenli VAR (TVAR / STVAR)
Threshold VAR and Smooth-Transition VAR are nonlinear multivariate time-series models in which the coefficients of a vector autoregression switch between regimes according to a threshold variable. Building on Tsay's 1998 treatment of multivariate threshold models, they capture different dynamic structures across phases such as the business cycle, financial crises, or policy differences.
Key highlights
- Captures regime-dependent dynamics that a single linear VAR cannot represent.
- Allows the response of variables to shocks to differ across states such as recession versus expansion or crisis versus calm.
- STVAR permits a gradual, smooth transition between regimes rather than an abrupt switch.
Intuition
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How it works
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When to use it
Use TVAR or STVAR for continuous multivariate time series where you suspect the joint dynamics change across regimes — for example expansion versus contraction, or low versus high uncertainty. They require at least about 60 observations, a meaningful threshold variable to be chosen, prior rejection of linearity, and enough data within each regime. They are well suited to forecasting and to studying regime-dependent relationships among economic and financial variables.
Strengths & limitations
- Captures regime-dependent dynamics that a single linear VAR cannot represent.
- Allows the response of variables to shocks to differ across states such as recession versus expansion or crisis versus calm.
- STVAR permits a gradual, smooth transition between regimes rather than an abrupt switch.
- Needs a meaningful threshold variable to be specified in advance.
- Requires that linearity has first been rejected; otherwise a simpler linear VAR is preferable.
- Each regime must contain enough observations, so the data demands are high and small samples are unreliable.
Common pitfalls
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Applications
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Frequently asked
How is TVAR different from a Markov-switching VAR?
In TVAR the regime is determined deterministically by an observed threshold variable crossing a threshold, whereas a Markov-switching model treats the regime as an unobserved state governed by probabilistic transitions. Choose TVAR when you have a clear observable indicator for the regime and Markov-switching when the regime is latent.
What is the difference between TVAR and STVAR?
TVAR switches sharply: once the threshold variable crosses its threshold, the dynamics jump to the other regime. STVAR uses a smooth transition function so the dynamics change gradually, blending the regimes rather than flipping instantly.
Do I need to test for linearity first?
Yes. A regime-switching VAR is only justified if linearity is rejected. If a linearity test does not reject the linear model, a standard linear VAR is the more parsimonious and reliable choice.
How much data does the model need?
At least about 60 observations overall, but the real constraint is that each regime must have enough observations of its own to estimate its coefficients reliably.
Sources
- 1.Tsay, R. S. (1998). Testing and Modeling Multivariate Threshold Models. Journal of the American Statistical Association, 93(443), 1188-1202.
- 2.Balcilar, M. et al. (2017). Regime-Dependent Effects of Uncertainty Shocks. Economic Modelling.
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Cite this page
ScholarGate. (2026, June 1). Threshold and Smooth-Transition VAR. ScholarGate. https://scholargate.app/econometrics/stvar