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Threshold-Switching Dynamic Regression Models

Threshold autoregressive (TAR), self-exciting TAR (SETAR), and smooth-transition autoregressive (STAR) models

The threshold-switching dynamic regression model is composed of a discrete, fixed-state variable St and a collection of dynamic regression (ARX or VARX) submodels that describe the dynamic behavior of a univariate or multivariate time series Yt within each state or regime. The level of an observed threshold variable zt determines the regime at time t (the value of St): St = j if rj − 1 ≤ zt < rj, where the parameters rj are unobserved thresholds. To specify a threshold variable, use threshold.

Threshold autoregressive models (TAR) treat zt as exogenous to the system, whereas self-exciting threshold transition models (SETAR) treat zt as endogenous, specifically zt = ykt. Where transitions between states of TAR models are abrupt, smooth-transition autoregressive models (STAR) allow for variable-rate state transitions. Continuous rate functions and associated parameters determine the width and rate of state transitions. To specify a threshold-switching model, use tsVAR.


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thresholdCreate threshold transitions (Since R2021b)
tsVARCreate threshold-switching dynamic regression model (Since R2021b)
arimaCreate univariate autoregressive integrated moving average (ARIMA) model
varmCreate vector autoregression (VAR) model
ttplotPlot threshold transitions (Since R2021b)
ttdataTransition function data (Since R2021b)
ttstatesThreshold variable data state path (Since R2021b)
estimateFit threshold-switching dynamic regression model to data (Since R2021b)
summarizeSummarize threshold-switching dynamic regression model estimation results (Since R2021b)
simulateSimulate sample paths of threshold-switching dynamic regression model (Since R2021b)
forecastForecast sample paths from threshold-switching dynamic regression model (Since R2021b)