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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. Whereas 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.

Functions

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