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 S_t and a collection of dynamic regression (ARX or VARX) submodels that describe the dynamic behavior of a univariate or multivariate time series Y_t within each state or regime. The level of an observed threshold variable z_t determines the regime at time t (the value of S_t): S_t = j if r_j − 1 ≤ z_t < r_j, where the parameters r_j are unobserved thresholds. To specify a threshold variable, use threshold.

Threshold autoregressive models (TAR) treat z_t as exogenous to the system, whereas self-exciting threshold transition models (SETAR) treat z_t as endogenous, specifically z_t = y_kt. 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.

Functions

expand all

Create Model

`threshold`	Create threshold transitions (Since R2021b)
`tsVAR`	Create threshold-switching dynamic regression model (Since R2021b)
`arima`	Create univariate autoregressive integrated moving average (ARIMA) model
`varm`	Create vector autoregression (VAR) model

Analyze Threshold Transitions

`ttplot`	Plot threshold transitions (Since R2021b)
`ttdata`	Transition function data (Since R2021b)
`ttstates`	Threshold variable data state path (Since R2021b)

Fit Model to Data

`estimate`	Fit threshold-switching dynamic regression model to data (Since R2021b)
`summarize`	Summarize threshold-switching dynamic regression model estimation results (Since R2021b)

Generate Monte Carlo Simulations

simulate Simulate sample paths of threshold-switching dynamic regression model (Since R2021b)

Generate Forecasts

forecast Forecast sample paths from threshold-switching dynamic regression model (Since R2021b)

Topics

Create Threshold Transitions
Create a threshold transition object and access its properties.
Visualize Threshold Transitions
Plot threshold transitions to compare transition function rates and view mixing rates of the threshold levels.
Evaluate Threshold Transitions
Evaluate transition functions and compute states of threshold transitions given transition variable data.
Create Threshold-Switching Dynamic Regression Models
Create fully and partially specified threshold-switching dynamic regression models by using the tsVAR function.
Estimate Threshold-Switching Dynamic Regression Models
Fit threshold-switching dynamic regression models to simulated data and to tune estimation by using the esitmate function.
Simulate Paths of Threshold-Switching Dynamic Regression Models
Generate random response, innovations, and state paths of various threshold-switching dynamic regression models by using the simulate function.
Forecast Threshold-Switching Dynamic Regression Models
Forecast paths of threshold-switching models by using the forecast function.
Analyze US Unemployment Rate Using Threshold-Switching Model
Describe the dynamics of the yearly US unemployment rate using a threshold-switching dynamic regression model.