MATLAB Code Implementation for Threshold Autoregressive Model

The Threshold Autoregressive (TAR) model is a nonlinear time series model suitable for describing systems with distinct dynamic behaviors. MATLAB provides robust tools for constructing and estimating this type of model. The implementation steps for a threshold autoregressive model in MATLAB include: Data Preparation: Begin by preparing time series data and performing stationarity tests. In MATLAB, this typically involves using functions like `adftest` for Augmented Dickey-Fuller tests or `pptest` for Phillips-Perron tests to verify stationarity. Determining Threshold Variables and Delay Parameters: Lagged variables are commonly used as threshold variables, with appropriate delay parameters selected. Code implementation may involve creating lagged matrices using the `lagmatrix` function and determining optimal delays through autocorrelation analysis with `autocorr`. Estimating Threshold Values: Optimal threshold values can be determined through grid search methods or other optimization techniques. This can be implemented using loops to test different threshold values and selecting the one that minimizes the sum of squared errors or maximizes likelihood. Segmented Regression Estimation: Data is partitioned according to threshold values, with autoregressive estimations performed within each regime. This involves using conditional statements to separate data subsets and applying `arima` or linear regression functions like `regress` to each segment. Model Validation: Model quality is assessed through residual analysis or prediction performance evaluation. MATLAB functions such as `lbqtest` for Ljung-Box Q-tests on residuals or cross-validation techniques can be employed for this purpose. MATLAB's `arima` and `nlarx` toolboxes can assist in modeling, while users can customize optimization algorithms using `fmincon` or `fminsearch` to improve estimation accuracy. Extended Applications: The threshold autoregressive model finds applications in economic fluctuation forecasting, financial risk management, and other domains where data exhibits structural changes, making it particularly valuable for regime-switching scenarios.