Forecast Performance of Threshold Autoregressive Models - A Monte Carlo Study

Threshold Autoregressive Models (TAR) along with other nonlinear time series models have attracted much attention in recent years in time series analysis. TAR models have been applied to a variety of time series. It has been reported that they have a good in sample fit but like many other non-linear time series models cannot improve out of sample forecast performance. Within a controlled simulation framework, we study the forecast performance under two types of non-linearity: shift in the mean and shift in the volatility of the process. We illustrate that estimation of the lag parameter and threshold value are crucial for forecast performance. Monte Carlo results show that TAR model performs much better than a Random Walk (RW) model; however, it provides no significant improvement over a linear Autoregressive (AR) model. Conclusions on the relative forecast performance of TAR models based on a single data set can be quite different than long run (Monte Carlo) results.