Moving Average Threshold Heterogeneous Autoregressive (MAT-HAR) Models

We propose moving average threshold heterogeneous autoregressive (MAT-HAR) models as a novel combination of heterogeneous autoregression (HAR) and threshold autoregression (TAR). The MAT-HAR has multiple groups of lags of a target series, and a threshold term can appear in each group. The threshold is a moving average of lagged target series, which guarantees time-varying thresholds and simple estimation via least squares. We show via Monte Carlo simulations that the MAT-HAR has sharp in-sample and out-of-sample performance. An empirical application on the industrial production of Japan suggests that significant threshold effects exist, and the MAT-HAR has a higher forecast accuracy than the HAR.