Moving average threshold heterogeneous autoregressive (MAT‐HAR) models

Abstract

Abstract 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.