Vector Moving Average Threshold Heterogeneous Autoregressive (VMAT-HAR) Model

The existing vector heterogeneous autoregression (VHAR) does not allow for threshold effects. The threshold autoregressions are well established in the literature, but the presence of an unknown threshold complicates inference. To resolve this dilemma, we propose the vector moving average threshold (VMAT) HAR model. Observed moving averages of lagged target series are used as thresholds, which guarantees time-varying thresholds and the least squares estimation. We show via simulations that the proposed model performs well in small samples. We analyze daily realized volatilities of the stock price indices of Hong Kong and Shanghai, detecting significant threshold effects and mutual Granger causality