Moving Average Threshold Heterogeneous Autoregressive (MAT-HAR) Models

A moving average heterogeneous autoregressive model for forecasting the realized volatility of the US stock market: Evidence from over a century of data

“…The threshold is an observed moving average of lagged target series, which guarantee time-varying thresholds and simple estimation with least squares estimator. As evident from the Monte Carlo simulation conducted by Motegi et al (2019), MAT-HAR was found to have higher forecast accuracy than the HAR baseline model. Earlier studies on the realized volatility of US stock market such as Bauer and Vorkink (2011), Chen et al (2019), Gong and Liu (2019), Gupta et al (2018), Wu and Wang (2019) and Yao et al (2019) have not considered moving average threshold effect as a modification to the conventional HAR model.…”

“…is an indicator function that equals 1 if 1 t y    and 0 otherwise. A naïve way to add threshold terms to the HAR model would be to specify as: We, as in Motegi et al, (2019), circumvent the above mentioned problems by specifying the thresholds to be the moving averages of the lagged target variable instead of specifying them to be mere constants. The proposed MAT-HAR model is thus specified as:…”

“…The threshold is an observed moving average of lagged target series, which guarantees time-varying thresholds and simple estimation with least squares estimator. As evident from the Monte Carlo simulation conducted by Motegi et al (2019), MAT-HAR was found to have higher forecast accuracy than the HAR baseline model.…”

“…Earlier studies on the realized volatility of US stock market such as Bauer andVorkink (2011), Chen et al (2019), Gong and Lin (2019), Gupta et al (2018), Wu andWang (2019) andYao et al (2019) have not considered moving average threshold effect as a modification to the conventional HAR model. While recent studies such as Gupta et al (2018) and Wu and Wang (2019) appear to account for time variation in the predictive model, they assume unknown threshold; which complicates both estimation and inferences (Motegi et al, 2019). Meanwhile, following Chen et al (2019), Qu et al, (2018) and Wu and Wang (2019) that find leverage effect to be significant in forecasting realized volatility, this study accounts for realized return volatility asymmetry by distinguishing between the good realized volatility and bad realized volatility.…”

“…This study contributes to the extant literature on forecasting realized volatility with heterogeneous autoregressive (HAR) model by accounting for threshold effect in a unique way with the adoption of a moving average threshold heterogeneous (MAT-HAR) model. Our proposed model, as developed by Motegi, Cai, Hamori, and Xu (2019), is a novel combination of HAR and threshold autoregressive (TAR) models. As in the HAR model, the MAT-HAR model has multiple groups of lags of a target series, where the groups are constructed from a viewpoint of sampling frequencies.…”