A multivariate HAR-RV model with heteroscedastic errors and its WLS estimation

Abstract

This work considers a multivariate heterogeneous autoregressive-realized volatility (HAR-RV) model in the presence of heteroscedasticity and aims to analyze realized volatilities of multiple assets that possess non-standard features, such as non-Gaussianity, time varying volatility and long-memory dependence. For capturing the long-memory, a HAR-RV model is employed, while for a heavy-tailed distribution, a GARCH process is adopted on the noise term. To estimate coefficients of the HAR-RV-GARCH model, we suggest weighted least squares estimator (WLSE) based on an observed weighting scheme and prove its asymptotic normality. Simulation results show a good performance on the WLSE. The multivariate HAR-RV-GARCH model fitted by the WLSE is illustrated with an application to realized volatilities of multiple financial data.