A Study Of Multivariate HAR Models Based On Cojumps And The Application In Asset Allocation

The covariance matrix among several assets, which is an important measurement for risk, plays a crucial role in asset allocation field. Therefore, how to forecast it accurately has always been the key problem for related researchers. As high-frequency data is now more accessible, the realized covariance (RCV) which is constructed with high-frequency data becomes popular as a proxy for multivariate volatility, so do the models based on it.The jump indicates a sharp movement of asset prices in a short time, whereas the cojump means a simultaneous jump among different assets. Cojump, which is also called common jumps, is not rare in financial markets, usually due to macro announcements and important economic events. In this case, to study the cojump has a great practical significance both in risk management and asset allocation field.The Heterogeneous Autoregressive model, i.e. HAR, is one of the representative high-frequency data based volatility models. Nevertheless, previous studies are generally restricted to univariate models, mainly focusing on market index volatility, while few researchers have paid attention to multi-asset covariance. Motivated by this, univariate HAR model is extended to multivariate HAR model (MHAR) with the regressors replaced by the realized covariance (RCV). Considering the non-positive definiteness of the RCV matrix, cholesky decomposing and logarithm transformation methods are applied, making cholesky factors and logarithm volatility the regression variables. Additionally, BLT test is used to identify the intraday cojump while the cojump intensity is estimated by Hawkes model. Both the cojump indicator variable JD, which is 1 if a cojump is detected and 0 if not, and also the cojump intensity JI are corporated into MHAR model for the first time, hence building three alternative models:MHAR-JD, MHAR-JI and MHAR-JDJI. In order to evaluate the cojump contribution to these models, both the in-sample model fitting and out-of-sample forecasting are implemented. Also, MCS test is utilized to evaluate which model is the best one. The result demonstrates that the cojump indicator has a weak connection with future covariance while the cojump intensity makes a positive contribution to RCV. Moreover, MHAR-JI model and MHAR-JDJI model significantly improve the model’s fitting ability and forecasting performance, while MHAR-JDJI is proved to be the best model.In addition, the global minimum variance portfolio strategy is utilized to examine the economic meaning of this study. By comparing the average returns, standard deviation, Sharpe Ratios and utilities of portfolios from different model forecasting values, the expanded models are further proved to be effective.