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abstract

This paper introduces a new model for detecting the presence of commonalities in a set of realized volatility measures. In particular, we propose a multivariate generalization of the heterogeneous autoregressive model (HAR) that is endowed with a common index structure. The vector heterogeneous autoregressive index model has the property of generating a common index that preserves the same temporal cascade structure as in the HAR model, a feature that is not shared by other aggregation methods (e.g., principal components). The parameters of this model can be estimated easily by a proper switching algorithm that increases the Gaussian likelihood at each step. We illustrate our approach using an empirical analysis that aims to combine several realized volatility measures of the same equity index for three different markets. © 2016 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.used as a predictor as our target variable, in order to avoid the risk of putting too much weight on it. We consider daily series of the measures that are reported in Table 2, spanning the period 01/01/2000 to 10/29/2015, for three equity indexes: SandP500 for the U.S., FTSE 100 for the U.K., and the Nikkei 225 for Japan. These series are downloaded from the webpage of the Oxford-Man Institute of Quantitative Finance (see Heber, Lunde, Shephard, & Sheppard, 2009).

6. Conclusions

This paper has proposed the VHARI model, a multivariate generalization of the HAR model of Corsi (2009), which allows for the parsimonious modelling of a vector of realized volatilities. In particular, the realized volatility measures can be explained as linear functions of a few indexes, which preserve the same temporal cascade structure as the autoregressive terms of the univariate HAR model. The parameters of the VHARI model can be estimated by means of a switching algorithm that increases the Gaussian likelihood at each step. Based on the work of Takeuchi (1976), we have modified traditional information criteria by allowing for non-Gaussianity and heteroskedasticity in the errors of our model. Finally, we have illustrated the practical value of the proposed methods by means of an empirical application to a set of ten realized volatility measures for the SandP500, FTSE and the Nikkei equity indexes.