A vector heterogeneous autoregressive index model for realized volatility measures

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 market

A Note on the Asymptotic Normality Theory of the Least Squares Estimates in Multivariate HAR-RV Models

“…Since its introduction, various adaptive versions of the HAR model are used to analyze the volatility along with empirical data analysis. Here, we refer to [2][3][4][5] for univariate data and [6][7][8][9][10][11] for multivariate data.…”

“…In particular, Bubak et al [6] used a multivariate extension of the HAR model to uncover volatility transmission between Central European currencies and the EUR/USA foreign exchange rate, whereas Soucek and Todorova [8] employ a bivariate HAR model to explore the relationship between equity and oil market volatility. Cubadda et al [9] proposed a vector HAR index model for detecting the presence of co-movements and analyzing the joint behavior in a set of daily realized volatility measures. Cech and Barunik [10] proposed a generalized HAR model for dynamic covariance matrix modelling and forecasting.…”

“…Furthermore, the least squares estimate (LSE) method has been popularly used as a tool of estimation in time series data analysis. The LSEs are used often in the literature to analyze the multivariate data in the multivariate HAR models and good performances on the volatility forecasting are obtained with forecast accuracy, for instance, see [9,12]. However, in the multivariate HAR models, rigorous formulation of asymptotic multivariate normality theory of the LSE has not yet been established in spite of the frequent uses of the LSEs.…”

Forecasting US stock market volatility: How to use international volatility information

“…In particular, the presence of volatility co-movement and spillover suggests that cross-market volatility information flows probably have significant predictive power for forecasting the future volatility of a major stock market. This predictive power can be attributed to common reactions of investors, policy-makers, and central banks to news relating to certain macroeconomic and financial variables (Cubadda, Guardabascio, & Hecq, 2017). Furthermore, Rizova (2010) argues that a two-country Lucas tree framework with gradual information diffusion (Hong & Stein, 1999;Hong, Torous, & Valkanov, 2007) causes the result that returns in one country predict returns in a trading-partner country.…”

Exponentially Weighted Multivariate HAR Model with Applications in the Stock Market

“…To assess the performance of the test, we use bivariate HAR models of orders p = 3, 6. We set h = (1,5,22), (1,7,14) if p = 3, and h = (1,5,7,9,14,22), (1,7,14,19,22,25) if p = 6. The sizes of the proposed test in the HAR(p, 2) models with λ 1 ∈ {0.5, 0.8}, λ 2 ∈ {0.1, 0.4}, are illustrated in Table 3.…”