Variance Targeting Research Articles

Realized BEKK-CAW Models

Abstract Estimating time-varying conditional covariance matrices of financial returns play important role in portfolio analysis, risk management, and financial econometrics research. The availability of high-frequency financial data can provide an additional data source for dynamic covariance modeling. In this paper, we propose to use the information of asset return vector and realized covariance measures simultaneously to develop a new conditional covariance matrix model. We derive the stationary condition of the new model. We use the normal and Wishart distributions to construct the quasi-log-likelihood function. We also consider the variance targeting (VT) method, which plugs in the weighted average of the sample covariance matrix of returns and the sample mean of realized covariance measure for the unconditional covariance matrix, in order to maximize the quasi-log-likelihood function. We show the consistency and asymptotic normality of the quasi-maximum likelihood (QML) and VT estimators. We investigate the finite sample property of these estimators via Monte Carlo experiments. The empirical example for the bivariate data of the Nikkei 225 index and its futures indicates that the first-step VT estimation could have non-negligible effects on the standard errors of the second-step VT estimates.

Feasible Panel GARCH Models: Variance-Targeting Estimation and Empirical Application

For the panel generalized autoregressive conditional heteroskedasticity (GARCH) model, the conditions for the stationarity and positive definiteness of conditional covariance processes are examined. A new feasible specification is constructed for the class of panel GARCH models, and a three-step estimation technique is developed based on a variance-targeting (VT) approach. The consistency and asymptotic normality of the VT estimator are shown when the time dimension tends to infinity and the cross-sectional dimension is fixed. The stationarity and asymptotic properties are discussed for both time and cross-sectional dimensions tend to infinity. The results of Monte Carlo experiments indicate that the finite sample property of the VT estimator is satisfactory, implying that increasing the cross-sectional dimension does not affect the speed of convergence, but shrinks the asymptotic covariance matrix. The empirical results of the analysis of the inflation rates of G7 countries and growth rates for the value of trade in four economic regions indicate that the feasible specification provides a competitive alternative to the class of panel GARCH models. The empirical results indicate that the global financial crisis affects the growth rates of trades, while the influence of the COVID-19 pandemic shows that its effect on inflation rates is insignificant.

Multivariate variance targeting in the BEKK-GARCH model

Summary In this paper, we consider asymptotic inference in the multivariate BEKK model based on (co)variance targeting (VT). By definition the VT estimator is a two-step estimator and the theory presented is based on expansions of the modified likelihood function, or estimating function, corresponding to these two steps. Strong consistency is established under weak moment conditions, while sixth-order moment restrictions are imposed to establish asymptotic normality. The simulations included indicate that the multivariately induced higher-order moment constraints are necessary.

Multivariate Variance Targeting in the BEKK-GARCH Model

This paper considers asymptotic inference in the multivariate BEKK model based on (co-)variance targeting (VT). By de finition the VT estimator is a two-step estimator and the theory presented is based on expansions of the modifi ed likelihood function, or estimating function, corresponding to these two steps. Strong consistency is established under weak moment conditions, while sixth order moment restrictions are imposed to establish asymptotic normality. Included simulations indicate that the multivariately induced higher order moment constraints are indeed necessary.