Modelling Multivariate Return Volatilities by Independent Components Using Johnson SU Likelihood

Abstract

Time-varying volatility modelling is crucial in financial econometrics. For multivariate data, time-varying correlations across securities are important to explain the co-movement of the data. Therefore, we need to estimate the covariance matrix. Estimating a large conditional covariance matrix requires the estimation of a large number of parameters, which is a hard task and often leads to convergence difficulties in the estimation algorithm. We introduce a framework for forecasting the conditional covariance matrix of a large data set by employing a factor model to reduce dimensionality, with the factors estimated using independent components. The main contribution of our article is the estimation of the unobserved independent components using Johnson SU likelihood, which captures the skewness and excess kurtosis—stylized facts in stock returns. First, we extract the independent components using the Johnson SU distribution, maximizing their non-Gaussianity. Second, we sorted the independent components in terms of their explained variability and fit a univariate GARCH process on a few common independent components. Next, we approximate the conditional covariance matrix of the data through a linear combination of the conditional variances of those select few independent components. We apply this procedure to 50 stock returns data (listed in Nifty 50) that exhibit excess kurtosis and skewness, and the findings show that our methodology dominates other algorithms in extracting the independent components. This method enables fund managers to accurately forecast a large conditional covariance matrix, facilitating effective risk management and portfolio construction.