A conditionally heteroskedastic independent factor model with an application to financial stock returns

Abstract

a b s t r a c t We propose a new conditionally heteroskedastic factor model, the GICA-GARCH model, which combines independent component analysis (ICA) and multivariate GARCH (MGARCH) models. This model assumes that the data are generated by a set of underlying independent components (ICs) that capture the co-movements among the observations, which are assumed to be conditionally heteroskedastic. The GICA-GARCH model separates the estimation of the ICs from their fitting with a univariate ARMA-GARCH model. Here, we will use two ICA approaches to find the ICs: the first estimates the components, maximizing their non-Gaussianity, while the second exploits the temporal structure of the data. After estimating and identifying the common ICs, we fit a univariate GARCH model to each of them in order to estimate their univariate conditional variances. The GICA- GARCH model then provides a new framework for modelling the multivariate conditional heteroskedasticity in which we can explain and forecast the conditional covariances of the observations by modelling the univariate conditional variances of a few common ICs. We report some simulation experiments to show the ability of ICA to discover leading factors in a multivariate vector of financial data. Finally, we present an empirical application to the Madrid stock market, where we evaluate the forecasting performances of the GICA-GARCH and two additional factor GARCH models: the orthogonal GARCH and the conditionally uncorrelated components GARCH.