Conditional Correlation Models of Autoregressive Conditional Heteroskedasticity with Nonstationary GARCH Equations
PRESENTER: Professor Timo Teräsvirta
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In this paper we investigate the effects of careful modelling the long-run dynamics of the volatilities of stock market returns on the conditional correlation structure. To this end we allow the individual unconditional variances in Conditional Correlation GARCH models to change smoothly over time by incorporating a nonstationary component in the variance equations. The modelling technique to determine the parametric structure of this time-varying component is based on a sequence of specification Lagrange multiplier-type tests derived in Amado and Teräsvirta (2012). The variance equations combine the long-run and the short-run dynamic behaviour of the volatilities. The structure of the conditional correlation matrix is assumed to be either time independent or to vary over time. We apply our model to pairs of seven daily stock returns belonging to the S&P 500 composite index and traded at the New York Stock Exchange. The results suggest that accounting for deterministic changes in the unconditional variances considerably improves the fit of the multivariate Conditional Correlation GARCH models to the data. The effect of careful specification of the variance equations on the estimated correlations is variable: in some cases rather small, in others more discernible. As a by-product, we generalize news impact surfaces to the situation in which both the GARCH equations and the conditional correlations contain a deterministic component that is a function of time.
Centre for Research in Econometric Analysis of Time Series
Timo Teräsvirta is Professor of Economics, Aarhus University, and member of CREATES. He received his DPolSc (Econometrics) from the University of Helsinki 1970. He has been Professor of Statistics, University of Helsinki, 1976-1980, Research Fellow, Research Institute of the Finnish Economy, 1980-1989, Research Fellow, Norges Bank, 1992-1993, 1994, 2000, and Professor of Econometrics, Stockholm School of Economics, 1994-2006. Teräsvirta is elected member of the International Statistical Institute (since 1978), Societas Scientiarum Fennica, Helsinki (since 1978), and the Royal Academy of Sciences, Stockholm (since 2001). He is Distinguished Author of Journal of Applied Econometrics and Fellow of Journal of Econometrics. His research and teaching interests include nonlinear time series econometrics and modelling volatility