Working Papers

From Kevin Sheppard

Evaluating Volatility and Correlation Forecasts , joint with Andrew Patton
This is a chapter in the forthcoming Handbook of Financial Time Series, edited by Torben G. Andersen, Richard A. Davis, Jens-Peter Kreiss, and Thomas Mikosch.

Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH with Robert F. Engle
The theoretical and empirical properties of a new class of multivariate GARCH models capable of estimating large time-varying covariance matrices, Dynamic Conditional Correlation (DCC) Multivariate GARCH are developed. We show that the problem of multivariate conditional covariance estimation can be simplified by estimating univariate GARCH models for each asset?s variance, and then, using transformed residuals resulting from the first stage, estimating a time-varying conditional correlation estimator. The standard errors of the first stage parameters remain consistent, and only the standard errors for the correlation parameters need be modified. We use the model to estimate the conditional covariance of up to 100 assets using S&P 500 Sector Indices and Dow Jones Industrial Average stocks, and conduct specification tests of the estimator using an industry standard benchmark for volatility models. This new estimator demonstrates very strong performance especially considering the ease of implementation of the estimator.

Economic factors and the covariance of Equity Returns
This paper examines the dynamics in the covariance of equity returns using a set of exogenous explanatory variables in place of lagged cross-products. A model is developed which allows for the inclusion of exogenous variables in the conditional covariance without requiring the variables to be non-negative. The model parameterizes the symmetric square-root of the conditional covariance as a linear process in the explanatory variables. Using a set of 6 market equity and BE/ME sorted portfolios, exogenous variables are able to explain up to 10% of the variation in conditional variances and up to 30% in the variation in conditional correlations. The model is extended to allow for ARCH effects where the effect of exogenous variables, while diminished, remains significant. Further, including exogenous variables lowers the persistence in conditional covariances as measured by the parameter on lagged covariance. These findings are consistent with a two time-scale interpretation of conditional covariances, a high frequency component lasting a few months, and a low frequency, business-cycle length component captured by the exogenous explanatory variables.