Template-type: ReDIF-Paper 1.0
Author-Name: Christian M. Hafner 

Author-Email: christian.hafner@uclouvain.be
Author-Person: pha77
Author-Workplace-Name: Institut de statistique, biostatistique et sciences actuarielles Université catholique de Louvain.
Author-Name: Michael McAleer
Author-Person: pmc90 
Author-Workplace-Name: Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute, 
	The Netherlands, Department of Quantitative Economics, Complutense University of Madrid, and Institute of Economic 
	Research, Kyoto University. 
Title: A One Line Derivation of DCC: Application of a Vector Random Coefficient Moving Average Process
Abstract: One of the most widely-used multivariate conditional volatility models is the dynamic conditional correlation (or DCC) 
	specification. However, the underlying stochastic process to derive DCC has not yet been established, which has made 
	problematic the derivation of asymptotic properties of the Quasi-Maximum Likelihood Estimators. The paper shows that the 
	DCC model can be obtained from a vector random coefficient moving average process, and derives the stationarity and 
	invertibility conditions. The derivation of DCC from a vector random coefficient moving average process raises three 
	important issues: (i) demonstrates that DCC is, in fact, a dynamic conditional covariance model of the returns shocks 
	rather than a dynamic conditional correlation model; (ii) provides the motivation, which is presently missing, for 
	standardization of the conditional covariance model to obtain the conditional correlation model; and (iii) shows that the 
	appropriate ARCH or GARCH model for DCC is based on the standardized shocks rather than the returns shocks. The derivation 
	of the regularity conditions should subsequently lead to a solid statistical foundation for the estimates of the DCC 
	parameters.
Classification-JEL: C22, C52, C58, G32.
Keywords: Dynamic conditional correlation, Dynamic conditional Covariance, Vector random.
 coefficient 
	moving average, stationarity, invertibility, asymptotic properties.
Note: The authors are most grateful to Gian Piero Aielli, Massimiliano Caporin and Yuk Tse for helpful comments and suggestions. 
	For financial support, the second author wishes to acknowledge the Australian Research Council and the National Science 
	Council, Taiwan. An earlier version of the paper was presented at the International Conference on Frontiers of Time Series 
	Econometrics and Related Fields, Hong Kong, July 2013.
Length: 14 pages
Creation-Date: 2014
Number: 2014-29 
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1429.txt
File-URL: https://eprints.ucm.es/id/eprint/27265/1/1429.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doicae:1429