Publication: A One Line Derivation of DCC: Application of a Vector Random Coefficient Moving Average Process
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2014-07
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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.
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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.
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