A One Line Derivation of DCC: Application of a Vector Random Coefficient Moving Average Process - Christian M. Hafner; Michael McAleer (Tinbergen Institute, 2014)
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 (QMLE). To date, the statistical properties of the QMLE of the DCC parameters have been derived under highly restrictive and unverifiable regularity conditions. 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.
Keywords: C22; C52; C58; G32; 330; Dynamic conditional correlation; dynamic conditional covariance; vector random coefficient moving average; stationarity; invertibility; asymptotic properties