Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/107800
Authors: 
Hafner, Christian M.
McAleer, Michael
Year of Publication: 
2014
Series/Report no.: 
Tinbergen Institute Discussion Paper 14-087/III
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 (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.
Subjects: 
Dynamic conditional correlation
dynamic conditional covariance
vector random coefficient moving average
stationarity
invertibility
asymptotic properties
JEL: 
C22
C52
C58
G32
Document Type: 
Working Paper

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