Stationarity and Invertibility of a Dynamic Correlation Matrix

DOI

10.2991/icefs-17.2017.2How to use a DOI?

Keywords

Eigen values and eigenvectors, dynamic conditional correlation, dynamic conditional covariance, vector random coefficient moving average, stationarity, invertibility, asymptotic properties.

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 regularity conditions, such as stationarity and invertibility, and 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, which essentially leads to proof by assumption. 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 of the DCC model. 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 univariate conditional volatility model for DCC is based on the standardized shocks rather than the returns shocks. The derivation of the regularity conditions, especially stationarity and invertibility, should subsequently lead to a solid statistical foundation for the estimates of the DCC parameters.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Christian Hafner
AU  - Michael McAleer
PY  - 2017/01
DA  - 2017/01
TI  - Stationarity and Invertibility of a Dynamic Correlation Matrix
BT  - Proceedings of the 2017 International Conference on Economics, Finance and Statistics (ICEFS 2017)
PB  - Atlantis Press
SP  - 8
EP  - 18
SN  - 2352-5428
UR  - https://doi.org/10.2991/icefs-17.2017.2
DO  - 10.2991/icefs-17.2017.2
ID  - Hafner2017/01
ER  -