Stationarity and Invertibility of a Dynamic Correlation Matrix

摘要：

　　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.

关键词： Eigen values and eigenvectors dynamic conditional correlation dynamic conditional covariance vector random coefficient moving average stationarity invertibility asymptotic properties

作者: Christian M.Hafner Michael McAleer

作者单位: ISBA and CORE Université Catholique de Louvain,Belgium Department of Quantitative Finance National Tsing Hua University,Taiwan

会议类型: 国际会议

会议名称: ICEFS2017(International Conference on Economics, Finance and Statistics 2017) (2017经济、金融与统计国际会议)

会议地点: 香港

会议语种:英文

页码: 8-18

在线出版日期: 2017-01-14（万方平台首次上网日期，不代表论文的发表时间）