# 16-071/III (2016-09-05)

Manabu Asai, Soka University, Japan; Michael McAleer, National Tsing Hua University, Taiwan; Erasmus University Rotterdam, the Netherlands; Complutense University of Madrid, Spain; Yokohama National University, Japan
Multivariate conditional volatility, Vector random coefficient autoregressive process, Asymmetry, Long memory, Dynamic conditional correlations, Regularity conditions, Asymptotic properties
JEL codes:
C13, C32, C58

The paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive asymptotic theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated asymptotic properties.