Asymptotic Theory for Multivariate GARCH Processes

Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes∗

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 whi...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Genetic and Evolutionary Algorithms and Programming

98. Nelson DB (1990) Stationarity and persistence in the GARCH(1,1) model. Econom Theory 6:318–334 99. Nelson DB (1991) Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59:347–370 100. Nelson DB, Cao CQ (1992) Inequality constraints in the univariate garchmodel. J Bus Econ Stat 10:229–235 101. Newey WK, Steigerwald DS (1997) Asymptotic bias for quasi maximum likelih...

Augmented GARCH sequences: Dependence structure and asymptotics

The augmented GARCH model is a unification of numerous extensions of the popular and widely used ARCH process. It was introduced by Duan and besides ordinary (linear) GARCH processes, it contains exponential GARCH, power GARCH, threshold GARCH, asymmetric GARCH, etc. In this paper, we study the probabilistic structure of augmented GARCH(1,1) sequences and the asymptotic distribution of various ...

Volatility Modelling of Multivariate Financial Time Series by Using ICA-GARCH Models

Volatility modelling of asset returns is an important aspect for many financial applications, e.g., option pricing and risk management. GARCH models are usually used to model the volatility processes of financial time series. However, multivariate GARCH modelling of volatilities is still a challenge due to the complexity of parameters estimation. To solve this problem, we suggest using Independ...