Multivariat ARCH and test for constant beta

Specialeforsvar ved Tobias Bedstrup Eiberg

Titel: Multivariat ARCH and test for constant beta 

Abstract: In this thesis two of the key multivariate GARCH models, the so-called BEKK and CCC models, are analyzed in detail. The focus will be the implications from multivariate GARCH modeling for conditional, or partial modeling, where one (or more) stock returns are conditioned upon one or more risk factors identified in the multivariate GARCH analysis. A key question posed here is the often maintained epirical hypothesis of a time constant conditional mean regression parameter(s) beta which here load the driving factor(s). Specifically, likelihood-based analysis of the mentioned multivariate GARCH models will be applied and discussed in detail. The multivariate GARCH covariance matrix will be estimated for the three stock returns Chevron, CitiGroup and Coca Cola as well as one driving factor the New York Stock Exchange Composite Index. In terms of estimation and theory the likelihood analysis for the GARCH models will be treated with both Gaussian- and t-distributed innovations respectively in order to identify a plausible model for the data. From the joint multivariate analysis the time varying regression parameter beta_t can be derived explicitly. Next is the investigation of parametrizations of the multivariate GARCH models which is empirically relevant and which allows testing for the hypothesis of a constant beta_t, beta_t=beta. The hypothesis will be investigated by likelihood-based inference for the mentioned time series. One expects a time varying beta_t, possibly with periods of time where constancy can't be rejected

Vejleder:    Anders Rahbek, Ø.I.
Censor:     Jesper Lund, CBS