Regular variation and related results for the multivariate GARCH(p,q) model with constant conditional correlations

AbstractWe establish the regular variation of the finite dimensional distributions of the multivariate GARCH(p,q) process with constant conditional correlations under mild assumptions on the noise distribution. We use this property for two main purposes: First, to describe the componentwise-maximum domain of attraction in which the process lies; and second, to relate the asymptotic behavior of the sample autocovariance function of the process to its regular variation index

Applications of М-GARCH Model for the Selection of Securities of Banks’ Investment Portfolio

The main aim of this article is to investigate the accuracy of the Multivariate Generalized Autoregressive Conditional Heteroskedasticity Model (M-GARCH) for the selection of the best investment portfolio. There is extended literature on M-GARCH in this field with a great number of studies using different sets of variables among them the returns of assets, the volatility of the assets in the investment portfolio, the maturity date of the asset etc. The origin of M-GARCH is associated with the elements of the Dynamic Conditional Correlations Model (DDCM) as proposed by Engle. An earlier version of DDCM with time variations in the correlation matrix has been developed by Bollerslev. DCCM offers flexibility by incorporating different levels of volatilities able to structure portfolios with a great number of assets. M-GARCH models take into account separate univariate GARCH models, associate with each asset in the portfolio, in order to form a complete M-GARCH model. The present article uses a multiple dimension classic M-GARCH volatility model on a data set consisting from three time series. The daily ASE index on stock returns (Athens), the DAX index (Germany) and the CAC index (France). For each national index, the continuously compounded return was estimated as rt=100[log(pt)-log(pt-1)], where pt is the price on day t