We provide a closed-form estimator based on the VARMA representation for the unrestricted multivariate GARCH(1,1). We show that all parameters can be derived using basic linear algebra tools. We show that the estimator is consistent and asymptotically normal distributed. Our results allow also to derive a closed form for the parameters in the context of temporal aggregation of multivariate GARC...

Abstract For large multivariate models of generalized autoregressive conditional heteroskedasticity (GARCH), it is important to reduce the number parameters cope with ‘curse dimensionality’. Recently, Laurent, Rombouts and Violante (2014 “Multivariate Rotated ARCH Models” Journal Econometrics 179 : 16–30) developed rotated GARCH model, which focuses on for standardized variables. This paper ext...

This paper provides a solution for the multiple changepoint detection problems in financial time series prediction without knowing the number and location of changepoints. The proposed approach is a Sequential Monte Carlo (SMC) method for estimating GARCH based volatility models which are subject to an unknown number of changepoints. Recent Auxiliary Particle Filtering (APF) techniques are used...

We propose a method for defining and measuring the spatial contagion between two financial markets. Next we investigate which from the large family of multivariate GARCH models is the best tool for modeling spatial contagion.

This paper stresses the importance of assessing the risk-return trade-off faced by environmental industries in financial markets. One of the most widely-used theoretical models in finance is the conditional CAPM, which describes the conditional risk-return tradeoff in financial markets, whereby both the conditional mean return and conditional beta risk are allowed to vary over time. This paper ...

Multivariate models of asset returns are very important in financial applications. Asset allocation, risk assessment and construction of an optimal portfolio require estimates of the covariance matrix between the returns of assets (see e.g. Aguilar and West (2000), Pajor (2005a, 2005b)). Similarly, hedges require a covariance matrix of all the assets in the hedge. There are two main types of vo...

The generalization from the univariate volatility model into a multivariate approach opens up a variety of modeling possibilities. This study aims to examine the performance of the two multivariate GARCH models BEKK and DCC, applied on ten years exchange rates data. Estimations and forecasts of the covariance matrix are made for the EUR/SEK and USD/SEK, whereby the forecasts are used in a pract...

This paper explains how the Gibbs sampler can be used to perform Bayesian inference on GARCH models. Although the Gibbs sampler is usually based on the analytical knowledge of the full conditional posterior densities, such knowledge is not available in regression models with GARCH errors. We show that the Gibbs sampler can be combined with a unidimensional deterministic integration rule applied...