Multivariate mixed normal conditional heteroskedasticity
Computational Statistics & Data Analysis
Asymmetric multivariate normal mixture GARCH
Computational Statistics & Data Analysis
Efficient estimation of copula-GARCH models
Computational Statistics & Data Analysis
Multivariate distribution models with generalized hyperbolic margins
Computational Statistics & Data Analysis
An extension of the Gauss-Newton algorithm for estimation under asymmetric loss
Computational Statistics & Data Analysis
Time-varying joint distribution through copulas
Computational Statistics & Data Analysis
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When forecasts are assessed by a general loss (cost-of-error) function, the optimal point forecast is, in general, not the conditional mean, and depends on the conditional volatility-which, for stock returns, is time-varying. In order to provide forecasts of daily returns of 30 DJIA stocks under a general multivariate loss function, the following issues are addressed. We discuss what conditions define a multivariate loss function, and a simple class of such functions is proposed. Based on suitable combinations of univariate losses, the suggested multivariate functions are convenient for practical applications with many variables. To keep the computational aspect tractable, a flexible multivariate GARCH model is employed in estimating the conditional forecast distributions. The model easily copes with large number of series while allowing for skewness, fat tails, non-ellipticity, and tail dependence. Based on Engle's DCC GARCH, it uses multivariate affine generalized hyperbolic distributions as conditional probability law, and the number of parameters to be estimated simultaneously does not depend on the number of series. The model is fitted using daily data from 2002 to 2007 (keeping data from 2008 for out-of-sample forecasts), and a bootstrap procedure is used to derive point forecasts under several multivariate loss functions of the proposed type.