Cholesky-GARCH models with applications to finance |
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Authors: | Petros Dellaportas Mohsen Pourahmadi |
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Institution: | 1.Department of Statistics,Athens University of Economics and Business,Athens,Greece;2.Department of Statistics,Texas A&M University,College Station,USA |
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Abstract: | Instantaneous dependence among several asset returns is the main reason for the computational and statistical complexities
in working with full multivariate GARCH models. Using the Cholesky decomposition of the covariance matrix of such returns,
we introduce a broad class of multivariate models where univariate GARCH models are used for variances of individual assets
and parsimonious models for the time-varying unit lower triangular matrices. This approach, while reducing the number of parameters
and severity of the positive-definiteness constraint, has several advantages compared to the traditional orthogonal and related
GARCH models. Its major drawback is the potential need for an a priori ordering or grouping of the stocks in a portfolio,
which through a case study we show can be taken advantage of so far as reducing the forecast error of the volatilities and
the dimension of the parameter space are concerned. Moreover, the Cholesky decomposition, unlike its competitors, decompose
the normal likelihood function as a product of univariate normal likelihoods with independent parameters, resulting in fast
estimation algorithms. Gaussian maximum likelihood methods of estimation of the parameters are developed. The methodology
is implemented for a real financial dataset with seven assets, and its forecasting power is compared with other existing models. |
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