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PozycjaFolia Oeconomica Cracoviensia, Vol. LIII(Krakowska Akademia im. Andrzeja Frycza Modrzewskiego, Polska Akademia Nauk - Oddział w Krakowie - Komisja Nauk Ekonomicznych i Statystyki, 2012) Marzec, Jerzy; Osiewalski, Jacek; Pipień, Mateusz; Prędki, Artur; Wróbel-Rotter, Renata; Iwasiewicz, Andrzej PozycjaKonstrukcja portfeli efektywnych z zastosowaniem wielorownaniowych modeli(Oficyna Wydawnicza AFM, 2007) Fiszeder, PiotrThe purpose of this paper is to present dynamic approach to selection of efficient port folios using a forecasts of variances and covar iances from the multivaria te GARCH models. Evaluation of efficiency for different methods of asset allocation is also performed for stocks from the WSE. Twelve specif ications o f the multivariate GARCH models, the univariate GARCH model and six other covariance matrix estimation methods are used. Taking in to consideration time varying variances and covariances of stock returns in portfolio selections increases, with some exceptions , efficiency of asset allocation process. Simple specifications of the multivariateGARCH models, which parame ters are estimated in one stage, are the best performing models. From economic point of view, the differences between the models are not significant, with exception of the factor and orthogonal models. RiskMetrics methodology commonly used by practitioners does not give good results for constructions of efficient portfolios . PozycjaOrthogonal transformation of coordinates in copula m-garch models - Bayesian analysis for wig20 spot and futures returns(Oficyna Wydawnicza AFM, 2012) Pipień, MateuszWe check the empirical importance of some generalisations of the conditional distribution in M-GARCH case. A copula M-GARCH model with coordinate free conditional distribution is considered, as a continuation of research concerning specification of the conditional distribution in multivariate volatility models, see Pipień (2007, 2010). The main advantage of the proposed family of probability distributions is that the coordinate axes, along which heavy tails and symmetry can be modelled, are subject to statistical inference. Along a set of specified coordinates both, linear and nonlinear dependence can be expressed in a decomposed form. In the empirical part of the paper w e considered a problem of modelling the dynamics of the returns on the spot and future quotations of the WIG20 index from the Warsaw Stock Exchange. On the basis of the posterior odds ratio we checked the data support of considered generalisation, comparing it with BEKK model with the conditional distribution simply constructed as a product of the univariate skewed components. Our example clearly showed the empirical importance of the proposed class of the coordinate free conditional distributions.