Consistent ranking of multivariate volatility models
AbstractA large number of parameterizations have been proposed to model conditional variance dynamics in a multivariate framework. This paper examines the ranking of multivariate volatility models in terms of their ability to forecast out-of-sample conditional variance matrices. We investigate how sensitive the ranking is to alternative statistical loss functions which evaluate the distance between the true covariance matrix and its forecast. The evaluation of multivariate volatility models requires the use of a proxy for the unobservable volatility matrix which may shift the ranking of the models. Therefore, to preserve this ranking conditions with respect to the choice of the loss function have to be discussed. To do this, we extend the conditions defined in Hansen and Lunde (2006) to the multivariate framework. By invoking norm equivalence we are able to extend the class of loss functions that preserve the true ranking. In a simulation study, we sample data from a continuous time multivariate diffusion process to illustrate the sensitivity of the ranking to different choices of the loss functions and to the quality of the proxy. An application to three foreign exchange rates, where we compare the forecasting performance of 16 multivariate GARCH specifications, is provided.
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Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2009002.
Date of creation: 01 Jan 2009
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volatility; multivariate GARCH; matrix norm and loss function; norm equivalence;
Find related papers by JEL classification:
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- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
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- Valeri Voev, 2009. "On the Economic Evaluation of Volatility Forecasts," CREATES Research Papers 2009-56, School of Economics and Management, University of Aarhus.
- Audrino, Francesco, 2011. "Forecasting correlations during the late-2000s financial crisis: short-run component, long-run component, and structural breaks," Economics Working Paper Series 1112, University of St. Gallen, School of Economics and Political Science.
- Manner, Hans & Reznikova, Olga, 2010. "Forecasting international stock market correlations: does anything beat a CCC?," Discussion Papers in Statistics and Econometrics 7/10, University of Cologne, Department for Economic and Social Statistics.
- Rasmus Tangsgaard Varneskov, 2011. "Flat-Top Realized Kernel Estimation of Quadratic Covariation with Non-Synchronous and Noisy Asset Prices," CREATES Research Papers 2011-35, School of Economics and Management, University of Aarhus.
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