On Loss Functions and Ranking Forecasting Performances of Multivariate Volatility Models

Sébastien Laurent, Jeroen Rombouts and Francesco Violante ()

Cahiers de recherche from CIRPEE

Abstract: A large number of parameterizations have been proposed to model conditional variance dynamics in a multivariate framework. However, little is known about the ranking of multivariate volatility models in terms of their forecasting ability. The ranking of multivariate volatility models is inherently problematic because it requires the use of a proxy for the unobservable volatility matrix and this substitution may severely affect the ranking. We address this issue by investigating the properties of the ranking with respect to alternative statistical loss functions used to evaluate model performances. We provide conditions on the functional form of the loss function that ensure the proxy-based ranking to be consistent for the true one – i.e., the ranking that would be obtained if the true variance matrix was observable. We identify a large set of loss functions that yield a consistent ranking. In a simulation study, we sample data from a continuous time multivariate diffusion process and compare the ordering delivered by both consistent and inconsistent loss functions. We further discuss the sensitivity of the ranking to the quality of the proxy and the degree of similarity between models. An application to three foreign exchange rates, where we compare the forecasting performance of 16 multivariate GARCH specifications, is provided.

Keywords: Volatility; multivariate GARCH; Matrix norm; Loss function; Model confidence set (search for similar items in EconPapers)
JEL-codes: C10 C32 C51 C52 C53 G10 (search for similar items in EconPapers)
Date: 2009
New Economics Papers: this item is included in nep-ecm and nep-for
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Citations: View citations in EconPapers (22)

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Related works:
Journal Article: On loss functions and ranking forecasting performances of multivariate volatility models (2013)
Working Paper: On Loss Functions and Ranking Forecasting Performances of Multivariate Volatility Models (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:lvl:lacicr:0948

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