On Loss Functions and Ranking Forecasting Performances of Multivariate Volatility Models
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.Download Info
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Paper provided by CIRPEE in its series Cahiers de recherche with number 0948.Length:
Date of creation: 2009
Date of revision:
Handle: RePEc:lvl:lacicr:0948
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Keywords: Volatility; multivariate GARCH; Matrix norm; Loss function; Model confidence set;Other versions of this item:
- Laurent, Sébastien & Rombouts, Jeroen V.K. & Violante, Francesco, 2013. "On loss functions and ranking forecasting performances of multivariate volatility models," Journal of Econometrics, Elsevier, vol. 173(1), pages 1-10.
- Sébastien Laurent & Jeroen Rombouts & Francesco Violente, 2009. "On Loss Functions and Ranking Forecasting Performances of Multivariate Volatility Models," CIRANO Working Papers 2009s-45, CIRANO.
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-11-14 (All new papers)
- NEP-ECM-2009-11-14 (Econometrics)
- NEP-FOR-2009-11-14 (Forecasting)
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Caporin, M. & McAleer, M.J., 2010.
"Ranking multivariate GARCH models by problem dimension,"
Econometric Institute Report
EI 2010-34, Erasmus University Rotterdam, Econometric Institute.
- Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," CIRJE F-Series CIRJE-F-742, CIRJE, Faculty of Economics, University of Tokyo.
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