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On loss functions and ranking forecasting performances of multivariate volatility models

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  • Laurent, Sébastien
  • Rombouts, Jeroen V.K.
  • Violante, Francesco

Abstract

The ranking of multivariate volatility models is inherently problematic because when the unobservable volatility is substituted by a proxy, the ordering implied by a loss function may be biased with respect to the intended one. We point out that the size of the distortion is strictly tied to the level of the accuracy of the volatility proxy. We propose a generalized necessary and sufficient functional form for a class of non-metric distance measures of the Bregman type which ensure consistency of the ordering when the target is observed with noise. An application to three foreign exchange rates is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:173:y:2013:i:1:p:1-10
    DOI: 10.1016/j.jeconom.2012.08.004
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    More about this item

    Keywords

    Volatility; Multivariate GARCH; Matrix norm; Loss function; Model confidence set;
    All these keywords.

    JEL classification:

    • 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; Diffusion Processes; State Space 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)

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