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The role of the information set for forecasting - with applications to risk management

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  • Hajo Holzmann
  • Matthias Eulert
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    Abstract

    Predictions are issued on the basis of certain information. If the forecasting mechanisms are correctly specified, a larger amount of available information should lead to better forecasts. For point forecasts, we show how the effect of increasing the information set can be quantified by using strictly consistent scoring functions, where it results in smaller average scores. Further, we show that the classical Diebold-Mariano test, based on strictly consistent scoring functions and asymptotically ideal forecasts, is a consistent test for the effect of an increase in a sequence of information sets on $h$-step point forecasts. For the value at risk (VaR), we show that the average score, which corresponds to the average quantile risk, directly relates to the expected shortfall. Thus, increasing the information set will result in VaR forecasts which lead on average to smaller expected shortfalls. We illustrate our results in simulations and applications to stock returns for unconditional versus conditional risk management as well as univariate modeling of portfolio returns versus multivariate modeling of individual risk factors. The role of the information set for evaluating probabilistic forecasts by using strictly proper scoring rules is also discussed.

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    File URL: http://arxiv.org/pdf/1404.7653
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1404.7653.

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    Date of creation: Apr 2014
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    Publication status: Published in Annals of Applied Statistics 2014, Vol. 8, No. 1, 595-621
    Handle: RePEc:arx:papers:1404.7653

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    Web page: http://arxiv.org/

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    1. Raffaella Giacomini & Halbert White, 2003. "Tests of conditional predictive ability," Boston College Working Papers in Economics 572, Boston College Department of Economics.
    2. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2005. "Evaluating Value-at-Risk models with desk-level data," Working Paper Series 010, North Carolina State University, Department of Economics, revised Dec 2006.
    3. Francis X. Diebold, 2012. "Comparing Predictive Accuracy, Twenty Years Later: A Personal Perspective on the Use and Abuse of Diebold-Mariano Tests," NBER Working Papers 18391, National Bureau of Economic Research, Inc.
    4. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
    5. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
    6. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
    7. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
    8. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
    9. repec:taf:jnlbes:v:30:y:2012:i:1:p:1-17 is not listed on IDEAS
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