Comparing density forecast models<FNR HREF="fn1"></FNR> <FN ID="fn1"><P>Previous versions of this paper have been circulated with the title, 'A Test for Density Forecast Comparison with Applications to Risk Management' since October 2003; see Bao <TOGGLE>et al.</TOGGLE> (2004).</P></FN>

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Comparing density forecast models
Previous versions of this paper have been circulated with the title, 'A Test for Density Forecast Comparison with Applications to Risk Management' since October 2003; see Bao et al. (2004).

Author Info

Tae-Hwy Lee (University of California, Riverside, California USA)
Yong Bao (University of Texas, San Antonio, Texas, USA)
Burak Saltoğlu (Bosphorous University, Istanbul, Turkey)

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Abstract

In this paper we discuss how to compare various (possibly misspecified) density forecast models using the Kullback-Leibler information criterion (KLIC) of a candidate density forecast model with respect to the true density. The KLIC differential between a pair of competing models is the (predictive) log-likelihood ratio (LR) between the two models. Even though the true density is unknown, using the LR statistic amounts to comparing models with the KLIC as a loss function and thus enables us to assess which density forecast model can approximate the true density more closely. We also discuss how this KLIC is related to the KLIC based on the probability integral transform (PIT) in the framework of Diebold et al. (1998). While they are asymptotically equivalent, the PIT-based KLIC is best suited for evaluating the adequacy of each density forecast model and the original KLIC is best suited for comparing competing models. In an empirical study with the S&P500 and NASDAQ daily return series, we find strong evidence for rejecting the normal-GARCH benchmark model, in favor of the models that can capture skewness in the conditional distribution and asymmetry and long memory in the conditional variance. Copyright © 2007 John Wiley & Sons, Ltd.

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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Forecasting.

Volume (Year): 26 (2007)
Issue (Month): 3 ()
Pages: 203-225
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:jof:jforec:v:26:y:2007:i:3:p:203-225

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This file is part of IDEAS, which uses RePEc data

Comparing density forecast models Previous versions of this paper have been circulated with the title, 'A Test for Density Forecast Comparison with Applications to Risk Management' since October 2003; see Bao et al. (2004).

Comparing density forecast models
Previous versions of this paper have been circulated with the title, 'A Test for Density Forecast Comparison with Applications to Risk Management' since October 2003; see Bao et al. (2004).