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Comparing density forecast models
Author(s) -
Bao Yong,
Lee TaeHwy,
Saltoğlu Burak
Publication year - 2007
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.1023
Subject(s) - skewness , econometrics , autoregressive conditional heteroskedasticity , conditional probability distribution , mathematics , probability integral transform , conditional variance , statistic , statistics , probability density function , volatility (finance) , moment generating function
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.