Articlegreen2007

Comparing density forecast models

154 citations0/0 files storedJournal of Forecasting

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Financial Risk and Volatility Modeling Forecasting Techniques and Applications Statistical Distribution Estimation and Applications

Abstract

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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References

1986Generalized autoregressive conditional heteroskedasticity 1982Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation 1991Conditional Heteroskedasticity in Asset Returns: A New Approach 1993On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks 1994Comparing Predictive Accuracy 1993A long memory property of stock market returns and a new model 1994Threshold heteroskedastic models 1998Evaluating Density Forecasts with Applications to Financial Risk Management

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2011Likelihood-based scoring rules for comparing density forecasts in tails 2010Do high-frequency measures of volatility improve forecasts of return distributions?2010Evaluating density forecasts: forecast combinations, model mixtures, calibration and sharpness 2012Modeling Realized Covariances and Returns 2010A Multi-Horizon Comparison of Density Forecasts for the S&P 500 Using Index Returns and Option Prices

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