Comparing Density Forecasts Via Weighted Likelihood Ratio Tests: Asymptotic and Bootstrap Methods

UCSD, Economics Working Paper No. 2002-12

37 Pages Posted: 10 Nov 2002

See all articles by Raffaella Giacomini

Raffaella Giacomini

University College London - Department of Economics; University of California, Los Angeles - Department of Economics

Date Written: June 2002

Abstract

This paper proposes and analyzes tests that can be used to compare the accuracy of alternative conditional density forecasts of a variable. The tests are also valid in the broader context of model selection based on out-of-sample predictive ability. We restrict attention to the case of density forecasts derived from non-nested parametric models, with known or estimated parameters. The evaluation makes use of scoring rules, which are loss functions defined over the density forecast and the realizations of the variable. In particular, we consider the logarithmic scoring rule, which leads to the development of asymptotic and bootstrap 'weighted likelihood ratio' tests. The name comes from the fact that the tests compare weighted averages of the scores over the available sample, as a way to focus attention on different regions of the distribution of the variable. For a uniform weight function, the asymptotic test can be interpreted as an extension of Vuong (1989)'s likelihood ratio test for non-nested hypotheses to time series data and to an out-of-sample testing framework. A Monte Carlo simulation explores the size and power properties of this last test in finite samples. An application using S&P500 daily returns shows how the tests can be used to compare the performance of density forecasts obtained from GARCH models with different distributional assumptions.

Keywords: Density Forecasting, Scoring Rules, Predictive Ability, Forecast Comparision

JEL Classification: C12, C22, C52, C53

Suggested Citation

Giacomini, Raffaella, Comparing Density Forecasts Via Weighted Likelihood Ratio Tests: Asymptotic and Bootstrap Methods (June 2002). UCSD, Economics Working Paper No. 2002-12, Available at SSRN: https://ssrn.com/abstract=340680 or http://dx.doi.org/10.2139/ssrn.340680

Raffaella Giacomini (Contact Author)

University College London - Department of Economics ( email )

Gower Street
London WC1E 6BT, WC1E 6BT
United Kingdom

University of California, Los Angeles - Department of Economics ( email )

405 Hilgard Avenue
Box 951361
Los Angeles, CA 90095-1361
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
178
Abstract Views
1,416
rank
234,438
PlumX Metrics