Nonparametric Tests for Superior Predictive Ability

64 Pages Posted: 12 Oct 2018 Last revised: 8 Mar 2020

See all articles by Stelios Arvanitis

Stelios Arvanitis

Athens University of Economics and Business

Selcuk Karabati

Koc University - College of Administrative Sciences and Economics

Thierry Post

Graduate School of Business of Nazarbayev University

Valerio Potì

University College Dublin

Date Written: June 13, 2019

Abstract

Abstract A nonparametric method for comparing multiple forecast models is developed and implemented. The hypothesis of Optimal Predictive Ability generalizes the Superior Predictive Ability hypothesis from a single given loss function to an entire class of loss functions. Distinction is drawn between General Loss functions, Convex Loss functions and Symmetric Convex Loss functions. The research hypothesis is formulated in terms of moment inequality conditions. The empirical moment conditions are reduced to an exact and finite system of linear inequalities based on piecewise-linear loss functions. The hypothesis can be tested in a statistically consistent way using a blockwise Empirical Likelihood Ratio test statistic. A computationally feasible test procedure computes the test statistic using Convex Optimization methods, and estimates conservative, data-dependent critical values using a majorizing chi-square limit distribution and a moment selection method. An empirical application to inflation forecasting reveals that a very large majority of thousands of forecast models are redundant, leaving predominantly Phillips Curve type models, when convexity and symmetry are assumed.

Keywords: Forecast Comparison, Stochastic Dominance, Empirical Likelihood, Inflation Forecasting

JEL Classification: C12, C44, C52, C53, C61, D81

Suggested Citation

Arvanitis, Stelios and Karabati, Selcuk and Post, Thierry and Potì, Valerio, Nonparametric Tests for Superior Predictive Ability (June 13, 2019). Available at SSRN: https://ssrn.com/abstract=3251944 or http://dx.doi.org/10.2139/ssrn.3251944

Stelios Arvanitis

Athens University of Economics and Business ( email )

76 Patission Street
Athens, 104 34
GREECE

Selcuk Karabati

Koc University - College of Administrative Sciences and Economics ( email )

Rumelifeneri Yolu
College of Administrative Sciences and Economics
Sariyer 34450, Istanbul
Turkey

Thierry Post (Contact Author)

Graduate School of Business of Nazarbayev University ( email )

53 Kabanbay Batyra Avenue
Astana, 010000
Kazakhstan

Valerio Potì

University College Dublin ( email )

M. Smurfit School of Business
Carysfort Avenue, Blackrock
Dublin, Co Dublin
Ireland

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