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ROBUST FORECAST COMPARISON

Published online by Cambridge University Press:  27 October 2016

Sainan Jin ,
Valentina Corradi  and
Norman R. Swanson
Sainan Jin*
Affiliation:
Singapore Management University
Valentina Corradi
Affiliation:
University of Surrey
Norman R. Swanson
Affiliation:
Rutgers University
*
*Address correspondence to Sainan Jin, School of Economics, Singapore Management University, 90 Stamford Road, Singapore 178903; e-mail: snjin@smu.edu.sg.
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Abstract

Forecast accuracy is typically measured in terms of a given loss function. However, as a consequence of the use of misspecified models in multiple model comparisons, relative forecast rankings are loss function dependent. In order to address this issue, a novel criterion for forecast evaluation that utilizes the entire distribution of forecast errors is introduced. In particular, we introduce the concepts of general-loss (GL) forecast superiority and convex-loss (CL) forecast superiority; and we develop tests for GL (CL) superiority that are based on an out-of-sample generalization of the tests introduced by Linton, Maasoumi, and Whang (2005, Review of Economic Studies 72, 735–765). Our test statistics are characterized by nonstandard limiting distributions, under the null, necessitating the use of resampling procedures to obtain critical values. Additionally, the tests are consistent and have nontrivial local power, under a sequence of local alternatives. The above theory is developed for the stationary case, as well as for the case of heterogeneity that is induced by distributional change over time. Monte Carlo simulations suggest that the tests perform reasonably well in finite samples, and an application in which we examine exchange rate data indicates that our tests can help identify superior forecasting models, regardless of loss function.

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Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 6 , December 2017 , pp. 1306 - 1351
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

We are grateful to the editor, Peter C. B. Phillips, the co-editor, Robert Taylor, two referees, Xu Cheng, Frank Diebold, Jesus Gonzalo, Simon Lee, Federico Martellosio, Chris Martin, Vito Polito, Barbara Rossi, Olivier Scaillet, Minchul Shin, Tang Srisuma, Liangjun Su; and to seminar participants at the University of Surrey, the University of Bath, the 2015 Princeton/QUT/SJTU/SMU Conference on the Frontier in Econometrics, the 2015 UK Econometric Study Group, 4th International Conference in Applied Econometrics, Universita’ Milano Bicocca, and the 2016 Winter Econometric Society Winter Meeting for useful comments and suggestions. For research support, Jin thanks the Singapore Ministry of Education for Academic Research Fund under grant number MOE2012-T2-2-021.

References

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