"Go Wild for a While!": A New Asymptotically Normal Test for Forecast Evaluation in Nested Models

36 Pages Posted: 12 Mar 2021

See all articles by Pablo M. Pincheira

Pablo M. Pincheira

Adolfo Ibanez University - School of Business

Nicolas Hardy

Universidad Finis Terrae

Felipe Muñoz

Institute for International Studies

Date Written: January 10, 2021

Abstract

In this paper we present a new asymptotically normal test for out-of-sample evaluation in nested models. Our approach is a simple modification of a traditional encompassing test that is commonly known as Clark and West test (CW). The key point of our strategy is to introduce an independent random variable that prevents the traditional CW test from becoming degenerate under the null hypothesis of equal predictive ability. Using the approach developed by West (1996), we show that in our test the impact of parameter estimation uncertainty vanishes asymptotically. Using a variety of Monte Carlo simulations in iterated multi-step-ahead forecasts we evaluate our test and CW in terms of size and power. These simulations reveal that our approach is reasonably well-sized even at long horizons when CW may present severe size distortions. In terms of power, results are mixed but CW has an edge over our approach. Finally, we illustrate the use of our test with an empirical application in the context of the commodity currencies literature.

Keywords: forecasting, random walk, out-of-sample, prediction, mean square prediction error

Suggested Citation

Pincheira, Pablo M. and Hardy, Nicolas and Muñoz, Felipe, "Go Wild for a While!": A New Asymptotically Normal Test for Forecast Evaluation in Nested Models (January 10, 2021). Available at SSRN: https://ssrn.com/abstract=3770402 or http://dx.doi.org/10.2139/ssrn.3770402

Pablo M. Pincheira

Adolfo Ibanez University - School of Business ( email )

Diagonal Las Torres 2640
Peñalolén
Santiago
Chile

Nicolas Hardy (Contact Author)

Universidad Finis Terrae ( email )

Av. Pedro de Valdivia 1509
Ñuñoa
Santiago, Santiago
Chile

Felipe Muñoz

Institute for International Studies ( email )

Av. Condell 249
Providencia
Santiago, R. Metropolitana 7500753
Chile

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