On bootstrapping tests of equal forecast accuracy for nested models

Firmin Doko Tchatoka and Qazi Haque

CAMA Working Papers from Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University

Abstract: The asymptotic distributions of the recursive out-of-sample forecast accuracy test statistics depend on stochastic integrals of Brownian motion when the models under comparison are nested. This often complicates their implementation in practice because the computation of their asymptotic critical values is costly. Hansen and Timmermann (2015, Econometrica) propose a Wald approximation of the commonly used recursive F-statistic and provide a simple characterization of the exact density of its asymptotic distribution. However, this characterization holds only when the larger model has one extra predictor or the forecast errors are homoscedastic. No such closed-form characterization is readily available when the nesting involves more than one predictor and heteroskedasticity is present. We first show both the recursive F-test and its Wald approximation have poor finite-sample properties, especially when the forecast horizon is greater than one. We then propose a hybrid bootstrap method consisting of a block moving bootstrap (which is nonparametric) and a residual based bootstrap for both statistics, and establish its validity. Simulations show that our hybrid bootstrap has good finite-sample performance, even in multi-step ahead forecasts with heteroscedastic or autocorrelated errors, and more than one predictor. The bootstrap method is illustrated on forecasting core inflation and GDP growth.

Keywords: Out-of-sample forecasts; HAC estimator; Moving block bootstrap; Bootstrap consistency (search for similar items in EconPapers)
JEL-codes: C12 C15 C32 (search for similar items in EconPapers)
Pages: 43 pages
Date: 2020-03
New Economics Papers: this item is included in nep-for and nep-ore
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Related works:
Journal Article: On bootstrapping tests of equal forecast accuracy for nested models (2023)
Working Paper: On bootstrapping tests of equal forecast accuracy for nested models (2020)
Working Paper: On bootstrapping tests of equal forecast accuracy for nested models (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:een:camaaa:2020-27

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