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Nonparametric tests for conditional symmetry

Miguel A. Delgado and Xiaojun Song

Journal of Econometrics, 2018, vol. 206, issue 2, 447-471

Abstract: We propose omnibus tests for symmetry of the conditional distribution of a time series process about a nonparametric regression function. The test statistic is a weighted version of the integrated squared difference between the restricted and unrestricted estimators of the joint characteristic function of nonparametric residuals and explanatory variables, whose critical values are estimated with the assistance of a bootstrap technique. The test is sensitive to local alternatives converging to the null at the parametric rate T−1∕2, with T the sample size. We investigate the finite sample performance of the test by means of Monte Carlo experiments and two empirical applications to test whether losses are more likely than gains in financial markets, and whether expansions and contractions are equally likely in business cycles, given the relevant information.

Keywords: Conditional symmetry; Nonparametric testing; Permutation; Smoothing; Time series data (search for similar items in EconPapers)
JEL-codes: C12 C14 C15 (search for similar items in EconPapers)
Date: 2018
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