A bootstrap approach to test the conditional symmetry in time series models

Abstract

This paper discusses how to test for conditional symmetry in time series regression models. To that end, we utilize the Bai and Ng test. We also examine the performance of some popular (unconditional) symmetry tests for observations when applied to regression residuals. The tests considered include the coeficient of skewness, a joint test of the third and fifth moments, the Runs test, the Wilcoxon signed-rank test and the Triples test. An easy-to-implement symmetric bootstrap procedure is proposed to calculate critical values for these tests. Consistency of the bootstrap procedure will be shown. A simple Monte Carlo experiment is conducted to explore the finite-sample properties of all the tests.Codes JEL: C12; C15; C22

Neoclassical versus Frontier Production Models? Testing for the Skewness of Regression Residuals*

“…In the symmetry test, we sample from the symmetrized residual distribution, whereas in the normality test we sample from the standard normal density. The power of the bootstrap method is evident from the Monte Carlo simulations reported by Pérez‐Alonso (2007).…”

“…The challenge of applying the test to the more general, non‐parametric H′ 0 arises from the fact that the true distribution under the null remains unspecified. Pérez‐Alonso (2007) has devised a non‐parametric bootstrap approach, which can be adapted to our purposes. The main idea is to find a bootstrap distribution that mimics the actual distribution of disturbances under the null hypothesis.…”

“…Pérez‐Alonso's (2007) bootstrap procedure can be adapted for our purposes as follows. We compute the critical values of the statistic under the H′ 0 of symmetry in five stages.…”

A nonparametric test for conditional symmetry in nonstationary and absolutely regular dynamical models

“…Our main objective in this paper is to test H 0 : F ∈ S against H 1 : F / ∈ S. This testing problem generalizes the one in Bai and Ng [1], Pérez-Alonso [5] or Ngatchou-Wandji [4], in the sense that if the ε i 's are iid, then all the F i 's equal the distribution function F . Another relevent paper is Delgado and Escanciano [2] where testing conditional symmetry in dynamical models has been considered for stationary observations and nonnecessarily independent errors.…”

“…Assume that (A1)-(A4), the conditions (4),(5) and (6) hold and F (t) is continuous. Then for F n (t) defined by (7), in probability,sup t∈R F n (t) − F (t) → 0, as n → ∞.Theorem 2.…”