A Nonparametric Goodness-of-fit-based Test for Conditional Heteroskedasticity

• Main Authors: SU, Liangjun, ULLAH, Aman
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2009
• Subjects: ANOVA; Conditional homoskedasticity; Consistency; Local polynomial regressions; Nonparametric R2; Nonparametric test; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1257; https://ink.library.smu.edu.sg/context/soe_research/article/2256/viewcontent/heteroskedasticity09.pdf
• Institution: Singapore Management University

In this paper we propose a nonparametric test for conditional heteroskedasticity based on a new measure of nonparametric goodness-of-fit (R2). In analogy with the ANOVA tools for classical linear regression models, the nonparametric R2 is obtained for the local polynomial regression of the residuals from a parametric regression on some covariates. It is close to 0 under the null hypothesis of conditional homoskedasticity and stays away from 0 otherwise. Unlike most popular parametric tests in the literature, the new test does not require the correct specification of parametric conditional heteroskedasticity form and thus is able to detect all kinds of conditional heteroskedasticity of unknown form. We show that after being appropriately centered and standardized, the nonparametric R2 is asymptotically normally distributed under the null hypothesis of conditional homoskedasticity and a sequence of Pitman local alternatives. We also prove the consistency of the test, propose a bootstrap method to obtain the critical values or bootstrap p-values, and justify the validity of the bootstrap method. We conduct a small set of Monte Carlo simulations and compare our test with some popular parametric and nonparametric tests in the literature. Applications to the U.S. real GDP growth rate data indicate that our nonparametric test can reveal certain conditional heteroskedasticity which the parametric tests fail to detect.