TY - JOUR

T1 - The Spurious Effect of ARCH Errors on Linearity Tests

T2 - A Theoretical Note and an Alternative Maximum Likelihood Approach

AU - Pavlidis, Efthymios

AU - Tsionas, Efthymios

N1 - Copyright © 2017 by Walter de Gruyter GmbH

PY - 2018/4

Y1 - 2018/4

N2 - Linearity tests against smooth transition nonlinearity are typically based on the standard least-squares (LS) covariance matrix estimator. We derive an expression for the bias of the LS estimator in the presence of ARCH errors. We show that the bias is downward, and increases dramatically with the persistence of the variance process. As a consequence, conventional tests spuriously indicate nonlinearity. Next, we examine an alternative maximum likelihood approach. Our findings suggest that this approach has substantially better size properties than tests based on least-squares and heteroskedasticity-consistent matrix estimators, and performs comparably to a bootstrap technique.

AB - Linearity tests against smooth transition nonlinearity are typically based on the standard least-squares (LS) covariance matrix estimator. We derive an expression for the bias of the LS estimator in the presence of ARCH errors. We show that the bias is downward, and increases dramatically with the persistence of the variance process. As a consequence, conventional tests spuriously indicate nonlinearity. Next, we examine an alternative maximum likelihood approach. Our findings suggest that this approach has substantially better size properties than tests based on least-squares and heteroskedasticity-consistent matrix estimators, and performs comparably to a bootstrap technique.

KW - ARCH

KW - linearity tests

KW - smooth transition models

KW - spurious inference

U2 - 10.1515/snde-2016-0055

DO - 10.1515/snde-2016-0055

M3 - Journal article

VL - 22

JO - Studies in Nonlinear Dynamics and Econometrics

JF - Studies in Nonlinear Dynamics and Econometrics

SN - 1558-3708

IS - 2

M1 - 20160055

ER -