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The spurious effect of ARCH errors on linearity tests: a theoretical note and an alternative maximum likelihood approach

Author

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  • Pavlidis Efthymios G.
  • Tsionas Mike

    (Lancaster University Management School, Department of Economics, Bailrigg, Lancaster, LA1 4YX, United Kingdom of Great Britain and Northern Ireland)

Abstract

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.

Suggested Citation

  • Pavlidis Efthymios G. & Tsionas Mike, 2018. "The spurious effect of ARCH errors on linearity tests: a theoretical note and an alternative maximum likelihood approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(2), pages 1-8, April.
    • Handle: RePEc:bpj:sndecm:v:22:y:2018:i:2:p:8:n:2
    DOI: 10.1515/snde-2016-0055
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