The spurious effect of ARCH errors on linearity tests: a theoretical note and an alternative maximum likelihood approach
-
Efthymios G. Pavlidis
and
Mike Tsionas
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.
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Supplemental Material
The online version of this article offers supplementary material (DOI: https://doi.org/10.1515/snde-2016-0055).
©2018 Walter de Gruyter GmbH, Berlin/Boston
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Articles in the same Issue
- Markov-switching quantile autoregression: a Gibbs sampling approach
- Uncertainty in the housing market: evidence from US states
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