Testing linearity against parametric alternatives

Timo Teräsvirta, Dag Tjøstheim and W. J. Granger

in Modelling Nonlinear Economic Time Series

Published in print December 2010 | ISBN: 9780199587148
Published online May 2011 | e-ISBN: 9780191595387 | DOI:

Series: Advanced Texts in Econometrics

Testing linearity against parametric alternatives

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The topic of this chapter is testing linearity of a model when the alternative is a parametric nonlinear model nesting a linear model. The case leading to standard asymptotic inference is discussed first. This is followed by a characterization of the identification problem present in many of these testing situations. Different ways of solving the identification problem are considered and their merits and disadvantages discussed. The chapter also covers tests designed for situations in which no well‐specified alternative to the linear model in question is available. Finally, there is a discussion of the concept asymptotic relative efficiency that is helpful in comparing power properties of various tests in different testing situastions and brief remarks on which test or tests to use in practice and when.

Keywords: testing linearity; Lagrange multiplier test; identification problem; nonstandard statistical inference; Rao's score test

Chapter.  13811 words. 

Subjects: Econometrics and Mathematical Economics

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