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Modelling Nonlinear Economic Time Series$
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Timo Teräsvirta, Dag Tjøstheim, and Clive W. J. Granger

Print publication date: 2010

Print ISBN-13: 9780199587148

Published to Oxford Scholarship Online: May 2011

DOI: 10.1093/acprof:oso/9780199587148.001.0001

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Testing linearity against parametric alternatives

Testing linearity against parametric alternatives

Chapter:
(p.65) 5 Testing linearity against parametric alternatives
Source:
Modelling Nonlinear Economic Time Series
Author(s):

Timo Teräsvirta

Dag Tjøstheim (Contributor Webpage)

W. J. Granger

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199587148.003.0005

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

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