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On the Limit Behavior of a Chi-Square Type Test if the Number of Conditional Moments Tested Approaches Infinity

Published online by Cambridge University Press:  11 February 2009

R.M. de Jong  and
H.J. Bierens
R.M. de Jong
Affiliation:
Free University Amsterdam
H.J. Bierens
Affiliation:
Southern Methodist University
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Abstract

In this paper, a consistent model specification test is proposed. Some consistent model specification tests have been discussed in econometrics literature. Those tests are consistent by randomization, display a discontinuity in sample size, or have an asymptotic distribution that depends on the data-generating process and on the model, whereas our test does not have one of those disadvantages. Our test can be viewed upon as a conditional moment test as proposed by Newey but instead of a fixed number of conditional moments, an asymptotically infinite number of moment conditions is employed. The use of an asymptotically infinite number of conditional moments will make it possible to obtain a consistent test. Computation of the test statistic is particularly simple, since in finite samples our statistic is equivalent to a chi-square conditional moment test of a finite number of conditional moments.

Type
Articles
Information
Econometric Theory , Volume 10 , Issue 1 , March 1994 , pp. 70 - 90
Copyright
Copyright © Cambridge University Press 1994

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