Testing for Neglected Nonlinearity Using Twofold Unidentified Models under the Null and Hexic Expansions (published in: Essays in Nonlinear Time Series Econometrics, Festschrift in Honor of Timo Terasvirta. Eds. Niels Haldrup, Mika Meitz, and Pentti Saikkonen (2014). Oxford: Oxford University Press.)

Jin Seo Cho (), Isao Ishida and Halbert White

No 2013rwp-55, Working papers from Yonsei University, Yonsei Economics Research Institute

Abstract: We revisit the twofold identification problem discussed by Cho, Ishida, and White (Neural Computation, 2011), which arises when testing for neglected nonlinearity by artificial neural networks. We do not use the so-called ¡°no-zero¡± condition and employ a sixth-order expansion to obtain the asymptotic null distribution of the quasi-likelihood ratio (QLR) test. In particular, we avoid restricting the number of explanatory variables in the activation function by using the distance and direction method discussed in Cho and White (Neural Computation, 2012). We find that the QLR test statistic can still be used to handle the twofold identification problem appropriately under the set of mild regularity conditions provided here, so that the asymptotic null distribution can be obtained in a manner similar to that in Cho, Ishida, and White (Neural Computation, 2011). This also implies that the weighted bootstrap in Hansen (Econometrica, 1996) can be successfully exploited when testing the linearity hypothesis using the QLR test.

Keywords: Artificial neural networks; Neglected nonlinearity; Quasi-likelihood ratio test; Distance and direction approach; Gaussian stochastic process; Twofold identification problem; Sixth-order (hexic) expansion; Weighted bootstrap (search for similar items in EconPapers)
Pages: 31 pages
Date: 2013-02
New Economics Papers: this item is included in nep-cmp and nep-ore
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Citations: View citations in EconPapers (11)

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