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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.)

Author

Listed:
  • JIN SEO CHO

    (School of Economics, Yonsei University)

  • ISAO ISHIDA

    (CSFI, Osaka University)

  • HALBERT WHITE

    (Department of Economics, University of California, San Diego)

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.

Suggested Citation

  • Jin Seo Cho & Isao Ishida & Halbert White, 2013. "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 Teras," Working papers 2013rwp-55, Yonsei University, Yonsei Economics Research Institute.
  • Handle: RePEc:yon:wpaper:2013rwp-55
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    References listed on IDEAS

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    1. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
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    Cited by:

    1. Yae Ji Jun & Jin Seo Cho, 2015. "Analyzing the Interrelationship of the Statistics for Testing Neglected Nonlinearity under the Null of Linearity," Working papers 2015rwp-78, Yonsei University, Yonsei Economics Research Institute.
    2. Baek, Yae In & Cho, Jin Seo & Phillips, Peter C.B., 2015. "Testing linearity using power transforms of regressors," Journal of Econometrics, Elsevier, vol. 187(1), pages 376-384.
    3. Jin Seo Cho & Peter C.B. Phillips, 2016. "Sequentially Testing Polynomial Model Hypotheses using Power Transforms of Regressors," Working papers 2016rwp-90, Yonsei University, Yonsei Economics Research Institute.
    4. Kyu Lee Shin & Jin Seo Cho, 2013. "Testing for Neglected Nonlinearity Using Extreme Learning Machines (published in: International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21, Suppl. 2 (2013), 117--129.)," Working papers 2013rwp-57, Yonsei University, Yonsei Economics Research Institute.
    5. Jin Seo Cho & Halbert White, 2017. "Supplements to ¡°Directionally Differentiable Econometric Models¡±," Working papers 2017rwp-103a, Yonsei University, Yonsei Economics Research Institute.
    6. Jin Seo Cho & Halbert White, 2017. "Directionally Differentiable Econometric Models," Working papers 2017rwp-103, Yonsei University, Yonsei Economics Research Institute.

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