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Specification for lattice processes

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  • Hidalgo, Javier
  • Seo, Myung Hwan

Abstract

We consider an omnibus test for the correct speci…cation of the dynamics of a sequence fx (t)gt2Zd in a lattice. As it happens with causal models and d = 1, its asymptotic distribution is not pivotal and depends on the estimator of the unknown parameters of the model under the null hypothesis. One of our main goals of the paper is to provide a transformation to obtain an asymptotic distribution that is free of nuisance parameters. Secondly, we propose a bootstrap analogue of the transformation and show its validity. Third, we discuss the results when fx (t)gt2Zd are the errors of a parametric regression model. As a by product, we also discuss the asymptotic normality of the least squares estimators under very mild conditions. Finally, we present a small Monte Carlo experiment to shed some light on the …nite sample behaviour of our test.

Suggested Citation

  • Hidalgo, Javier & Seo, Myung Hwan, 2013. "Specification for lattice processes," LSE Research Online Documents on Economics 58191, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:58191
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    References listed on IDEAS

    as
    1. Hidalgo, J. & Kreiss, J.-P., 2006. "Bootstrap specification tests for linear covariance stationary processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 807-839, August.
    2. Jun Zhu & Hsin‐Cheng Huang & Perla E. Reyes, 2010. "On selection of spatial linear models for lattice data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 389-402, June.
    3. Delgado, Miguel A. & Hidalgo, Javier & Velasco, Carlos, 2011. "Bootstrap Assisted Specification Tests For The Arfima Model," Econometric Theory, Cambridge University Press, vol. 27(5), pages 1083-1116, October.
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    More about this item

    Keywords

    specification test; spatial processes; lattice; spectral domain; CUSUM; bootstrap;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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