Specification For Lattice Processes
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.
|Date of creation:||May 2013|
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- Peter M. Robinson & J. Vidal Sanz, 2005.
"Modified whittle estimation of multilateral models on a lattice,"
LSE Research Online Documents on Economics
4545, London School of Economics and Political Science, LSE Library.
- Robinson, P.M. & Vidal Sanz, J., 2006. "Modified Whittle estimation of multilateral models on a lattice," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1090-1120, May.
- Peter M Robinson & J Vidal Sanz, 2005. "Modified Whittle Estimation of Multilateral Models on a Lattice," STICERD - Econometrics Paper Series /2005/492, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
- 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.
- Yoshihiro Yajima & Yasumasa Matsuda, 2008. "Asymptotic Properties of the LSE of a Spatial Regression in both Weakly and Strongly Dependent Stationary Random Fields," CIRJE F-Series CIRJE-F-587, CIRJE, Faculty of Economics, University of Tokyo.
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