lattice processes
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2014 ◽  
Vol 31 (2) ◽  
pp. 294-336 ◽  
Author(s):  
Javier Hidalgo ◽  
Myung Hwan Seo

We consider an omnibus test for the correct specification of the dynamics of a sequence $\left\{ {x\left( t \right)} \right\}_{t \in Z^d } $ 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 first main goal of the paper is to provide a transformation to obtain an asymptotic distribution that is free of nuisance parameters. Secondly, we propose a bootstrap analog of the transformation and show its validity. Thirdly, we discuss the results when $\left\{ {x\left( t \right)} \right\}_{t \in Z^d } $ are the errors of a parametric regression model. As a by product, we also discuss the asymptotic normality of the least squares estimator of the parameters of the regression model under very mild conditions. Finally, we present a small Monte Carlo experiment to shed some light on the finite sample behavior of our test.


2012 ◽  
Vol 26 (4) ◽  
pp. 479-490 ◽  
Author(s):  
Emilio Porcu ◽  
Jorge Mateu ◽  
Pablo Gregori ◽  
Martin Ostoja-Starzewski

2009 ◽  
Vol 100 (10) ◽  
pp. 2178-2194 ◽  
Author(s):  
Jan Beran ◽  
Sucharita Ghosh ◽  
Dieter Schell

2009 ◽  
Vol 151 (2) ◽  
pp. 113-128 ◽  
Author(s):  
Javier Hidalgo

2006 ◽  
pp. 260-273 ◽  
Author(s):  
Wei Qian ◽  
Wenyu Huang ◽  
Qusai Darugar ◽  
Mostafa A. El-Sayed

1998 ◽  
Vol 27 (12) ◽  
pp. 3095-3111 ◽  
Author(s):  
Ronit Nirel ◽  
Moira A. Mugglestone ◽  
Vic Barnett

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