{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T17:40:09Z","timestamp":1717263609487},"reference-count":51,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,8,19]],"date-time":"2014-08-19T00:00:00Z","timestamp":1408406400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2015,4]]},"abstract":"<jats:p>We consider an omnibus test for the correct specification of the dynamics of a sequence<jats:inline-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0266466614000310_inline1\"\/><jats:tex-math>$\\left\\{ {x\\left( t \\right)} \\right\\}_{t \\in Z^d } $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>in a lattice. As it happens with causal models and<jats:italic>d<\/jats:italic>= 1, its asymptotic distribution is not pivotal and depends on the estimator of the unknown parameters of the model under the null hypothesis. One first main goal of the paper is to provide a transformation to obtain an asymptotic distribution that is free of nuisance parameters. Secondly, we propose a bootstrap analog of the transformation and show its validity. Thirdly, we discuss the results when<jats:inline-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0266466614000310_inline2\"\/><jats:tex-math>$\\left\\{ {x\\left( t \\right)} \\right\\}_{t \\in Z^d } $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>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. 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