{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T11:37:03Z","timestamp":1791977823593,"version":"4.4.0"},"reference-count":73,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":4882,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1995,10]]},"abstract":"<jats:p>The primary purpose of this paper is to review a very few results on some basic elements of large sample theory in a restricted <jats:italic>structural<\/jats:italic> framework, as described in detail in the recent book by LeCam and Yang (1990, <jats:italic>Asymptotics in Statistics: Some Basic Concepts<\/jats:italic>. New York: Springer), and to illustrate how the asymptotic inference problems associated with a wide variety of time series regression models fit into such a structural framework. The models illustrated include many linear time series models, including cointegrated models and autoregressive models with unit roots that are of wide current interest. The general treatment also includes nonlinear models, including what have become known as ARCH models. The possibility of replacing the density of the error variables of such models by an estimate of it (adaptive estimation) based on the observations is also considered.<\/jats:p><jats:p>Under the framework in which the asymptotic problems are treated, only the approximating structure of the likelihood ratios of the observations, together with auxiliary estimates of the parameters, will be required. Such approximating structures are available under quite general assumptions, such as that the Fisher information of the common density of the error variables is finite and nonsingular, and the more specific assumptions, such as Gaussianity, are not required. In addition, the construction and the form of inference procedures will not involve any additional complications in the non-Gaussian situations because the approximating quadratic structure actually will reduce the problems to the situations similar to those involved in the Gaussian cases.<\/jats:p>","DOI":"10.1017\/s0266466600009907","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:40:44Z","timestamp":1236699644000},"page":"818-887","source":"Crossref","is-referenced-by-count":133,"title":["Some Aspects of Asymptotic Theory with Applications to Time Series Models"],"prefix":"10.1017","volume":"11","author":[{"given":"P.","family":"Jeganathan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600009907_ref069","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(85)90051-X"},{"key":"S0266466600009907_ref067","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176343056"},{"key":"S0266466600009907_ref016","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345457"},{"key":"S0266466600009907_ref062","volume-title":"An Adaptive Estimator of the Autocorrelation Coefficient in a Semiparametric Regression Model with Autoregressive Errors","author":"Schick","year":"1993"},{"key":"S0266466600009907_ref060","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350055"},{"key":"S0266466600009907_ref057","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012408"},{"key":"S0266466600009907_ref056","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(88)90039-5"},{"key":"S0266466600009907_ref054","doi-asserted-by":"publisher","DOI":"10.2307\/1913237"},{"key":"S0266466600009907_ref053","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5769-1"},{"key":"S0266466600009907_ref050","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600013402"},{"key":"S0266466600009907_ref049","volume-title":"Work in Progress","author":"Negal","year":"1988"},{"key":"S0266466600009907_ref048","volume-title":"Probability Theory","volume":"II","author":"Lo\u00e9ve","year":"1978"},{"key":"S0266466600009907_ref046","volume-title":"Testing Statistical Hypotheses","author":"Lehmann","year":"1959"},{"key":"S0266466600009907_ref045","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0377-0"},{"key":"S0266466600009907_ref043","volume-title":"Asymptotic Methods in Statistical Decision Theory","author":"LeCam","year":"1986"},{"key":"S0266466600009907_ref064","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316481"},{"key":"S0266466600009907_ref041","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177696960"},{"key":"S0266466600009907_ref040","first-page":"37","article-title":"Locally asymptotically normal families of distributions","volume":"3","author":"LeCam","year":"1960","journal-title":"University of California Publications in Statistics"},{"key":"S0266466600009907_ref052","volume-title":"Probability and Measure","author":"Parthasarathy","year":"1977"},{"key":"S0266466600009907_ref036","first-page":"59","article-title":"On adaptive estimation in autoregressive models when there are nuisance parameters","volume":"5","author":"Kreiss","year":"1987","journal-title":"Statistics and Decisions"},{"key":"S0266466600009907_ref068","doi-asserted-by":"publisher","DOI":"10.1007\/BF00635962"},{"key":"S0266466600009907_ref066","first-page":"187","article-title":"Efficient non-parametric testing and estimation","volume":"1","author":"Stein","year":"1956","journal-title":"Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability"},{"key":"S0266466600009907_ref032","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-6592-2"},{"key":"S0266466600009907_ref059","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804373"},{"key":"S0266466600009907_ref030","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(89)90036-5"},{"key":"S0266466600009907_ref055","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.3.535"},{"key":"S0266466600009907_ref042","first-page":"383","volume-title":"A Survey of Statistical Design and Linear Models","author":"LeCam","year":"1975"},{"key":"S0266466600009907_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(79)90051-6"},{"key":"S0266466600009907_ref021","volume-title":"Theory of Rank Tests","author":"H\u00e1jek","year":"1967"},{"key":"S0266466600009907_ref065","volume-title":"Adaptive Estimation in Time Series Regression Models. 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