A general asymptotic theory for time-series models |
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| Authors: | Shiqing Ling, Michael McAleer&dagger |
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| Affiliation: | Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China;
Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute, The Netherlands and Center for International Research on the Japanese Economy (CIRJE) Faculty of Economics, University of Tokyo, Tokyo, Japan |
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| Abstract: | This paper develops a general asymptotic theory for the estimation of strictly stationary and ergodic time–series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the asymptotic normality of a general class of estimators that includes LSE, MLE and some M-type estimators. As an application, we verify the assumptions for the long-memory fractional ARIMA model. Other examples include the GARCH(1,1) model, random coefficient AR(1) model and the threshold MA(1) model. |
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| Keywords: | asymptotic normality estimation rate of strong convergence strong consistency time-series models |
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