A general asymptotic theory for time-series models
Shiqing Ling
Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China
Search for more papers by this authorMichael McAleer
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
Search for more papers by this authorShiqing Ling
Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China
Search for more papers by this authorMichael McAleer
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
Search for more papers by this authorAbstract
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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