A General Asymptotic Theory for Time Series Models

16 Pages Posted: 1 Nov 2009

See all articles by Shiqing Ling

Shiqing Ling

Hong Kong University of Science & Technology (HKUST)

Michael McAleer

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute; Tinbergen Institute; University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Date Written: October 31, 2009

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.

Keywords: Asymptotic normality, estimation, rate of strong convergence, strong consistency, time series models.

JEL Classification: C12, C13, C22.

Suggested Citation

Ling, Shiqing and McAleer, Michael, A General Asymptotic Theory for Time Series Models (October 31, 2009). Available at SSRN: https://ssrn.com/abstract=1497459 or http://dx.doi.org/10.2139/ssrn.1497459

Shiqing Ling

Hong Kong University of Science & Technology (HKUST) ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

Michael McAleer (Contact Author)

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute ( email )

Rotterdam
Netherlands

Tinbergen Institute

Rotterdam
Netherlands

University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Tokyo
Japan

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