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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