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A general asymptotic theory for time‐series models
Author(s) -
Ling Shiqing,
McAleer Michael
Publication year - 2010
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2009.00447.x
Subject(s) - asymptotic distribution , estimator , mathematics , strong consistency , ergodic theory , asymptotic analysis , series (stratigraphy) , autoregressive integrated moving average , consistency (knowledge bases) , autoregressive conditional heteroskedasticity , rate of convergence , simple (philosophy) , convergence (economics) , econometrics , time series , statistics , mathematical analysis , computer science , discrete mathematics , key (lock) , volatility (finance) , computer security , epistemology , economics , economic growth , paleontology , biology , philosophy
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.