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Statistica Sinica 16(2006), 721-740





A MAXIMAL MOMENT INEQUALITY FOR LONG RANGE

DEPENDENT TIME SERIES WITH APPLICATIONS

TO ESTIMATION AND MODEL SELECTION


Ching-Kang Ing$^{1,2}$ and Ching-Zong Wei$^2$


$^1$National Taiwan University and $^2$Academia Sinica


Abstract: We establish a maximal moment inequality for the weighted sum of a sequence of random variables with finite second moments. An extension to the Hájek-Rény and Chow inequalities is then obtained. When certain second-moment properties are fulfilled, it enables us to deduce a strong law for the weighted sum of a time series having long-range dependence. Applications to estimation and model selection in multiple regression models with long-range dependent errors are also given.



Key words and phrases: Autoregressive fractionally integrated moving average, convergence system, long-range dependence, maximal inequality, model selection, strong consistency.

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