A maximal moment inequality for long range dependent time series with applications to estimation and model selection (Running Head: A maximal moment inequality with applications)

We establish a maximal moment inequality for the weighted sum of a sequence of random variables with finite second moments. An extension to Hájek-Rény and Chow’s type inequality 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 longrange dependence. Applications to estimation and model selection in multiple regression models with long-range dependent errors are also given. Abstract. We establish a maximal moment inequality for the weighted sum of a sequence of random variables with finite second moments. An extension to Hájek-Rény and Chow’s type inequality 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 longrange dependent errors are also given. We establish a maximal moment inequality for the weighted sum of a sequence of random variables with finite second moments. An extension to Hájek-Rény and Chow’s type inequality 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 longrange dependent errors are also given. AMS 1991 subject classifications. Primary 60E15; secondary 62M10.