Moving Average Processes
نویسنده
چکیده
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Blackwell Publishing and Royal Statistical Society are collaborating with JSTOR to digitize, preserve and extend access to Journal of the Royal Statistical Society. Series D (The Statistician). Properties of Moving Average processes are discussed, amongst these being the closure under addition of independent MA models, the sometimes possible "orthogonal" decomposition of an MA process, and stronger restrictions on the autocorrelation function. These ideas would seem to be relevant to practical time series modelling, and some examples of their use are given. 1. Introduction to Box-Jenkins Process Time Series analysis is concerned with data which is not independent, but serially correlated, and where the relations between consecutive observations are of interest. It is a rapid growth area in statistical practice, and the mass of research and application, currently taking place, has already left its mark on nearly all the numerate disciplines in the sciences, business and technology. The approach to time series developed in the 60s by Professors Box and Jenkins, and summarized in their book (1970), is attracting more and more attention, and is being applied by accountants, sociologists, statisticians, civil, mechanical and telephone engineers, economists, physicists and process chemists, to name but a few.
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Complete convergence of moving-average processes under negative dependence sub-Gaussian assumptions
The complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. As a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.
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