Short Range and Long Range Dependence
A discussion of the evolution of a notion of strong mixing as a measure of short range dependence and with additional restrictions a sufficient condition for a central limit theorem, is given. A characterization of strong mixing for stationary Gaussian sequences is noted. Examples of long range dependence leading to limit theorems with nonnormal limiting distributions are specified. Open questions concerning limit theorems for finite Fourier transforms are remarked on. There are also related queries on the use of Fourier methods for a class of nonstationary sequences.
KeywordsSpectral Density Central Limit Theorem Gaussian Process Asymptotic Normality Gaussian Stationary Process
I thank Professor Rafal Kulik for his help in putting this paper into coherent form.
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