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Non-singularity and asymptotic independence

Published online by Cambridge University Press:  14 July 2016

Peter Bloomfield
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Abstract

A stationary stochastic process must satisfy various requirements to make it a realistic model for a phenomenon in the real world. Some of these requirements are quantitative, such as agreement of distribution or moments. Other, more qualitative requirements deal with the general behavior of the process. Two such requirements are non-singularity and asymptotic independence. Each will be discussed from a variety of points of view, and given precise definition in a succession of progressively stronger forms.

Keywords

DETERMINISM AND NON-DETERMINISMPREDICTABILITYMINIMALITYCANONICAL AND ESSENTIAL CORRELATIONCOMPLETE AND ABSOLUTE REGULARITY

Information

Type
Part 1—Structure and General Methods for Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 9 - 21
Copyright
Copyright © 1986 Applied Probability Trust 

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