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Consistency of several variants of the standardized time series area variance estimator

✍ Scribed by Halim Damerdji; David Goldsman

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
901 KB
Volume
42
Category
Article
ISSN
0894-069X

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✦ Synopsis

In statistical analysis of stationary time series or in steady-state simulation output analysis, it is desired to find consistent estimates of the process variance parameter. Here, we consider variants of the area estimator ofstandardized time series, namely, the weighted area and the Cram&-von Mises area estimators, and provide their consistency, in the strong sense and mean-square sense. A sharp bound for the (asymptotic) variance of these estimators is obtained. We also present a central limit theorem for the weighted area estimator: this gives a rate of convergence of this estimator, as well as a confidence interval for the variance parameter.

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Estimations of the time-average variance for meteorological time series play a central role in climatic studies. They depend on the finite sample length and the correlation structure of the climatic time series. A general equation for these estimations is derived theoretically for autoregressive int