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Asymptotic confidence intervals for variograms of stationary time series
Author(s) -
Bisgaard Søren,
Khachatryan Davit
Publication year - 2010
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1052
Subject(s) - variogram , autocorrelation , series (stratigraphy) , statistics , confidence interval , stationary process , mathematics , time series , interval (graph theory) , sample (material) , econometrics , kriging , geology , combinatorics , chemistry , chromatography , paleontology
Industrial processes are often monitored via data sampled at a high frequency and hence are likely to be autocorrelated time series that may or may not be stationary. To determine if a time series is stationary or not the standard approach is to check whether sample autocorrelation function fades out relatively quickly. An alternative and somewhat sounder approach is to use the variogram. In this article we review the basic properties of the variogram and then derive a general expression for asymptotic confidence intervals for variogram based on the Delta method. We illustrate the computations with an industrial process example. Copyright © 2009 John Wiley & Sons, Ltd.