AStA Advances in Statistical Analysis

, Volume 101, Issue 1, pp 67–94 | Cite as

Control charts for multivariate spatial autoregressive models

  • Robert Garthoff
  • Philipp OttoEmail author
Original Paper


This paper deals with spatial detection of changes in model parameters of spatial autoregressive processes. The respective sequential testing problems are formulated. Moreover, we introduce characteristic quantities to monitor means or covariances of multivariate spatial autoregressive processes. Additionally, we also take into account the simultaneous surveillance of the mean vector and the covariance matrix. The aim is to apply control charts, important tools of sequential analysis, to these quantities. The considered control procedures are based on either cumulative sums or exponential smoothing. Further, we illustrate the methodology of statistical process control studying the spectrum of additive colors in a satellite photograph. Via simulation studies, the proposed control procedures are calibrated for a predefined average run length. In addition, we compare the performance of the control procedures considering the out-of-control situation. Eventually, the control charts are applied, and the signals of the different schemes are visualized. The final results are critically discussed.


Multivariate CUSUM charts Multivariate EWMA charts Spatial autoregressive model 

Mathematics Subject Classification

62H11 62L10 62M30 91B72 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.European University ViadrinaFrankfurt (Oder)Germany

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