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Control charts for multivariate spatial autoregressive models

Author

Listed:
  • Robert Garthoff

    (European University Viadrina)

  • Philipp Otto

    (European University Viadrina)

Abstract

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.

Suggested Citation

  • Robert Garthoff & Philipp Otto, 2017. "Control charts for multivariate spatial autoregressive models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 67-94, January.
    • Handle: RePEc:spr:alstar:v:101:y:2017:i:1:d:10.1007_s10182-016-0276-x
    DOI: 10.1007/s10182-016-0276-x
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    References listed on IDEAS

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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    2. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    3. Bernard Fingleton, 2009. "A generalized method of moments estimator for a spatial model with moving average errors, with application to real estate prices," Studies in Empirical Economics, in: Giuseppe Arbia & Badi H. Baltagi (ed.), Spatial Econometrics, pages 35-57, Springer.
    4. Kelejian, Harry H. & Prucha, Ingmar R., 2004. "Estimation of simultaneous systems of spatially interrelated cross sectional equations," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 27-50.
    5. Robert Garthoff & Iryna Okhrin & Wolfgang Schmid, 2014. "Statistical surveillance of the mean vector and the covariance matrix of nonlinear time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 225-255, July.
    6. Sutton, Paul C. & Costanza, Robert, 2002. "Global estimates of market and non-market values derived from nighttime satellite imagery, land cover, and ecosystem service valuation," Ecological Economics, Elsevier, vol. 41(3), pages 509-527, June.
    7. Lazariv, Taras & Okhrin, Yarema & Schmid, Wolfgang, 2015. "Behavior of EWMA type control charts for small smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 115-125.
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    1. Robert Garthoff & Philipp Otto, 2018. "Verfahren zur Überwachung räumlicher autoregressiver Prozesse mit externen Regressoren [Statistical surveillance of spatial autoregressive processes with exogenous regressors]," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 12(2), pages 107-133, September.

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