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Verfahren zur Überwachung räumlicher autoregressiver Prozesse mit externen Regressoren

Statistical surveillance of spatial autoregressive processes with exogenous regressors

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Zusammenfassung

Der vorliegende Beitrag befasst sich mit der statistischen Prozesskontrolle räumlicher autoregressiver Prozesse mit externen Regressoren. Das Ziel ist die Weiterentwicklung etablierter Methoden der zeitlichen Prozesskontrolle. Diese Ansätze werden für Anwendungen in der räumlichen Prozesskontrolle modifiziert. Wir illustrieren dieses Vorgehen anhand eines sozialstatistischen Beispiels, welches sich mit der Bevölkerungsentwicklung in den Landkreisen und Kreisfreien Städten der Bundesrepublik Deutschland befasst. Mittels Faktorenanalyse werden zunächst nicht beobachtbare Variablen basierend auf den zuvor gewählten manifesten Variablen identifiziert, denn für die nachfolgende Analyse sind voneinander unabhängige Faktoren erforderlich. Daraufhin sind anhand einer Clusteranalyse die Regionen in Gruppen einzuteilen. Mit Hilfe der gebildeten Cluster sind diejenigen Regionen, welche die Grundlage der Modellanpassung darstellen, im Zustand unter Kontrolle auszuwählen. Anhand der zuvor ermittelten Faktorwerte erfolgt eine Modellanpassung mit Hilfe der verallgemeinerten Momenten-Methode. Im Rahmen der statistischen Prozesskontrolle werden in einem weiteren Schritt multivariate Kontrollkarten basierend auf entweder exponentieller Glättung oder kumulierter Summe herangezogen, um Kreise außerhalb der Region im Zustand unter Kontrolle hinsichtlich ihres Kontrollzustandes zu beurteilen. Wir stellen verschiedene Ansätze vor, um die zu überwachenden Regionen für eine Prozesskontrolle zu sortieren. Schlussendlich möchten wir zeigen, dass die modifizierten Kontrollkarten strukturelle Veränderungen in Bezug auf ein zuvor geschätztes Modell signalisieren, ohne dass eine permanente Schätzung erforderlich ist.

Abstract

This paper deals with statistical process control of spatial autoregressive models with exogenous regressors. The main purpose is the extension of conventional methods of process control in time series analysis. These approaches are modified for applications of spatial monitoring. The method is illustrated by an example of social statistics dealing with natural as well as spatial population change regarding administrative districts of Germany. Via factor analysis latent variables are identified based on manifest variables, because independent factors are needed for the following analysis. Afterwards, the considered regions are divided into groups via cluster analysis. The results of cluster analysis helps to find a specific region of one cluster that is used for in-control estimation. The previously mentioned model is fitted to factor scores using the generalized method of moments. Multivariate control charts based on either exponential smoothing or cumulative sum are used to evaluate full-sample data regarding their control situation. Accordingly, we propose different approaches to sort the regions to be monitored. Eventually, the modified charts signalize structural changes regarding the model based on in-control data without permanent re-estimation.

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  1. Europa-Universität Viadrina, Große Scharrnstraße 59, 15230, Frankfurt (Oder), Deutschland

    Robert Garthoff & Philipp Otto

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  1. Robert Garthoff
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  2. Philipp Otto
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Correspondence to Robert Garthoff.

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Garthoff, R., Otto, P. Verfahren zur Überwachung räumlicher autoregressiver Prozesse mit externen Regressoren. AStA Wirtsch Sozialstat Arch 12, 107–133 (2018). https://doi.org/10.1007/s11943-018-0224-1

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  • DOI: https://doi.org/10.1007/s11943-018-0224-1

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