STOCHASTIC INEQUALITIES FOR THE RUN LENGTH OF THE EWMA CHART FOR LONG-MEMORY PROCESSES

* In this paper the properties of the modified EWMA control chart for detecting changes in the mean of an ARFIMA process are discussed. The central question is related to the false alarm probability and its behavior for different autocorrelation structures and parameters of the underlying process. I...

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Bibliographic Details
Published inRevstat Vol. 17; no. 1; p. 67
Main Authors Okhrin, Yarema, Schmid, Wolfgang
Format Journal Article
LanguageEnglish
Published Instituto Nacional de Estatistica 01.01.2019
Instituto Nacional de Estatística | Statistics Portugal
Subjects
ARFIMA process
EWMA control chart
Inequalities (Mathematics)
long-memory process
Mathematical research
Memory
Moving averages
statistical process control
Stochastic models
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ISSN1645-6726
2183-0371
DOI10.57805/revstat.v17i1.259

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Summary:* In this paper the properties of the modified EWMA control chart for detecting changes in the mean of an ARFIMA process are discussed. The central question is related to the false alarm probability and its behavior for different autocorrelation structures and parameters of the underlying process. It is shown under which conditions the false alarm probability of an ARFIMA(p,d,q) process is larger than that of the pure ARFIMA(0,d,0) process. Furthermore, it is shown that the false alarm probability for ARFIMA(0,d,0) and ARFIMA(1,d,1) is monotonic in d for common parameter values of the processes. Key-Words: * statistical process control; EWMA control chart; long-memory process; ARFIMA process. AMS Subject Classification: * 62L10, 62M10.
ISSN:1645-6726
2183-0371
DOI:10.57805/revstat.v17i1.259