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Locating Multiple Change-Points Using a Combination of Methods
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2014 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Lokalisering av multipla brytpunkter med en kombination av metoder (Swedish)
Abstract [en]

The aim of this study is to find a method that is able to locate multiple change-points in a time series with unknown properties. The methods that are investigated are the CUSUM and CUSUM of squares test, the CUSUM test with OLS residuals, the Mann-Whitney test and Quandt’s log likelihood ratio. Since all methods are detecting single change-points, the binary segmentation technique is used to find multiple change-points. The study shows that the CUSUM test with OLS residuals, Mann-Whitney test and Quandt’s log likelihood ratio work well on most samples while the CUSUM and CUSUM of squares are not able to detect the location of the change-points. Furthermore the study shows that the binary segmentation technique works well with all methods and is able to detect multiple change-points in most circumstances. The study also shows that the results can, most of the time, be improved by using a combination of the methods.

Abstract [sv]

Syftet med studien är att hitta en metod som identifierar tidpunkterna för strukturella brott i en tidsserie med okända egenskaper. De metoder som undersöks är CUSUM och CUSUM av kvadrater, CUSUM test med OLS-residualer, Mann-Whitney-test samt Quandts log likelihood ratio. Eftersom alla metoder identifierar enbart en brytpunkt används binära uppdelningstekniken för att hitta multipla brytpunkter. Studien visar att CUSUM-test med OLS-residualer, Mann-Whitney-test och Quandt’s log likelihood ratio fungerar bra för de flesta stickproven medan CUSUM och CUSUM av kvadrater inte hittar tidpunkten för brytpunkterna. Vidare så visar studien att binära uppdelningstekniken fungerar bra med alla metoder och kan identifiera multipla brytpunkter i de flesta fallen. Studien visar också att resultaten för det mesta kan förbättras genom att använda en kombination av metoderna.

Place, publisher, year, edition, pages
TRITA-MAT-E, 2014:30
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-146271OAI: diva2:723400
Subject / course
Mathematical Statistics
Educational program
Master of Science - Industrial Engineering and Management
Available from: 2014-06-10 Created: 2014-06-10 Last updated: 2014-06-10Bibliographically approved

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