A unified approach to structural change tests based on F statistics, OLS residuals, and ML scores

Achim Zeileis

Publication: Working/Discussion PaperWU Working Paper

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Abstract

Three classes of structural change tests (or tests for parameter instability) which have been receiving much attention in both the statistics and econometrics communities but have been developed in rather loosely connected lines of research are unified by embedding them into the framework of generalized M-fluctuation tests (Zeileis and Hornik, 2003). These classes are tests based on F statistics (supF, aveF, expF tests), on OLS residuals (OLS-based CUSUM and MOSUM tests) and on maximum likelihood scores (including the Nyblom-Hansen test). We show that (represantives from) these classes are special cases of the generalized M-fluctuation tests, based on the same functional central limit theorem, but employing different functionals for capturing excessive fluctuations. After embedding these tests into the same framework and thus understanding the relationship between these procedures for testing in historical samples, it is shown how the tests can also be extended to a monitoring situation. This is achieved by establishing a general M-fluctuation monitoring procedure and then applying the different functionals corresponding to monitoring with F statistics, OLS residuals and ML scores. In particular, an extension of the supF test to a monitoring scenario is suggested and illustrated on a real-world data set.
Original languageEnglish
Place of PublicationVienna
PublisherInstitut für Statistik und Mathematik, WU Vienna University of Economics and Business
DOIs
Publication statusPublished - 2005

Publication series

SeriesResearch Report Series / Department of Statistics and Mathematics
Number13

WU Working Paper Series

  • Research Report Series / Department of Statistics and Mathematics

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