Page’s sequential procedure for change-point detection in time series regression
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Date
2013-12-16
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Abstract
In a variety of different settings cumulative sum (CUSUM) procedures have been applied for
the sequential detection of structural breaks in the parameters of stochastic models. Yet their
performance depends strongly on the time of change and is best under early-change scenarios. For
later changes their finite sample behavior is rather questionable. We therefore propose modified
CUSUM procedures for the detection of abrupt changes in the regression parameter of multiple
time series regression models, that show a higher stability with respect to the time of change
than ordinary CUSUM procedures. The asymptotic distributions of the test statistics and the
consistency of the procedures are provided. In a simulation study it is shown that the proposed
procedures behave well in finite samples. Finally the procedures are applied to a set of capital
asset pricing data related to the Fama-French extension of the capital asset pricing model.
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Keywords
CUSUM, Fama-French model, CAPM, invariance principle, asymptotic distribution, sequential test, change-point, linear model