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Abstract:
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We consider detection of multiple changes in the distribution of periodic and autocorrelated data. We show that periodicity and autocorrelation degrade existing change detection methods since they blur the changes that these procedures aim to discover. To account for periodicity we transform the sequence of vector observations by embedding them in matrices and thereby producing a sequence of i.i.d. matrix observations. We propose methods of testing the equality of matrix distribution functions and offer change detection algorithms that can be applied to matrix observations. In particular, we use the E-divisive algorithm and apply clustering methods to a sample of observation matrices. Methods that ignore the periodicity have very low statistical power to detect changes in the mean or the variance of periodic data when the periodic effects overwhelm the actual changes, while the proposed methods detect such changes with high power. We illustrate the proposed methods by detecting changes in the total revenue for accounting, tax preparation, bookkeeping, and payroll services, provided by US Bureau of the Census.
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