Research paper
Tests for detecting a shift in the mean of hydrological time series

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Abstract

A practical problem in time-series analysis of hydrological and meteorological data is to find statistical techniques for testing for an abrupt change in the mean at an unknown time. Suitable techniques have been developed in the situation of a single time series, {yi}. Attention is paid to the likelihood ratio statistic V and to a Bayesian statistic U.

Complications arise if we want to test for a shift in the mean using a regression on a second correlated sequence, {xi}, because the critical values of the test statistic in general depend on the configuration of the xi's. For the statistic U, this problem can be solved using techniques similar to those for testing for serial correlation in least-squares regression. A so-called bounds test can be performed on the least-squares residuals. Unfortunately, there is quite a large possibility that this test is inconclusive. As an alternative to the bounds test, the statistic U can be applied to transformed residuals. The tests are illustrated with runoff and precipitation data for the Colorado River Basin, U.S.A., and the River Thames at Teddington, U.K.

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