The Effect of Serial Correlation on the Performance of CUSUM Tests II

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Abstract
We continue the study by developing another approximation to the cumrdative sums which allows one to study the run length distribution after a change in level occurred. This approximate distribution is doubly important because it also applies to the situation of stable operation when the reference value is such that the terms of the sum have a non-zero mean. The major emphasis here is on the effects on the run length distribution caused by the presence of serial correlation. The approximation introduced holds for first order moving average models and first order autoregressive models and particular attention is paid to these error structures. A Monte Carlo study with normal observations is used to check the accuracy of the approximations. The presence of serial correlation is seen to have quite a major influence on the run length distribution.

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