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Slowly decaying serial correlations have, if ignored, disastrous effects on classical tests and confidence intervals. We propose a modified t test for the location parameter which takes into account such correlations. An approximate distribution function of the test statistic is given under the assumption of fractional Gaussian noise. The results are generalized to prediction intervals for a future average. An example is given to illustrate the methods.
Jan Beran (Sun,) studied this question.