Comparison of pivotals for confidence bounds and intervals for the mean of a stationary time series

ABSTRACT

We construct new pivotals to obtain confidence bounds and confidence intervals for the mean of a stationary process. These follow the approach based on estimating functions. The new pivotals are compared with the standard pivotal based on studentization. We study the first four cumulants of each of these pivotals and explain why the pivotals based on the estimating function approach result in better coverage probabilities. Some simulation results comparing these pivotals have been reported.

KEYWORDS:

• Confidence bounds
• Confidence intervals
• Cumulants
• Estimating function
• Mean
• Stationary time series.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62M99
• 62G15

Acknowledgments

Thanks are due to the University Grants Commission, India, for a research fellowship. I thank the reviewers for their helpful suggestions. I also thank Dr Akanksha Kashikar for a careful reading of the manuscript.