On sequential confidence interval in a stationary Gaussian process

Abstract

In this article we concentrate on fixed accuracy intervals of the common variance when the data arise from a Gaussian process with order 1 autoregressive covariance structure. Our approach includes the maximum likelihood method and least squares method for estimating the parameters in this process. We provide necessary asymptotic results and carry out numerical evaluations.

KEYWORDS:

• Fixed accuracy confidence interval
• Gaussian process
• martingale
• serial correlation

SUBJECT CLASSIFICATIONS:

• 62F25
• 62L12

ACKNOWLEDGMENTS

We are grateful to the Editor-in-Chief Professor Nitis Mukhopadhyay for his discerning observations and the reviewers for their helpful feedback.

DISCLOSURE

The authors have no conflicts of interest to report.