Fixed Precision Estimation in the Blum-Rosenblatt Time Series

SYNOPTIC ABSTRACT

The problem of fixed length confidence interval for the parameters of a discrete m-dependent stationary Gaussian process is considered. Blum and Rosenblatt (1969) proved that if m is unknown such estimation is impossible. We show that if a number of independent copies of such process are available then the fixed precision estimation is possible and we effectively construct such estimator.

Key Words and Phrases:

• fixed precision estimation
• Gaussian time series
• m-dependent processes