The Annals of Statistics
- Ann. Statist.
- Volume 24, Number 5 (1996), 2233-2249.
Sequential estimation for the autocorrelations of linear processes
This paper considers sequential point estimation of the autocorrelations of stationary linear processes within the framework of the sequential procedure initiated by Robbins. The sequential estimator proposed here is based on the usual sample autocorrelations and is shown to be risk efficient in the sense of Starr as the cost per observation approaches zero. To achieve the asymptotic risk efficiency, we are led to study the uniform integrability and random central limit theorem of the sample autocorrelations. Some moment conditions are provided for the errors of the linear processes to establish the uniform integrability and random central limit theorem.
Ann. Statist., Volume 24, Number 5 (1996), 2233-2249.
First available in Project Euclid: 20 November 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62L12: Sequential estimation
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Lee, Sangyeol. Sequential estimation for the autocorrelations of linear processes. Ann. Statist. 24 (1996), no. 5, 2233--2249. doi:10.1214/aos/1069362319. https://projecteuclid.org/euclid.aos/1069362319