The Annals of Statistics

Sequential estimation for the autocorrelations of linear processes

Sangyeol Lee

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Abstract

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.

Article information

Source
Ann. Statist., Volume 24, Number 5 (1996), 2233-2249.

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362319

Digital Object Identifier
doi:10.1214/aos/1069362319

Mathematical Reviews number (MathSciNet)
MR1421170

Zentralblatt MATH identifier
0898.62099

Subjects
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]

Keywords
Sequential estimation linear processes sample autocorrelations asymptotic risk efficiency uniform integrability random central limit theorem

Citation

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


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