Sequential estimation for the autocorrelations of linear processes. (English) Zbl 0898.62099

Lee, Sangyeol

Ann. Stat. 24, No. 5, 2233-2249 (1996).

Summary: This paper considers sequential point estimation of the autocorrelations of stationary linear processes within the framework of the sequential procedure initiated by H. Robbins [Probability and Statistics, H. Cramér Vol., 235-245 (1959; Zbl 0095.13005)]. The sequential estimator proposed here is based on the usual sample autocorrelations and is shown to be risk efficient in the sense of N. Starr [Ann. Math. Stat. 37, 1173-1185 (1966; Zbl 0144.40801)] 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.

MSC:

62L12	Sequential estimation
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G40	Stopping times; optimal stopping problems; gambling theory

Keywords:

stationary linear processes; sample autocorrelations; asymptotic risk efficiency; uniform integrability; random central limit theorem

Citations:

Zbl 0095.13005; Zbl 0144.40801