The Annals of Probability

Weak Convergence of Serial Rank Statistics Under Dependence with Applications in Time Series and Markov Processes

Michel Harel and Madan L. Puri

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Abstract

The asymptotic normality of linear serial rank statistics introduced by Hallin, Ingenbleek and Puri (1985) for the problem of testing white noise against ARMA alternatives is established for $\varphi$-mixing as well as strong mixing sequences of random variables. Applications in Markov processes and ARMA processes in time series are provided.

Article information

Source
Ann. Probab., Volume 18, Number 3 (1990), 1361-1387.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990749

Digital Object Identifier
doi:10.1214/aop/1176990749

Mathematical Reviews number (MathSciNet)
MR1062072

Zentralblatt MATH identifier
0705.62083

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60J05: Discrete-time Markov processes on general state spaces 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Serial rank statistics $\varphi$-mixing strong mixing graduate empirical process graduate rank process Skorohod topology weak convergence Markov process ARMA process

Citation

Harel, Michel; Puri, Madan L. Weak Convergence of Serial Rank Statistics Under Dependence with Applications in Time Series and Markov Processes. Ann. Probab. 18 (1990), no. 3, 1361--1387. doi:10.1214/aop/1176990749. https://projecteuclid.org/euclid.aop/1176990749


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