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.
Publié le : 1990-07-14
Classification:
Serial rank statistics,
$\varphi$-mixing,
strong mixing,
graduate empirical process,
graduate rank process,
Skorohod topology,
weak convergence,
Markov process,
ARMA process,
60F05,
60J05,
62M10
@article{1176990749,
author = {Harel, Michel and Puri, Madan L.},
title = {Weak Convergence of Serial Rank Statistics Under Dependence with Applications in Time Series and Markov Processes},
journal = {Ann. Probab.},
volume = {18},
number = {4},
year = {1990},
pages = { 1361-1387},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990749}
}
Harel, Michel; Puri, Madan L. Weak Convergence of Serial Rank Statistics Under Dependence with Applications in Time Series and Markov Processes. Ann. Probab., Tome 18 (1990) no. 4, pp. 1361-1387. http://gdmltest.u-ga.fr/item/1176990749/