A method of deriving asymptotics for linear processes is introduced which uses an explicit algebraic decomposition of the linear filter. The technique is closely related to Gordin's method but has some advantages over it, especially in terms of its range of application. The method offers a simple unified approach to strong laws, central limit theory and invariance principles for linear processes. Sample means and sample covariances are covered. The results accommodate both homogeneous and heterogeneous innovations as well as innovations with undefined means and variances.
Publié le : 1992-06-14
Classification:
BN decomposition,
central limit theory,
functional limit laws,
infinite variance errors,
law of iterated logarithm,
linear process,
stable process,
strong laws,
60F05,
60F17,
60F15
@article{1176348666,
author = {Phillips, Peter C. B. and Solo, Victor},
title = {Asymptotics for Linear Processes},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 971-1001},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348666}
}
Phillips, Peter C. B.; Solo, Victor. Asymptotics for Linear Processes. Ann. Statist., Tome 20 (1992) no. 1, pp. 971-1001. http://gdmltest.u-ga.fr/item/1176348666/