A number of statistics that arise in time series analysis can be represented as the sum of a partial realization of a possibly serially dependent and nonstationary discrete-parameter stochastic process. The almost sure and $L_p, p > 1$, convergence of such statistics is investigated, under various moment conditions. The results are applied to the least squares estimates of multiple regressions.
Publié le : 1978-01-14
Classification:
Almost sure convergence,
$L_p$ convergence,
martingale inequalities,
time series regression,
60F15,
62M10,
60G45
@article{1176344080,
author = {Robinson, P. M.},
title = {On Consistency in Time Series Analysis},
journal = {Ann. Statist.},
volume = {6},
number = {1},
year = {1978},
pages = { 215-223},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344080}
}
Robinson, P. M. On Consistency in Time Series Analysis. Ann. Statist., Tome 6 (1978) no. 1, pp. 215-223. http://gdmltest.u-ga.fr/item/1176344080/