A recursive estimate of the stochastic structure of a stationary time series is constructed based on the assumption that the true structure is ARMA, i.e., has a rational spectrum. The estimate is recursive in the sense that each successive estimate is obtained from the previous one by a relatively simple adjustment, that could be effected in a "real time" situation. The procedure is basically that of updating a regression when all variates involved are constructed from previous estimates of the parameter vector. The strong convergence of the estimate to the true value is established as well as a result relating to the rate of convergence.
Publié le : 1980-07-14
Classification:
ARMA models,
recursive estimation,
strong convergence,
martingales,
real time calculation,
62M10,
62N15,
62L12
@article{1176345069,
author = {Hannan, E. J.},
title = {Recursive Estimation Based on ARMA Models},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 762-777},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345069}
}
Hannan, E. J. Recursive Estimation Based on ARMA Models. Ann. Statist., Tome 8 (1980) no. 1, pp. 762-777. http://gdmltest.u-ga.fr/item/1176345069/