We consider an autoregressive moving average process of order (p,q)(ARMA(p,q)) with stationary, white noise error variables having uniformly bounded fourth order moments. The characteristic polynomials of both the autoregressive and moving average components involve stable and explosive roots. The autoregressive parameters are estimated by using the instrumental variable technique while the moving average parameters are estimated through a derived autoregressive process using the same sample. The asymptotic distribution of the estimators is then derived.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-1,
author = {Sugata Sen Roy and Sankha Bhattacharya},
title = {Asymptotic distribution of the estimated parameters of an ARMA(p,q) process in the presence of explosive roots},
journal = {Applicationes Mathematicae},
volume = {39},
year = {2012},
pages = {257-272},
zbl = {1273.62220},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-1}
}
Sugata Sen Roy; Sankha Bhattacharya. Asymptotic distribution of the estimated parameters of an ARMA(p,q) process in the presence of explosive roots. Applicationes Mathematicae, Tome 39 (2012) pp. 257-272. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-1/