Geodesic
Asymptotic distribution of the estimated parameters of an ${\rm ARMA}(p, q)$ process in the presence of explosive roots
Sugata Sen Roy1 ; Sankha Bhattacharya2
1 Department of Statistics University of Calcutta 35, Ballygunge Circular Road Calcutta 700019, India
2 R.K.M.R. College Narendrapur 743508, India
Applicationes Mathematicae, Tome 39 (2012) no. 3, pp. 257-272.

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We consider an autoregressive moving average process of order $(p,q)$ $({\rm ARMA}(p,q))$ 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.
DOI : 10.4064/am39-3-1
Keywords: consider autoregressive moving average process order arma stationary white noise error variables having uniformly bounded fourth order moments characteristic polynomials autoregressive moving average components involve stable explosive roots autoregressive parameters estimated using instrumental variable technique while moving average parameters estimated through derived autoregressive process using sample asymptotic distribution estimators derived

Sugata Sen Roy 1 ; Sankha Bhattacharya 2

1 Department of Statistics University of Calcutta 35, Ballygunge Circular Road Calcutta 700019, India
2 R.K.M.R. College Narendrapur 743508, India 
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Sugata Sen Roy; Sankha Bhattacharya. Asymptotic distribution of the estimated parameters of an ${\rm ARMA}(p, q)$ process in the presence of explosive roots. Applicationes Mathematicae, Tome 39 (2012) no. 3, pp. 257-272. doi : 10.4064/am39-3-1. http://geodesic.mathdoc.fr/articles/10.4064/am39-3-1/

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