Asymptotic distribution of the estimated parameters of an ${\rm ARMA}(p, q)$ process in the presence of explosive roots

Tom 39 / 2012

Sugata Sen Roy, Sankha Bhattacharya Applicationes Mathematicae 39 (2012), 257-272 MSC: Primary 62M10, 62E20. DOI: 10.4064/am39-3-1


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.


  • Sugata Sen RoyDepartment of Statistics
    University of Calcutta
    35, Ballygunge Circular Road
    Calcutta 700019, India
  • Sankha BhattacharyaR.K.M.R. College
    Narendrapur 743508, India

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