Estimation of parameters in ARUMA models (Q917202)

An ARUMA (p,d,q) process X(n) is defined by \(U(B)A(B)X(n)=C(B)W(n)\), where B is the back-shift operator, and A, B and C are polynomials of degrees d, p and q, respectively. It is assumed that C is relatively prime to UA and that W(n) is a martingale difference. Let all roots of U have absolute value 1 and let all roots of A lie outside the unit circle. The author proposes estimates of d and of the coefficients of U. It is proved that the estimates are weakly consistent. Weakly consistent estimates of p, q and of the coefficients of A are also given.