This paper is concerned with the unstable autoregressive process which satisfies the unstable autoregressive(AR) model U(B)G(B)xt=εt , where all the roots of the polynomials U(z) and G(z)lie on and outside the unit c...This paper is concerned with the unstable autoregressive process which satisfies the unstable autoregressive(AR) model U(B)G(B)xt=εt , where all the roots of the polynomials U(z) and G(z)lie on and outside the unit circle respectively. We propose several procedures to estimate the coefficients of U(z) and G(z) separately, in order to guarantee that the estimated polynomials of U(z) and G(z) have all the roots lying on and outside the unit circle respectively. The estimators of the coefficients of U(z) and G(z) are shown to be of strong consistency. The limiting distribution of the estimators of the coefficients of U(B)G(B) are obtained for some special cases.展开更多
文摘This paper is concerned with the unstable autoregressive process which satisfies the unstable autoregressive(AR) model U(B)G(B)xt=εt , where all the roots of the polynomials U(z) and G(z)lie on and outside the unit circle respectively. We propose several procedures to estimate the coefficients of U(z) and G(z) separately, in order to guarantee that the estimated polynomials of U(z) and G(z) have all the roots lying on and outside the unit circle respectively. The estimators of the coefficients of U(z) and G(z) are shown to be of strong consistency. The limiting distribution of the estimators of the coefficients of U(B)G(B) are obtained for some special cases.
