Sequential Estimation of the Parameters in Unstable AR(2)

摘要

For a second-order nonexplosive autoregressive process with unknown vector parameter θ=(θ_1, θ_2)', it is shown that the sequential least squares estimate with a particular stopping time is asymptotically normally distributed uniformly in θ belonging to any compact set in the stability region of the process supplemented with the part of its boundary corresponding to complex roots of the characteristic polynomial.