Sequential Estimation of the Parameters in Unstable AR(2)

Abstract

For a second-order nonexplosive autoregressive process with unknown vector parameter Θ = (Θ₁,Θ₂)^′, 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.

Keywords:

• Autoregressive process
• Least squares estimate
• Sequential estimation
• Uniform asymptotic normality
• Unstable autoregressive process

Mathematics Subject Classification:

• 62L10
• 62L12

ACKNOWLEDGMENTS

The authors are grateful to the referee for helpful comments and constructive suggestions. The second author is partially supported by the RFFI-DFG-Grant 02-01-04001 and RFFI-Grant 04-01-00855.

Recommended by T. N. Sriram