Limiting Distributions of Least Squares Estimates of Unstable Autoregressive Processes

Reversals of Least-Squares Estimates

An adjusted estimate may be opposite the original estimate. This paper presents necessary and sufficient conditions for such a reversal, in the context of linear modeling, where adjustment is obtained through considering additional explanatory data associated with lurking variables.

On asymptotic normality of sequential LS-estimates of unstable autoregressive processes

For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting distribution of the sequential LSE is shown to be normal for the parameter vector lying both inside the stability region and on some part of its boundary in contr...

Weighted Least Squares Approximate Restricted Maximum Likelihood Estima - tion of Vector Autoregressive Processes

4 Appendix S-1 4.1 Proof of Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-1 4.2 Proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-4 4.3 Proof of Theorem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-8 4.4 Proof of Theorem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Limiting Distributions for Branching Processes

Asymptotic Theory of Least Squares Estimators for Nearly Unstable Processes under Strong Dependence by Boris Buchmann

This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures converge to functionals of fractional Ornstein–Uhlenbeck processes. We use fractional integrated noise as an example to illustrate the important ideas. In this...