Uniform moment bounds of Fisher's information with applications to time series

TL;DR

This paper establishes uniform moment bounds for Fisher's information matrix inverse and applies these results to derive bounds for least squares estimates in time series models, aiding model selection.

Contribution

It introduces a novel uniform moment bound for Fisher's information inverse and applies it to time series, enhancing understanding of estimator behavior and model selection criteria.

Findings

Derived asymptotic mean squared prediction error for ARMA models

Provided theoretical foundation for model selection criteria

Established uniform bounds for Fisher's information inverse

Abstract

In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher's information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear) stochastic regression models. The usefulness of these results is illustrated using time series models. In particular, an asymptotic expression for the mean squared prediction error of the least squares predictor in autoregressive moving average models is obtained. This asymptotic expression provides a solid theoretical foundation for some model selection criteria.