Best linear unbiased estimators in continuous time regression models

TL;DR

This paper investigates the explicit form of best linear unbiased estimators (BLUE) in continuous-time regression models, especially with smooth error processes, providing formulas for specific models like AR(2) and integrated Brownian motion.

Contribution

It derives explicit BLUE formulas for various continuous-time models, including cases with smooth error processes and specific error structures, advancing estimation theory in continuous-time regression.

Findings

Explicit BLUE formulas for models with smooth errors

BLUE derivations for AR(2) and integrated Brownian motion errors

Illustrative examples demonstrating estimator applications

Abstract

In this paper the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular when the error process is a smooth process with one or several derivatives of the response process available for construction of the estimators. We derive the explicit form of the BLUE for many specific models including the cases of continuous autoregressive errors of order two and integrated error processes (such as integrated Brownian motion). The results are illustrated by several examples.