An Investigation into Regression Models with Autocorrelated Errors and Applications.

Abstract

Estimation of regression models with autocorrelated errors is an important problem in many practical applications, especially in finance, economics, and medical research. This research reviews the theory of conditional and exact least squares estimation in regression models with autoregressive (AR) errors. It also investigates the theory of exact parameter estimation in regression models with higher-order autoregressive errors by extending the Prais-Winsten approach. The Prais-Winsten method for higher-order AR errors, using a computationally efficient zig-zag algorithm, is discussed and assessed through a simulation study. The theoretical incorporation of small-sample analysis with AR errors within the Prais-Winsten conceptual framework is also explored. The findings are further substantiated by applying the theory to time series data in the health sector, demonstrating its applicability and usefulness in real world scenarios. These contributions highlight the importance of addressing AR errors in regression models and offer novel methodologies to improve predictive accuracy in practical applications.