Theory of Ridge Regression Estimation with Applications

9Regression Models with Autoregressive Errors

9.1 Introduction

One of the important assumptions of the linear model is that observed responses of the model are independent. However, in reality, significant serial correlation might occur when data are collected sequentially in time. Autocorrelation, also known as serial correlation, occurs when successive items in a series are correlated so that their covariance is not zero and they are not independent. The main objective of this chapter is to develop some penalty and improved estimators, namely, ridge regression estimator (RRE) and the least absolute shrinkage and selection operator (LASSO) and the Stein‐type estimators for the linear regression model with AR(1) errors when some of the coefficients are not statistically significant.

To describe the problem of autocorrelation, we consider the following regression model,

(9.1)

where 's are responses, is a known vector of regressors, is an unknown vector of unknown regression parameters, ...