Revisiting simple linear regression with autocorrelated errors

Minimax Regression Designs for Approximately Linear Models with Autocorrelated Errors

We study the construction of regression designs, when the random errors are autocorrelated. Our model of dependence assumes that the spectral density g(~o) of the error process is of the form g ( o ) = (1 -a)go(~O ) + ~gl(o), where go(CO) is uniform (corresponding to uncorrelated errors), ct ~ [0, 1) is fixed, and gx(to) is arbitrary. We consider regression responses which are exactly, or only ...

Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors

More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors

We propose a modification of kernel time series regression estimators that improves efficiency when the innovation process is autocorrelated. The procedure is based on a pre-whitening transformation of the dependent variable that has to be estimated from the data. We establish the asymptotic distribution of our estimator under weak dependence conditions. It is shown that the proposed estimation...

The Linear Regression Model with Autocorrelated Errors: Just Say No to Error Autocorrelation

This paper focuses on the practice of serial correlation correcting of the Linear Regression Model (LRM) by modeling the error. Simple Monte Carlo experiments are used to demonstrate the following points regarding this practice. First, the common factor restrictions implicitly imposed on the temporal structure of yt and xt appear to be completely unreasonable for any real world application. Sec...

Mixtures of Linear Regression with Measurement Errors

Existing research on mixtures of regression models are limited to directly observed predictors. The estimation of mixtures of regression for measurement error data imposes challenges for statisticians. For linear regression models with measurement error data, the naive ordinary least squares method, which directly substitutes the observed surrogates for the unobserved error-prone variables, yie...