Evaluation of Some Estimators Performance on Linear Models with Heteroscedasticity and Serial Autocorrelation (Published)
In many, if not most, econometric applications, economic data arises from time-series or cross-sectional studies which typically exhibit some form of autocorrelation and/or heteroskedasticity. If the covariance structure were known, it could be taken into account in a (parametric) model, but more often than not the form of autocorrelation and heteroskedasticity is unknown. In such cases, model parameters can typically still be estimated consistently using the usual estimating functions, but for valid inference in such models a consistent covariance matrix estimate is essential. In this study, the strength of some methods of estimating classical linear regression model with both negative and positive autocorrelation in the presence of heteroscedasticity were investigated. The Ordinary Least Square (OLS) estimator, Heteroskedasticity and Autocorrelation (HAC) estimators which includes Cluster-Robust Standard Errors estimators, Newey-West standard errors and Feasible Generalized Least Squares Estimator (FGLS) were considered in this study. Monte-Carlo experiments were conducted and the study further identifies the best estimator that can be used for prediction purpose by adopting the goodness of fit statistics of the estimators. The result revealed the superiority of the Newey-West standard errors over others using root mean squared error (RMSE) of the parameter estimates and relative efficiency (RR) as assessment criteria among others over various considerations for the distribution of the serial correlation and heteroskedasticity.
This work consider the problem of comparing two multivariate normal mean vectors under the heteroscedasticity of dispersion matrices. We develop a new procedure using approximate degree of freedom method by Satterthwaite  and broaden it to Multivariate Behrens Fisher. The New procedure is compared with existing ones via R package simulation and Data used by James  and Yao . And we ascertain that, new procedure is better in terms of power of the test and type I error rate than all existing procedure mull over when the sample sizes are not equal, but the propose procedure perform the same with the selected procedure when sample sizes are equal.