Understanding GLS
GLS stands for Generalized Least Squares, which is a statistical method used in regression analysis to estimate the parameters of a model with errors that have autocorrelation or heteroscedasticity. It is an extension of ordinary least squares (OLS) regression, which assumes that the errors are uncorrelated and have constant variance.
How GLS works
In GLS, the errors are no longer assumed to be independent and identically distributed. Instead, GLS accounts for the correlation structure of the errors by using a weighting matrix that captures the covariance structure of the errors. This allows for more efficient estimation of the model parameters and more accurate inferential results.
Examples of GLS
One common application of GLS is in finance, where stock returns often exhibit autocorrelation and heteroscedasticity. By using GLS, researchers can better estimate the risk and return characteristics of a portfolio and make more informed investment decisions.
Case studies
A study by economists on the impact of education on earnings used GLS to account for the correlation between individuals’ education levels and their family backgrounds. By using GLS, the researchers were able to obtain more reliable estimates of the effect of education on earnings.
Statistics on GLS
According to a survey of statisticians, GLS is increasingly being used in various fields such as economics, finance, and environmental science due to its ability to handle complex error structures. In a recent study, over 60% of researchers reported using GLS in their regression analyses.
