Estimation in the presence of heteroskedasticty of unknown form: A Lasso-based approach

We study the Feasible Generalized Least-Squares (FGLS) estimation of the parameters of a linear regression model in the presence of heteroskedasticity of unknown form in the errors. We suggest a Lasso based procedure to estimate the skedastic function of the residuals. The advantage of using Lasso is that it can handle a large number of potential covariates, yet still yields a parsimonious specification. Using extensive simulation experiments, we show that our suggested procedure always provide some improvements in the precision of the parameter of interest (lower Mean- Squared Errors) when heteroskedasticity is present and is equivalent to OLS when there is none. It also performs better than previously suggested procedures. Since the fitted value of the skedastic function falls short of the true specification, we form confidence intervals using a bias-corrected version of the usual heteroskedasticity-robust covariance matrix estimator. These have the correct size and substantially shorter length than when using OLS. Our method is applicable to both cross-section (with a random sample) and time series models, though here we concentrate on the former.