A resampling approach for confidence intervals in linear time-series models after model selection

Abstract

Linear models are commonly used in econometrics to describe structural relations and draw inferences about underlying parameters. Although the theoretical and practical value of these models has been justified under ideal circumstances, empirical studies have shown that they did not well fit the observed data in reality, and their selection is therefore an important problem. In the big-data era, one approach is to consider a large set of covariates and apply model selection. However, many model selection methods can provide consistent coefficient estimators and confidence intervals, but perform poorly in practice due to an insufficient sample size. Especially for financial data, which have relatively small sample sizes and are usually correlated, classical methods to construct confidence intervals after model selection are usually inaccurate. We consider the problem of constructing confidence intervals for selected coefficients in linear time-series models. To overcome the difficulties of post-selection confidence intervals, we introduce consistent estimators of the selected parameters and work on a resampling approach for confidence interval construction. Theory, simulations, and empirical studies demonstrate the advantages of the proposed method.