Oracle Properties, Bias Correction, and Inference of the Adaptive Lasso for Time Series Extremum Estimators
38 Pages Posted: 14 Oct 2013 Last revised: 4 May 2015
Date Written: May 2015
Abstract
We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for time series regression models. In particular we investigate the question of how to conduct finite sample inference on the parameters given an adaptive lasso model for some fixed value of the shrinkage parameter. Central in this study is the test of the hypothesis that a given adaptive lasso parameter equals zero, which therefore tests for a false positive. To this end we construct a simple (conservative) testing procedure and show, theoretically and empirically through extensive Monte Carlo simulations, that the adaptive lasso combines efficient parameter estimation, variable selection, and valid finite sample inference in one step. Moreover, we analytically derive a bias correction factor that is able to significantly improve the empirical coverage of the test on the active variables. Finally, we apply the introduced testing procedure to investigate the relation between the short rate dynamics and the economy, thereby providing a statistical foundation (from a model choice perspective) to the classic Taylor rule monetary policy model.
Keywords: Adaptive lasso, Time series, Oracle properties, Finite sample inference, Taylor rule monetary policy model
JEL Classification: C12, C22, E43
Suggested Citation: Suggested Citation
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