Oracle Properties Bias Correction And Inference Of The Adaptive Lasso For Time Series Extremum Estimators
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Oracle Properties, Bias Correction, and Inference of the Adaptive Lasso for Time Series Extremum Estimators
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.
Oracle Properties, Bias Correction, and Bootstrap Inference for Adaptive Lasso for Time Series M-Estimators
We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for possibly nonlinear time series models. In particular, we investigate the question of how to conduct inference on the parameters given an adaptive lasso model. Central to 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 introduce a recentered bootstrap procedure and show, theoretically and empirically through extensive Monte Carlo simulations, that the adaptive lasso can combine efficient parameter estimation, variable selection, and 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 adaptive lasso and the recentered bootstrap procedure to investigate the relation between the short rate dynamics and the economy, thereby providing a statistical foundation (from a model choice perspective) for the classic Taylor rule monetary policy model.
Extended Oracle Properties of Adaptive Lasso Estimators
We study the asymptotic properties of adaptive lasso estimators when some components of the parameter of interest are strictly different than zero, while other components may be zero or may converge to zero with rate n^(-delta), with delta> 0, where n denotes the sample size. First, we derive conditions that allow to select tuning parameters in order to ensure that adaptive lasso estimates of n^(-delta)-components indeed collapse to zero. Second, in this case we also derive asymptotic distributions of adaptive lasso estimators for nonzero components. When delta > 1=2, we obtain the usual n1/2-asymptotic normal distribution, while when 0