Oracle Properties, Bias Correction, and Bootstrap Inference for Adaptive Lasso for Time SeriesM‐Estimators
研究了自适应Lasso在非线性时间序列模型中的理论性质，提出了一种重中心化Bootstrap方法，可同时实现参数估计、变量选择和推断，并推导了偏差校正因子以改进检验的覆盖概率。
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.