  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 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.
