13,877 research outputs found
Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models
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
Time-varying signal processing using multi-wavelet basis functions and a modified block least mean square algorithm
This paper introduces a novel parametric modeling and identification method for linear time-varying systems using a modified block least mean square (LMS) approach where the time-varying parameters are approximated using multi-wavelet basis functions. This approach can be used to track rapidly or even sharply varying processes and is more suitable for recursive estimation of process parameters by combining wavelet approximation theory with a modified block LMS algorithm. Numerical examples are provided to show the effectiveness of the proposed method for dealing with severely nonstatinoary processes
Integrated Pre-Processing for Bayesian Nonlinear System Identification with Gaussian Processes
We introduce GP-FNARX: a new model for nonlinear system identification based
on a nonlinear autoregressive exogenous model (NARX) with filtered regressors
(F) where the nonlinear regression problem is tackled using sparse Gaussian
processes (GP). We integrate data pre-processing with system identification
into a fully automated procedure that goes from raw data to an identified
model. Both pre-processing parameters and GP hyper-parameters are tuned by
maximizing the marginal likelihood of the probabilistic model. We obtain a
Bayesian model of the system's dynamics which is able to report its uncertainty
in regions where the data is scarce. The automated approach, the modeling of
uncertainty and its relatively low computational cost make of GP-FNARX a good
candidate for applications in robotics and adaptive control.Comment: Proceedings of the 52th IEEE International Conference on Decision and
Control (CDC), Firenze, Italy, December 201
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