Penalised estimation of semi-parametric additive time-series models

Abstract: 

This work studies oracle properties of L1 -penalized least squares estimator, such as the LASSO, in a semi-parametric regression setting with dependent data. We extend previous results in the literature of semi-parametric models and show that sparsity oracle inequalities for the LASSO also hold in a time-series environment. The results are valid even when the dimension of the model is (much) larger than the sample size and the regression matrix is not positive definite. Our results are derived when the nonparametric component is approximated by a linear combination of known basis functions (sieves), such that the approximating model is linear in the parameters. We advocate the use of a set of randomly generated logistic functions to approximate the nonparametric component of the model. Both simulations and an empirical exercise with Brazilian energy consumption data deliver promising results.