A1168
Title: Penalized QMLE and model selection of time series regressions
Authors: Julie Schnaitmann - University of Tuebingen (Germany) [presenting]
Christian Francq - CREST and University Lille III (France)
Sebastien Laurent - AMU (France)
Abstract: The purpose is to examine a linear regression model applied to the components of a time series, aiming to identify time-varying, constant as well as zero conditional beta coefficients. To address the non-identifiability of parameters when a conditional beta is constant, a Lasso-type estimator is employed. This penalized estimator simplifies the model by shrinking the estimates in favor of natural constant beta representations. A multistep estimator that first captures the dynamics of the regressors is proposed before estimating the dynamics of the betas. This strategy breaks down a large-dimensional optimization problem into several lower-dimensional ones. Since making strict parametric assumptions is avoided about the innovation distributions, quasi-maximum likelihood estimators are used. The non-Markovian nature of the global model means that standard convex optimization results cannot be applied. The asymptotic distribution of the multistep Lasso estimator and its adaptive version are analyzed, deriving bounds on the maximum value of the penalty term. A nonlinear coordinate-wise descent algorithm is also proposed, which is demonstrated to find stationary points of the objective function. The finite-sample properties of these estimators are further explored through a Monte Carlo simulation and illustrated with an application to financial data.
