arXiv subjects

Etienne Wijler

Publications and source records attributed to Etienne Wijler.

4 recordsLinked to original sources

arXiv2022

A restricted eigenvalue condition for unit-root non-stationary data

In this paper, we develop a restricted eigenvalue condition for unit-root non-stationary data and derive its validity under the assumption of independent Gaussian innovations that may be contemporaneously correlated. The method of proof relies on matrix concentration inequalities and offers sufficient flexibility to enable extensions of our results to alternative time series settings. As an application of this result, we show the consistency of the lasso estimator on ultra high-dimensional cointegrated data in which the number of integrated regressors may grow exponentially in relation to the sample size.

econ.EM↗

arXiv2021

Sparse Generalized Yule-Walker Estimation for Large Spatio-temporal Autoregressions with an Application to NO2 Satellite Data

We consider a high-dimensional model in which variables are observed over time and space. The model consists of a spatio-temporal regression containing a time lag and a spatial lag of the dependent variable. Unlike classical spatial autoregressive models, we do not rely on a predetermined spatial interaction matrix, but infer all spatial interactions from the data. Assuming sparsity, we estimate the spatial and temporal dependence fully data-driven by penalizing a set of Yule-Walker equations. This regularization can be left unstructured, but we also propose customized shrinkage procedures when observations originate from spatial grids (e.g. satellite images). Finite sample error bounds are derived and estimation consistency is established in an asymptotic framework wherein the sample size and the number of spatial units diverge jointly. Exogenous variables can be included as well. A simulation exercise shows strong finite sample performance compared to competing procedures. As an empirical application, we model satellite measured NO2 concentrations in London. Our approach delivers forecast improvements over a competitive benchmark and we discover evidence for strong spatial interactions.

econ.EM↗

arXiv2020

An Automated Approach Towards Sparse Single-Equation Cointegration Modelling

In this paper we propose the Single-equation Penalized Error Correction Selector (SPECS) as an automated estimation procedure for dynamic single-equation models with a large number of potentially (co)integrated variables. By extending the classical single-equation error correction model, SPECS enables the researcher to model large cointegrated datasets without necessitating any form of pre-testing for the order of integration or cointegrating rank. Under an asymptotic regime in which both the number of parameters and time series observations jointly diverge to infinity, we show that SPECS is able to consistently estimate an appropriate linear combination of the cointegrating vectors that may occur in the underlying DGP. In addition, SPECS is shown to enable the correct recovery of sparsity patterns in the parameter space and to posses the same limiting distribution as the OLS oracle procedure. A simulation study shows strong selective capabilities, as well as superior predictive performance in the context of nowcasting compared to high-dimensional models that ignore cointegration. An empirical application to nowcasting Dutch unemployment rates using Google Trends confirms the strong practical performance of our procedure.

econ.EM↗

arXiv2019

High-Dimensional Forecasting in the Presence of Unit Roots and Cointegration

We investigate how the possible presence of unit roots and cointegration affects forecasting with Big Data. As most macroeoconomic time series are very persistent and may contain unit roots, a proper handling of unit roots and cointegration is of paramount importance for macroeconomic forecasting. The high-dimensional nature of Big Data complicates the analysis of unit roots and cointegration in two ways. First, transformations to stationarity require performing many unit root tests, increasing room for errors in the classification. Second, modelling unit roots and cointegration directly is more difficult, as standard high-dimensional techniques such as factor models and penalized regression are not directly applicable to (co)integrated data and need to be adapted. We provide an overview of both issues and review methods proposed to address these issues. These methods are also illustrated with two empirical applications.

econ.EM↗