Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/266091 
Year of Publication: 
2022
Series/Report no.: 
LEM Working Paper Series No. 2022/21
Publisher: 
Scuola Superiore Sant'Anna, Laboratory of Economics and Management (LEM), Pisa
Abstract: 
This paper characterizes the impact of serial dependence on the non-asymptotic estimation error bound of penalized regressions (PRs). Focusing on the direct relationship between the degree of cross-correlation of covariates and the estimation error bound of PRs, we show that orthogonal or weakly cross-correlated stationary AR processes can exhibit high spurious cross-correlations caused by serial dependence. In this respect, we study analytically the density of sample cross-correlations in the simplest case of two orthogonal Gaussian AR(1) processes. Simulations show that our results can be extended to the general case of weakly cross-correlated non Gaussian AR processes of any autoregressive order. To improve the estimation performance of PRs in a time series regime, we propose an approach based on applying PRs to the residuals of ARMA models fit on the observed time series. We show that under mild assumptions the proposed approach allows us both to reduce the estimation error and to develop an effective forecasting strategy. The estimation accuracy of our proposal is numerically evaluated through simulations. To assess the effectiveness of the forecasting strategy, we provide the results of an empirical application to monthly macroeconomic data relative to the Euro Area economy.
Subjects: 
Serial dependence
spurious correlation
minimum eigenvalue
penalized regressions
estimation accuracy
JEL: 
C13
C18
C22
C31
C46
Document Type: 
Working Paper

Files in This Item:
File
Size
768.71 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.