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On the impact of serial dependence on penalized regression methods

Simone ToniniFrancesca ChiaromonteAlessandro Giovannelli
Aug 2022
摘要
This paper characterizes the impact of serial dependence on thenon-asymptotic estimation error bound of penalized regressions (PRs). Focusingon the direct relationship between the degree of cross-correlation ofcovariates and the estimation error bound of PRs, we show that orthogonal orweakly cross-correlated stationary AR processes can exhibit high spuriouscross-correlations caused by serial dependence. In this respect, we studyanalytically the density of sample cross-correlations in the simplest case oftwo orthogonal Gaussian AR(1) processes. Simulations show that our results canbe extended to the general case of weakly cross-correlated non Gaussian ARprocesses of any autoregressive order. To improve the estimation performance ofPRs in a time series regime, we propose an approach based on applying PRs tothe residuals of ARMA models fit on the observed time series. We show thatunder mild assumptions the proposed approach allows us both to reduce theestimation error and to develop an effective forecasting strategy. Theestimation accuracy of our proposal is numerically evaluated throughsimulations. To assess the effectiveness of the forecasting strategy, weprovide the results of an empirical application to monthly macroeconomic datarelative to the Euro Area economy.
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