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Article overview
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On the impact of serial dependence on penalized regression methods | | Simone Tonini
; Francesca Chiaromonte
; Alessandro Giovannelli
; | | Date: |
1 Aug 2022 | | 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. | | Source: | arXiv, 2208.00727 | | Services: | Forum | Review | PDF | Favorites | |
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