Regression with Autocorrelated Errors Using Design-Adapted Haar Wavelets

Porto Rogério F., Morettin Pedro A. and Aubin Elisete C. Q.
Additional contact information
Porto Rogério F.: Bank of Brazil
Morettin Pedro A.: University of São Paulo, Brazil
Aubin Elisete C. Q.: University of São Paulo, Brazil

Journal of Time Series Econometrics, 2012, vol. 4, issue 1, 30

Abstract: We present some theoretical results on semi-parametric regression models in the presence of autocorrelated errors using design-adapted Haar wavelets. We prove that the risks for the linear and nonlinear estimators are asymptotically almost minimax when the errors have absolutely summable autocovariances. For the nonlinear estimator, we also need a strong mixing property with a specific coefficient and a condition on the errors' higher-order moments. Some simulations ilustrate the theoretical achievements.

Keywords: autocorrelation; denoising; design-adapted wavelets; semi-parametric estimation; smoothing; unbalanced Haar wavelets (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1515/1941-1928.1067

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