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Regression with Autocorrelated Errors Using Design-Adapted Haar Wavelets

Author

Listed:
  • Porto Rogério F.

    (Bank of Brazil)

  • Morettin Pedro A.

    (University of São Paulo, Brazil)

  • Aubin Elisete C. Q.

    (University of São Paulo, Brazil)

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.

Suggested Citation

  • Porto Rogério F. & Morettin Pedro A. & Aubin Elisete C. Q., 2012. "Regression with Autocorrelated Errors Using Design-Adapted Haar Wavelets," Journal of Time Series Econometrics, De Gruyter, vol. 4(1), pages 1-30, May.
    • Handle: RePEc:bpj:jtsmet:v:4:y:2012:i:1:n:4
    DOI: 10.1515/1941-1928.1067
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    References listed on IDEAS

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    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
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    Cited by:

    1. Luz M. Gómez & Rogério F. Porto & Pedro A. Morettin, 2021. "Nonparametric regression with warped wavelets and strong mixing processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1203-1228, December.

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