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Nonparametric regression with warped wavelets and strong mixing processes

Author

Listed:
  • Luz M. Gómez

    (University of São Paulo)

  • Rogério F. Porto

    (Bank of Brazil)

  • Pedro A. Morettin

    (University of São Paulo)

Abstract

We consider the situation of a univariate nonparametric regression where either the Gaussian error or the predictor follows a stationary strong mixing stochastic process and the other term follows an independent and identically distributed sequence. Also, we estimate the regression function by expanding it in a wavelet basis and applying a hard threshold to the coefficients. Since the observations of the predictor are unequally distant from each other, we work with wavelets warped by the density of the predictor variable. This choice enables us to retain some theoretical and computational properties of wavelets. We propose a unique estimator and show that some of its properties are the same for both model specifications. Specifically, in both cases the coefficients are unbiased and their variances decay at the same rate. Also the risk of the estimator, measured by the mean integrated square error is almost minimax and its maxiset remains unaltered. Simulations and an application illustrate the similarities and differences of the proposed estimator in both situations.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:aistmt:v:73:y:2021:i:6:d:10.1007_s10463-021-00789-0
    DOI: 10.1007/s10463-021-00789-0
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    1. Danthine, Jean-Pierre & Donaldson, John B., 2014. "Intermediate Financial Theory," Elsevier Monographs, Elsevier, edition 3, number 9780123865496.
    2. Erdos, Péter & Ormos, Mihály & Zibriczky, Dávid, 2011. "Non-parametric and semi-parametric asset pricing," Economic Modelling, Elsevier, vol. 28(3), pages 1150-1162, May.
    3. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    4. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    5. Gómez-González, José Eduardo & Sanabria-Buenaventura, Elioth Mirsha, 2014. "Non-parametric and semi-parametric asset pricing: An application to the Colombian stock exchange," Economic Systems, Elsevier, vol. 38(2), pages 261-268.
    6. Yhlas Sovbetov, 2018. "Factors Influencing Cryptocurrency Prices: Evidence from Bitcoin, Ethereum, Dash, Litcoin, and Monero," Journal of Economics and Financial Analysis, Tripal Publishing House, vol. 2(2), pages 1-27.
    7. Baumöhl, Eduard, 2019. "Are cryptocurrencies connected to forex? A quantile cross-spectral approach," Finance Research Letters, Elsevier, vol. 29(C), pages 363-372.
    8. Wolfgang Härdle & Helmut Lütkepohl & Rong Chen, 1997. "A Review of Nonparametric Time Series Analysis," International Statistical Review, International Statistical Institute, vol. 65(1), pages 49-72, April.
    9. Donald W.K. Andrews, 1983. "First Order Autoregressive Processes and Strong Mixing," Cowles Foundation Discussion Papers 664, Cowles Foundation for Research in Economics, Yale University.
    10. Antoniadis, A. & Grégoire, G. & Vial, P., 1997. "Random design wavelet curve smoothing," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 225-232, October.
    11. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    12. Cai, T. Tony & Brown, Lawrence D., 1999. "Wavelet estimation for samples with random uniform design," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 313-321, April.
    13. Christophe Chesneau, 2014. "A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under -Mixing Dependence," Journal of Probability and Statistics, Hindawi, vol. 2014, pages 1-12, January.
    14. Antoniadis A. & Fan J., 2001. "Regularization of Wavelet Approximations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 939-967, September.
    15. 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.
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