IDEAS home Printed from https://ideas.repec.org/p/fam/rpseri/rp144.html
   My bibliography  Save this paper

Multiariate Wavelet-based sahpe preserving estimation for dependant observation

Author

Listed:
  • Antonio Cosma
  • Olivier Scaillet
  • Rainer von Sachs

Abstract

We present a new approach on shape preserving estimation of probability distribution and density functions using wavelet methodology for multivariate dependent data. Our estimators preserve shape constraints such as monotonicity, positivity and integration to one, and allow for low spatial regularity of the underlying functions. As important application, we discuss conditional quantile estimation for financial time series data. We show that our methodology can be easily implemented with B-splines, and performs well in a finite sample situation, through Monte Carlo simulations.

Suggested Citation

  • Antonio Cosma & Olivier Scaillet & Rainer von Sachs, 2005. "Multiariate Wavelet-based sahpe preserving estimation for dependant observation," FAME Research Paper Series rp144, International Center for Financial Asset Management and Engineering.
    • Handle: RePEc:fam:rpseri:rp144
    as

    Download full text from publisher

    File URL: http://www.swissfinanceinstitute.ch/rp144.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    2. K. Tribouley, 1995. "Practical estimation of multivariate densities using wavelet methods," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 49(1), pages 41-62, March.
    3. Kerkyacharian, G. & Picard, D., 1992. "Density estimation in Besov spaces," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 15-24, January.
    4. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(1), pages 169-192, February.
    5. Masry, Elias, 1994. "Probability density estimation from dependent observations using wavelets orthonormal bases," Statistics & Probability Letters, Elsevier, vol. 21(3), pages 181-194, October.
    6. Lee, Jin & Hong, Yongmiao, 2001. "Testing For Serial Correlation Of Unknown Form Using Wavelet Methods," Econometric Theory, Cambridge University Press, vol. 17(2), pages 386-423, April.
    7. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    8. Masry, Elias, 1997. "Multivariate probability density estimation by wavelet methods: Strong consistency and rates for stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 177-193, May.
    9. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    10. Pinheiro, Aluisio & Vidakovic, Brani, 1997. "Estimating the square root of a density via compactly supported wavelets," Computational Statistics & Data Analysis, Elsevier, vol. 25(4), pages 399-415, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:wyi:journl:002095 is not listed on IDEAS
    2. Morettin Pedro A. & Toloi Clelia M.C. & Chiann Chang & de Miranda José C.S., 2011. "Wavelet Estimation of Copulas for Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-31, October.
    3. R H Spady & S Stouli, 2018. "Dual regression," Biometrika, Biometrika Trust, vol. 105(1), pages 1-18.
    4. Cosma, Antonio & Galluccio, Stefano & Scaillet, Olivier, 2012. "Valuing American options using fast recursive projections," Working Papers unige:41856, University of Geneva, Geneva School of Economics and Management.
    5. Benjamin Beckers & Helmut Herwartz & Moritz Seidel, 2017. "Risk forecasting in (T)GARCH models with uncorrelated dependent innovations," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 121-137, January.
    6. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    7. Lu Ou & Zhibiao Zhao, 2021. "Value‐at‐risk forecasting via dynamic asymmetric exponential power distributions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 291-300, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:cte:werepe:we1211 is not listed on IDEAS
    2. Rodney V. Fonseca & Aluísio Pinheiro, 2020. "Wavelet estimation of the dimensionality of curve time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1175-1204, October.
    3. repec:wyi:journl:002095 is not listed on IDEAS
    4. Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.
    5. Taoufik Bouezmarni & Abderrahim Taamouti, 2014. "Nonparametric tests for conditional independence using conditional distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 697-719, December.
    6. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    7. Zongwu Cai & Xian Wang, 2013. "Nonparametric Methods for Estimating Conditional VaR and Expected Shortfall," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    8. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    9. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.
    10. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Time Series Nonparametric Regression Using Asymmetric Kernels with an Application to Estimation of Scalar Diffusion Processes," CIRJE F-Series CIRJE-F-573, CIRJE, Faculty of Economics, University of Tokyo.
    11. Gérard, Kerkyacharian & Dominique, Picard, 1997. "Limit of the quadratic risk in density estimation using linear methods," Statistics & Probability Letters, Elsevier, vol. 31(4), pages 299-312, February.
    12. Jürgen Franke & Peter Mwita & Weining Wang, 2015. "Nonparametric estimates for conditional quantiles of time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 107-130, January.
    13. Marianna Pensky, 2002. "Locally Adaptive Wavelet Empirical Bayes Estimation of a Location Parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 83-99, March.
    14. Sun, Haoze & Weng, Chengguo & Zhang, Yi, 2017. "Optimal multivariate quota-share reinsurance: A nonparametric mean-CVaR framework," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 197-214.
    15. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    16. Leorato, Samantha & Peracchi, Franco & Tanase, Andrei V., 2012. "Asymptotically efficient estimation of the conditional expected shortfall," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 768-784.
    17. Xu, Ke-Li & Phillips, Peter C. B., 2011. "Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 518-528.
    18. Sun, Yiguo, 2006. "A Consistent Nonparametric Equality Test Of Conditional Quantile Functions," Econometric Theory, Cambridge University Press, vol. 22(4), pages 614-632, August.
    19. Cai, Zongwu & Li, Qi, 2008. "Nonparametric Estimation Of Varying Coefficient Dynamic Panel Data Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1321-1342, October.
    20. Ke Zhu, 2016. "Bootstrapping the portmanteau tests in weak auto-regressive moving average models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 463-485, March.
    21. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    22. Masry, Elias, 1997. "Multivariate probability density estimation by wavelet methods: Strong consistency and rates for stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 177-193, May.

    More about this item

    Keywords

    Conditional quantile; time series; shape preserving wavelet estimation; B-splines; multivariate process;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fam:rpseri:rp144. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ridima Mittal (email available below). General contact details of provider: https://edirc.repec.org/data/fameech.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.