IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i4p624-d752022.html
   My bibliography  Save this article

Nonparametric Estimation of the Density Function of the Distribution of the Noise in CHARN Models

Author

Listed:
  • Joseph Ngatchou-Wandji

    (EHESP French School of Public Health, 35043 Rennes, France
    Institut Élie Cartan de Lorraine, University of Lorraine, 54052 Vandoeuvre-Lès-Nancy, France)

  • Marwa Ltaifa

    (Institut Élie Cartan de Lorraine, University of Lorraine, 54052 Vandoeuvre-Lès-Nancy, France)

  • Didier Alain Njamen Njomen

    (Department of Mathematics and Computer Science, Faculty of Science, University of Maroua, Maroua P.O. Box 814, Cameroon)

  • Jia Shen

    (Department of Statistics, Fudan University, Shanghai 200433, China)

Abstract

This work is concerned with multivariate conditional heteroscedastic autoregressive nonlinear (CHARN) models with an unknown conditional mean function, conditional variance matrix function and density function of the distribution of noise. We study the kernel estimator of the latter function when the former are either parametric or nonparametric. The consistency, bias and asymptotic normality of the estimator are investigated. Confidence bound curves are given. A simulation experiment is performed to evaluate the performance of the results.

Suggested Citation

  • Joseph Ngatchou-Wandji & Marwa Ltaifa & Didier Alain Njamen Njomen & Jia Shen, 2022. "Nonparametric Estimation of the Density Function of the Distribution of the Noise in CHARN Models," Mathematics, MDPI, vol. 10(4), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:624-:d:752022
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/4/624/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/4/624/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. S. Chandra & Masanobu Taniguchi, 2001. "Estimating Functions for Nonlinear Time Series Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 125-141, March.
    3. Neumeyer, Pablo A. & Perri, Fabrizio, 2005. "Business cycles in emerging economies: the role of interest rates," Journal of Monetary Economics, Elsevier, vol. 52(2), pages 345-380, March.
    4. Chesneau, Christophe & Fadili, Jalal & Maillot, Bertrand, 2015. "Adaptive estimation of an additive regression function from weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 77-94.
    5. Kazuo Noda, 1976. "Estimation of a regression function by the parzen kernel-type density estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 28(1), pages 221-234, December.
    6. Ziegelmann, Flavio A., 2002. "Nonparametric Estimation Of Volatility Functions: The Local Exponential Estimator," Econometric Theory, Cambridge University Press, vol. 18(4), pages 985-991, August.
    7. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 159-199.
    8. Holger Dette & Natalie Neumeyer & Ingrid Van Keilegom, 2007. "A new test for the parametric form of the variance function in non‐parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 903-917, November.
    9. Collomb, Gérard & Härdle, Wolfgang, 1986. "Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 77-89, October.
    10. Azzedine, Nadjia & Laksaci, Ali & Ould-Saïd, Elias, 2008. "On robust nonparametric regression estimation for a functional regressor," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3216-3221, December.
    11. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    12. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    13. Neumeyer, N. & Van Keilegom, I., 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," LIDAM Reprints ISBA 2010006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Li, David X & Turtle, H J, 2000. "Semiparametric ARCH Models: An Estimating Function Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 174-186, April.
    15. Oliver B. Linton & Yang Yan, 2011. "Semi- and Nonparametric ARCH Processes," Journal of Probability and Statistics, Hindawi, vol. 2011, pages 1-17, August.
    16. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    17. Nils-Bastian Heidenreich & Anja Schindler & Stefan Sperlich, 2013. "Bandwidth selection for kernel density estimation: a review of fully automatic selectors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 403-433, October.
    18. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    19. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    20. Franke, Jurgen & Neumann, Michael H. & Stockis, Jean-Pierre, 2004. "Bootstrapping nonparametric estimators of the volatility function," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 189-218.
    21. Hiroomi Kanai & Hiroaki Ogata & Masanobu Taniguchi, 2010. "Estimating function approach for CHARN Models," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 1-21.
    22. M. S. Al‐Qassam & J. A. Lane, 1989. "Forecasting Exponential Autoregressive Models Of Order 1," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(2), pages 95-113, March.
    23. Zu, Yang & Peter Boswijk, H., 2014. "Estimating spot volatility with high-frequency financial data," Journal of Econometrics, Elsevier, vol. 181(2), pages 117-135.
    24. C. Crambes & L. Delsol & A. Laksaci, 2008. "Robust nonparametric estimation for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 573-598.
    25. Kristensen, Dennis, 2010. "Nonparametric Filtering Of The Realized Spot Volatility: A Kernel-Based Approach," Econometric Theory, Cambridge University Press, vol. 26(1), pages 60-93, February.
    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. Jenny Farmer & Eve Allen & Donald J. Jacobs, 2022. "Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities," Mathematics, MDPI, vol. 11(1), pages 1-19, December.
    2. Piotr Powroźnik & Paweł Szcześniak & Krzysztof Turchan & Miłosz Krysik & Igor Koropiecki & Krzysztof Piotrowski, 2022. "An Elastic Energy Management Algorithm in a Hierarchical Control System with Distributed Control Devices," Energies, MDPI, vol. 15(13), pages 1-24, June.

    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. Biqing Cai & Dag Tjøstheim, 2015. "Nonparametric Regression Estimation for Multivariate Null Recurrent Processes," Econometrics, MDPI, vol. 3(2), pages 1-24, April.
    2. Enno Mammen & Jens Perch Nielsen & Michael Scholz & Stefan Sperlich, 2019. "Conditional Variance Forecasts for Long-Term Stock Returns," Risks, MDPI, vol. 7(4), pages 1-22, November.
    3. Comte, F. & Rozenholc, Y., 2002. "Adaptive estimation of mean and volatility functions in (auto-)regressive models," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 111-145, January.
    4. Matthieu Garcin & Clément Goulet, 2015. "Non-parameteric news impact curve: a variational approach," Documents de travail du Centre d'Economie de la Sorbonne 15086rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Feb 2017.
    5. Gloria González-Rivera & Tae-Hwy Lee, 2007. "Nonlinear Time Series in Financial Forecasting," Working Papers 200803, University of California at Riverside, Department of Economics, revised Feb 2008.
    6. Jürgen Franke & Jean-Pierre Stockis & Joseph Tadjuidje, 2007. "Quantile Sieve Estimates For Time Series," SFB 649 Discussion Papers SFB649DP2007-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Saliha Derrar & Ali Laksaci & Elias Ould Saïd, 2020. "M-estimation of the regression function under random left truncation and functional time series model," Statistical Papers, Springer, vol. 61(3), pages 1181-1202, June.
    8. Mailand, Wilhelm, 1998. "Zum Einfluß von Unsicherheit auf die gesamtwirtschaftliche Investitionstätigkeit," HWWA Discussion Papers 57, Hamburg Institute of International Economics (HWWA).
    9. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    10. Adam Clements & Scott White, 2005. "Non-linear filtering with state dependant transition probabilities: A threshold (size effect) SV model," School of Economics and Finance Discussion Papers and Working Papers Series 191, School of Economics and Finance, Queensland University of Technology.
    11. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    12. Härdle, Wolfgang & Horowitz, Joel L. & Kreiss, Jens-Peter, 2001. "Bootstrap methods for time series," SFB 373 Discussion Papers 2001,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    13. Feve, Frederique & Florens, Jean-Pierre & Van Keilegom, Ingrid, 2012. "Estimation of conditional ranks and tests of exogeneity in nonparametric nonseparable models," LIDAM Discussion Papers ISBA 2012036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Maurício Yoshinori Une & Marcelo Savino Portugal, 2005. "Fear of disruption: a model of Markov-switching regimes for the Brazilian country risk conditional volatility," Econometrics 0509005, University Library of Munich, Germany.
    15. Linton, Oliver & Mammen, Enno, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.
    16. Mailand, Wilhelm, 1998. "Zum Einfluss von Unsicherheit auf die gesamtwirtschaftliche Investitionstatigkeit," Discussion Paper Series 26305, Hamburg Institute of International Economics.
    17. Shields, Kalvinder K, 1997. "Threshold Modelling of Stock Return Volatility on Eastern European Markets," Economic Change and Restructuring, Springer, vol. 30(2-3), pages 107-125.
    18. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    19. Lijian Yang & Wolfgang Hardle & Jens Nielsen, 1999. "Nonparametric Autoregression with Multiplicative Volatility and Additive mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 579-604, September.
    20. Boente, Graciela & Vahnovan, Alejandra, 2015. "Strong convergence of robust equivariant nonparametric functional regression estimators," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 1-11.

    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:gam:jmathe:v:10:y:2022:i:4:p:624-:d:752022. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.