IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v83y2020i4d10.1007_s00184-019-00735-4.html
   My bibliography  Save this article

Comparing two nonparametric regression curves in the presence of long memory in covariates and errors

Author

Listed:
  • Hira L. Koul

    (Michigan State University)

  • Fang Li

    (Indiana University Purdue University Indianapolis (IUPUI))

Abstract

This paper discusses the problem of testing the equality of two nonparametric regression functions against two-sided alternatives in the presence of long memory in the common covariate and errors. The proposed test is based on a marked empirical process of the differences between the response variables. We discuss asymptotic null distribution of this process and consistency of the test for a class of general alternatives. We also conduct a Monte Carlo simulation study to evaluate the finite sample level and power behavior of the test at some alternatives.

Suggested Citation

  • Hira L. Koul & Fang Li, 2020. "Comparing two nonparametric regression curves in the presence of long memory in covariates and errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 499-517, May.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:4:d:10.1007_s00184-019-00735-4
    DOI: 10.1007/s00184-019-00735-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-019-00735-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-019-00735-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 442-447, September.
    2. Scheike, Thomas H., 2000. "Comparison of non-parametric regression functions through their cumulatives," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 21-32, January.
    3. Ferreira, E. & Stute, W., 2004. "Testing for Differences Between Conditional Means in a Time Series Context," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 169-174, January.
    4. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameter for nonlinear time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 211-251, March.
    5. Dalla, Violetta & Giraitis, Liudas & Hidalgo, Javier, 2006. "Consistent estimation of the memory parameter for nonlinear time series," LSE Research Online Documents on Economics 6813, London School of Economics and Political Science, LSE Library.
    6. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    7. Hira Koul & Donatas Surgailis & Nao Mimoto, 2015. "Minimum distance lack-of-fit tests under long memory errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 119-143, February.
    8. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
    9. Härdle, W. & Marron, S.J., 1990. "Semiparametric comparison of regression curves," LIDAM Reprints CORE 890, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Koul, Hira L. & Baillie, Richard T. & Surgailis, Donatas, 2004. "Regression Model Fitting With A Long Memory Covariate Process," Econometric Theory, Cambridge University Press, vol. 20(3), pages 485-512, June.
    11. Javier Hidalgo & Peter M. Robinson, 2002. "Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory," Econometrica, Econometric Society, vol. 70(4), pages 1545-1581, July.
    12. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameterfor nonlinear time series," STICERD - Econometrics Paper Series 497, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. Robinson, Peter M., 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
    Full references (including those not matched with items on IDEAS)

    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. Fabrizio Iacone, 2010. "Local Whittle estimation of the memory parameter in presence of deterministic components," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 37-49, January.
    2. Karim M. Abadir & Walter Distaso & Liudas Giraitis, 2011. "An I() model with trend and cycles," Post-Print hal-00834425, HAL.
    3. La Spada Gabriele & Lillo Fabrizio, 2014. "The effect of round-off error on long memory processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(4), pages 1-38, September.
    4. Frank S. Nielsen, 2009. "Local Whittle estimation of multivariate fractionally integrated processes," CREATES Research Papers 2009-38, Department of Economics and Business Economics, Aarhus University.
    5. Frank S. Nielsen, 2011. "Local Whittle estimation of multi‐variate fractionally integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(3), pages 317-335, May.
    6. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2011. "An I(d) model with trend and cycles," Journal of Econometrics, Elsevier, vol. 163(2), pages 186-199, August.
    7. Ruiz Esther & Pérez Ana, 2012. "Maximally Autocorrelated Power Transformations: A Closer Look at the Properties of Stochastic Volatility Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-33, September.
    8. Faÿ, Gilles & Moulines, Eric & Roueff, François & Taqqu, Murad S., 2009. "Estimators of long-memory: Fourier versus wavelets," Journal of Econometrics, Elsevier, vol. 151(2), pages 159-177, August.
    9. Hira Koul & Nao Mimoto & Donatas Surgailis, 2013. "Goodness-of-fit tests for long memory moving average marginal density," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(2), pages 205-224, February.
    10. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers 2008-28, Department of Economics and Business Economics, Aarhus University.
    11. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2009. "Two estimators of the long-run variance: Beyond short memory," Journal of Econometrics, Elsevier, vol. 150(1), pages 56-70, May.
    12. repec:hal:journl:peer-00834425 is not listed on IDEAS
    13. Fabrizio Iacone, 2009. "A Semiparametric Analysis of the Term Structure of the US Interest Rates," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(4), pages 475-490, August.
    14. Baillie, Richard T. & Kapetanios, George, 2008. "Nonlinear models for strongly dependent processes with financial applications," Journal of Econometrics, Elsevier, vol. 147(1), pages 60-71, November.
    15. Dalla, Violetta, 2015. "Power transformations of absolute returns and long memory estimation," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 1-18.
    16. Jean‐Marc Bardet & Paul Doukhan & José Rafael León, 2008. "Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 906-945, September.
    17. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
    18. Pedro H. C. Sant'Anna & Xiaojun Song & Qi Xu, 2022. "Covariate distribution balance via propensity scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1093-1120, September.
    19. Miguel A. Delgado & Juan Carlos Escanciano, 2013. "Conditional Stochastic Dominance Testing," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 16-28, January.
    20. Hidalgo, Javier, 2007. "Specification testing for regression models with dependent data," LSE Research Online Documents on Economics 6799, London School of Economics and Political Science, LSE Library.
    21. Gørgens, Tue, 2002. "Nonparametric comparison of regression curves by local linear fitting," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 81-89, November.

    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:spr:metrik:v:83:y:2020:i:4:d:10.1007_s00184-019-00735-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.