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Estimation and model specification testing in nonparametric and semiparametric econometric models

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  • Gao, Jiti
  • King, Maxwell

Abstract

This paper considers two classes of semiparametric nonlinear regression models, in which nonlinear components are introduced to reflect the nonlinear fluctuation in the mean. A general estimation and testing procedure for nonparametric time series regression under the strong-mixing condition is introduced. Several test statistics for testing nonparametric significance, linearity and additivity in nonparametric and semi-parametric time series econometric models are then constructed. The proposed test statistics are shown to have asymptotic normal distributions under their respective null hypotheses. Moreover, the proposed testing procedures are illustrated by several simulated examples. In addition, one of the proposed testing procedures is applied to a continuous-time model and implemented through a set of the US Federal interest rate data. Our research suggests that it is unreasonable to assume the linearity in the drift for the given data as required by some existing studies.

Suggested Citation

  • Gao, Jiti & King, Maxwell, 2003. "Estimation and model specification testing in nonparametric and semiparametric econometric models," MPRA Paper 11989, University Library of Munich, Germany, revised Feb 2006.
    • Handle: RePEc:pra:mprapa:11989
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    References listed on IDEAS

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    1. Linton, Oliver B., 2000. "Efficient Estimation Of Generalized Additive Nonparametric Regression Models," Econometric Theory, Cambridge University Press, vol. 16(4), pages 502-523, August.
    2. Gao, Jiti & Tong, Howell & Wolff, Rodney, 2002. "Model Specification Tests in Nonparametric Stochastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 324-359, November.
    3. Wooldridge, Jeffrey M., 1992. "A Test for Functional Form Against Nonparametric Alternatives," Econometric Theory, Cambridge University Press, vol. 8(4), pages 452-475, December.
    4. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
    5. Peter C. B. Phillips & Mico Loretan, 1991. "Estimating Long-run Economic Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 407-436.
    6. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, February.
    7. Lavergne, Pascal, 2001. "An equality test across nonparametric regressions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 307-344, July.
    8. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    9. Jiti Gao & Hua Liang, 1997. "Statistical Inference in Single-Index and Partially Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 493-517, September.
    10. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    11. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
    12. Shively, Thomas S. & Kohn, Robert & Ansley, Craig F., 1994. "Testing for linearity in a semiparametric regression model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 77-96.
    13. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-1159, September.
    14. Li, Q. & Hsiao, C., 1998. "Testing serial correlation in semiparametric panel data models," Journal of Econometrics, Elsevier, vol. 87(2), pages 207-237, September.
    15. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
    16. Lavergne, Pascal & Vuong, Quang, 2000. "Nonparametric Significance Testing," Econometric Theory, Cambridge University Press, vol. 16(4), pages 576-601, August.
    17. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    18. Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 449-487.
    19. Gozalo, Pedro L., 1993. "A Consistent Model Specification Test for Nonparametric Estimation of Regression Function Models," Econometric Theory, Cambridge University Press, vol. 9(3), pages 451-477, June.
    20. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
    21. Sperlich, Stefan & Tjøstheim, Dag & Yang, Lijian, 2002. "Nonparametric Estimation And Testing Of Interaction In Additive Models," Econometric Theory, Cambridge University Press, vol. 18(2), pages 197-251, April.
    22. Granger, Clive W. J. & Inoue, Tomoo & Morin, Norman, 1997. "Nonlinear stochastic trends," Journal of Econometrics, Elsevier, vol. 81(1), pages 65-92, November.
    23. Whang, Yoon-Jae & Andrews, Donald W. K., 1993. "Tests of specification for parametric and semiparametric models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 277-318.
    24. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(4), pages 435-451, December.
    25. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(5), pages 615-645, October.
    26. P. M. Robinson, 1989. "Hypothesis Testing in Semiparametric and Nonparametric Models for Econometric Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(4), pages 511-534.
    27. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    28. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, vol. 104(1), pages 1-48, August.
    29. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    30. Lavergne, Pascal & Vuong, Quang H, 1996. "Nonparametric Selection of Regressors: The Nonnested Case," Econometrica, Econometric Society, vol. 64(1), pages 207-219, January.
    31. Song Xi Chen & Wolfgang Härdle & Ming Li, 2003. "An empirical likelihood goodness‐of‐fit test for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 663-678, August.
    32. Yacine Aït-Sahalia, 2001. "Transition Densities For Interest Rate And Other Nonlinear Diffusions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 1, pages 1-34, World Scientific Publishing Co. Pte. Ltd..
    33. David A. Chapman & Neil D. Pearson, 1998. "Is the Short Rate Drift Actually Nonlinear?," Finance 9808005, University Library of Munich, Germany.
    34. P. Lavergne & Q.H. Vuong, 1996. "Nonparametric selection of regressors : the nonnested case [[Sélection non paramétrique de régresseurs : le cas de régressions non emboîtées]]," Post-Print hal-02689500, HAL.
    35. 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.
    36. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    37. Hjellvik, Vidar & Yao, Qiwei & Tjostheim, Dag, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
    38. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
    39. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
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    1. El Ghouch, Anouar & Genton, Marc G. & Bouezmarni , Taoufik, 2012. "Measuring the Discrepancy of a Parametric Model via Local Polynomial Smoothing," LIDAM Discussion Papers ISBA 2012001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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    More about this item

    Keywords

    Estimation; model specification; semi-parametric error correction model; stochastic process;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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