IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2012-21.html
   My bibliography  Save this paper

Semiparametric Methods in Nonlinear Time Series Analysis: A Selective Review

Author

Listed:
  • Patrick Saart
  • Jiti Gao

Abstract

Time series analysis is a tremendous research area in statistics and econometrics. As remarked in a review by Howell Tong in 2001, for about 100 years up to 2001 Biometrika (alone) published over 400 papers on the subject. [Tong (2001)] Furthermore, in the review, Howell Tong is able break down up to fifteen key areas of research interest in time series analysis. Nonetheless, unlike that of Howell Tong, the aim of the review in this paper is not to cover a wide range of topics on the subject, but is to concentrate on a small, but extremely essential, point he made on the semiparametric methods in nonlinear time series analysis and to explore into various aspect of this research area in much more detail. It is also an objective of this review to provide some discussion on a future research where appropriate.

Suggested Citation

  • Patrick Saart & Jiti Gao, 2012. "Semiparametric Methods in Nonlinear Time Series Analysis: A Selective Review," Monash Econometrics and Business Statistics Working Papers 21/12, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2012-21
    as

    Download full text from publisher

    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp21-12.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    2. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    3. Jiti Gao & Maxwell King, 2012. "An Improved Nonparametric Unit-Root Test," Monash Econometrics and Business Statistics Working Papers 16/12, Monash University, Department of Econometrics and Business Statistics.
    4. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
    5. Gao, Jiti & Gijbels, Irène, 2008. "Bandwidth Selection in Nonparametric Kernel Testing," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1584-1594.
    6. Gao, Jiti & Lu, Zudi & Tjostheim, Dag, 2003. "Estimation in semiparametric spatial regression," MPRA Paper 11971, University Library of Munich, Germany.
    7. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    8. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, December.
    9. Fan, Yanqin & Li, Qi, 1997. "A consistent nonparametric test for linearity of AR(p) models," Economics Letters, Elsevier, vol. 55(1), pages 53-59, August.
    10. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
    11. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    12. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
    13. Fan, Y. & Li, Q. & Stengos, T., 1992. "Root-Consistent Semiparametric Regression with Conditionally Heteroskedastic Disturbances," Working Papers 1992-17, University of Guelph, Department of Economics and Finance.
    14. 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.
    15. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    16. Jiti Gao & Howell Tong, 2004. "Semiparametric non‐linear time series model selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 321-336, May.
    17. Phillips, Peter C.B., 2009. "Local Limit Theory And Spurious Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1466-1497, December.
    18. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    19. Arthur Lewbel & Oliver Linton, 2007. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Econometrica, Econometric Society, vol. 75(4), pages 1209-1227, July.
    20. Jiti Gao & Kim Hawthorne, 2006. "Semiparametric estimation and testing of the trend of temperature series," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 332-355, July.
    21. Patrick W. Saart & Jiti Gao & David E. Allen, 2015. "Semiparametric Autoregressive Conditional Duration Model: Theory and Practice," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 849-881, December.
    22. 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.
    23. Aurora Galego & João Pereira, 2010. "Evidence On Gender Wage Discrimination In Portugal: Parametric And Semi‐Parametric Approaches," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(4), pages 651-666, December.
    24. Maria Pacurar, 2008. "Autoregressive Conditional Duration Models In Finance: A Survey Of The Theoretical And Empirical Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 22(4), pages 711-751, September.
    25. Wang, Qiying & Phillips, Peter C.B., 2011. "Asymptotic Theory For Zero Energy Functionals With Nonparametric Regression Applications," Econometric Theory, Cambridge University Press, vol. 27(2), pages 235-259, April.
    26. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 710-738, June.
    27. 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.
    28. Gao, Jiti & King, Maxwell, 2004. "Adaptive Testing In Continuous-Time Diffusion Models," Econometric Theory, Cambridge University Press, vol. 20(5), pages 844-882, October.
    29. Nam H Kim & Patrick W Saart & Jiti Gao, 2013. "Semi-parametric Analysis of Shape-Invariant Engel Curves with Control Function Approach," Monash Econometrics and Business Statistics Working Papers 10/13, Monash University, Department of Econometrics and Business Statistics.
    30. Gao, Jiti & King, Maxwell & Lu, Zudi & Tjøstheim, Dag, 2009. "Nonparametric Specification Testing For Nonlinear Time Series With Nonstationarity," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1869-1892, December.
    31. Racine, Jeffrey & Su, Liangjun & Ullah, Aman, 2014. "The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics," OUP Catalogue, Oxford University Press, number 9780199857944.
    32. Lance Bachmeier, 2002. "Is the term structure nonlinear? A semiparametric investigation," Applied Economics Letters, Taylor & Francis Journals, vol. 9(3), pages 151-153.
    33. J. P. Nielsen & O. B. Linton, 1998. "An optimization interpretation of integration and back‐fitting estimators for separable nonparametric models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 217-222.
    34. Stefan Sperlich & Juan M. Rodríguez-Póo & Ana I. Fernández, 2005. "Semiparametric three-step estimation methods for simultaneous equation systems," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(6), pages 699-721.
    35. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
    36. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    37. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    38. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    39. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    40. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    41. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    42. Qiying Wang & Peter C. B. Phillips, 2009. "Structural Nonparametric Cointegrating Regression," Econometrica, Econometric Society, vol. 77(6), pages 1901-1948, November.
    43. Jiti Gao & Dag Tjøstheim & Jiying Yin, 2012. "Model Specification between Parametric and Nonparametric Cointegration," Monash Econometrics and Business Statistics Working Papers 18/12, Monash University, Department of Econometrics and Business Statistics.
    44. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    45. Gao, Jiti, 2012. "Identification, Estimation and Specification in a Class of Semi-Linear Time Series Models," MPRA Paper 39256, University Library of Munich, Germany, revised 14 May 2012.
    46. Young K. Truong & Charles J. Stone, 1994. "Semiparametric Time Series Regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(4), pages 405-428, July.
    47. Fan, Jianqing & Yao, Qiwei & Tong, Howell, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," LSE Research Online Documents on Economics 6704, London School of Economics and Political Science, LSE Library.
    48. Li, Qi & Wooldridge, Jeffrey M., 2002. "Semiparametric Estimation Of Partially Linear Models For Dependent Data With Generated Regressors," Econometric Theory, Cambridge University Press, vol. 18(3), pages 625-645, June.
    49. Buhlmann, Peter & McNeil, Alexander J., 2002. "An algorithm for nonparametric GARCH modelling," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 665-683, October.
    50. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    51. Stefan Sperlich, 2009. "A note on non-parametric estimation with predicted variables," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 382-395, July.
    52. Jia Chen & Jiti Gao & Degui Li, 2010. "Estimation in Semiparametric Time Series Regression," School of Economics and Public Policy Working Papers 2010-27, University of Adelaide, School of Economics and Public Policy.
    53. Oxley, Les & McAleer, Michael, 1993. "Econometric Issues in Macroeconomic Models with Generated Regressors," Journal of Economic Surveys, Wiley Blackwell, vol. 7(1), pages 1-40.
    54. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-247, February.
    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. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    2. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    3. Jiti Gao & Peter C.B. Phillips, 2011. "Semiparametric Estimation in Multivariate Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 17/11, Monash University, Department of Econometrics and Business Statistics.
    4. Gao, Jiti & Phillips, Peter C.B., 2013. "Semiparametric estimation in triangular system equations with nonstationarity," Journal of Econometrics, Elsevier, vol. 176(1), pages 59-79.
    5. Song Xi Chen & Jiti Gao, 2010. "Simultaneous Testing of Mean and Variance Structures in Nonlinear Time Series Models," School of Economics and Public Policy Working Papers 2010-28, University of Adelaide, School of Economics and Public Policy.
    6. Gao, Jiti & Kim, Nam Hyun & Saart, Patrick W., 2015. "A misspecification test for multiplicative error models of non-negative time series processes," Journal of Econometrics, Elsevier, vol. 189(2), pages 346-359.
    7. Kim, Namhyun & W. Saart, Patrick, 2021. "Estimation in partially linear semiparametric models with parametric and/or nonparametric endogeneity," Cardiff Economics Working Papers E2021/9, Cardiff University, Cardiff Business School, Economics Section.
    8. Patrick W Saart & Jiti Gao & Nam Hyun Kim, 2014. "Econometric Time Series Specification Testing in a Class of Multiplicative Error Models," Monash Econometrics and Business Statistics Working Papers 1/14, Monash University, Department of Econometrics and Business Statistics.
    9. Jia Chen & Jiti Gao & Degui Li & Zhengyan Lin, 2015. "Specification testing in nonstationary time series models," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 117-136, February.
    10. Dong, Chaohua & Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2017. "Specification testing for nonlinear multivariate cointegrating regressions," Journal of Econometrics, Elsevier, vol. 200(1), pages 104-117.
    11. Escanciano, Juan Carlos & Jacho-Chávez, David T. & Lewbel, Arthur, 2014. "Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 426-443.
    12. Gao, Jiti, 2012. "Identification, Estimation and Specification in a Class of Semi-Linear Time Series Models," MPRA Paper 39256, University Library of Munich, Germany, revised 14 May 2012.
    13. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.
    14. Xin Geng & Carlos Martins-Filho & Feng Yao, 2015. "Estimation of a Partially Linear Regression in Triangular Systems," Working Papers 15-46, Department of Economics, West Virginia University.
    15. Tu, Yundong & Wang, Ying, 2022. "Spurious functional-coefficient regression models and robust inference with marginal integration," Journal of Econometrics, Elsevier, vol. 229(2), pages 396-421.
    16. George Athanasopoulos & Minfeng Deng & Gang Li & Haiyan Song, 2013. "Domestic and outbound tourism demand in Australia: a System-of-Equations Approach," Monash Econometrics and Business Statistics Working Papers 6/13, Monash University, Department of Econometrics and Business Statistics.
    17. Patrick W. Saart & Jiti Gao & David E. Allen, 2015. "Semiparametric Autoregressive Conditional Duration Model: Theory and Practice," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 849-881, December.
    18. Jiti Gao, 2012. "Identification, Estimation and Specification in a Class of Semiparametic Time Series Models," Monash Econometrics and Business Statistics Working Papers 6/12, Monash University, Department of Econometrics and Business Statistics.
    19. Chen, Song Xi & Gao, Jiti & Tang, Chenghong, 2005. "A test for model specification of diffusion processes," MPRA Paper 11976, University Library of Munich, Germany, revised Feb 2007.
    20. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.

    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:msh:ebswps:2012-21. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/dxmonau.html .

    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: Professor Xibin Zhang (email available below). General contact details of provider: https://edirc.repec.org/data/dxmonau.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.