IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v26y2014i1p141-169.html
   My bibliography  Save this article

Semiparametric methods in nonlinear time series analysis: a selective review

Author

Listed:
  • Patrick Saart
  • Jiti Gao
  • Nam Hyun Kim

Abstract

Time series analysis is a tremendous research area in statistics and econometrics. In a previous review, the author was able to break down up 15 key areas of research interest in time series analysis. Nonetheless, the aim of the review in this current paper is not to cover a wide range of somewhat unrelated topics on the subject, but the key strategy of the review in this paper is to begin with a core the 'curse of dimensionality' in nonparametric time series analysis, and explore further in a metaphorical domino-effect fashion into other closely related areas in semiparametric methods in nonlinear time series analysis.

Suggested Citation

  • Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
  • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:141-169
    DOI: 10.1080/10485252.2013.840724
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2013.840724
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/10485252.2013.840724?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 look for a different version below or search for a different version of it.

    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, November.
    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. 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.
    11. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
    12. 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.
    13. 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.
    14. 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..
    15. 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.
    16. Phillips, Peter C.B., 2009. "Local Limit Theory And Spurious Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1466-1497, December.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. Gao, Jiti & King, Maxwell, 2004. "Adaptive Testing In Continuous-Time Diffusion Models," Econometric Theory, Cambridge University Press, vol. 20(5), pages 844-882, October.
    25. 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.
    26. 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.
    27. 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.
    28. Lance Bachmeier, 2002. "Is the term structure nonlinear? A semiparametric investigation," Applied Economics Letters, Taylor & Francis Journals, vol. 9(3), pages 151-153.
    29. 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.
    30. 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.
    31. 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.
    32. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    33. 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.
    34. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    35. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    36. 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.
    37. Qiying Wang & Peter C. B. Phillips, 2009. "Structural Nonparametric Cointegrating Regression," Econometrica, Econometric Society, vol. 77(6), pages 1901-1948, November.
    38. 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.
    39. 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.
    40. 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.
    41. 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.
    42. Buhlmann, Peter & McNeil, Alexander J., 2002. "An algorithm for nonparametric GARCH modelling," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 665-683, October.
    43. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    44. Stefan Sperlich, 2009. "A note on non-parametric estimation with predicted variables," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 382-395, July.
    45. Jia Chen & Jiti Gao & Degui Li, 2010. "Estimation in Semiparametric Time Series Regression," School of Economics Working Papers 2010-27, University of Adelaide, School of Economics.
    46. 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.
    47. 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. 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.
    3. 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.
    4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    5. 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.
    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. 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.
    8. 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.
    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. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Honda, Toshio, 2013. "Nonparametric LAD cointegrating regression," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 150-162.
    15. Song Xi Chen & Jiti Gao, 2010. "Simultaneous Testing of Mean and Variance Structures in Nonlinear Time Series Models," School of Economics Working Papers 2010-28, University of Adelaide, School of Economics.
    16. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
    17. 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.
    18. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    19. 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.
    20. Pipat Wongsaart & Jiti Gao, 2011. "Nonparametric Kernel Testing in Semiparametric Autoregressive Conditional Duration Model," Monash Econometrics and Business Statistics Working Papers 18/11, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    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:taf:gnstxx:v:26:y:2014:i:1:p:141-169. 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: http://www.tandfonline.com/GNST20 .

    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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.