IDEAS home Printed from https://ideas.repec.org/p/tiu/tiutis/c849e96f-3ad1-461e-96c6-f095affc1053.html
   My bibliography  Save this paper

Jump-Preserving Varying-Coefficient Models for Nonlinear Time Series

Author

Listed:
  • Cizek, Pavel

    (Tilburg University, School of Economics and Management)

  • Koo, Chao

    (Tilburg University, School of Economics and Management)

Abstract

An important and widely used class of semiparametric models is formed by the varying-coefficient models. Although the varying coefficients are traditionally assumed to be smooth functions, the varying-coefficient model is considered here with the coefficient functions containing a finite set of discontinuities. Contrary to the existing nonparametric and varying-coefficient estimation of piecewise smooth functions, the varying-coefficient models are considered here under dependence and are applicable in time series with heteroskedastic and serially correlated errors. Additionally, the conditional error variance is allowed to exhibit discontinuities at a finite set of points too. The (uniform) consistency and asymptotic normality of the proposed estimators are established and the finite-sample performance is tested via a simulation study and in a real-data example.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Cizek, Pavel & Koo, Chao, 2017. "Jump-Preserving Varying-Coefficient Models for Nonlinear Time Series," Other publications TiSEM c849e96f-3ad1-461e-96c6-f, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:c849e96f-3ad1-461e-96c6-f095affc1053
    as

    Download full text from publisher

    File URL: https://pure.uvt.nl/ws/portalfiles/portal/15842820/2017_017.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1291-1320, October.
    2. Boldea, Otilia & Hall, Alastair R., 2013. "Estimation and inference in unstable nonlinear least squares models," Journal of Econometrics, Elsevier, vol. 172(1), pages 158-167.
    3. Kang, Kee-Hoon & Koo, Ja-Yong & Park, Cheol-Woo, 2000. "Kernel estimation of discontinuous regression functions," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 277-285, April.
    4. Jianqing Fan & Qiwei Yao & Zongwu Cai, 2003. "Adaptive varying‐coefficient linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 57-80, February.
    5. Henderson, Daniel J. & Kumbhakar, Subal C. & Li, Qi & Parmeter, Christopher F., 2015. "Smooth coefficient estimation of a seemingly unrelated regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 148-162.
    6. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    7. Zhao, Yan-Yong & Lin, Jin-Guan & Huang, Xing-Fang & Wang, Hong-Xia, 2016. "Adaptive jump-preserving estimates in varying-coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 65-80.
    8. Cai, Zongwu & Li, Qi, 2008. "Nonparametric Estimation Of Varying Coefficient Dynamic Panel Data Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1321-1342, October.
    9. Ahmad, Saad, 2016. "A multiple threshold analysis of the Fed's balancing act during the Great Moderation," Economic Modelling, Elsevier, vol. 55(C), pages 343-358.
    10. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
    11. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    12. Sun, Yiguo & Cai, Zongwu & Li, Qi, 2013. "Semiparametric Functional Coefficient Models With Integrated Covariates," Econometric Theory, Cambridge University Press, vol. 29(3), pages 659-672, June.
    13. 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.
    14. Lixia Hu & Tao Huang & Jinhong You, 2019. "Estimation and Identification of a Varying-Coefficient Additive Model for Locally Stationary Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1191-1204, July.
    15. Zhou Zhou & Wei Biao Wu, 2010. "Simultaneous inference of linear models with time varying coefficients," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 513-531, September.
    16. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    17. Yan-Yong Zhao & Jin-Guan Lin & Hong-Xia Wang & Xing-Fang Huang, 2017. "Jump-detection-based estimation in time-varying coefficient models and empirical applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 574-599, September.
    18. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
    19. Moritz Schularick & Alan M. Taylor, 2012. "Credit Booms Gone Bust: Monetary Policy, Leverage Cycles, and Financial Crises, 1870-2008," American Economic Review, American Economic Association, vol. 102(2), pages 1029-1061, April.
    20. Cukierman Alex & Muscatelli Anton, 2008. "Nonlinear Taylor Rules and Asymmetric Preferences in Central Banking: Evidence from the United Kingdom and the United States," The B.E. Journal of Macroeconomics, De Gruyter, vol. 8(1), pages 1-31, February.
    21. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
    22. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    23. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
    24. J. Fan & J.‐T. Zhang, 2000. "Two‐step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
    25. Jiti Gao & Peter C.B. Phillips, 2013. "Functional Coefficient Nonstationary Regression," Cowles Foundation Discussion Papers 1911, Cowles Foundation for Research in Economics, Yale University.
    26. Isabel Casas & Irene Gijbels, 2009. "Unstable volatility functions: the break preserving local linear estimator," CREATES Research Papers 2009-48, Department of Economics and Business Economics, Aarhus University.
    27. Jianhua Z. Huang & Haipeng Shen, 2004. "Functional Coefficient Regression Models for Non‐linear Time Series: A Polynomial Spline Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 515-534, December.
    28. Neuenkirch, Matthias & Tillmann, Peter, 2014. "Inflation targeting, credibility, and non-linear Taylor rules," Journal of International Money and Finance, Elsevier, vol. 41(C), pages 30-45.
    29. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 235-272, June.
    30. Andrew Patton & Dimitris Politis & Halbert White, 2009. "Correction to “Automatic Block-Length Selection for the Dependent Bootstrap” by D. Politis and H. White," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 372-375.
    31. Spokoiny, Vladimir G., 1998. "Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice," SFB 373 Discussion Papers 1998,1, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    32. Huang, Bwo-Nung & Hwang, M.J. & Peng, Hsiao-Ping, 2005. "The asymmetry of the impact of oil price shocks on economic activities: An application of the multivariate threshold model," Energy Economics, Elsevier, vol. 27(3), pages 455-476, May.
    33. Zhang, Wenyang & Lee, Sik-Yum & Song, Xinyuan, 2002. "Local Polynomial Fitting in Semivarying Coefficient Model," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 166-188, July.
    34. 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.
    35. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    36. Xiangjin B. Chen & Jiti Gao & Degui Li & Param Silvapulle, 2018. "Nonparametric Estimation and Forecasting for Time-Varying Coefficient Realized Volatility Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 88-100, January.
    37. Sun, Yanqing & Zhang, Yuanqing & Huang, Jianhua Z., 2019. "Estimation of a semiparametric varying-coefficient mixed regressive spatial autoregressive model," Econometrics and Statistics, Elsevier, vol. 9(C), pages 140-155.
    38. Gao, Jiti & Gijbels, Irene & Van Bellegem, Sebastien, 2008. "Nonparametric simultaneous testing for structural breaks," Journal of Econometrics, Elsevier, vol. 143(1), pages 123-142, March.
    39. C. A. Nebot & J. Garcia-Solanes & A. Beyaert, 2019. "New insights into the non-linearity of the ECB Taylor Rule," Applied Economics Letters, Taylor & Francis Journals, vol. 26(12), pages 1044-1048, July.
    40. Isabel Casas & Irene Gijbels, 2012. "Unstable volatility: the break-preserving local linear estimator," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 883-904, December.
    41. Racine, Jeff, 2000. "Consistent cross-validatory model-selection for dependent data: hv-block cross-validation," Journal of Econometrics, Elsevier, vol. 99(1), pages 39-61, November.
    42. Hongtu Zhu & Jianqing Fan & Linglong Kong, 2014. "Spatially Varying Coefficient Model for Neuroimaging Data With Jump Discontinuities," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1084-1098, September.
    43. Taylor, John B., 1993. "Discretion versus policy rules in practice," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 39(1), pages 195-214, December.
    44. J. Polzehl & V. G. Spokoiny, 2000. "Adaptive weights smoothing with applications to image restoration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 335-354.
    45. Górecki, Tomasz & Horváth, Lajos & Kokoszka, Piotr, 2018. "Change point detection in heteroscedastic time series," Econometrics and Statistics, Elsevier, vol. 7(C), pages 63-88.
    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. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.

    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. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    2. Yan-Yong Zhao & Jin-Guan Lin & Hong-Xia Wang & Xing-Fang Huang, 2017. "Jump-detection-based estimation in time-varying coefficient models and empirical applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 574-599, September.
    3. Casas Villalba, Maria Isabel, 2020. "Adaptative predictability of stock market returns," DES - Working Papers. Statistics and Econometrics. WS 31648, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    5. Chuanhua Wei & Lijie Wan, 2015. "Efficient Estimation in Heteroscedastic Varying Coefficient Models," Econometrics, MDPI, vol. 3(3), pages 1-7, July.
    6. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    7. Lujia Bai & Weichi Wu, 2021. "Detecting long-range dependence for time-varying linear models," Papers 2110.08089, arXiv.org, revised Mar 2023.
    8. Henderson, Daniel J. & Kumbhakar, Subal C. & Li, Qi & Parmeter, Christopher F., 2015. "Smooth coefficient estimation of a seemingly unrelated regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 148-162.
    9. Zongwu Cai, 2013. "Functional Coefficient Models for Economic and Financial Data," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    10. Hu, Lixia & Huang, Tao & You, Jinhong, 2019. "Two-step estimation of time-varying additive model for locally stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 94-110.
    11. Fu, Zhonghao & Hong, Yongmiao, 2019. "A model-free consistent test for structural change in regression possibly with endogeneity," Journal of Econometrics, Elsevier, vol. 211(1), pages 206-242.
    12. Xialu Liu & Zongwu Cai & Rong Chen, 2015. "Functional coefficient seasonal time series models with an application of Hawaii tourism data," Computational Statistics, Springer, vol. 30(3), pages 719-744, September.
    13. Isabel Casas & Eva Ferreira & Susan Orbe, 2021. "Time-Varying Coefficient Estimation in SURE Models. Application to Portfolio Management," Journal of Financial Econometrics, Oxford University Press, vol. 19(4), pages 707-745.
    14. repec:wyi:journl:002112 is not listed on IDEAS
    15. Isabel Casas & Xiuping Mao & Helena Veiga, 2018. "Reexamining financial and economic predictability with new estimators of realized variance and variance risk premium," CREATES Research Papers 2018-10, Department of Economics and Business Economics, Aarhus University.
    16. Yuying Sun & Shaoxin Hong & Zongwu Cai, 2023. "Optimal Local Model Averaging for Divergent-Dimensional Functional-Coefficient Regressions," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202309, University of Kansas, Department of Economics, revised Sep 2023.
    17. Yang, Guangren & Zhou, Yong, 2014. "Semiparametric varying-coefficient study of mean residual life models," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 226-238.
    18. Yarovaya, Larisa & Matkovskyy, Roman & Jalan, Akanksha, 2021. "The effects of a “black swan” event (COVID-19) on herding behavior in cryptocurrency markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 75(C).
    19. Sun, Yiguo & Hsiao, Cheng & Li, Qi, 2011. "Measuring correlations of integrated but not cointegrated variables: A semiparametric approach," Journal of Econometrics, Elsevier, vol. 164(2), pages 252-267, October.
    20. Li, Kunpeng & Li, Weiming, 2013. "Estimation of varying coefficient models with time trend and integrated regressors," Economics Letters, Elsevier, vol. 119(1), pages 89-93.
    21. Aslanidis, Nektarios & Casas, Isabel, 2013. "Nonparametric correlation models for portfolio allocation," Journal of Banking & Finance, Elsevier, vol. 37(7), pages 2268-2283.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:tiu:tiutis:c849e96f-3ad1-461e-96c6-f095affc1053. 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: Richard Broekman (email available below). General contact details of provider: https://www.tilburguniversity.edu/about/schools/economics-and-management/ .

    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.