IDEAS home Printed from https://ideas.repec.org/p/ecl/riceco/2003-18.html
   My bibliography  Save this paper

Strong Approximations for Nonlinear Transformations of Integrated Time Series

Author

Listed:
  • Park, Joon

    (Rice U)

Abstract

In this paper we establish the strong approximations for the nonlinear transformations of integrated time series. Both the asymptotically homogeneous and integrable transformations are considered, and the explicit rates for the convergence to their limit distributions are obtained under mild regularity conditions that are satisfied by virtually all nonlinear models used in practical applications. The first order asymptotics are also derived under the conditions that are significantly weaker than those required by earlier works.

Suggested Citation

  • Park, Joon, 2003. "Strong Approximations for Nonlinear Transformations of Integrated Time Series," Working Papers 2003-18, Rice University, Department of Economics.
    • Handle: RePEc:ecl:riceco:2003-18
    as

    Download full text from publisher

    File URL: http://www.ruf.rice.edu/~econ/papers/2003papers/18park.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chang, Yoosoon, 2002. "Nonlinear IV unit root tests in panels with cross-sectional dependency," Journal of Econometrics, Elsevier, vol. 110(2), pages 261-292, October.
    2. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
    3. Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May.
    4. Ross Williams, 2013. "Introduction," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 46(4), pages 460-461, December.
    5. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    6. Phillips, Peter C. B. & Park, Joon Y. & Chang, Yoosoon, 2004. "Nonlinear instrumental variable estimation of an autoregression," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 219-246.
    7. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    8. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    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. Park, Joon, 2003. "Nonstationary Nonlinearity: An Outlook for New Opportunities," Working Papers 2003-05, Rice University, Department of Economics.
    2. Chang, Yoosoon, 2003. "Nonlinear IV Panel Unit Root Tests," Working Papers 2003-06, Rice University, Department of Economics.
    3. Chung, Heetaik & Park, Joon Y., 2007. "Nonstationary nonlinear heteroskedasticity in regression," Journal of Econometrics, Elsevier, vol. 137(1), pages 230-259, March.

    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. Park, Joon, 2003. "Nonstationary Nonlinearity: An Outlook for New Opportunities," Working Papers 2003-05, Rice University, Department of Economics.
    2. Chang, Yoosoon, 2003. "Nonlinear IV Panel Unit Root Tests," Working Papers 2003-06, Rice University, Department of Economics.
    3. Miller J. Isaac, 2010. "A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-38, September.
    4. Matei Demetrescu & Christoph Hanck & Adina I. Tarcolea, 2014. "Iv-Based Cointegration Testing In Dependent Panels With Time-Varying Variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 393-406, August.
    5. Demetrescu Matei, 2009. "Panel Unit Root Testing with Nonlinear Instruments for Infinite-Order Autoregressive Processes," Journal of Time Series Econometrics, De Gruyter, vol. 1(2), pages 1-30, December.
    6. Tu, Yundong & Liang, Han-Ying & Wang, Qiying, 2022. "Nonparametric inference for quantile cointegrations with stationary covariates," Journal of Econometrics, Elsevier, vol. 230(2), pages 453-482.
    7. Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
    8. Arai, Yoichi, 2016. "Testing For Linearity In Regressions With I(1) Processes," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 57(1), pages 111-138, June.
    9. Hu, Zhishui & Phillips, Peter C.B. & Wang, Qiying, 2021. "Nonlinear Cointegrating Power Function Regression With Endogeneity," Econometric Theory, Cambridge University Press, vol. 37(6), pages 1173-1213, December.
    10. Kim, Chang Sik & Kim, In-Moo, 2008. "Nonlinear regression for unit root models with autoregressive errors," Economics Letters, Elsevier, vol. 100(3), pages 326-329, September.
    11. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2021. "Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice," Papers 2111.02023, arXiv.org.
    12. K. Hassanain, 2004. "Purchasing Power Parity And Cross‐Sectional Dependency," South African Journal of Economics, Economic Society of South Africa, vol. 72(2), pages 238-257, June.
    13. Chan, Nigel & Wang, Qiying, 2015. "Nonlinear regressions with nonstationary time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 182-195.
    14. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
    15. Yoosoon Chang & Wonho Song, 2002. "Panel Unit Root Tests in the Presence of Cross-Sectional Dependency and Heterogeneity," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 B5-2, International Conferences on Panel Data.
    16. Marmer, Vadim, 2008. "Nonlinearity, nonstationarity, and spurious forecasts," Journal of Econometrics, Elsevier, vol. 142(1), pages 1-27, January.
    17. Wagner, Martin, 2008. "The carbon Kuznets curve: A cloudy picture emitted by bad econometrics?," Resource and Energy Economics, Elsevier, vol. 30(3), pages 388-408, August.
    18. Chang, Yoosoon, 2002. "Nonlinear IV unit root tests in panels with cross-sectional dependency," Journal of Econometrics, Elsevier, vol. 110(2), pages 261-292, October.
    19. Im, K.S. & Pesaran, M.H., 2003. "On The Panel Unit Root Tests Using Nonlinear Instrumental Variables," Cambridge Working Papers in Economics 0347, Faculty of Economics, University of Cambridge.
    20. Liang, Hanying & Phillips, Peter C.B. & Wang, Hanchao & Wang, Qiying, 2016. "Weak Convergence To Stochastic Integrals For Econometric Applications," Econometric Theory, Cambridge University Press, vol. 32(6), pages 1349-1375, December.

    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:ecl:riceco:2003-18. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/dericus.html .

    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.