Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v31y2015i04p753-777_00.html
   My bibliography  Save this article

Estimation And Inference For Varying-Coefficient Models With Nonstationary Regressors Using Penalized Splines

Author

Listed:
  • Chen, Haiqiang
  • Fang, Ying
  • Li, Yingxing
Abstract
This paper considers estimation and inference for varying-coefficient models with nonstationary regressors. We propose a nonparametric estimation method using penalized splines, which achieves the same optimal convergence rate as kernel-based methods, but enjoys computation advantages. Utilizing the mixed model representation of penalized splines, we develop a likelihood ratio test statistic for checking the stability of the regression coefficients. We derive both the exact and the asymptotic null distributions of this test statistic. We also demonstrate its optimality by examining its local power performance. These theoretical findings are well supported by simulation studies.

Suggested Citation

  • Chen, Haiqiang & Fang, Ying & Li, Yingxing, 2015. "Estimation And Inference For Varying-Coefficient Models With Nonstationary Regressors Using Penalized Splines," Econometric Theory, Cambridge University Press, vol. 31(4), pages 753-777, August.
    • Handle: RePEc:cup:etheor:v:31:y:2015:i:04:p:753-777_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466614000541/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    2. 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.
    3. In Choi & Pentti Saikkonen, 2004. "Testing linearity in cointegrating smooth transition regressions," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 341-365, December.
    4. Taimur Baig & Ilan Goldfajn, 2002. "Monetary Policy in the Aftermath of Currency Crises: The Case of Asia," Review of International Economics, Wiley Blackwell, vol. 10(1), pages 92-112, February.
    5. 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.
    6. Paye, Bradley S. & Timmermann, Allan, 2006. "Instability of return prediction models," Journal of Empirical Finance, Elsevier, vol. 13(3), pages 274-315, June.
    7. Peter Hall & J. D. Opsomer, 2005. "Theory for penalised spline regression," Biometrika, Biometrika Trust, vol. 92(1), pages 105-118, March.
    8. Hao, K., 1996. "Testing for Structural Change in Cointegrated Regression Models: Some Comparisons and Generalizations," Monash Econometrics and Business Statistics Working Papers 3/96, Monash University, Department of Econometrics and Business Statistics.
    9. Søren Johansen & Rocco Mosconi & Bent Nielsen, 2000. "Cointegration analysis in the presence of structural breaks in the deterministic trend," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 216-249.
    10. Martin Lettau & Sydney Ludvigson, 2001. "Consumption, Aggregate Wealth, and Expected Stock Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 815-849, June.
    11. Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1373-1403, October.
    12. Park, Joon Y. & Hahn, Sang B., 1999. "Cointegrating Regressions With Time Varying Coefficients," Econometric Theory, Cambridge University Press, vol. 15(5), pages 664-703, October.
    13. Yingxing Li & David Ruppert, 2008. "On the asymptotics of penalized splines," Biometrika, Biometrika Trust, vol. 95(2), pages 415-436.
    14. Ciprian Crainiceanu & David Ruppert & Gerda Claeskens & M. P. Wand, 2005. "Exact likelihood ratio tests for penalised splines," Biometrika, Biometrika Trust, vol. 92(1), pages 91-103, March.
    15. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    16. Henrik Hansen & Søren Johansen, 1999. "Some tests for parameter constancy in cointegrated VAR-models," Econometrics Journal, Royal Economic Society, vol. 2(2), pages 306-333.
    17. Amit Goyal & Ivo Welch, 2003. "Predicting the Equity Premium with Dividend Ratios," Management Science, INFORMS, vol. 49(5), pages 639-654, May.
    18. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    19. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
    20. Kuo, Biing-Shen, 1998. "Test for partial parameter instability in regressions with I(1) processes," Journal of Econometrics, Elsevier, vol. 86(2), pages 337-368, June.
    21. Søren Johansen & Rocco Mosconi & Bent Nielsen, 2000. "Cointegration analysis in the presence of structural breaks in the deterministic trend," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 216-249.
    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. Cui, Liyuan & Hong, Yongmiao & Li, Yingxing, 2021. "Solving Euler equations via two-stage nonparametric penalized splines," Journal of Econometrics, Elsevier, vol. 222(2), pages 1024-1056.
    2. Poeschel, Friedrich, 2012. "Assortative matching through signals," VfS Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62061, Verein für Socialpolitik / German Economic Association.
    3. Lin, Yingqian & Tu, Yundong, 2024. "Functional coefficient cointegration models with Box–Cox transformation," Economics Letters, Elsevier, vol. 234(C).
    4. Brantley Liddle & George Messinis, 2018. "Revisiting carbon Kuznets curves with endogenous breaks modeling: evidence of decoupling and saturation (but few inverted-Us) for individual OECD countries," Empirical Economics, Springer, vol. 54(2), pages 783-798, 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. repec:wyi:journl:002195 is not listed on IDEAS
    2. repec:hum:wpaper:sfb649dp2013-033 is not listed on IDEAS
    3. Haiqi Li Author-Name-First: Haiqi & Jing Zhang & Chaowen Zheng, 2023. "Estimating and Testing for Functional Coefficient Quantile Cointegrating Regression," Economics Discussion Papers em-dp2023-07, Department of Economics, University of Reading.
    4. Miller, Stephen M. & Martins, Luis Filipe & Gupta, Rangan, 2019. "A Time-Varying Approach Of The Us Welfare Cost Of Inflation," Macroeconomic Dynamics, Cambridge University Press, vol. 23(2), pages 775-797, March.
    5. repec:ipg:wpaper:2014-474 is not listed on IDEAS
    6. Martins, Luis F. & Gabriel, Vasco J., 2014. "Modelling long run comovements in equity markets: A flexible approach," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 288-295.
    7. Chen, Haiqiang, 2015. "Robust Estimation And Inference For Threshold Models With Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 31(4), pages 778-810, August.
    8. 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.
    9. Sonja Greven & Ciprian Crainiceanu, 2013. "On likelihood ratio testing for penalized splines," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 387-402, October.
    10. Chew Lian Chua & Sarantis Tsiaplias, 2014. "A Bayesian Approach to Modelling Bivariate Time-Varying Cointegration and Cointegrating Rank," Melbourne Institute Working Paper Series wp2014n27, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    11. Feng, Yuanhua & Härdle, Wolfgang Karl, 2020. "A data-driven P-spline smoother and the P-Spline-GARCH models," IRTG 1792 Discussion Papers 2020-016, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    12. repec:wyi:journl:002108 is not listed on IDEAS
    13. Li, Degui & Li, Runze, 2016. "Local composite quantile regression smoothing for Harris recurrent Markov processes," Journal of Econometrics, Elsevier, vol. 194(1), pages 44-56.
    14. Nakashima, Kiyotaka & Saito, Makoto, 2012. "On the comparison of alternative specifications for money demand: The case of extremely low interest rate regimes in Japan," Journal of the Japanese and International Economies, Elsevier, vol. 26(3), pages 454-471.
    15. Wu, Ximing & Sickles, Robin, 2018. "Semiparametric estimation under shape constraints," Econometrics and Statistics, Elsevier, vol. 6(C), pages 74-89.
    16. Takuma Yoshida, 2016. "Asymptotics and smoothing parameter selection for penalized spline regression with various loss functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(4), pages 278-303, November.
    17. 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.
    18. Rong Chen & Hua Liang & Jing Wang, 2011. "Determination of linear components in additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 367-383.
    19. Holland, Ashley D., 2017. "Penalized spline estimation in the partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 211-235.
    20. Haug Alfred A & Beyer Andreas & Dewald William, 2011. "Structural Breaks and the Fisher Effect," The B.E. Journal of Macroeconomics, De Gruyter, vol. 11(1), pages 1-31, May.
    21. Annie Qu & Runze Li, 2006. "Quadratic Inference Functions for Varying-Coefficient Models with Longitudinal Data," Biometrics, The International Biometric Society, vol. 62(2), pages 379-391, June.
    22. Jean-Philippe Gervais, 2011. "Disentangling nonlinearities in the long- and short-run price relationships: an application to the US hog/pork supply chain," Applied Economics, Taylor & Francis Journals, vol. 43(12), pages 1497-1510.
    23. Christou, Christina & Gupta, Rangan & Nyakabawo, Wendy & Wohar, Mark E., 2018. "Do house prices hedge inflation in the US? A quantile cointegration approach," International Review of Economics & Finance, Elsevier, vol. 54(C), pages 15-26.
    24. Lee, Wang-Sheng, 2014. "Is the BMI a Relic of the Past?," IZA Discussion Papers 8637, Institute of Labor Economics (IZA).

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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:cup:etheor:v:31:y:2015:i:04:p:753-777_00. 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    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.