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Estimation and testing for varying coefficients in additive models with marginal integration

Author

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  • Yang, Lijian
  • Härdle, Wolfgang
  • Park, Byeong U.

Abstract

We propose marginal integration estimation and testing methods for the coefficients of varying coefficient multivariate regression model. Asymptotic distribution theory is developed for the estimation method which enjoys the same rate of convergence as univariate function estimation. For the test statistic, asymptotic normal theory is established. These theoretical results are derived under the fairly general conditions of absolute regularity (ß-mixing). Application of the test procedure to the West German real GNP data reveals that a partially linear varying coefficient model fits best the data dynamics, a fact that is also confirmed with residual diagnostics.

Suggested Citation

  • Yang, Lijian & Härdle, Wolfgang & Park, Byeong U., 2002. "Estimation and testing for varying coefficients in additive models with marginal integration," SFB 373 Discussion Papers 2002,75, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200275
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    References listed on IDEAS

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    1. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
    2. 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.
    3. Yang, Lijian & Tschernig, Rolf, 2002. "Non- And Semiparametric Identification Of Seasonal Nonlinear Autoregression Models," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1408-1448, December.
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    6. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(02), pages 258-289, February.
    7. J. FAN & Wolfgang HÄRDLE & Enno MAMMEN, 1996. "Direct estimation of low dimensional components in additive models," SFB 373 Discussion Papers 1996,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(02), pages 214-252, April.
    9. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    10. Sperlich, Stefan & Tj stheim, Dag & Yang, Lijian, 2002. "Nonparametric Estimation And Testing Of Interaction In Additive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 197-251, April.
    11. O. B. LINTON & Wolfgang HÄRDLE, 1995. "Estimation of Additive Regression Models with Links," SFB 373 Discussion Papers 1995,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Citations

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    Cited by:

    1. Stefan Sperlich & Raoul Theler, 2015. "Modeling heterogeneity: a praise for varying-coefficient models in causal analysis," Computational Statistics, Springer, vol. 30(3), pages 693-718, September.
    2. repec:eee:csdana:v:123:y:2018:i:c:p:50-65 is not listed on IDEAS
    3. Stefan Trück & Wolfgang Härdle & Rafal Weron, 2012. "The relationship between spot and futures CO2 emission allowance prices in the EU-ETS," HSC Research Reports HSC/12/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    4. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 663-690, September.
    5. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    6. Yang, Seong J. & Park, Byeong U., 2014. "Efficient estimation for partially linear varying coefficient models when coefficient functions have different smoothing variables," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 100-113.
    7. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    8. Park, Byeong U. & Mammen, Enno & Härdle, Wolfgang & Borak, Szymon, 2009. "Time Series Modelling With Semiparametric Factor Dynamics," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 284-298.
    9. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Center for Research in Economics and Statistics.
    10. 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.

    More about this item

    Keywords

    Equivalent kernels; German real GNP; Local polynomial; Marginal Integration; Rate of convergence;

    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
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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