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Functional-coefficient models under unit root behaviour

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  • Ted Juhl

Abstract

We analyze the statistical properties of non-parametrically estimated functions in a functional-coefficient model if the data have a unit root. We show that the estimated function converges at a faster rate than under the stationary case. However, the estimator has a mixed normal distribution so that point-wise confidence intervals are calculated using the usual normal distribution theory rather than a Dickey--Fuller distribution. The results are used to show how one can discriminate between a unit root process and a non-linear functional-coefficient process. We illustrate the procedure using U.S. unemployment and interest rate data. Copyright 2005 Royal Economic Society

Suggested Citation

  • Ted Juhl, 2005. "Functional-coefficient models under unit root behaviour," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 197-213, July.
    • Handle: RePEc:ect:emjrnl:v:8:y:2005:i:2:p:197-213
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    Cited by:

    1. repec:wyi:journl:002112 is not listed on IDEAS
    2. 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.
    3. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
    4. Banerjee Anurag & Pitarakis Jean-Yves, 2014. "Functional cointegration: definition and nonparametric estimation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(5), pages 1-14, December.
    5. repec:wyi:journl:002195 is not listed on IDEAS
    6. Phillips, Peter C.B. & Wang, Ying, 2023. "When bias contributes to variance: True limit theory in functional coefficient cointegrating regression," Journal of Econometrics, Elsevier, vol. 232(2), pages 469-489.
    7. 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.
    8. 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.
    9. 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.
    10. Zongwu Cai & Bingyi Jing & Xinbing Kong & Zhi Liu, 2017. "Nonparametric regression with nearly integrated regressors under long‐run dependence," Econometrics Journal, Royal Economic Society, vol. 20(1), pages 118-138, February.
    11. Chen, Xirong & Huang, Ta-Cheng & Li, Qi, 2017. "An alternative bandwidth selection method for estimating functional coefficient models," Economics Letters, Elsevier, vol. 156(C), pages 27-31.
    12. Irina Murtazashvili & Di Liu & Artem Prokhorov, 2015. "Two-sample nonparametric estimation of intergenerational income mobility in the United States and Sweden," Canadian Journal of Economics, Canadian Economics Association, vol. 48(5), pages 1733-1761, December.
    13. Zongwu Cai & Qi Li, 2013. "Some Recent Develop- ments on Nonparametric Econometrics," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    14. Likai Chen & Ekaterina Smetanina & Wei Biao Wu, 2022. "Estimation of nonstationary nonparametric regression model with multiplicative structure [Income and wealth distribution in macroeconomics: A continuous-time approach]," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 176-214.
    15. Gan, Li & Hsiao, Cheng & Xu, Shu, 2014. "Model specification test with correlated but not cointegrated variables," Journal of Econometrics, Elsevier, vol. 178(P1), pages 80-85.
    16. repec:wyi:journl:002096 is not listed on IDEAS
    17. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    18. Zongwu Cai & Henong Li, 2013. "Convergency and Divergency of Functional Coefficient Weak Instrumental Variables Models," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.

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