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Nonparametric Transformation to White Noise

Author

Listed:
  • Oliver Linton
  • Enno Mammen

Abstract

We consider a semiparametric distributed lag model in which the "news impact curve" m isnonparametric but the response is dynamic through some linear filters. A special case ofthis is a nonparametric regression with serially correlated errors. We propose an estimatorof the news impact curve based on a dynamic transformation that produces white noiseerrors. This yields an estimating equation for m that is a type two linear integral equation.We investigate both the stationary case and the case where the error has a unit root. In thestationary case we establish the pointwise asymptotic normality. In the special case of anonparametric regression subject to time series errors our estimator achieves efficiencyimprovements over the usual estimators, see Xiao, Linton, Carroll, and Mammen (2003). Inthe unit root case our procedure is consistent and asymptotically normal unlike the standardregression smoother. We also present the distribution theory for the parameter estimates,which is non-standard in the unit root case. We also investigate its finite sampleperformance through simulation experiments.

Suggested Citation

  • Oliver Linton & Enno Mammen, 2006. "Nonparametric Transformation to White Noise," STICERD - Econometrics Paper Series 503, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:503
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    References listed on IDEAS

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    1. Hendry, David F. & Pagan, Adrian R. & Sargan, J.Denis, 1984. "Dynamic specification," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 18, pages 1023-1100, Elsevier.
    2. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-853, October.
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    4. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, May.
    5. Zudi Lu, 2001. "Asymptotic Normality of Kernel Density Estimators under Dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 447-468, September.
    6. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    7. Geweke, John F, 1978. "Temporal Aggregation in the Multiple Regression Model," Econometrica, Econometric Society, vol. 46(3), pages 643-661, May.
    8. 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.
    9. Xiao Z. & Linton O.B. & Carroll R.J. & Mammen E., 2003. "More Efficient Local Polynomial Estimation in Nonparametric Regression With Autocorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 980-992, January.
    10. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-563, May.
    11. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    12. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
    13. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    14. Javier Hidalgo, 1997. "Non‐Parametric Estimation With Strongly Dependent Multivariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(2), pages 95-122, March.
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    Citations

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    Cited by:

    1. Xilong Chen & Eric Ghysels, 2011. "News--Good or Bad--and Its Impact on Volatility Predictions over Multiple Horizons," The Review of Financial Studies, Society for Financial Studies, vol. 24(1), pages 46-81, October.
    2. Linton, Oliver & Wang, Qiying, 2016. "Nonparametric Transformation Regression With Nonstationary Data," Econometric Theory, Cambridge University Press, vol. 32(1), pages 1-29, February.
    3. Mammen, Enno & Park, Byeong U. & Schienle, Melanie, 2012. "Additive models: Extensions and related models," SFB 649 Discussion Papers 2012-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    5. repec:hum:wpaper:sfb649dp2012-045 is not listed on IDEAS
    6. Gregory Connor & Matthias Hagmann & Oliver Linton, 2007. "Efficient Estimation of a Semiparametric Characteristic- Based Factor Model of Security Returns," Swiss Finance Institute Research Paper Series 07-26, Swiss Finance Institute.
    7. Degui Li & Oliver Linton & Zudi Lu, 2012. "A Flexible Semiparametric Model for Time Series," Monash Econometrics and Business Statistics Working Papers 17/12, Monash University, Department of Econometrics and Business Statistics.
    8. Koo, Bonsoo & Linton, Oliver, 2012. "Estimation of semiparametric locally stationary diffusion models," Journal of Econometrics, Elsevier, vol. 170(1), pages 210-233.
    9. Juliane Geller & Michael H. Neumann, 2018. "Improved local polynomial estimation in time series regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 1-27, January.
    10. Ioannis Kyriakou & Parastoo Mousavi & Jens Perch Nielsen & Michael Scholz, 2020. "Longer-Term Forecasting of Excess Stock Returns—The Five-Year Case," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    11. Ioannis Kyriakou & Parastoo Mousavi & Jens Perch Nielsen & Michael Scholz, 2021. "Short-Term Exuberance and Long-Term Stability: A Simultaneous Optimization of Stock Return Predictions for Short and Long Horizons," Mathematics, MDPI, vol. 9(6), pages 1-19, March.
    12. Mammen, Enno & Martínez-Miranda, María Dolores & Nielsen, Jens Perch & Vogt, Michael, 2021. "Calendar effect and in-sample forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 31-52.
    13. Deniz Ozabaci & Daniel Henderson, 2015. "Additive kernel estimates of returns to schooling," Empirical Economics, Springer, vol. 48(1), pages 227-251, February.
    14. Enno Mammen & Jens Perch Nielsen & Michael Scholz & Stefan Sperlich, 2019. "Conditional Variance Forecasts for Long-Term Stock Returns," Risks, MDPI, vol. 7(4), pages 1-22, November.
    15. Ioannis Kyriakou & Parastoo Mousavi & Jens Perch Nielsen & Michael Scholz, 2019. "Machine Learning for Forecasting Excess Stock Returns The Five-Year-View," Graz Economics Papers 2019-06, University of Graz, Department of Economics.
    16. Ioannis Kyriakou & Parastoo Mousavi & Jens Perch Nielsen & Michael Scholz, 2020. "Short-Term Exuberance and long-term stability: A simultaneous optimization of stock return predictions for short and long horizons," Graz Economics Papers 2020-20, University of Graz, Department of Economics.
    17. Li, Degui & Linton, Oliver & Lu, Zudi, 2015. "A flexible semiparametric forecasting model for time series," Journal of Econometrics, Elsevier, vol. 187(1), pages 345-357.
    18. Liangjun Su & Aman Ullah & Yun Wang, 2013. "Nonparametric regression estimation with general parametric error covariance: a more efficient two-step estimator," Empirical Economics, Springer, vol. 45(2), pages 1009-1024, October.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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