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Efficient estimation of nonparametric regression in the presence of dynamic heteroskedasticity

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  • Linton, Oliver
  • Xiao, Zhijie

Abstract

We study the efficient estimation of nonparametric regression in the presence of heteroskedasticity. We focus our analysis on local polynomial estimation of nonparametric regressions with conditional heteroskedasticity in a time series setting. We introduce a weighted local polynomial regression smoother that takes account of the dynamic heteroskedasticity. We show that, although traditionally it is advised that one should not weight for heteroskedasticity in nonparametric regressions, in many popular nonparametric regression models our method has lower asymptotic variance than the usual unweighted procedures. We conduct a Monte Carlo investigation that confirms the efficiency gain over conventional nonparametric regression estimators in finite samples.

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  • Linton, Oliver & Xiao, Zhijie, 2019. "Efficient estimation of nonparametric regression in the presence of dynamic heteroskedasticity," Journal of Econometrics, Elsevier, vol. 213(2), pages 608-631.
    • Handle: RePEc:eee:econom:v:213:y:2019:i:2:p:608-631
    DOI: 10.1016/j.jeconom.2019.01.016
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    1. Su, Liangjun & Ullah, Aman, 2006. "More Efficient Estimation In Nonparametric Regression With Nonparametric Autocorrelated Errors," Econometric Theory, Cambridge University Press, vol. 22(1), pages 98-126, February.
    2. Martins-Filho, Carlos & Yao, Feng, 2009. "Nonparametric regression estimation with general parametric error covariance," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 309-333, March.
    3. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," The Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
    4. Ang, Andrew & Kristensen, Dennis, 2012. "Testing conditional factor models," Journal of Financial Economics, Elsevier, vol. 106(1), pages 132-156.
    5. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    6. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    7. Linton, Oliver & Xiao, Zhijie, 2007. "A Nonparametric Regression Estimator That Adapts To Error Distribution Of Unknown Form," Econometric Theory, Cambridge University Press, vol. 23(3), pages 371-413, June.
    8. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, May.
    9. Jianqing Fan & Qiwei Yao & Zongwu Cai, 2003. "Adaptive varying‐coefficient linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 57-80, February.
    10. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
    11. Jin, Sainan & Su, Liangjun & Xiao, Zhijie, 2015. "Adaptive Nonparametric Regression With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1153-1191, December.
    12. Connor, Gregory & Korajczyk, Robert A, 1993. "A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-1291, September.
    13. Chen, Xiaohong & Jacho-Chávez, David T. & Linton, Oliver, 2016. "Averaging Of An Increasing Number Of Moment Condition Estimators," Econometric Theory, Cambridge University Press, vol. 32(1), pages 30-70, February.
    14. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    15. M Hashem Pesaran & Takashi Yamagata, 2024. "Testing for Alpha in Linear Factor Pricing Models with a Large Number of Securities," Journal of Financial Econometrics, Oxford University Press, vol. 22(2), pages 407-460.
    16. 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.
    17. Naisyin Wang, 2003. "Marginal nonparametric kernel regression accounting for within-subject correlation," Biometrika, Biometrika Trust, vol. 90(1), pages 43-52, March.
    18. Roll, Richard, 1977. "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory," Journal of Financial Economics, Elsevier, vol. 4(2), pages 129-176, March.
    19. Hall, Peter G. & Racine, Jeffrey S., 2015. "Infinite order cross-validated local polynomial regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 510-525.
    20. Amemiya, Takeshi, 1983. "Partially generalized least squares and two-stage least squares estimators," Journal of Econometrics, Elsevier, vol. 23(2), pages 275-283, October.
    21. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
    22. Peng, Liang & Yao, Qiwei, 2003. "Least absolute deviations estimation for ARCH and GARCH models," LSE Research Online Documents on Economics 5828, London School of Economics and Political Science, LSE Library.
    23. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
    24. Connor, Gregory & Linton, Oliver, 2007. "Semiparametric estimation of a characteristic-based factor model of common stock returns," Journal of Empirical Finance, Elsevier, vol. 14(5), pages 694-717, December.
    25. Linton, Oliver & Wang, Qiying, 2016. "Nonparametric Transformation Regression With Nonstationary Data," Econometric Theory, Cambridge University Press, vol. 32(1), pages 1-29, February.
    26. J. Fan & M. Farmen & I. Gijbels, 1998. "Local maximum likelihood estimation and inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 591-608.
    27. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    28. Chen, Yixin & Wang, Qin & Yao, Weixin, 2015. "Adaptive estimation for varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 17-31.
    29. Diebold, Francis X. & Nason, James A., 1990. "Nonparametric exchange rate prediction?," Journal of International Economics, Elsevier, vol. 28(3-4), pages 315-332, May.
    30. Liu, Jun M. & Chen, Rong & Yao, Qiwei, 2010. "Nonparametric transfer function models," LSE Research Online Documents on Economics 28868, London School of Economics and Political Science, LSE Library.
    31. Kristensen, Dennis & Linton, Oliver, 2006. "A Closed-Form Estimator For The Garch(1,1) Model," Econometric Theory, Cambridge University Press, vol. 22(2), pages 323-337, April.
    32. Liu, Jun M. & Chen, Rong & Yao, Qiwei, 2010. "Nonparametric transfer function models," Journal of Econometrics, Elsevier, vol. 157(1), pages 151-164, July.
    33. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    34. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.
    35. Kevin Q. Wang, 2003. "Asset Pricing with Conditioning Information: A New Test," Journal of Finance, American Finance Association, vol. 58(1), pages 161-196, February.
    36. Linton, Oliver & Mammen, Enno & Nielsen, Jens Perch & Van Keilegom, Ingrid, 2011. "Nonparametric regression with filtered data," LIDAM Reprints ISBA 2011008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    37. Yao, Weixin, 2013. "A note on EM algorithm for mixture models," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 519-526.
    38. 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.
    39. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 88-100, February.
    40. Panagiotis Avramidis, 2016. "Adaptive likelihood estimator of conditional variance function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 132-151, March.
    41. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    42. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    43. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    44. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    2. Cui, Qiurong & Xu, Yuqing & Zhang, Zhengjun & Chan, Vincent, 2021. "Max-linear regression models with regularization," Journal of Econometrics, Elsevier, vol. 222(1), pages 579-600.
    3. Hwang, Eunju & Hong, Won-Tak, 2021. "A multivariate HAR-RV model with heteroscedastic errors and its WLS estimation," Economics Letters, Elsevier, vol. 203(C).
    4. Dong, Chaohua & Linton, Oliver & Peng, Bin, 2021. "A weighted sieve estimator for nonparametric time series models with nonstationary variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 909-932.

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    More about this item

    Keywords

    Efficiency; Heteroskedasticity; Local polynomial estimation; Nonparametric regression;
    All these keywords.

    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

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