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Recent Developments in Non- and Semiparametric Regression with Fractional Time Series Errors

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  • Beran, Jan
  • Feng, Yuanhua

Abstract

This paper summarizes recent developments in non- and semiparametric regres- sion with stationary fractional time series errors, where the error process may be short-range, long-range dependent or antipersistent. The trend function in this model is estimated nonparametrically, while the dependence structure of the error process is estimated by approximate maximum likelihood. Asymptotic properties of these estimators are described briefly. The focus is on describing the developments of bandwidth selection in this context based on the iterative plug-in idea (Gasser et al., 1991) and some detailed computational aspects. Applications in the framework of the SEMIFAR (semiparametric fractional autoregressive) model (Beran, 1999) illustrate the practical usefulness of the methods described here.

Suggested Citation

  • Beran, Jan & Feng, Yuanhua, 2002. "Recent Developments in Non- and Semiparametric Regression with Fractional Time Series Errors," CoFE Discussion Papers 02/13, University of Konstanz, Center of Finance and Econometrics (CoFE).
    • Handle: RePEc:zbw:cofedp:0213
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    References listed on IDEAS

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    1. Beran, Jan & Feng, Yuanhua & Ghosh, Sucharita & Sibbertsen, Philipp, 2002. "On robust local polynomial estimation with long-memory errors," International Journal of Forecasting, Elsevier, vol. 18(2), pages 227-241.
    2. Beran, Jan, 1999. "SEMIFAR Models - A Semiparametric Framework for Modelling Trends, Long Range Dependence and Nonstationarity," CoFE Discussion Papers 99/16, University of Konstanz, Center of Finance and Econometrics (CoFE).
    3. Yuanhua Feng & Jan Beran, 2013. "Optimal convergence rates in non-parametric regression with fractional time series errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 30-39, January.
    4. Hall, Peter & Hart, Jeffrey D., 1990. "Nonparametric regression with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 339-351, December.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Chiu, Shean-Tsong, 1989. "Bandwidth selection for kernel estimate with correlated noise," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 347-354, September.
    7. Beran, Jan & Ocker, Dirk, 2001. "Volatility of Stock-Market Indexes--An Analysis Based on SEMIFAR Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 103-116, January.
    8. Beran, Jan & Feng, Yuanhua, 2002. "SEMIFAR models--a semiparametric approach to modelling trends, long-range dependence and nonstationarity," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 393-419, August.
    9. Beran, Jan & Feng, Yuanhua & Heiler, Siegfried, 2000. "Modifying the double smoothing bandwidth selector in nonparametric regression," CoFE Discussion Papers 00/37, University of Konstanz, Center of Finance and Econometrics (CoFE).
    10. Beran, Jan & Feng, Yuanhua, 2001. "Supplement to the Paper "Interative plug-in algorithms for SEMIFAR models - definition, convergence and asymptotic properties": Detailed Simulation Results," CoFE Discussion Papers 01/12, University of Konstanz, Center of Finance and Econometrics (CoFE).
    11. Feng, Yuanhua, 2004. "Simultaneously Modeling Conditional Heteroskedasticity And Scale Change," Econometric Theory, Cambridge University Press, vol. 20(3), pages 563-596, June.
    12. HÄRDLE, Wolfgang & HALL, Peter & MARRON, Steve, 1992. "Regression smoothing parameters that are not far from their optimum," LIDAM Reprints CORE 978, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Beran, Jan & Ocker, Dirk, 1999. "SEMIFAR Forecasts, with Applications to Foreign Exchange Rates," CoFE Discussion Papers 99/13, University of Konstanz, Center of Finance and Econometrics (CoFE).
    14. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    15. Jan Beran & Yuanhua Feng, 2002. "Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 291-311, June.
    16. Feng, Yuanhua, 2002. "An Iterative Plug-In Algorithm for Nonparametric Modelling of Seasonal Time Series," CoFE Discussion Papers 02/04, University of Konstanz, Center of Finance and Econometrics (CoFE).
    17. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    Full references (including those not matched with items on IDEAS)

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