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Bandwidth selection for kernel estimate with correlated noise

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  • Chiu, Shean-Tsong

Abstract

The problem of selecting the bandwidth for the kernel estimate is considered. It is shown that Mallows' criterion does not select a proper bandwidth when the noise are correlated. A simple modification of Mallows' criterion is suggested, which significantly improves the performance of the kernel estimate. Since the modified criterion needs an estimate for the noise spectrum at frequency zero, an estimation procedure for the parameter of the noise spectrum is proposed. Under some regularity conditions, it is shown that the procedure gives strongly consistent estimates. The asymptotic distribution of the estimate is also given.

Suggested Citation

  • Chiu, Shean-Tsong, 1989. "Bandwidth selection for kernel estimate with correlated noise," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 347-354, September.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:4:p:347-354
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    Citations

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    Cited by:

    1. Mohamed Chikhi & Claude Diebolt, 2010. "Nonparametric analysis of financial time series by the Kernel methodology," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(5), pages 865-880, August.
    2. Kim, Tae Yoon & Park, Byeong U. & Moon, Myung Sang & Kim, Chiho, 2009. "Using bimodal kernel for inference in nonparametric regression with correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1487-1497, August.
    3. 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).
    4. CHIKHI, Mohamed, 2009. "Identification non paramétrique d’un processus non linéaire hétéroscédastique [Nonparametric identification of heteroscedastic nonlinear process]," MPRA Paper 82108, University Library of Munich, Germany, revised 2009.
    5. 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.
    6. Chikhi, Mohamed & Terraza, Michel, 2002. "Un essai de prévision non paramétrique de l'action France Télécom [A nonparametric prediction test of the France Telecom stock proces]," MPRA Paper 77268, University Library of Munich, Germany, revised Dec 2003.
    7. Beran, Jan & Feng, Yuanhua & Franke, Günter & Hess, Dieter & Ocker, Dirk, 1999. "SEMIFAR Models, with Applications to Commodities, Exchange Rates and the Volatility of Stock Market Indices," CoFE Discussion Papers 99/18, University of Konstanz, Center of Finance and Econometrics (CoFE).
    8. D. Benelmadani & K. Benhenni & S. Louhichi, 2020. "The reproducing kernel Hilbert space approach in nonparametric regression problems with correlated observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1479-1500, December.
    9. Krivobokova, Tatyana & Serra, Paulo & Rosales, Francisco & Klockmann, Karolina, 2022. "Joint non-parametric estimation of mean and auto-covariances for Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    10. 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).
    11. 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.
    12. CHIKHI, Mohamed, 2017. "Chocs exogènes et non linéarités dans les séries boursières: Application à la modélisation non paramétrique du cours de l'action Orange [Exogenous Shocks and nonlinearity in the stock exchange seri," MPRA Paper 76691, University Library of Munich, Germany, revised 2017.
    13. del Rio, Alejandro Quintela, 1996. "Comparison of bandwidth selectors in nonparametric regression under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 21(5), pages 563-580, May.
    14. Beran, Jan, 2002. "Prediction of 0-1-events for short- and long-memory time series," CoFE Discussion Papers 02/11, University of Konstanz, Center of Finance and Econometrics (CoFE).
    15. 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).

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