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Nearest neighbor conditional estimation for Harris recurrent Markov chains

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  • Sancetta, Alessio

Abstract

This paper is concerned with consistent nearest neighbor time series estimation for data generated by a Harris recurrent Markov chain on a general state space. It is shown that nearest neighbor estimation is consistent in this general time series context, using simple and weak conditions. The results proved here, establish consistency, in a unified manner, for a large variety of problems, e.g. autoregression function estimation, and, more generally, extremum estimators as well as sequential forecasting. Finally, under additional conditions, it is also shown that the estimators are asymptotically normal.

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  • Sancetta, Alessio, 2009. "Nearest neighbor conditional estimation for Harris recurrent Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2224-2236, November.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2224-2236
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    1. Rychlik, Tomasz, 1994. "Distributions and expectations of order statistics for possibly dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 48(1), pages 31-42, January.
    2. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
    3. Nicolau, João, 2002. "Stationary Processes That Look Like Random Walks— The Bounded Random Walk Process In Discrete And Continuous Time," Econometric Theory, Cambridge University Press, vol. 18(1), pages 99-118, February.
    4. Yakowitz, Sid, 1993. "Nearest neighbor regression estimation for null-recurrent Markov time series," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 311-318, November.
    5. van Garderen, Kees Jan, 1997. "Curved Exponential Models in Econometrics," Econometric Theory, Cambridge University Press, vol. 13(06), pages 771-790, December.
    6. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    7. Granger, Clive W. J. & Jeon, Yongil, 2004. "Thick modeling," Economic Modelling, Elsevier, vol. 21(2), pages 323-343, March.
    8. Hall, Peter & Yao, Qiwei, 2005. "Approximating conditional distribution functions using dimension reduction," LSE Research Online Documents on Economics 16333, London School of Economics and Political Science, LSE Library.
    9. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 4, pages 135-196, Elsevier.
    10. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    11. Capistrán, Carlos & Timmermann, Allan, 2009. "Forecast Combination With Entry and Exit of Experts," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 428-440.
    12. de Haan, Laurens & Resnick, Sidney I. & Rootzén, Holger & de Vries, Casper G., 1989. "Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 213-224, August.
    13. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    14. Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, vol. 71(4), pages 1049-1082, July.
    15. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    16. Nze, Patrick Ango & Doukhan, Paul, 2004. "Weak Dependence: Models And Applications To Econometrics," Econometric Theory, Cambridge University Press, vol. 20(6), pages 995-1045, December.
    17. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
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    Cited by:

    1. Nengxiang Ling & Germán Aneiros & Philippe Vieu, 2020. "kNN estimation in functional partial linear modeling," Statistical Papers, Springer, vol. 61(1), pages 423-444, February.
    2. Battey, Heather & Sancetta, Alessio, 2013. "Conditional estimation for dependent functional data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 1-17.
    3. Linton, Oliver & Sancetta, Alessio, 2009. "Consistent estimation of a general nonparametric regression function in time series," Journal of Econometrics, Elsevier, vol. 152(1), pages 70-78, September.

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