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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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    Cited by:

    1. Battey, Heather & Sancetta, Alessio, 2013. "Conditional estimation for dependent functional data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 1-17.
    2. Nengxiang Ling & Germán Aneiros & Philippe Vieu, 2020. "kNN estimation in functional partial linear modeling," Statistical Papers, Springer, vol. 61(1), pages 423-444, February.
    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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