Uniform consistency rate of kNN regression estimation for functional time series data

ABSTRACT

In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried out to illustrate the finite sample performances and the usefulness of the kNN approach.

KEYWORDS:

• kNN estimation
• nonparametric functional data analysis
• strong mixing dependence
• uniform almost complete convergence rate

Acknowledgments

The authors would like to thank the Editor in Chief, the A.E and the two anonymous reviewers for their valuable comments and suggestions that are very helpful for them to improve the quality and presentation of the paper significantly.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is supported by the National Social Science Funds of China (14ATJ005), the National Nature Science Funds of China (51579059). the National Key Research and Development Program of China (2017YFC1502405, 2016YFC0401303) and Anhui Provincial Natural Science Foundation (1808085MA18).