Predicting temperature curve based on fast k NN local linear estimation of the conditional distribution function

PeerJ. 2021 Jul 9:9:e11719. doi: 10.7717/peerj.11719. eCollection 2021.


Predicting the yearly curve of the temperature, based on meteorological data, is essential for understanding the impact of climate change on humans and the environment. The standard statistical models based on the big data discretization in the finite grid suffer from certain drawbacks such as dimensionality when the size of the data is large. We consider, in this paper, the predictive region problem in functional time series analysis. We study the prediction by the shortest conditional modal interval constructed by the local linear estimation of the cumulative function of Y given functional input variable X . More precisely, we combine the k -Nearest Neighbors procedure to the local linear algorithm to construct two estimators of the conditional distribution function. The main purpose of this paper is to compare, by a simulation study, the efficiency of the two estimators concerning the level of dependence. The feasibility of these estimators in the functional times series prediction is examined at the end of this paper. More precisely, we compare the shortest conditional modal interval predictive regions of both estimators using real meteorological data.

Keywords: Conditional predictive region; Distribution function; Functional time series; Kernel weighting; Local linear fitting; Meteorological data; k-nearest neighbors smoothing.

Grants and funding

This work was supported by the Deanship of Scientific Research at King Khalid University through the Research Groups Program under the grant number R.G.P. 1/64/42. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.