Stochastic temporal data upscaling using the generalized k-nearest neighbor algorithm

TL;DR

This paper introduces a generalized k-nearest neighbor (GkNN) method for stochastic temporal data upscaling, analyzing its accuracy and statistical properties, with applications in simulating rainwater tank yields from climatic data.

Contribution

It develops a new GkNN framework for temporal data upscaling, including theoretical analysis and properties under stochastic dependence assumptions.

Findings

GkNN can accurately simulate monthly yields with large training data

The method preserves statistical properties of the original data

Application demonstrated in rainwater yield simulation

Abstract

Three methods of temporal data upscaling, which may collectively be called the generalized k-nearest neighbor (GkNN) method, are considered. The accuracy of the GkNN simulation of month by month yield is considered (where the term yield denotes the dependent variable). The notion of an eventually well distributed time series is introduced and on the basis of this assumption some properties of the average annual yield and its variance for a GkNN simulation are computed. The total yield over a planning period is determined and a general framework for considering the GkNN algorithm based on the notion of stochastically dependent time series is described and it is shown that for a sufficiently large training set the GkNN simulation has the same statistical properties as the training data. An example of the application of the methodology is given in the problem of simulating yield of a rainwater tank given monthly climatic data.