Expectile-based probabilistic forecasting for spatio-temporal river network data

In this paper, we present a novel approach for probabilistic forecasting based on expectile smoothing of river network data. The Miho River dataset, which is the focus of this study, contains spatio-temporal observations across a stream network. As the inherent structure of the stream network should be taken into account and time points are irregular and vary across observation sites, developing a forecasting method presents significant challenges. To address this, we extend the flexible smoothing method of spatio-temporal river stream network data by incorporating expectile regression. We represent expectile curves of annual observations as a function of time and employ the forecasting method of functional time series. Through expectile regression, we extract information beyond the mean response for river network data analysis and develop a probabilistic forecasting method by predicting the expectile process. We demonstrate the results of the proposed method with the Miho River data and evaluate its performance.