Robust streamflow forecasting: a Student’s t-mixture vector autoregressive model

Abstract

Accurate streamflow forecasting is one of the main challenges in the management of reservoirs, where autoregressive models have been commonly used. Typically, the noise of these models is considered Gaussian. However, this assumption can overestimate the presence of outliers, generally presented in water inflow real-world data. Motivated by this, we propose a novel streamflow forecasting method by modeling the noise of a vector autoregressive model as a multivariate Student’s t-mixture based on the use of the variational expectation-maximization algorithm. The proposed model is able to capture the trend, seasonality, and spatio-temporal correlations of hydro inflows, along with both asymmetry and multimodal features of the vector autoregressive process’ residuals. Based on 12 of the main inflows of the Chilean hydroelectric network, our experiments show the proposed model’s efficiency and improvements for forecasting medium to long-term inflows over a classical vector autoregressive model. Results show that the expected forecasts are improved with theproposed model and the predictive distributions present tighter intervals based on standard and state-of-the-art metrics.