Análisis clúster para series de tiempo estacionales y modelización de caudales de ríos del Brasil.

Abstract

This paper deals with the application of the Cluster Analysis for Time Series oriented to the modeling of stream flows of the main rivers of Brazil, which were measured in 179 stations distributed in them, this from climatic variables and the combination of techniques of modeling as SARIMA, SARIMAX and Cluster Analysis. Specifically, what is done is to create a small number of clusters (from 2 to 4 clusters) from the 179 stations, where each group will contain stations in which their flows have a temporal behavior similar possible, then for each of these clusters, two models are proposed, the first is a SARIMA model built for the functional mean of the series of each cluster, and the second, a SARIMAX model built for the time series most centrally located (medoid) inside each cluster and considering as exogenous variables climatic series measured in the nearest geographical station. We will show later the advantages and the efficiency of modeling a huge amount of time series with the use of these techniques, this because the model that explains each cluster can be extended (using the same delays and explanatory variables) to each one of the time series that compose it. We carry out comparative studies between both models, obtaining close results in terms of information criteria and predictive power, but which indicate that the SARIMAX model offers better results in general terms.