Linear Models Applied to Monthly Seasonal Streamflow Series Prediction

Abstract

Linear models are widely used to perform time series forecasting. The Autoregressive models stand out, due to their simplicity in the parameters adjustment based on close-form solution. The Autoregressive and Moving Average models (ARMA) and Infinite Impulse Response filters (IIR) are also good alternatives, since they are recurrent structures. However, their adjustment is more complex, since the problem has no analytical solution. This investigation performs linear models to predict monthly seasonal streamflow series, from to Brazilian hydroelectric plants. The goal is to reach the best achievable performance addressing linear approaches. We propose the application of recurrent models, estimating their parameters via an immune algorithm. To compare the optimization performance, the Least Mean Square (LMS) and Recursive Prediction Error (RPE) algorithms are utilized. Also, the AR model and the Holt-Winters method were performed. The results showed that the insertion of feedback loops increases the quality of the responses. The ARMA models optimized by the immune algorithms achieved the best overall performance.