Wind speed forecasting by the extraction of the multifractal patterns of time series through the multiplicative cascade technique

Abstract

In this work, the forecasting errors produced by the Autoregressive Integrated Moving Average, Deep Learning, and Persistence models were analyzed when these models were applied to two time series for predicting the wind speed one-step-ahead. The analysis consisted of verified, with the aid of the Multifractal Detrended Fluctuation Analysis, whether there were multifractal patterns in the forecasting errors. Then, the multifractal patterns of the errors were extracted by a Multiplicative Cascade model. The sum of the patterns extracted from the models generated new hybrid models such as Autoregressive Integrated Moving Average-Multiplicative Cascade, Deep Learning-Multiplicative Cascade, and Persistence-Multiplicative Cascade. Those new models showed a diminution of the final forecasting error. The wind speed time series used for this study were measured at two wind farms of the State of Oaxaca, Mexico, namely La Mata and La Venta. The first time series has five years of ten-minutes averaged data, while the second one has six years and eleven months of hourly data. Both time series were provided by Mexico’s Federal Electricity Commission. The typical performance metrics tools were used for the quantitative analysis of the forecasting results, where the simple models were compared against the hybrid models by using the Mean Squared Error, the Mean Absolute Error, the Root Mean Squared Error, the Mean Absolute Percentage Error, and the Inter-rater Agreement. The latter was done to find out the actual input in a one-step-ahead forecast. The obtained results showed a gain between 0.331% and 5.285% in the fit of hybrid models in the metrics, which demonstrates the convenience of analyzing the forecasting errors generated by the models aforementioned to improve forecasts and therefore help in planning and dispatching energy flow.