This paper presents a study of a wind speed time series from La Venta, Oaxaca, Mexico. The time series consists of anemometric measurements taken by the Federal Electricity Commission of Mexico throughout a little over 6 years. The study was conducted to calculate the Hurst correlation coefficient using: box counting, rescaled range, power spectrum, detrended fluctuation analysis, and multifractal detrended fluctuation analysis techniques. The main objective of this research is to know the correlation among wind speed data to obtain a better description of real conditions of the time series, which is not always available, and to define the structure of its behavior. In this way, more suitable wind speed prediction models can be achieved. Results obtained from techniques above were used to generate fractals time series for a typical month, using the Hurst coefficient and a self‐affine trace generator, which produces fractals time series whose probability distribution is always normal. These time series were compared against time series generated by using random numbers with Gaussian behavior and the characteristics of a typical month. Fractals time series highlight in the qualitative part regarding the modeling of wind speed variability and the descriptive statistics (average, standard deviation, and coefficient of variation), which is similar to the real series. Discordance tests were applied to the datasets to detect deviated values, and so ensure the normal behavior of the samples. These tests showed the existence of different populations with normal behavior in the samples that had bimodal characteristics. By separating the samples, it was possible to apply the self‐affine trace generator to each population found, to generate the fractal time series. An additional objective was to find the level of change in the structure of the original series concerning its statistical and fractal characteristics at different window widths of the time series (daily, monthly, seasonal, and annual) to identify either a specific tendency or dynamic behavior. The results showed a wind speed time series with a negative correlation (antipersistent), a high degree of scale invariance (homothetic), and a fractal dimension very close to 2, thus indicating that the time series is more irregular than a random process.

Forecast models for wind speed and wind turbine power generation are valuable support tools for operators of Control Energy Center. In this work, a year of daily energy output of a wind turbine is analyzed. The original time series was separated into a high-power sample and a low-power sample. High-power sample has a seasonal pattern while low-power sample does not. Afterward, a sARIMA model was produced for high-power sample forecast, with a good performance, while for low-power sample any ARIMA model defeated persistence model; thus, a couple of nonlinear autoregressive artificial neural networks are proposed. Mean absolute error and mean square error are reported and demonstrate that the sARIMA model can predict satisfactorily high-power sample, even with limited data, while to forecast low-power sample, it is necessary to use a neural networks approach and all data available to produce accurate forecasts. In each case, a normalized comparison with persistence model is also reported. Finally, a method which uses previous data of daily output energy and forecasted future wind speed values from a numeric weather prediction model is presented to objectively identify whether the current time is in a high-power or low-power regime to choose the ad hoc daily output energy forecast model.

The main objective of this work is to analyze and configure appropriately the input vectors to enhance the performance of NARX models to forecast solar radiation one hour ahead. For this study, Engle–Granger causality tests were implemented. Additionally, collinearity among the meteorological variables of the databases was examined. Different databases were used to test the contribution of these analyses in the improvement of the input vectors. For that, databases from three cities of Mexico with different climates were obtained, namely: Chihuahua, Temixco, and Zacatecas. These databases consisted of hourly measurements of the following variables: solar radiation (SR), wind speed (WS), relative humidity (RH), pressure (P), and temperature (T). Results showed that, in all three cases, proper NARX models were produced even when using input vectors formed only with solar radiation and temperature data. Consequently, it was inferred that pressure, wind speed, and relative humidity could be excluded from the input vectors of the forecasting models since, according to the causality tests, they did not provide relevant information to improve the solar radiation forecast in the studied cases. Conversely, these variables could generate spurious results. Forecasting results obtained with the NARX model were compared to the smart persistence model, commonly used to validate SR prediction. Error measures, such as mean absolute error (MAE) and root mean squared error (RMSE), were used to compare prediction results obtained from different models. In all cases, results obtained from the enhanced NARX model surpassed the results of the smart persistence, namely: in Chihuahua up to $11.5\%$ , in Temixco up to $15.7\%$ , and in Zacatecas up to $27.2\%$ .