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 $27.2\%$ .

In this paper, a methodology for short-term forecasting of power generated by a photovoltaic module is reported. The method incorporates a nonlinear autoregressive with exogenous inputs (NARX) fed by the solar radiation and temperature times series, as well as an estimation of power time series obtained by implementing an ideal single diode model. This synthetic time series was validated against an actual photovoltaic module. The NARX model has been implemented in conjunction with the corrective vector multiplier (CVM) technique, which uses solar radiation under clear sky conditions to adjust the forecasting results. In addition, collinearity and the Granger causality tests were used to choose the input variables. The forecasting horizon was 24-h-ahead. The hybrid NARX-CVM model was compared to a nonlinear autoregressive neural network and persistence model using the typic forecasting error measures such as the mean bias error, mean squared error, root mean squared error and forecast skill. The results showed that the forecasting skills of the hybrid model are about 34% against the NAR model and about 42% against the Persistence model. The model was validated by blind forecasting. The results demonstrated evidence of the quality of the conformed forecasting model and the convenience of its implementation and building.

Time series classification is a challenging and exciting problem in data mining. Some diseases are classified and diagnosed based on time series. Such is the case for diabetes mellitus, which can be analyzed based on data from the oral glucose tolerance test (OGTT). Prompt diagnosis of diabetes mellitus is essential for disease management. Diabetes mellitus does not appear suddenly; instead, the patient presents symptoms of impaired glucose tolerance that can also be diagnosed via glucose tolerance testing. This work presents a classification and diagnosis scheme for diseases, specifically diabetes mellitus and poor glucose tolerance, using deep neural networks based on time series data. In addition, data from virtual patients were obtained through the Dalla Man and UVA/Padova models; the validation was carried out with data from actual patients. The results show that deep neural networks have an accuracy of 96%. This indicates that DNNs is a helpful tool that can improve the diagnosis and classification of diseases in early detection.

This paper uses collinearity and causality tests to choose variables for an input vector to forecast the electrical power generated by a photovoltaic system. The collinearity test determines redundant variables, and the causality test determines which variables cause the electric power. The chosen input vector is used to train nonlinear autoregressive models with external inputs neural networks (NARX-NN). We develop an algorithm to generate NARX models with an all variable combinations algorithm (AVCA) to validate the results. Finally, we compare the results of the proposed methodology against the best results obtained by the AVCA; the algorithm tests 502 input vectors with the NARX model to forecast 26 steps (a day ahead) of the electrical power. The best model chosen using the collinearity and causality techniques has an RMSE of 308 W for the electric power using four variables in the input vector; the best model using the AVCA has an RMSE of 305 W using five variables in the input vector. Results show that the collinearity and causality techniques are a direct way to select the input vector without affecting the models performance and results in a reduction of the input vector length.

Photovoltaic power forecasting is important because solar generation varies with weather conditions. Accurate forecasts help improve grid operation, reduce costs, enhance system stability, and support battery management. This paper presents a hybrid methodology that combines statistical analysis and machine learning to forecast photovoltaic power generation. First, the data are cleaned and preprocessed. Then, the input vector is selected using two criteria: collinearity analysis to remove redundant variables, and Granger causality to identify variables with predictive value in a nonlinear autoregressive with exogenous inputs artificial neural network (NARX-ANN) framework. Next, an experimental design is used to evaluate two training algorithms and activation functions for the hidden layer available in Matlab^® version 26.1.0.3276743 (R2026a Update 3, MathWorks Inc., Natick, MA, USA). The methodology is validated by comparing hundreds of input-variable combinations generated through binomial coefficients. A case study using data from Sonora, Mexico, shows that the best model is the Collinearity–Causality (CC)-NARX-4 model, which uses four input variables, a radial basis function in the hidden layer, and Bayesian regularization backpropagation. This model achieves a root-mean-square error (RMSE) of approximately 132 watts (W) for the forecasting stage/forecasting horizon. The results are also compared with a nonlinear autoregressive (NAR) model to assess the predictive benefit of including exogenous inputs. The final outcome is a robust methodology for improving multivariable neural networks through (i) optimized input-vector selection using collinearity and causality tests, validated by an exhaustive combinatorial algorithm; and (ii) a systematic procedure for configuring the hidden-layer transfer function and the neural network training function.