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This paper tackles the challenge of time series forecasting in the presence of missing data. Traditional methods often struggle with such data, which leads to inaccurate predictions. We propose a novel framework that combines the strengths of Generative Adversarial Networks (GANs) and Bayesian inference. The framework utilizes a Conditional GAN (C-GAN) to realistically impute missing values in the time series data. Subsequently, Bayesian inference is employed to quantify the uncertainty associated with the forecasts due to the missing data. This combined approach improves the robustness and reliability of forecasting compared to traditional methods. The effectiveness of our proposed method is evaluated on a real-world dataset of air pollution data from Mexico City. The results demonstrate the framework's capability to handle missing data and achieve improved forecasting accuracy. [ABSTRACT FROM AUTHOR]

When conducting an analysis of nature's time series, such as meteorological ones, an important matter is a long-range dependence to quantify the global behavior of the series and connect it with other physical characteristics of the region of study. In this paper, we applied the Higuchi fractal dimension and the Hurst exponent (rescaled range) to quantify the relative trend underlying the time series of historical data from 17 of the 34 weather stations located in the Río Bravo-San Juan Basin, Mexico; these data were provided by the National Water Commission CONAGUA) in Mexico. In this way, this work aims to perform a comparative study about the level of persistency obtained by using the Higuchi fractal dimension and Hurst exponent for each station of the basin. The comparison is supported by a climate clustering of the stations, according to the Köppen classification. Results showed a better fitting between the climate of each station and its Higuchi fractal dimension obtained than when using the Hurst exponent. In fact, we found that the more the aridity of the zone the more the persistency of rainfall, according to Higuchi's values. In turn, we found more relation between the Hurst exponent and the accumulated amount of rainfall. These are relations between the climate and the long-term persistency of rainfall in the basin that could help to better understand and complete the climatological models of the study region. Trends between the fractal exponents used and the accumulated annual rainfall were also analyzed. [ABSTRACT FROM AUTHOR]

Understanding the behavior of suspended pollutants in the atmosphere has become of paramount importance to determine air quality. For this purpose, a variety of simulation software packages and a large number of algorithms have been used. Among these techniques, recurrent deep neural networks (RNN) have been used lately. These are capable of learning to imitate the chaotic behavior of a set of continuous data over time. In the present work, the results obtained from implementing three different RNNs working with the same structure are compared. These RNNs are long-short term memory network (LSTM), a recurrent gated unit (GRU), and the Elman network, taking as a case study the records of particulate matter PM 10 and PM 2.5 from 2005 to 2019 of Mexico City, obtained from the Red Automatica de Monitoreo Ambiental (RAMA) database. The results were compared for these three topologies in execution time, root mean square error (RMSE), and correlation coefficient (CC) metrics. [ABSTRACT FROM AUTHOR]