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This study explores market efficiency and behavior by integrating key theories such as the Efficient Market Hypothesis (EMH), Adaptive Market Hypothesis (AMH), Informational Efficiency and Random Walk theory. Using LSTM enhanced by optimizers like Stochastic Gradient Descent (SGD), Adam, AdaGrad, and RMSprop, we analyze market inefficiencies in the Standard and Poor's (SPX) index over a 22-year period. Our results reveal "pockets in time" that challenge EMH predictions, particularly with the AdaGrad optimizer at a size of the hidden layer (HS) of 64. Beyond forecasting, we apply the Dominguez–Lobato (DL) and General Spectral (GS) tests as part of the Martingale Difference Hypothesis to assess statistical inefficiencies and deviations from the Random Walk model. By emphasizing "informational efficiency", we examine how quickly new information is reflected in stock prices. We argue that market inefficiencies are transient phenomena influenced by structural shifts and information flow, challenging the notion that forecasting alone can refute EMH. Additionally, we compare LSTM with ARIMA with Exponential Smoothing, and LightGBM to highlight the strengths and limitations of these models in financial forecasting. The LSTM model excels at capturing temporal dependencies, while LightGBM demonstrates its effectiveness in detecting non-linear relationships. Our comprehensive approach offers a nuanced understanding of market dynamics and inefficiencies. [ABSTRACT FROM AUTHOR]

This research is devoted to the determination of hidden dependencies between the flow of particles that come from the Sun and precipitation-induced floods in the United Kingdom (UK). The analysis covers 20 flood events during the period from October 2001 to December 2019. The parameters of solar activity were used as model input data, while precipitations data in the period 10 days before and during each flood event were used as model output. The time lag of 0–9 days was taken into account in the research. Correlation analysis was conducted to determine the degree of randomness for the time series of input and output parameters. For establishing a potential causative link, machine learning classification predictive modeling was applied. Two approaches, the decision tree, and the random forest were used. We analyzed the accuracy of classification models forecast from 0 to 9 days in advance. It was found that the most important factors for flood forecasting are proton density with a time lag of 9, differential proton flux in the range of 310–580 keV, and ion temperature. Research in this paper has shown that the decision tree model is more accurate and adequate in predicting the appearance of precipitation-induced floods up to 9 days ahead with an accuracy of 91%. The results of this study confirmed that by increasing technical capabilities, using improved machine learning techniques and large data sets, it is possible to improve the understanding of the physical link between the solar wind and tropospheric weather and help improve severe weather forecasting. [ABSTRACT FROM AUTHOR]