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Economic unions are international agreements oriented to increase economic efficiency and establishing political and cultural ties between the member countries. Becoming a member of an existing union usually requires the approval of both the candidate and members, while leaving it may require only the unilateral will of the exiting country. There are many examples of accession of states to previously consolidated economic unions, and a recent example of leaving is the withdrawal of the United Kingdom from the European Union. Motivated by the Brexit process, in this paper we propose an agent-based model to study the determinant factors driving withdrawals from an economic union. We show that both Union and local taxes promote the exits, whereas customs fees out of the Union boost cohesion. Furthermore, heterogeneity in both business conditions and wealth distribution promotes withdrawals, while countries' size diversity does not have a significant effect on them. We also deep into the individual causes that lead to dissatisfaction and, ultimately, to exits. We found that, for low Union taxes, the wealth inequality within the country is the leading cause of anti-Union opinion spreading. Conversely, for high Union taxes, the country's performance turns out to be the main driving force, resulting in a risk of wealthier countries leaving the Union. These findings will be helpful for the design of economic policies and effective informative campaigns. • Agent-based modeling is helpful to study opinion dynamics in economic unions. • Taxes promote economic unions withdrawals, whereas customs fees boost cohesion. • Heterogeneity in both business conditions and wealth distribution promotes exits. • For low taxes, within-country wealth inequality fosters anti-Union opinion spreading. • High Union taxes involves a risk of wealthier countries leaving the Union. [ABSTRACT FROM AUTHOR]

• Feed-forward and LSTM networks are compared in the forecasting of noisy chaotic time series. • Observation noise strongly affects the performance of all the neural predictors. • Recurrent architectures are more suitable for learning the non-stationary dynamics caused by structural noise. • LSTM trained without teacher forcing shows the greatest ability of mitigating the different sources of noise. Recurrent neural networks have recently proved the state-of-the-art approach in forecasting complex oscillatory time series on a multi-step horizon. Researchers in the field investigated different machine learning techniques and training approaches on dynamical systems with different degrees of complexity. Still, these analyses are usually limited to noise-free chaotic time series. This paper extends the analysis from a deterministic to a noisy environment, by considering both observation and structural noise. Observation noise is evaluated by adding different levels of artificially-generated random values on deterministic processes obtained from the simulation of four archetypal chaotic systems. A case of structural noise is implemented through a time-varying version of the logistic map, which exhibits a slow structural change of the system's dynamic that makes the system non-stationary. Finally, a time series of ozone concentration in Northern Italy is considered to test the theoretical findings on a real-world case study in which both forms of noise play a significant role. Recurrent neural networks formed by LSTM cells are compared with two benchmark feed-forward architectures. LSTM trained without the standard teacher forcing approach, i.e., with training that replicates the setting used in inference mode, proved to have the best performance in compensating the stochasticity generated by the observation noise and reproducing the structural non-stationarity of the process. [ABSTRACT FROM AUTHOR]

• LSTM nets outperform feed-forward competitors in forecasting noise-free chaotic time series. • Training without teacher forcing (no-TF) enhances the forecasting accuracy and the robustness of the LSTM predictors. • The robustness to the number of data samples provided as input (lags) is especially relevant for real-world applications. • LSTM-no-TF also ensure a uniform predictive power within the chaotic attractor. • LSTM-no-TF nets well predict chaotic dynamics up to 7 Lyapunov times. Recurrent neurons (and in particular LSTM cells) demonstrated to be efficient when used as basic blocks to build sequence to sequence architectures, which represent the state-of-the-art approach in many sequential tasks related to natural language processing. In this work, these architectures are proposed as general purposes, multi-step predictors for nonlinear time series. We analyze artificial, noise-free data generated by chaotic oscillators and compare LSTM nets with the benchmarks set by feed-forward, one-step-recursive and multi-output predictors. We focus on two different training methods for LSTM nets. The traditional one makes use of the so-called teacher forcing, i.e. the ground truth data are used as input for each time step ahead, rather than the outputs predicted for the previous steps. Conversely, the second feeds the previous predictions back into the recurrent neurons, as it happens when the network is used in forecasting. LSTM predictors robustly show the strengths of the two benchmark competitors, i.e., the good short-term performance of one-step-recursive predictors and greatly improved mid-long-term predictions with respect to feed-forward, multi-output predictors. Training LSTM predictors without teacher forcing is recommended to improve accuracy and robustness, and ensures a more uniform distribution of the predictive power within the chaotic attractor. We also show that LSTM architectures maintain good performances when the number of time lags included in the input differs from the actual embedding dimension of the dataset, a feature that is very important when working on real data. [ABSTRACT FROM AUTHOR]

• An ARED (adaptive rational equilibrium dynamics) asset pricing model where agents trade according to heterogeneous and adaptive beliefs on the future prices. • The effects of the "uptick rule". • The investigation underlines that the uptick rule meets its intended objective. • The analysis suggests also possible and unwanted side effects of the regulation, such as an excessive swelling of speculative bubbles. This paper investigates the effects of the "uptick rule" (a short selling regulation formally known as Exchange Act Rule 10a-1) by means of a simple stock market model, based on the ARED (adaptive rational equilibrium dynamics) modeling framework, where heterogeneous and adaptive beliefs on the future prices of a risky asset were first shown to be responsible for endogenous price fluctuations. The dynamics of stock prices generated by the model, with and without the uptick-rule restriction, are analyzed by pairing the classical fundamental prediction with beliefs based on both linear and nonlinear forecasting rules deriving from the technical analysis of the financial markets. The comparison shows a reduction of downward price movements of undervalued shares when the short selling restriction is imposed. This gives evidence that the uptick rule meets its intended objective. However, the effects of the short selling regulation fade when the intensity of choice to switch trading strategies is high. In addition, the analysis suggests possible side effects of the regulation on price dynamics, such as an excessive swelling of speculative bubbles. [ABSTRACT FROM AUTHOR]