Search Results (37)

Financial time series in volatile markets often exhibit non-stationary behavior and signatures of stochastic chaos, challenging traditional forecasting methods based on stationarity assumptions. In this paper, we introduce a novel multi-expert forecasting system (MES) that leverages ensemble machine learning techniques—including bagging, boosting, and stacking—to enhance prediction accuracy and support robust risk management decisions. The proposed framework integrates diverse “weak learner” models, ranging from linear extrapolation and multidimensional regression to sentiment-based text analytics, into a unified decision-making architecture. Each expert is designed to capture distinct aspects of the underlying market dynamics, while the supervisory module aggregates their outputs using adaptive weighting schemes that account for evolving error characteristics. Empirical evaluations using high-frequency currency data, notably for the EUR/USD pair, demonstrate that the ensemble approach significantly improves forecast reliability, as evidenced by higher winning probabilities and better net trading results compared to individual forecasting models. These findings contribute both to the theoretical understanding of ensemble forecasting under chaotic market conditions and to its practical application in financial risk management, offering a reproducible methodology for managing uncertainty in highly dynamic environments. Full article

The inherent challenges of financial time series forecasting demand advanced modeling techniques for reliable predictions. Effective financial time series forecasting is crucial for financial risk management and the formulation of investment decisions. The accurate prediction of stock prices is a subject of study in the domains of investing and national policy. This problem appears to be challenging due to the presence of multi-noise, nonlinearity, volatility, and the chaotic nature of stocks. This paper proposes a novel financial time series forecasting model based on the deep learning ensemble model LSTM-mTrans-MLP, which integrates the long short-term memory (LSTM) network, a modified Transformer network, and a multilayered perception (MLP). By integrating LSTM, the modified Transformer, and the MLP, the suggested model demonstrates exceptional performance in terms of forecasting capabilities, robustness, and enhanced sensitivity. Extensive experiments are conducted on multiple financial datasets, such as Bitcoin, the Shanghai Composite Index, China Unicom, CSI 300, Google, and the Amazon Stock Market. The experimental results verify the effectiveness and robustness of the proposed LSTM-mTrans-MLP network model compared with the benchmark and SOTA models, providing important inferences for investors and decision-makers. Full article

Although data-driven machine learning methods have been successfully applied to predict complex nonlinear dynamics, forecasting future evolution based on incomplete past information remains a significant challenge. This paper proposes a novel data-driven approach that leverages the dynamical relationships among variables. By integrating Non-Stationary Transformers with LightGBM, we construct a robust model where LightGBM builds a fitting function to capture and simulate the complex coupling relationships among variables in dynamically evolving chaotic systems. This approach enables the reconstruction of missing data, restoring sequence completeness and overcoming the limitations of existing chaotic time series prediction methods in handling missing data. We validate the proposed method by predicting the future evolution of variables with missing data in both dissipative and conservative chaotic systems. Experimental results demonstrate that the model maintains stability and effectiveness even with increasing missing rates, particularly in the range of 30% to 50%, where prediction errors remain relatively low. Furthermore, the feature importance extracted by the model aligns closely with the underlying dynamic characteristics of the chaotic system, enhancing the method’s interpretability and reliability. This research offers a practical and theoretically sound solution to the challenges of predicting chaotic systems with incomplete datasets. Full article

Recently, reservoir computing (RC) has emerged as one of the most effective algorithms to model and forecast volatile and chaotic time series. In this paper, we aim to contribute to the understanding of the uncertainty associated with the predictions made by RC models and to propose a methodology to generate RC prediction intervals. As an illustration, we analyze the error distribution for the RC model when predicting the price time series of several agri-commodities. Results show that the error distributions are best modeled using a Normal Inverse Gaussian (NIG). In fact, NIG outperforms the Gaussian distribution, as the latter tends to overestimate the width of the confidence intervals. Hence, we propose a methodology where, in the first step, the RC generates a forecast for the time series and, in the second step, the confidence intervals are generated by combining the prediction and the fitted NIG distribution of the RC forecasting errors. Thus, by providing confidence intervals rather than single-point estimates, our approach offers a more comprehensive understanding of forecast uncertainty, enabling better risk assessment and more informed decision-making in business planning based on forecasted prices. Full article

The atmosphere is a complex nonlinear system, with the information of its temperature, water vapor, pressure, and cloud being crucial aspects of remote-sensing data analysis. There exist intricate interactions among these internal components, such as convection, radiation, and humidity exchange. Atmospheric phenomena span multiple spatial and temporal scales, from small-scale thunderstorms to large-scale events like El Niño. The dynamic interactions across different scales, along with external disturbances to the atmospheric system, such as variations in solar radiation and Earth surface conditions, contribute to the chaotic nature of the atmosphere, making long-term predictions challenging. Grasping the intrinsic chaotic dynamics is essential for advancing atmospheric analysis, which holds profound implications for enhancing meteorological forecasts, mitigating disaster risks, and safeguarding ecological systems. To validate the chaotic nature of the atmosphere, this paper reviewed the definitions and main features of chaotic systems, elucidated the method of phase space reconstruction centered on Takens’ theorem, and categorized the qualitative and quantitative methods for determining the chaotic nature of time series data. Among quantitative methods, the Wolf method is used to calculate the Largest Lyapunov Exponents, while the G–P method is used to calculate the correlation dimensions. A new method named Improved Saturated Correlation Dimension method was proposed to address the subjectivity and noise sensitivity inherent in the traditional G–P method. Subsequently, the Largest Lyapunov Exponents and saturated correlation dimensions were utilized to conduct a quantitative analysis of FY-4A and Himawari-8 remote-sensing infrared observation data, and ERA5 reanalysis data. For both short-term remote-sensing data and long-term reanalysis data, the results showed that more than 99.91% of the regional points have corresponding sequences with positive Largest Lyapunov exponents and all the regional points have correlation dimensions that tended to saturate at values greater than 1 with increasing embedding dimensions, thereby proving that the atmospheric system exhibits chaotic properties on both short and long temporal scales, with extreme sensitivity to initial conditions. This conclusion provided a theoretical foundation for the short-term prediction of atmospheric infrared radiation field variables and the detection of weak, time-sensitive signals in complex atmospheric environments. Full article

The applications of deep learning and artificial intelligence have permeated daily life, with time series prediction emerging as a focal area of research due to its significance in data analysis. The evolution of deep learning methods for time series prediction has progressed from the Convolutional Neural Network (CNN) and the Recurrent Neural Network (RNN) to the recently popularized Transformer network. However, each of these methods has encountered specific issues. Recent studies have questioned the effectiveness of the self-attention mechanism in Transformers for time series prediction, prompting a reevaluation of approaches to LTSF (Long Time Series Forecasting) problems. To circumvent the limitations present in current models, this paper introduces a novel hybrid network, Temporal Convolutional Network-Linear (TCN-Linear), which leverages the temporal prediction capabilities of the Temporal Convolutional Network (TCN) to enhance the capacity of LSTF-Linear. Time series from three classical chaotic systems (Lorenz, Mackey–Glass, and Rossler) and real-world stock data serve as experimental datasets. Numerical simulation results indicate that, compared to classical networks and novel hybrid models, our model achieves the lowest RMSE, MAE, and MSE with the fewest training parameters, and its R² value is the closest to 1. Full article

The existence of chaos is particularly relevant, as the identification of a chaotic behavior in a time series could lead to reliable short-term forecasting. This paper evaluates the existence of nonlinearity and chaos in the underlying process of the spot prices of the Spanish electricity market. To this end, we used daily data spanning from 1 January 2013, to 31 March 2021 and we applied a comprehensive framework that encompassed a wide range of techniques. Nonlinearity was analyzed using the BDS method, while the existence of a chaotic structure was studied through Lyapunov exponents, recurrence plots, and quantitative recurrence analysis. While nonlinearity was detected in the underlying process, conclusive evidence supporting chaos was not found. In addition, the generalized autoregressive conditional heteroscedastic (GARCH) model accounts for part of the nonlinear structure that is unveiled in the electricity market. These findings hold substantial value for electricity market forecasters, traders, producers, and market regulators. Full article

Accurate forecasting remains a challenge, even with advanced techniques like deep learning (DL), ARIMA, and Holt–Winters (H&W), particularly for chaotic phenomena such as those observed in several areas, such as COVID-19, energy, and financial time series. Addressing this, we introduce a Forecasting Method with Filters and Residual Analysis (FMFRA), a hybrid methodology specifically applied to datasets of COVID-19 time series, which we selected for their complexity and exemplification of current forecasting challenges. FMFFRA consists of the following two approaches: FMFRA-DL, employing deep learning, and FMFRA-SSA, using singular spectrum analysis. This proposed method applies the following three phases: filtering, forecasting, and residual analysis. Initially, each time series is split into filtered and residual components. The second phase involves a simple fine-tuning for the filtered time series, while the third phase refines the forecasts and mitigates noise. FMFRA-DL is adept at forecasting complex series by distinguishing primary trends from insufficient relevant information. FMFRA-SSA is effective in data-scarce scenarios, enhancing forecasts through automated parameter search and residual analysis. Chosen for their geographical and substantial populations and chaotic dynamics, time series for Mexico, the United States, Colombia, and Brazil permitted a comparative perspective. FMFRA demonstrates its efficacy by improving the common forecasting performance measures of MAPE by 22.91%, DA by 13.19%, and RMSE by 25.24% compared to the second-best method, showcasing its potential for providing essential insights into various rapidly evolving domains. Full article

Reservoir computing (RC) systems can efficiently forecast chaotic time series using the nonlinear dynamical properties of an artificial neural network of random connections. The versatility of RC systems has motivated further research on both hardware counterparts of traditional RC algorithms and more-efficient RC-like schemes. Inspired by the nonlinear processes in a living biological brain and using solitary waves excited on the surface of a flowing liquid film, in this paper, we experimentally validated a physical RC system that substitutes the effect of randomness that underpins the operation of the traditional RC algorithm for a nonlinear transformation of input data. Carrying out all operations using a microcontroller with minimal computational power, we demonstrate that the so-designed RC system serves as a technically simple hardware counterpart to the ‘next-generation’ improvement of the traditional RC algorithm. Full article

This study explores the modified Oskolkov equation, which depicts the behavior of the incompressible viscoelastic Kelvin–Voigt fluid. The primary focus of this research lies in several key areas. Firstly, the Lie symmetries of the considered equation are identified. These symmetries are utilized to transform the discussed model into an ordinary differential equation. Analytical solutions are subsequently derived using the new auxiliary equation technique. Next, a comprehensive analysis of the equation’s dynamic nature is undertaken from multiple aspects. Bifurcation is carried out at fixed points within the system, and chaotic behavior is unveiled by introducing an external force to the dynamic system. Various tools, including 3D and 2D phase plots, time series, Poincaré maps, and multistability analysis, are employed to identify the chaotic nature of the system. Furthermore, the sensitivity of the model is explored across diverse initial conditions. In general, comprehending the dynamic characteristics of systems holds immense significance in forecasting outcomes and innovating new technologies. Full article

We present an algorithm for extracting basis functions from the chaotic Lorenz system along with timing and bit-sequence statistics. Previous work focused on modifying Lorenz waveforms and extracting the basis function of a single state variable. Importantly, these efforts initiated the development of solvable chaotic systems with simple matched filters, which are suitable for many spread spectrum applications. However, few solvable chaotic systems are known, and they are highly dependent upon an engineered basis function. Non-solvable, Lorenz signals are often used to test time-series prediction schemes and are also central to efforts to maximize spectral efficiency by joining radar and communication waveforms. Here, we provide extracted basis functions for all three Lorenz state variables, their timing statistics, and their bit-sequence statistics. Further, we outline a detailed algorithm suitable for the extraction of basis functions from many chaotic systems such as the Lorenz system. These results promote the search for engineered basis functions in solvable chaotic systems, provide tools for joining radar and communication waveforms, and give an algorithmic process for modifying chaotic Lorenz waveforms to quantify the performance of chaotic time-series forecasting methods. The results presented here provide engineered test signals compatible with quantitative analysis of predicted amplitudes and regular timing. Full article

Predicting stock prices has long been the holy grail for providing guidance to investors. Extracting effective information from Limit Order Books (LOBs) is a key point in high-frequency trading based on stock-movement forecasting. LOBs offer many details, but at the same time, they are very noisy. This paper proposes a differential transformer neural network model, dubbed DTNN, to predict stock movement according to LOB data. The model utilizes a temporal attention-augmented bilinear layer (TABL) and a temporal convolutional network (TCN) to denoise the data. In addition, a prediction transformer module captures the dependency between time series. A differential layer is proposed and incorporated into the model to extract information from the messy and chaotic high-frequency LOB time series. This layer can identify the fine distinction between adjacent slices in the series. We evaluate the proposed model on several datasets. On the open LOB benchmark FI-2010, our model outperforms other comparative state-of-the-art methods in accuracy and F1 score. In the experiments using actual stock data, our model also shows great stock-movement forecasting capability and generalization performance. Full article

In this study, we present a statistical forecasting framework and assess its efficacy using a range of established machine learning algorithms for predicting Particulate Matter (PM) concentrations in the Arctic, specifically in Pallas (FI), Reykjavik (IS), and Tromso (NO). Our framework leverages historical ground measurements and 24 h predictions from nine models by the Copernicus Atmosphere Monitoring Service (CAMS) to provide PM₁₀ predictions for the following 24 h. Furthermore, we compare the performance of various memory cells based on artificial neural networks (ANN), including recurrent neural networks (RNNs), gated recurrent units (GRUs), long short-term memory networks (LSTMs), echo state networks (ESNs), and windowed multilayer perceptrons (MLPs). Regardless of the type of memory cell chosen, our results consistently show that the proposed framework outperforms the CAMS models in terms of mean squared error (MSE), with average improvements ranging from 25% to 40%. Furthermore, we examine the impact of outliers on the overall performance of the model. Full article

This study aims to focus on using the Volterra series and machine learning for forecasting random and chaotic wind speed regimes, since calm weather is mostly noticed at the local site, making dataset selection difficult. A novel method is proposed to predict Volterra kernels up to the third order, using a forward–back propagation neural network with 12-month measurements at Fujairah site (United Arab Emirates). Both daily and monthly wind speed datasets are investigated for forecasting. The three dominant hourly and daily kernels are extracted for each day and each month. Predicted future Volterra kernels are estimated from past values using both statistical analysis and individual neuro networks for each of the Volterra kernel coefficients. Using the evolved Volterra kernels, the hourly and daily wind speeds are forecasted with similar patterns of the measured values. Due to the random nature of wind speed at the local site, a two-layer with four neurons per layer neuro network is used to locate the most variable and intense speed during 8 h in the day. Forecasted wind speed is determined with errors arising from different sources, such as the utilization of only third-order Volterra kernels and the difficulty of machine training of the employed shallow network. Nevertheless, this work depicts a useful algorithm to forecast chaotic and random wind speed regimes. Computational time is a trade of the complexity of Volterra mathematical analysis. Full article

Forecasting and modeling time series is a crucial aspect of economic research for academics and business practitioners. The ability to predict the direction of stock prices is vital for creating an investment plan or determining the optimal time to make a trade. However, market movements can be complex to predict, non-linear, and chaotic, making it difficult to forecast their evolution. In this paper, we investigate modeling and forecasting the daily prices of the new Morocco Stock Index 20 (MSI 20). To this end, we propose a comparative study between the results obtained from the application of the various Machine Learning (ML) methods: Support Vector Regression (SVR), eXtreme Gradient Boosting (XGBoost), Multilayer Perceptron (MLP), and Long Short-Term Memory (LSTM) models. The results show that using the Grid Search (GS) optimization algorithm, the SVR and MLP models outperform the other models and achieve high accuracy in forecasting daily prices. Full article