Modern portfolio construction demands robust methods for integrating data-driven insights into asset allocation. The Black-Litterman model offers a powerful Bayesian approach to adjust equilibrium returns using investor views to form a posterior expectation along with market priors. Mainstream research mainly generates subjective views through statistical models or machine learning methods, among which hybrid models combined with decomposition algorithms perform well. However, most hybrid models do not pay enough attention to noise, and time series decomposition methods based on single variables make it difficult to fully utilize information between multiple variables. Multivariate decomposition also has problems of low efficiency and poor component quality. In this study, we propose a novel hybrid forecasting model SSA-MAEMD-TCN to automate and improve the view generation process. The proposed model combines Singular Spectrum Analysis (SSA) for denoising, Multivariate Aligned Empirical Mode Decomposition (MA-EMD) for frequency-aligned decomposition, and Temporal Convolutional Networks (TCNs) for deep sequence learning to capture complex temporal patterns across multiple financial indicators. Empirical tests on the Nasdaq 100 Index stocks show a significant improvement in forecasting performance compared to baseline models based on MAEMD and MEMD. The optimized portfolio performs well, with annualized returns and Sharpe ratios far exceeding those of the traditional portfolio over a short holding period, even after accounting for transaction costs.

We investigated the use of Empirical Mode Decomposition (EMD) combined with Gaussian Mixture Models (GMM), feature engineering and machine learning algorithms to optimize trading decisions. We used five, two, and one year samples of hourly candle data for GameStop, Tesla, and XRP (Ripple) markets respectively. Applying a 15 hour rolling window for each market, we collected several features based on a linear model and other classical features to predict the next hour's movement. Subsequently, a GMM filtering approach was used to identify clusters among these markets. For each cluster, we applied the EMD algorithm to extract high, medium, low and trend components from each feature collected. A simple thresholding algorithm was applied to classify market movements based on the percentage change in each market's close price. We then evaluated the performance of various machine learning models, including Random Forests (RF) and XGBoost, in classifying market movements. A naive random selection of trading decisions was used as a benchmark, which assumed equal probabilities for each outcome, and a temporal cross-validation approach was used to test models on 40%, 30%, and 20% of the dataset. Our results indicate that transforming selected features using EMD improves performance, particularly for ensemble learning algorithms like Random Forest and XGBoost, as measured by accumulated profit. Finally, GMM filtering expanded the range of learning algorithm and data source combinations that outperformed the top percentile of the random baseline.

The decomposition of a signal is a fundamental tool in many fields of research, including signal processing, geophysics, astrophysics, engineering, medicine, and many more. By breaking down complex signals into simpler oscillatory components we can enhance the understanding and processing of the data, unveiling hidden information contained in them. Traditional methods, such as Fourier analysis and wavelet transforms, which are effective in handling mono-dimensional stationary signals struggle with non-stationary data sets and they require, this is the case of the wavelet, the selection of predefined basis functions. In contrast, the Empirical Mode Decomposition (EMD) method and its variants, such as Iterative Filtering (IF), have emerged as effective nonlinear approaches, adapting to signals without any need for a priori assumptions. To accelerate these methods, the Fast Iterative Filtering (FIF) algorithm was developed, and further extensions, such as Multivariate FIF (MvFIF) and Multidimensional FIF (FIF2), have been proposed to handle higher-dimensional data. In this work, we introduce the Multidimensional and Multivariate Fast Iterative Filtering (MdMvFIF) technique, an innovative method that extends FIF to handle data that vary simultaneously in space and time. This new algorithm is capable of extracting Intrinsic Mode Functions (IMFs) from complex signals that vary in both space and time, overcoming limitations found in prior methods. The potentiality of the proposed method is demonstrated through applications to artificial and real-life signals, highlighting its versatility and effectiveness in decomposing multidimensional and multivariate nonstationary signals. The MdMvFIF method offers a powerful tool for advanced signal analysis across many scientific and engineering disciplines.

This paper introduces a novel method for effectively removing artifacts from EEG signals by combining the Empirical Mode Decomposition (EMD) method with a machine learning architecture. The proposed method addresses the limitations of existing artifact removal techniques by enhancing the EMD method through interpolation of the upper and lower. For conventional artifact removal methods, the EMD technique is commonly employed. However, the challenge lies in accurately interpolating the missing components of the signal while preserving its inherent frequency components. To overcome this limitation, we incorporated machine learning technique, which enables us to carefully handle the interpolation process without directly manipulating the data. The key advantage of our approach lies in the preservation of the natural characteristics of the EEG signal during artifact removal. By utilizing machine learning for interpolation, we ensure that the average component obtained through the EMD method retains the crucial frequency components of the original signal. This preservation is essential for maintaining the integrity and fidelity of the EEG data, allowing for accurate analysis and interpretation. The results obtained from our evaluation serve to validate the effectiveness of our approach and pave the way for further advancements in EEG signal processing and analysis.

Unmanned boats, while navigating at sea, utilize active compensation systems to mitigate wave disturbances experienced by onboard instruments and equipment. However, there exists a lag in the measurement of unmanned boat attitudes, thus introducing unmanned boat motion attitude prediction to compensate for the lag in the signal acquisition process. This paper, based on the basic principles of waves, derives the disturbance patterns of waves on unmanned boats from the wave energy spectrum. Through simulation analysis of unmanned boat motion attitudes, motion attitude data is obtained, providing experimental data for subsequent work. A combined prediction model based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Particle Swarm Optimization (PSO), and Support Vector Machine (SVM) is designed to predict the motion attitude of unmanned boats. Simulation results validate its superior prediction accuracy compared to traditional prediction models. For example, in terms of mean absolute error, it improves by 17% compared to the EMD-PSO-SVM model.

Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. They also exhibit limitations when applied to nonlinear and non-stationary signals. To address this challenge, a series of nonlinear and adaptive methods, pioneered by the empirical mode decomposition method have been proposed. Their aim is to decompose a non-stationary signal into quasi-stationary components which reveal better features in the time-frequency analysis. Recently, inspired by deep learning, we proposed a novel method called residual recursive convolutional neural network (RRCNN). Not only RRCNN can achieve more stable decomposition than existing methods while batch processing large-scale signals with low computational cost, but also deep learning provides a unique perspective for non-stationary signal decomposition. In this study, we aim to further improve RRCNN with the help of several nimble techniques from deep learning and optimization to ameliorate the method and overcome some of the limitations of this technique.

The decomposition of non-stationary signals is an important and challenging task in the field of signal time-frequency analysis. In the recent two decades, many signal decomposition methods led by the empirical mode decomposition, which was pioneered by Huang et al. in 1998, have been proposed by different research groups. However, they still have some limitations. For example, they are generally prone to boundary and mode mixing effects and are not very robust to noise. Inspired by the successful applications of deep learning in fields like image processing and natural language processing, and given the lack in the literature of works in which deep learning techniques are used directly to decompose non-stationary signals into simple oscillatory components, we use the convolutional neural network, residual structure and nonlinear activation function to compute in an innovative way the local average of the signal, and study a new non-stationary signal decomposition method under the framework of deep learning. We discuss the training process of the proposed model and study the convergence analysis of the learning algorithm. In the experiments, we evaluate the performance of the proposed model from two points of view: the calculation of the local average and the signal decomposition. Furthermore, we study the mode mixing, noise interference, and orthogonality properties of the decomposed components produced by the proposed method. All results show that the proposed model allows for better handling boundary effect, mode mixing effect, robustness, and the orthogonality of the decomposed components than existing methods.

A univariate time series with high variability can pose a challenge even to Deep Neural Network (DNN). To overcome this, a univariate time series is decomposed into simpler constituent series, whose sum equals the original series. As demonstrated in this article, the conventional one-time decomposition technique suffers from a leak of information from the future, referred to as a data leak. In this work, a novel Moving Front (MF) method is proposed to prevent data leakage, so that the decomposed series can be treated like other time series. Indian Summer Monsoon Rainfall (ISMR) is a very complex time series, which poses a challenge to DNN and is therefore selected as an example. From the many signal processing tools available, Empirical Wavelet Transform (EWT) was chosen for decomposing the ISMR into simpler constituent series, as it was found to be more effective than the other popular algorithm, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). The proposed MF method was used to generate the constituent leakage-free time series. Predictions and forecasts were made by state-of-the-art Long and Short-Term Memory (LSTM) network architecture, especially suitable for making predictions of sequential patterns. The constituent MF series has been divided into training, testing, and forecasting. It has been found that the model (EWT-MF-LSTM) developed here made exceptionally good train and test predictions, as well as Walk-Forward Validation (WFV), forecasts with Performance Parameter ($PP$) values of 0.99, 0.86, and 0.95, respectively, where $PP$ = 1.0 signifies perfect reproduction of the data.

Green bonds, which are designed to finance for environmental-friendly or sustainable projects, have attracted more and more investors' attention. However, the study in this field is still relatively limited, especially in forecasting the market's future trends. In this paper, a hybrid model combining Complete Ensemble Empirical Mode Decomposition (CEEMDAN) and Long Short-Term Memory (LSTM) is introduced to predict CUFE-CNI Green Bond Index. In order to evaluate the performance of our model, we also use Empirical Mode Decomposition (EMD) to decompose the green bond index. Our empirical result suggests that, compared with EMD-LSTM and LSTM models, CEEMDAN-LSTM is the most accurate model in green bond index forecasting. Meanwhile, we find that indices from energy commodity markets and green stock markets are both effective predictors, which also provides ground on the correlations between the green bond market and other financial markets.

The ageing process may lead to cognitive and physical impairments, which may affect elderly everyday life. In recent years, the use of Brain Computer Interfaces (BCIs) based on Electroencephalography (EEG) has revealed to be particularly effective to promote and enhance rehabilitation procedures, especially by exploiting motor imagery experimental paradigms. Moreover, BCIs seem to increase patients' engagement and have proved to be reliable tools for elderly overall wellness improvement. However, EEG signals usually present a low signal-to-noise ratio and can be recorded for a limited time. Thus, irrelevant information and faulty samples could affect the BCI performance. Introducing a methodology that allows the extraction of informative components from the EEG signal while maintaining its intrinsic characteristics, may provide a solution to both the described issues: noisy data may be avoided by having only relevant components and combining relevant components may represent a good strategy to substitute the data without requiring long or repeated EEG recordings. Moreover, substituting faulty trials may significantly improve the classification performances of a BCI when translating imagined movement to rehabilitation systems. To this end, in this work the EEG signal decomposition by means of multivariate empirical mode decomposition is proposed to obtain its oscillatory modes, called Intrinsic Mode Functions (IMFs). Subsequently, a novel procedure for relevant IMF selection criterion based on the IMF time-frequency representation and entropy is provided. After having verified the reliability of the EEG signal reconstruction with the relevant IMFs only, the relevant IMFs are combined to produce new artificial data and provide new samples to use for BCI training.