Financial time series forecasting model based on CEEMDAN and LSTM

In this study, different kinds of hybrid Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithms with forecasting models including Random Forest (RF), Gated Recurrent Unit (GRU), and Long Short-Term Memory (LSTM) neural networks, are developed to estimate the mean daily wind speed at the height of 2 m in Ağrı city (WS st12 ), Turkey. In these hybrid models, different layer networks of single and integrated LSTM and GRU models include general single LSTM, general single GRU, simple coupled LSTM-GRU, and novel coupled LSTM with GRU through Addition layer (i.e., LSTM + GRU model) structures are applied. The most effective parameters on the WS st12 , from a list of on-site potential meteorological parameters and wind speed values in its adjacent cities of Ağrı province from Jan 2015–Dec 2019 through the Pearson correlation coefficient method, are determined. In the hybrid CEEMDAN and DNNs-based models, State activation functions (SAF), numbers of hidden neurons (NHN), dropout rates (P-rate), and network structural architect (NSA) as the meta-parameters are tuned for lessening the impact of overfitting/underfitting dilemmas and improving modeling performance. According to the comparison plots, performance evaluation measures, and total learnable parameter (TLP), the novel developed hybrid CEEMDAN-RF-(LSTM + GRU) model is confirmed as the best approach with an R 2 of 0.86 while, in the optimal scenario using the RF model, R 2 was 0.47. Graphical Abstract Based on the graphical snapshot, this study focuses on estimating daily mean wind speed at a 2-meter height in Ağrı, Turkey, using hybrid data-driven models. The research integrates the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm with advanced forecasting techniques, including Random Forest (RF), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU) neural networks. The modeling framework explores various configurations, such as standalone LSTM and GRU, coupled LSTM-GRU structures, and a novel LSTM + GRU model using an Addition layer to enhance predictive accuracy.

Long-short term memory (LSTM) is a state-of-art and widely used model to forecast financial time series. However, primitive LSTM networks do not perform well due to over-fitting problems of the deep learning model and nonlinear and non-stationary characteristics of financial time series data. In addition, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is an outstanding data frequency decomposition technique that can decompose original time series into several intrinsic mode functions and a residue. Thus, this paper proposed a novel hybrid network CEEMDAN-LSTM-BN based on LSTM. Specifically, to avoid over-fitting, the modified LSTM-BN network consists of two LSTM layers, two Batch Normalization (BN) layers following each LSTM layer, and a dropout layer. Each of the intrinsic mode functions and the residue would be processed by CEEMDAN-LSTM-BN and the final prediction results are obtained by reconstructing each predictive series. The advantages of the proposed CEEMDANLSTM-BN networks are verified by comparing them to primitive LSTM, other hybrid models, and some famous machine learning models. Moreover, the robustness of the networks is assessed by numerical experiments on different stock indices datasets.

The performance of tissue imaging is improved by tissue harmonic imaging (THI) to expand and enhance the range and level of clinical diagnosis for many diseases. The separation based on High-pass filtering (S_HPF) is a commonly used method for extracting harmonic components from ultrasonic echo signals. However, the cut-off frequency, order and algorithm to realize a high-pass filter have a great influence on the separation accuracy of harmonic signals. In present study, a novel separation method (S_CEEMDAN) based on the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm is proposed for adaptively separating harmonic components from ultrasonic echo signals. First, we calculate the ensemble size of CEEMDAN adaptively based on the added noise level, and draw a sum of intrinsic mode functions (IMFs) from the ultrasonic echo signals by CEEMDAN. Then, the spectrum of each IMF is computed and evaluated, and the IMFs containing both fundamental and harmonic components are further decomposed by using the CEEMDAN algorithm. This separation process is end until all of IMFs have been divided into either fundamental or harmonic categories. Finally, the corresponding fundamental and harmonic echo signals are yielded by accumulating separately these two categories. In experiments, simulated ultrasonic echo signals with a center frequency of 3.5MHz are separated by the proposed S_CEEMDAN method, and the results are compared with those processed by S_HPF. The edge of the harmonic image by S_CEEMDAN marginally better defined than S_HPF. The indices for the harmonic signals separated by S_CEEMDAN and S_HPF, respectively, are as follows: the center frequencies of 6.66 MHz and 6.65 MHz, 3 dB bandwidths of 1.04 MHz and 1.05 MHz, 6 dB bandwidths of 1.59 MHz and 1.55 MHz, signal-to-noise ratios (SNRs) of 14.00 and 13.63, and image contrasts of 7.01 and 7.06. In conclusion, due to good adaptive characteristics, and lower reconstruction errors, the proposed S_CEEMD method is superior to S_HPF in the performance of spectral accuracy and harmonic imaging. This method could be potentially alternative to the current method for the ultrasonic harmonic separation.

I335 the training of Support Vector Machine (SVM) classification model, some problems such as over-fitting, under-fitting, slow training speed and prediction affected by penalty and kernel function parameters are exposed. A fault classification method of rolling bearing based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Grey Wolf Optimization (GWO) -SVM is proposed. Firstly, the acquire signals are adaptively decomposed into a plurality of Intrinsic Mode Function(IMF) component by CEEMDAN, and the energy entropy of each IMF component is extracted to form a set of high dimensional feature vector. Then, the processed feature vectors are introduced into the diagnosis network of GWO-SVM algorithm to build a fault classification model of motor rolling bearing. The classification results show that the CEEMDAN and GWO-SVM fault classification network of motor rolling bearing has higher accuracy and shorter diagnosis time than Particle Swarm Optimization (PSO) -SVM and Cross Validation (CV) -SVM.

Warships play an important role in the modern sea battlefield. Research on the line spectrum features of warship radio noise signals is helpful to realize the classification and recognition of different types of warships, and provides critical information for sea battlefield. In this paper, we proposed a novel linear spectrum frequency feature extraction technique for warship radio noise based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), duffing chaotic oscillator (DCO), and weighted-permutation entropy (W-PE). The proposed linear spectrum frequency feature extraction technique, named CEEMDAN-DCO-W-PE has the following advantages in comparison with other linear spectrum frequency feature extraction techniques; (i) as an adaptive data-driven algorithm, CEEMDAN has more accurate and more reliable decomposition performance than empirical mode decomposition (EMD) and ensemble EMD (EEMD), and there is no need for presetting parameters, such as decomposition level and basis function; (ii) DCO can detect the linear spectrum of narrow band periodical warship signals by way of utilizing its properties of sensitivity for weak periodical signals and the immunity for noise; and (iii) W-PE is used in underwater acoustic signal feature extraction for the first time, and compared with traditional permutation entropy (PE), W-PE increases amplitude information to some extent. Firstly, warship radio noise signals are decomposed into some intrinsic mode functions (IMFs) from high frequency to low frequency by CEEMDAN. Then, DCO is used to detect linear spectrum of low-frequency IMFs. Finally, we can determine the linear spectrum frequency of low-frequency IMFs using W-PE. The experimental results show that the proposed technique can accurately extract the line spectrum frequency of the simulation signals, and has a higher classification and recognition rate than the traditional techniques for real warship radio noise signals.

Accurate prediction of Global Navigation Satellite System-derived precipitable water vapor (GNSS-PWV), which is a crucial indicator for climate change monitoring, holds significant scientific value for climate disaster prevention and mitigation. In the study of GNSS-PWV prediction, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm within a decomposition–integration framework effectively addresses the non-stationarity and complexity of PWV sequences, enhancing prediction accuracy. However, residual noise and pseudo-modes from decomposition can distort signals, reducing the predictor system’s reliability. Additionally, independent modeling of all decomposed components decreases computational efficiency. To address these challenges, this paper proposes a hybrid model combining the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), autoregressive integrated moving average (ARIMA), and long short-term memory (LSTM) networks. Enhanced by local mean optimization and adaptive noise regulation, the ICEEMDAN algorithm effectively suppresses pseudo-modes and minimizes residual noise, enabling its decomposed intrinsic mode functions (IMFs) to more accurately capture the multi-scale features of GNSS-PWV. Sample entropy (SE) is used to quantify the complexity of IMFs, and components with similar entropy values are reconstructed into the following three sub-sequences: high-frequency, low-frequency, and trend. This process significantly reduces modeling complexity and improves computational efficiency. We propose different modeling strategies tailored to the dynamics of various subsequences. For the nonlinear and non-stationary high-frequency components, the LSTM network is used to effectively capture their complex patterns. The LSTM’s gating mechanism and memory cell design proficiently address the long-term dependency issue. For the stationary and weakly nonlinear low-frequency and trend components, linear patterns are extracted using ARIMA. Differencing eliminates trends and moving average operations capture random fluctuations, effectively addressing periodicity and trends in the time series. Finally, the prediction results of the three components are linearly combined to obtain the final prediction value. To validate the model performance, experiments were conducted using measured GNSS-PWV data from several stations in Hong Kong. The results demonstrate that the proposed model reduces the root mean square error by 56.81%, 37.91%, and 13.58% at the 1 h scale compared to the LSTM, EMD-LSTM, and ICEEMDAN-SE-LSTM benchmark models, respectively. Furthermore, it exhibits strong robustness in cross-month forecasts (accounting for seasonal influences) and multi-step predictions over the 1–6 h period. By improving the accuracy and efficiency of PWV predictions, this model provides reliable technical support for the real-time monitoring and early warning of extreme weather events in Hong Kong while offering a universal methodological reference for multi-scale modeling of geophysical parameters.

In this paper, we propose a novel ECG signal enhancement method based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Higher Order Statistics (HOS). In our scheme, the noisy ECG signal is first decomposed adaptively into oscillatory components called intrinsic mode functions (IMFs) by using Empirical Mode Decomposition (EMD) or its variants. Therefore, the obtained modes are separated into two groups of noisy signal modes and one group of useful signal modes, by using a novel criterion derived from the HOS namely the fourth order cumulant or kurtosis. After that, a modified shrinkage scheme based on Interval Thresholding technique is adaptively applied to each selected IMF from the noise-dominant groups in order to reduce the noise and to preserve the QRS complex. The overall filtered ECG signal is then reconstructed by combining the thresholded IMFs and the retained unprocessed lower frequency relevant IMFs. Various tests and simulations are investigated to evaluate the performance of our proposed approach in combination with the EMD, Ensemble EMD (EEMD) and CEEMDAN algorithms. The simulation results carried on MIT-BIH Arrhythmia database, show that CEEMDAN method gives better performance than the two other methods, and outperforms some state-of-the-art methods in terms of Signal to Noise Ratio (SNR) and Root Mean Square Error (RMSE).

ABSTRACTThis study aims to forecast the S&P 500 ESG index using the mixture model of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and long short‐term memory (LSTM) prediction models. CEEMDAN enables decomposing the index's original return series into different intrinsic mode functions (IMFs) and a residual series. The decomposed IMFs are then regrouped into aggregate series depicting high frequency and medium frequency, while the residual series represent the trend component. LSTM algorithm is used on the aggregated series to obtain predicted values of the same. The study compares different prediction algorithms to identify their performance and explore the predictive power of the hybrid models.

A method of planetary gear fault diagnosis based on the fuzzy entropy of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and multi-layer perceptron (MLP) neural network is proposed. The vibration signal is decomposed into multiple intrinsic mode functions (IMFs) by CEEMDAN, and the fuzzy entropy that combines the fuzzy function and sample entropy is proposed and used to extract the feature information contained in each IMF. The fuzzy entropies of each IMF are defined as the input of the MLP neural network, and the planetary gear status can be recognized by the output. The experiments prove the proposed method is effective.

The drift signal of Fiber Optic Gyroscope (FOG) is often buried in noise. It is difficult to compensate drift directly, and three filtering methods based on Empirical Mode Decomposition (EMD) are applied. Comparison analysis with filtering methods based on EMD, Ensemble Empirical Mode Decomposition (EEMD) and the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is done. Experimental analysis results show that CEEMDAN outperforms than other denoising methods based on EMD and EEMD. The CEEMDAN method saves computational cost, requiring only 29.7% of the sifting iterations of the EEMD. Meanwhile, the rate white noise, bias instability and quantization noise involved in original signal is decreased from 0.0029°/√h , 0.0313°/h and 0.7814° to 0.0003°/√h , 0.0034°/h and 0.0111°, respectively, after applying CEEMDAN method.

Nowadays, effective prediction of Software Defined Network (SDN) traffic is one of the important ways to improve network service quality and secure network services. In order to improve the prediction accuracy of SDN network traffic, this paper proposes a combined prediction model combining decomposition algorithm, hybrid kernel least squares support vector machine, and optimization algorithm, considering the characteristics of network traffic such as nonlinearity and non-smoothness. Firstly, the original data series is decomposed into a series of Intrinsic Mode Function (IMF) using the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) to smooth the series. Then, the fuzzy C-mean algorithm (FCM) is used to classify each component into three classes based on its amplitude-frequency characteristics. Next, based on the different characteristics of the kernel functions, least-squares support vector machine (LSSVM) prediction models with corresponding kernel functions are constructed for each class of components, and the parameters of each model are optimized using the artificial bee colony algorithm (ABC). Finally, the prediction results of each component are cumulatively reconstructed to obtain the final prediction results. Through experimental comparison, the prediction accuracy of the proposed model (CEEMDAN-FCM-LSSVM-ABC) is better than that of CEEMDAN-LSSVM, EMD-LSSVM, LSSVM, and other models.

Electricity load demand is the fundamental building block for all utilities planning. The load demand data has nonlinear and non-stationary characteristics, which make it difficult to be predicted accurately by just computational intelligence or ensemble methods. Ensemble methods like Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is a powerful tool to forecast power load demand time series. Heterogeneous ensemble, a combination of two base models, will be distinct or more powerful in forecasting power load demand. In this paper, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) method is hybridized with three computational intelligence-based predictors: support vector regression (SVR), artificial neural network (ANN) and random forest (RF). The basis of this paper was to conduct a comparative study on the accuracy of the forecasting result from using heterogeneous ensemble method to individual computational intelligence or ensemble method for four different horizons. The performances of the heterogeneous method are compared and discussed. It shows that heterogeneous method has outperformed the individual computational intelligence and ensemble methods. Possible future works are also recommended for power load demand forecasting.

Numerous studies show that it is reasonable and effective to apply decomposition technology to deal with the complex carbon price series. However, the existing research ignores the residual term containing complex information after applying single decomposition technique. Considering the demand for higher accuracy of the carbon price series prediction and following the existing research path, this paper proposes a new hybrid prediction model VMD-CEEMDAN-LSSVM-LSTM, which combines a new quadratic decomposition technique with the optimized long short term memory (LSTM). In the decomposition part of the hybrid model, the original carbon price series is processed by variational mode decomposition (VMD), and then the residual term obtained by decomposition is further decomposed by complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). In the prediction part of the hybrid model, least squares support vector machine (LSSVM) is introduced, and LSSVM-LSTM model is constructed to predict the components obtained by decomposition. The empirical research of this paper selects two different case data from the European Union emissions trading system (EU ETS) as samples. Taking the results of Case Ⅰ in the 1-step ahead forecasting scenario as an example, the prediction evaluation indexes eMAPE, eRMSE and R2 of the VMD-CEEMDAN-LSSVM-LSTM hybrid model constructed in this paper are 0.3087, 0.0921 and 0.9987 respectively, which are significantly better than other benchmark models. The empirical results confirm the superiority and robustness of the hybrid model proposed in this paper for carbon price forecasting.

The electrical energy supply relies on the satisfactory operation of insulators. The ultrasound recorded from insulators in different conditions has a time series output, which can be used to classify faulty insulators. The random convolutional kernel transform (Rocket) algorithms use convolutional filters to extract various features from the time series data. This paper proposes a combination of Rocket algorithms, machine learning classifiers, and empirical mode decomposition (EMD) methods, such as complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), empirical wavelet transform (EWT), and variational mode decomposition (VMD). The results show that the EMD methods, combined with MiniRocket, significantly improve the accuracy of logistic regression in insulator fault diagnosis. The proposed strategy achieves an accuracy of 0.992 using CEEMDAN, 0.995 with EWT, and 0.980 with VMD. These results highlight the potential of incorporating EMD methods in insulator failure detection models to enhance the safety and dependability of power systems.

Accurate photovoltaic (PV) power prediction technology plays a crucial role in effectively addressing the challenges posed by the integration of large-scale PV systems into the grid. In this article, we propose a novel PV power combination prediction model based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) in conjunction with a hybrid neural network. To mitigate the influence of strong fluctuations in PV power on prediction outcomes, we employ CEEMDAN to decompose the PV data into several subsequences. Subsequently, sample entropy (SE) is used to quantify the complexity of each subsequence. Subsequences with similar SE values are then restructured to reduce computational load. Moreover, to overcome the limitations of a single neural network in capturing historical data features of PV power, a hybrid sequential convolutional neural network-gate recurrent unit (CNN-GRU) neural network is proposed. The effectiveness of our proposed model is validated through case studies involving PV power stations in two regions. To provide a comprehensive assessment, we conduct comparative validation by building and evaluating alternative models, including long-short term memory (LSTM), GRU, CEEMDAN-LSTM, CEEMDAN-GRU, and CNN-GRU. The results unequivocally demonstrate that the model presented in this article exhibits exceptional prediction performance, characterized by high accuracy and robust generalization.