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Abstract Commodity markets, such as crude oil and precious metals, play a strategic role in the economic development of nations, with crude oil prices influencing geopolitical relations and the global economy. Moreover, gold and silver are argued to hedge the stock and cryptocurrency markets during market downsides. Therefore, accurate forecasting of crude oil and precious metals prices is critical. Nevertheless, due to the nonlinear nature, substantial fluctuations, and irregular cycles of crude oil and precious metals, predicting their prices is a challenging task. Our study contributes to the commodity market price forecasting literature by implementing and comparing advanced deep-learning models. We address this gap by including silver alongside gold in our analysis, offering a more comprehensive understanding of the precious metal markets. This research expands existing knowledge and provides valuable insights into predicting commodity prices. In this study, we implemented 16 deep- and machine-learning models to forecast the daily price of the West Texas Intermediate (WTI), Brent, gold, and silver markets. The employed deep-learning models are long short-term memory (LSTM), BiLSTM, gated recurrent unit (GRU), bidirectional gated recurrent units (BiGRU), T2V-BiLSTM, T2V-BiGRU, convolutional neural networks (CNN), CNN-BiLSTM, CNN-BiGRU, temporal convolutional network (TCN), TCN-BiLSTM, and TCN-BiGRU. We compared the forecasting performance of deep-learning models with the baseline random forest, LightGBM, support vector regression, and k-nearest neighborhood models using mean absolute error (MAE), mean absolute percentage error, and root mean squared error as evaluation criteria. By considering different sliding window lengths, we examine the forecasting performance of our models. Our results reveal that the TCN model outperforms the others for WTI, Brent, and silver, achieving the lowest MAE values of 1.444, 1.295, and 0.346, respectively. The BiGRU model performs best for gold, with an MAE of 15.188 using a 30-day input sequence. Furthermore, LightGBM exhibits comparable performance to TCN and is the best-performing machine-learning model overall. These findings are critical for investors, policymakers, mining companies, and governmental agencies to effectively anticipate market trends, mitigate risk, manage uncertainty, and make timely decisions and strategies regarding crude oil, gold, and silver markets.

Abstract The notion that investors shift to gold during economic market crises remains unverified for many cryptocurrency markets. This paper investigates the connectedness between the 10 most traded cryptocurrencies and gold as well as crude oil markets pre-COVID-19 and during COVID-19. Through the application of various statistical techniques, including cointegration tests, vector autoregressive models, vector error correction models, autoregressive distributed lag models, and Granger causality analyses, we explore the relationship between these markets and assess the safe-haven properties of gold and crude oil for cryptocurrencies. Our findings reveal that during the COVID-19 pandemic, gold is a strong safe-haven for Bitcoin, Litecoin, and Monero while demonstrating a weaker safe-haven potential for Bitcoin Cash, EOS, Chainlink, and Cardano. In contrast, gold only exhibits a strong safe-haven characteristic before the pandemic for Litecoin and Monero. Additionally, Brent crude oil emerges as a strong safe-haven for Bitcoin during COVID-19, while West Texas Intermediate and Brent crude oils demonstrate weaker safe-haven properties for Ether, Bitcoin Cash, EOS, and Monero. Furthermore, the Granger causality analysis indicates that before the COVID-19 pandemic, the causal relationship predominantly flowed from gold and crude oil toward the cryptocurrency markets; however, during the COVID-19 period, the direction of causality shifted, with cryptocurrencies exerting influence on the gold and crude oil markets. These findings provide subtle implications for policymakers, hedge fund managers, and individual or institutional cryptocurrency investors. Our results highlight the need to adapt risk exposure strategies during financial turmoil, such as the crisis precipitated by the COVID-19 pandemic.

Abstract This study examines the market efficiency in the prices and volumes of transactions of 41 cryptocurrencies. Specifically, the correlation dimension (CD), Lyapunov Exponent (LE), and approximate entropy (AE) were estimated before and during the COVID-19 pandemic. Then, we applied Student’s t-test and F-test to check whether the estimated nonlinear features differ across periods. The empirical results show that (i) the COVID-19 pandemic has not affected the means of CD, LE, and AE in prices, (ii) the variances of CD, LE, and AE estimated from prices are different across pre-pandemic and during pandemic periods, and specifically (iii) the variance of CD decreased during the pandemic; however, the variance of LE and the variance of AE increased during the pandemic period. Furthermore, the pandemic has not affected all three features estimated from the volume series. Our findings suggest that investing in cryptocurrencies is advantageous during a pandemic because their prices become more regular and stable, and the latter has not affected the volume of transactions.

In this study, we adapt three spatial-temporal graph neural network models to the unique characteristics of crude oil, gold, and silver markets for forecasting purposes. It aims to be the first to (i) explore the potential of spatial-temporal graph neural networks family for price forecasting of these markets, (ii) examine the role of attention mechanism in improving forecasting accuracy, and (iii) integrate various sources of predictors for better performance. Specifically, we present three distinct models: Multivariate Time Series Graph Neural Networks with Temporal Attention and Learnable Adjacency matrix (MTGNN-TAttLA), Spatial Attention Graph with Temporal Convolutional Networks (SAG-TCN), and Attention-based Spatial-Temporal Graph Convolutional Networks (ASTGCN), to capture the intricate interplay of spatial and temporal dependencies within crude oil and precious metals markets. Moreover, the effectiveness of the attention mechanism in improving models' accuracies is shown. Our empirical results reveal remarkable prediction accuracy, with all three models outperforming conventional deep learning methods such as Temporal Convolutional Networks (TCN), long short-term memory networks (LSTM) and convolutional neural networks (CNN). The MTGNN-TAttLA model, enriched with a temporal attention mechanism, exhibits exceptional performance in predicting the direction of price movement in the WTI, Brent, and silver markets, while ASTGCN is the best-performing model for the gold market. Additionally, we observed that incorporating technical indicators from the crude oil and precious metal markets into the graph structure has improved the classification accuracy of spatial-temporal graph neural networks.

Wind energy is a clean, sustainable, and renewable source. It is receiving a large amount of attention from governments and energy companies worldwide as it plays a significant role as an alternative source of energy in reducing carbon emissions. However, due to long-term operation in reduced and difficult weather conditions, wind turbine blades are always seriously damaged. Hence, damage detection in blade structure is essential to evaluate its operational condition and ensure its structural integrity and safety. We aim to use fractal, entropy, and chaos concepts as descriptors for the diagnosis of wind turbine blade condition. They are, respectively, estimated by the correlation dimension, approximate entropy, and the Lyapunov exponent. Formal statistical tests are performed to check how they are different across wind turbine blade conditions. The experimental results follow. First, the correlation dimension is not able to distinguish between all conditions of wind turbine blades. Second, approximate entropy is suitable to distinguish between healthy and erosion conditions and between healthy and mass imbalance conditions. Third, chaos is not a discriminative feature to distinguish between wind turbine blade conditions. Fourth, wind turbine blades with either erosion or mass imbalance exhibit less irregularity in their respective signals than healthy wind turbine blades.

This study proposes a wavelet leaders method with multiscale entropy measures to analyze multiscale complexities in electrocardiogram (ECG) signals to characterize arrhythmia (ARR), congestive heart failure (CHF), and normal sinus rhythm (NSR). The statistical results show evidence of multiscale fractal and multiscale entropy in all health conditions. In addition, ECG signals under NSR conditions display the largest complexity compared to ARR and CHF. Further, statistical tests confirm the presence of differences in terms of multifractals between health conditions in ECG signals. Finally, multiscale entropy increases with scale. The results from statistical analyses indicate that healthy ECG signals are more complex than abnormal ones. Hence, abnormality alters and reduces complexity in arrhythmia and congestive heart failure signals.

Congestive heart failure (CHF) and arrhythmia (ARR) are common heart diseases that affect a growing population of patients worldwide. In this work, we employ multi-scale analysis (MSA) to estimate generalized Hurst exponent (GHE) from electrocardiogram (ECG) records under CHF, ARR, and normal sinus rhythm (NSR). As a result, fractal correlations in short and long fluctuations of CHF, ARR, and NSR are measured. Then, a set of six statistical tests are applied to GHE estimates to check how they are different at each time scale between two different ECG conditions. Particularly, the goal is verify if two different ECG conditions can be statistically differentiated by short or by long fluctuations. The battery of statistical tests includes Kolmogorov–Smirnov, Kruskal–Wallis, Wilcoxon rank sum, Student t-test, Ansari–Bradley, and F-test. The results from MSA show evidence that CHF, ARR, and NSR all exhibit multi-fractal properties. Besides, the results from statistical tests revealed that long fluctuations statistically differentiate CHF and ARR, ARR and NSR, and CHF and NSR. Therefore, long fluctuations account most for the characterization of CHF, ARR, and NSR. Our findings are helpful to better understand the mechanics of heart disease and normal heart beats, and also promising to eventually designing computer-aided diagnosis systems for CHF and ARR classification.

Fault detection and identification are critical for the accurate maintenance and management of industrial machinery. In this regard, data-driven condition monitoring models play an important role in machinery fault diagnosis and management. This study investigates the applicability of various statistical machine learning systems in modeling large data in the condition monitoring of electric drive trains in supply chains. Large data is used to train linear discriminant analysis, K-nearest neighbor algorithm, naïve Bayes, kernel naïve Bayes, decision trees, and support vector machine to distinguish between eleven fault states. The experimental results from the testing data set show that the decision trees achieved 93.8% accuracy, followed by kernel naïve Bayes (91.9%), radial basis function (Gaussian) support vector machine (89.3%), linear discriminant analysis (84.5%), k-NN algorithm (80.5%), and Gaussian naïve Bayes (71.3%). Accordingly, the choice of statistical machine learning algorithm influences classification accuracy related to electric drive fault diagnosis. In addition, decision trees take only few seconds to learn and classify new instances from big data. This makes the selection of decision trees trivial for condition monitoring and management of electric drive trains.

The combination of Deep Learning and GARCH-type models has been proved to be superior to the single models in forecasting of volatility in various markets such as energy, main metals, and especially stock markets. To verify this hypothesis for cryptocurrencies market, we constructed various Deep Learning models based on Feed Forward Neural Networks (DFFNNs) and Long Short-Term Memory (LSTM) networks and evaluated their performance in forecasting the volatility of 27 cryptocurrencies. Then, different hybrid models were built in which the outputs of three GARCH-type models, namely GARCH, EGARCH, and APGARCH, with three different assumptions for the residuals’ distribution were fed into the DFFNN and LSTM networks. In other words, GARCH-type models were utilized as feature extractors and the deep learning models leveraged a sequence of extracted features as their inputs to produce the volatility of the next day. Our findings revealed that not only the deep learning models improve the forecasts of GARCH-type models with any distribution assumption, the forecasts of GARCH-type models as informative features can significantly increase the predictive power of the studied deep learning models; namely, the DFFNN and LSTM models.

Multifractal behavior in the cepstrum representation of healthy and unhealthy infant cry signals is examined by means of wavelet leaders and compared using the Student t-test. The empirical results show that both expiration and inspiration signals exhibit clear evidence of multifractal properties under healthy and unhealthy conditions. In addition, expiration and inspiration signals exhibit more complexity under healthy conditions than under unhealthy conditions. Furthermore, distributions of multifractal characteristics are different across healthy and unhealthy conditions. Hence, this study improves the understanding of infant crying by providing a complete description of its intrinsic dynamics to better evaluate its health status.

The main purpose of our paper is to evaluate the impact of the COVID-19 pandemic on randomness in volatility series of world major markets and to examine its effect on their interconnections. The data set includes equity (Bitcoin and Standard and Poor’s 500), precious metals (Gold and Silver), and energy markets (West Texas Instruments, Brent, and Gas). The generalized autoregressive conditional heteroskedasticity model is applied to the return series. The wavelet packet Shannon entropy is calculated from the estimated volatility series to assess randomness. Hierarchical clustering is employed to examine interconnections between volatilities. We found that (i) randomness in volatility of the S&P500 and in the volatility of precious metals were the most affected by the COVID-19 pandemic, while (ii) randomness in energy markets was less affected by the pandemic than equity and precious metal markets. Additionally, (iii) we showed an apparent emergence of three volatility clusters: precious metals (Gold and Silver), energy (Brent and Gas), and Bitcoin and WTI, and (iv) the S&P500 volatility represents a unique cluster, while (v) the S&P500 market volatility was not connected to the volatility of Bitcoin, energy, and precious metal markets before the pandemic. Moreover, (vi) the S&P500 market volatility became connected to volatility in energy markets and volatility in Bitcoin during the pandemic, and (vii) the volatility in precious metals is less connected to volatility in energy markets and to volatility in Bitcoin market during the pandemic. It is concluded that (i) investors may diversify their portfolios across single constituents of clusters, (ii) investing in energy markets during the pandemic period is appealing because of lower randomness in their respective volatilities, and that (iii) constructing a diversified portfolio would not be challenging as clustering structures are fairly stable across periods.

This paper presents a forecasting model that integrates the discrete wavelet transform (DWT) and backpropagation neural networks (BPNN) for predicting financial time series. The presented model first uses the DWT to decompose the financial time series data. Then, the obtained approximation (low-frequency) and detail (high-frequency) components after decomposition of the original time series are used as input variables to forecast future stock prices. Indeed, while high-frequency components can capture discontinuities, ruptures and singularities in the original data, low-frequency components characterize the coarse structure of the data, to identify the long-term trends in the original data. As a result, high-frequency components act as a complementary part of low-frequency components. The model was applied to seven datasets. For all of the datasets, accuracy measures showed that the presented model outperforms a conventional model that uses only low-frequency components. In addition, the presented model outperforms both the well-known auto-regressive moving-average (ARMA) model and the random walk (RW) process.

This study employs the generalized autoregressive conditionally heteroskedastic in the mean (GARCH-M) methodology to investigate the return generating process of Jordan, Kingdom of Saudi Arabia (KSA), Kuwait, and Morocco stock market indices. The tradeoff between returns and the conditional variance is found to be positive in all markets. In other words, the empirical findings show that investors are rewarded for their exposure to more risk in these financial markets. This result is consistent with both financial theory and empirical finance.

In this research, three variance ratio tests: the standard variance ratio test, the wild bootstrap multiple variance ratio test, and the non-parametric rank scores test are adopted to test the random walk hypothesis (RWH) of stock markets in Middle East and North Africa (MENA) region using most recent data from January 2010 to September 2012. The empirical results obtained by all three econometric tests show that the RWH is strongly rejected for Kuwait, Tunisia, and Morocco. However, the standard variance ratio test and the wild bootstrap multiple variance ratio test reject the null hypothesis of random walk in Jordan and KSA, while non-parametric rank scores test do not. We may conclude that Jordan and KSA stock market are weak efficient. In sum, the empirical results suggest that return series in Kuwait, Tunisia, and Morocco are predictable. In other words, predictable patterns that can be exploited in these markets still exit. Therefore, investors may make profits in such less efficient markets.

Haemorrhages (HAs) presence in fundus images is one of the most important indicators of diabetic retinopathy that causes blindness. In this regard, accurate grading of HAs in fundus images is crucial for appropriate medical treatment. The purpose of this Letter is to assess the relative performance of statistical features obtained with three different multi-resolution analysis (MRA) techniques and fed to support vector machine in grading retinal HAs. Considered MRA techniques are the common discrete wavelet transform (DWT), empirical mode decomposition (EMD), and variational mode decomposition (VMD). The obtained experimental results show that statistical features obtained by EMD, VMD, and DWT, respectively, achieved 88.31% ± 0.0832, 71% ± 0.1782, and 64% ± 0.0949 accuracies. It also outperformed VMD and DWT in terms of sensitivity and specificity. Thus, the EMD-based features are promising for grading retinal HAs.

Variational mode decomposition (VMD) is a new adaptive multi-resolution technique suitable for signal denoising purpose. The main focus of this work has been to study the feasibility of several image denoising techniques in empirical mode decomposition (EMD) and VMD domains. A comparative study is made using 11 techniques widely used in the literature, including Wiener filter, first-order local statistics, fourth partial differential equation, nonlinear complex diffusion process, linear complex diffusion process (LCDP), probabilistic non-local means, non-local Euclidean medians, non-local means, non-local patch regression, discrete wavelet transform and wavelet packet transform. On the basis of comparison of 396 denoising based on peak signal-to-noise ratio, it is found that the best performances are obtained in VMD domain when appropriate denoising techniques are applied. Particularly, it is found that LCDP in combination with VMD performs the best and that VMD is faster than EMD.

This paper investigates the dynamics of the NASDAQ topology before, during, and after 2008 financial crisis. First, multiresolution analysis by virtue of wavelet transform is employed to denoise each NASDAQ sector return series. Second, the correlation matrix of sectors is built and analyzed in each time period to view comovements of sectors. Third, hierarchical clustering trees are constructed in each time period to find out how the structure of the NASDAQ market evolves through time. Our results suggest that interrelationships between sectors become stronger in times of crisis and especially in post-crisis period. In addition, some markets tend to form the same cluster in all time periods; for instance the Industrial and Bank sectors and the Telecommunication and Computer sectors. However, the general topology of the NASDAQ market has been considerably changed over periods. In sum, the complex structure of the NASDAQ market is dynamic and is more integrated after 2008 financial crisis. This result indicates that there are less diversification opportunities in the post-crisis period in comparison with pre-crisis period. These empirical findings are important for the development of subsequent portfolio strategies.

Autoregressive moving average (ARMA) process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX) are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF) to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE) and mean absolute deviation (MAD) statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction.

In this study, the backpropagation neural network (BPNN) is tested for the ability to forecast the daily volatility of two stock market indices from the Middle East and North Africa (MENA) region using volume; namely Morocco and Saudi Arabia. Volatility series were estimated using the Exponential Auto-Regressive Conditional Heteroskedasticity (EGARCH) model. The simulation results show that trading volume helps improving the forecasting accuracy of BPNN in Morocco but not in Saudi Arabia. As a result, volume represents valuable information flow to be used in the modeling and prediction of volatility in Morocco. In addition, it is found that BPNN overpredicts volatility during high volatile periods. This finding is important in financial applications such as asset allocation and derivatives pricing.

In financial industry, the accurate forecasting of the stock market is a major challenge to optimize and update portfolios and also to evaluate several financial derivatives. Artificial neural networks and technical analysis are becoming widely used by industry experts to predict stock market moves. In this paper, different technical analysis measures and resilient back-propagation neural networks are used to predict the price level of five major developed international stock markets, namely the US S&P500, Japanese Nikkei, UK FTSE100, German DAX, and the French CAC40. Four categories of technical analysis measures are compared. They are indicators, oscillators, stochastics, and indexes. The out-of-sample simulation results show a strong evidence of the effectiveness of the indicators category over the oscillators, stochastics, and indexes. In addition, it is found that combining all these measures lead to an increase of the prediction error. In sum, technical analysis indicators provide valuable information to predict the S&P500, Nikkei, FTSE100, DAX, and the CAC40 price level.

The purpose of this paper is to predict the S&P500 down moves with technical analysis indicators using learning vector quantization (LVQ) neural networks and probabilistic neural networks (PNN). In addition, entropy-based input selection technique is employed to improve the prediction accuracies. The out-of-sample simulations show that LVQ outperforms PNN. In addition, the Entropy-LVQ system achieved higher accuracy in comparison with the literature.

The risk‒return trade-off is a fundamental relationship that has received a large amount of attention in financial and economic analysis. Indeed, it has important implications for understanding linear dynamics in price returns and active quantitative portfolio optimization. The main contributions of this work include, firstly, examining such a relationship in five major fertilizer markets through different time periods: a period of low variability in returns and a period of high variability such as that during which the recent global financial crisis occurred. Secondly, we explore how entropy in those markets varies during the investigated time periods. This requires us to assess their inherent informational dynamics. The empirical results show that higher volatility is associated with a larger return in diammonium phosphate, potassium chloride, triple super phosphate, and urea market, but not rock phosphate. In addition, the magnitude of this relationship is low during a period of high variability. It is concluded that key statistical patterns of return and the relationship between return and volatility are affected during high variability periods. Our findings indicate that entropy in return and volatility series of each fertilizer market increase significantly during time periods of high variability.