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Since financial assets on stock exchanges were created, investors have sought to predict their future values. Currently, cryptocurrencies are also seen as assets. Machine learning is increasingly adopted to assist and automate investments. The main objective of this paper is to make daily predictions about the movement direction of financial time series through classification models, financial time series preprocessing methods, and feature selection with genetic algorithms. The target time series are Bitcoin, Ibovespa, and Vale. The methodology of this paper includes the following steps: collecting time series of financial assets; data preprocessing; feature selection with genetic algorithms; and the training and testing of machine learning models. The results were obtained by evaluating the models with the area under the ROC curve metric. For the best prediction models for Bitcoin, Ibovespa, and Vale, values of 0.61, 0.62, and 0.58 were obtained, respectively. In conclusion, the feature selection allowed the improvement of performance in most models, and the input series in the form of percentage variation obtained a good performance, although it was composed of fewer attributes in relation to the other sets tested. [ABSTRACT FROM AUTHOR]

Due to its capacity to unveil the dynamic characteristics of time series data, entropy has attracted growing interest. However, traditional entropy feature extraction methods, such as permutation entropy, fall short in concurrently considering both the absolute amplitude information of signals and the temporal correlation between sample points. Consequently, this limitation leads to inadequate differentiation among different time series and susceptibility to noise interference. In order to augment the discriminative power and noise robustness of entropy features in time series analysis, this paper introduces a novel method called Tsallis entropy-based complexity-improved permutation entropy casualty plane (TC-IPE-CP). TC-IPE-CP adopts a novel symbolization approach that preserves both absolute amplitude information and inter-point correlations within sequences, thereby enhancing feature separability and noise resilience. Additionally, by incorporating Tsallis entropy and weighting the probability distribution with parameter q, it integrates with statistical complexity to establish a feature plane of complexity and entropy, further enriching signal features. Through the integration of multiscale algorithms, a multiscale Tsallis-improved permutation entropy algorithm is also developed. The simulation results indicate that TC-IPE-CP requires a small amount of data, exhibits strong noise resistance, and possesses high separability for signals. When applied to the analysis of heart rate signals, fault diagnosis, and underwater acoustic signal recognition, experimental findings demonstrate that TC-IPE-CP can accurately differentiate between electrocardiographic signals of elderly and young subjects, achieve precise bearing fault diagnosis, and identify four types of underwater targets. Particularly in underwater acoustic signal recognition experiments, TC-IPE-CP achieves a recognition rate of 96.67%, surpassing the well-known multi-scale dispersion entropy and multi-scale permutation entropy by 7.34% and 19.17%, respectively. This suggests that TC-IPE-CP is highly suitable for the analysis of complex time series. [ABSTRACT FROM AUTHOR]

Slope Entropy (SlpEn) is a novel method recently proposed in the field of time series entropy estimation. In addition to the well-known embedded dimension parameter, m, used in other methods, it applies two additional thresholds, denoted as δ and γ , to derive a symbolic representation of a data subsequence. The original paper introducing SlpEn provided some guidelines for recommended specific values of these two parameters, which have been successfully followed in subsequent studies. However, a deeper understanding of the role of these thresholds is necessary to explore the potential for further SlpEn optimisations. Some works have already addressed the role of δ , but in this paper, we extend this investigation to include the role of γ and explore the impact of using an asymmetric scheme to select threshold values. We conduct a comparative analysis between the standard SlpEn method as initially proposed and an optimised version obtained through a grid search to maximise signal classification performance based on SlpEn. The results confirm that the optimised version achieves higher time series classification accuracy, albeit at the cost of significantly increased computational complexity. [ABSTRACT FROM AUTHOR]

The echo state network (ESN) is a recurrent neural network that has yielded state-of-the-art results in many areas owing to its rapid learning ability and the fact that the weights of input neurons and hidden neurons are fixed throughout the learning process. However, the setting procedure for initializing the ESN's recurrent structure may lead to difficulties in designing a sound reservoir that matches a specific task. This paper proposes an improved pre-training method to adjust the model's parameters and topology to obtain an adaptive reservoir for a given application. Two strategies, namely global random selection and ensemble training, are introduced to pre-train the randomly initialized ESN model. Specifically, particle swarm optimization is applied to optimize chosen fixed and global weight values within the network, and the reliability and stability of the pre-trained model are enhanced by employing the ensemble training strategy. In addition, we test the feasibility of the model for time series prediction on six benchmarks and two real-life datasets. The experimental results show a clear enhancement in the ESN learning results. Furthermore, the proposed global random selection and ensemble training strategies are also applied to pre-train the extreme learning machine (ELM), which has a similar training process to the ESN model. Numerical experiments are subsequently carried out on the above-mentioned eight datasets. The experimental findings consistently show that the performance of the proposed pre-trained ELM model is also improved significantly. The suggested two strategies can thus enhance the ESN and ELM models' prediction accuracy and adaptability. [ABSTRACT FROM AUTHOR]

Continuous real-time location data is very important in the big data era, but the privacy issues involved is also a considerable topic. It is not only necessary to protect the location privacy at each release moment, but also have to consider the impact of data correlation. Correlated Laplace Mechanism (CLM) is a sophisticated method to implement differential privacy on correlated time series. This paper aims to solve the key problems of applying CLM in continuous location release. Based on the finding that the location increment is approximately stationary in many scenarios, a location correlation estimation method based on the location increment is proposed to solve the problem of nonstationary location data correlation estimation; an adaptive adjustment model for the CLM filter based on parameter quantization idea (QCLM) as well as its effective implementation named QCLM-Lowpass utilizing the lowpass spectral characteristics of location data series is proposed to solve the problem of output deviations due to the undesired transient response of the CLM filter in time-varying environments. Extensive simulations and real data experiments validate the effectiveness of the proposed approach and show that the privacy scheme based on QCLM-Lowpass can offer a better balance between the ability to resist correlation-based attacks and data availability. [ABSTRACT FROM AUTHOR]

Spiking neural networks (SNNs) are recurrent models that can leverage sparsity in input time series to efficiently carry out tasks such as classification. Additional efficiency gains can be obtained if decisions are taken as early as possible as a function of the complexity of the input time series. The decision on when to stop inference and produce a decision must rely on an estimate of the current accuracy of the decision. Prior work demonstrated the use of conformal prediction (CP) as a principled way to quantify uncertainty and support adaptive-latency decisions in SNNs. In this paper, we propose to enhance the uncertainty quantification capabilities of SNNs by implementing ensemble models for the purpose of improving the reliability of stopping decisions. Intuitively, an ensemble of multiple models can decide when to stop more reliably by selecting times at which most models agree that the current accuracy level is sufficient. The proposed method relies on different forms of information pooling from ensemble models and offers theoretical reliability guarantees. We specifically show that variational inference-based ensembles with p-variable pooling significantly reduce the average latency of state-of-the-art methods while maintaining reliability guarantees. [ABSTRACT FROM AUTHOR]

The demand for complex equipment aftermarket parts is mostly sporadic, showing typical intermittent characteristics as a whole, resulting in the evolution law of a single demand series having insufficient information, which restricts the prediction effect of existing methods. To solve this problem, this paper proposes a prediction method of intermittent feature adaptation from the perspective of transfer learning. Firstly, to extract the intermittent features of the demand series, an intermittent time series domain partitioning algorithm is proposed by mining the demand occurrence time and demand interval information in the series, then constructing the metrics, and using a hierarchical clustering algorithm to divide all the series into different sub-source domains. Secondly, the intermittent and temporal characteristics of the sequence are combined to construct a weight vector, and the learning of common information between domains is accomplished by weighting the distance of the output features of each cycle between domains. Finally, experiments are conducted on the actual after-sales datasets of two complex equipment manufacturing enterprises. Compared with various prediction methods, the method in this paper can effectively predict future demand trends, and the prediction's stability and accuracy are significantly improved. [ABSTRACT FROM AUTHOR]

The profound impacts of severe air pollution on human health, ecological balance, and economic stability are undeniable. Precise air quality forecasting stands as a crucial necessity, enabling governmental bodies and vulnerable communities to proactively take essential measures to reduce exposure to detrimental pollutants. Previous research has primarily focused on predicting air quality using only time-series data. However, the importance of remote-sensing image data has received limited attention. This paper proposes a new multi-modal deep-learning model, Res-GCN, which integrates high spatial resolution remote-sensing images and time-series air quality data from multiple stations to forecast future air quality. Res-GCN employs two deep-learning networks, one utilizing the residual network to extract hidden visual information from remote-sensing images, and another using a dynamic spatio-temporal graph convolution network to capture spatio-temporal information from time-series data. By extracting features from two different modalities, improved predictive performance can be achieved. To demonstrate the effectiveness of the proposed model, experiments were conducted on two real-world datasets. The results show that the Res-GCN model effectively extracts multi-modal features, significantly enhancing the accuracy of multi-step predictions. Compared to the best-performing baseline model, the multi-step prediction's mean absolute error, root mean square error, and mean absolute percentage error increased by approximately 6%, 7%, and 7%, respectively. [ABSTRACT FROM AUTHOR]

The detection of instability inception is favorable to avoid compressor instability. In this paper, a multiscale entropy-based feature extraction is developed for the detection of the instability inception in axial compressors. Nonlinear and statistical features of the short-time instability inception are extracted by generally combining multiscale entropy and statistical features. First, nonlinear features are extracted by refined composite multiscale entropy to avoid the inaccurate estimation or undefined entropy of multiscale entropy for short time series. Second, the time-domain-based statistical features are chosen to capture more information on instability inception, and the dominant statistical features are determined by random forests implemented with the mean decrease accuracy algorithm at each time scale. The obtained refined composite dominant statistical features are regarded as weighting factors and integrated with the refined composite multiscale entropy to generate a combined feature. Finally, numerical simulation results on two synthetic noise datasets and a compressor instability model dataset are presented to demonstrate the effectiveness, efficiency, and robustness of the combined features under different conditions. [ABSTRACT FROM AUTHOR]

Driven by the variety of available measures intended to estimate predictability of diverse objects such as time series and network links, this paper presents a comprehensive overview of the existing literature in this domain. Our overview delves into predictability from two distinct perspectives: the intrinsic predictability, which represents a data property independent of the chosen forecasting model and serves as the highest achievable forecasting quality level, and the realized predictability, which represents a chosen quality metric for a specific pair of data and model. The reviewed measures are used to assess predictability across different objects, starting from time series (univariate, multivariate, and categorical) to network links. Through experiments, we establish a noticeable relationship between measures of realized and intrinsic predictability in both generated and real-world time series data (with the correlation coefficient being statistically significant at a 5% significance level). The discovered correlation in this research holds significant value for tasks related to evaluating time series complexity and their potential to be accurately predicted. [ABSTRACT FROM AUTHOR]

Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach that can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent homology (PH), which can extract topological properties from data at various scales. The aim of this article is to introduce TDA concepts to a statistical audience and provide an approach to analyzing multivariate time series data. The application's focus will be on multivariate brain signals and brain connectivity networks. Finally, this paper concludes with an overview of some open problems and potential application of TDA to modeling directionality in a brain network, as well as the casting of TDA in the context of mixed effect models to capture variations in the topological properties of data collected from multiple subjects. [ABSTRACT FROM AUTHOR]

Orthogonal time frequency space (OTFS) is a novel modulation scheme that enables reliable communication in high-mobility environments. In this paper, we propose a Transformer-based channel estimation method for OTFS systems. Initially, the threshold method is utilized to obtain preliminary channel estimation results. To further enhance the channel estimation, we leverage the inherent temporal correlation between channels, and a new method of channel response prediction is performed. To enhance the accuracy of the preliminary results, we utilize a specialized Transformer neural network designed for processing time series data for refinement. The simulation results demonstrate that our proposed scheme outperforms the threshold method and other deep learning (DL) methods in terms of normalized mean squared error and bit error rate. Additionally, the temporal complexity and spatial complexity of different DL models are compared. The results indicate that our proposed algorithm achieves superior accuracy while maintaining an acceptable computational complexity. [ABSTRACT FROM AUTHOR]

This paper proposes a class of algorithms for analyzing event count time series, based on state space modeling and Kalman filtering. While the dynamics of the state space model is kept Gaussian and linear, a nonlinear observation function is chosen. In order to estimate the states, an iterated extended Kalman filter is employed. Positive definiteness of covariance matrices is preserved by a square-root filtering approach, based on singular value decomposition. Non-negativity of the count data is ensured, either by an exponential observation function, or by a newly introduced "affinely distorted hyperbolic" observation function. The resulting algorithm is applied to time series of the daily number of seizures of drug-resistant epilepsy patients. This number may depend on dosages of simultaneously administered anti-epileptic drugs, their superposition effects, delay effects, and unknown factors, making the objective analysis of seizure counts time series arduous. For the purpose of validation, a simulation study is performed. The results of the time series analysis by state space modeling, using the dosages of the anti-epileptic drugs as external control inputs, provide a decision on the effect of the drugs in a particular patient, with respect to reducing or increasing the number of seizures. [ABSTRACT FROM AUTHOR]

Prediction markets are heralded as powerful forecasting tools, but models that describe them often fail to capture the full complexity of the underlying mechanisms that drive price dynamics. To address this issue, we propose a model in which agents belong to a social network, have an opinion about the probability of a particular event to occur, and bet on the prediction market accordingly. Agents update their opinions about the event by interacting with their neighbours in the network, following the Deffuant model of opinion dynamics. Our results suggest that a simple market model that takes into account opinion formation dynamics is capable of replicating the empirical properties of historical prediction market time series, including volatility clustering and fat-tailed distribution of returns. Interestingly, the best results are obtained when there is the right level of variance in the opinions of agents. Moreover, this paper provides a new way to indirectly validate opinion dynamics models against real data by using historical data obtained from PredictIt, which is an exchange platform whose data have never been used before to validate models of opinion diffusion. [ABSTRACT FROM AUTHOR]

Time series data are usually characterized by having missing values, high dimensionality, and large data volume. To solve the problem of high-dimensional time series with missing values, this paper proposes an attention-based sequence-to-sequence model to imputation missing values in time series (ASSM), which is a sequence-to-sequence model based on the combination of feature learning and data computation. The model consists of two parts, encoder and decoder. The encoder part is a BIGRU recurrent neural network and incorporates a self-attentive mechanism to make the model more capable of handling long-range time series; The decoder part is a GRU recurrent neural network and incorporates a cross-attentive mechanism into associate with the encoder part. The relationship weights between the generated sequences in the decoder part and the known sequences in the encoder part are calculated to achieve the purpose of focusing on the sequences with a high degree of correlation. In this paper, we conduct comparison experiments with four evaluation metrics and six models on four real datasets. The experimental results show that the model proposed in this paper outperforms the six comparative missing value interpolation algorithms. [ABSTRACT FROM AUTHOR]

This study investigated information spillovers across crude oil time series at different time scales, using a network combined with a wavelet transform. It can detect the oil price, which plays an important role in the dynamic process of spillovers, and it can also analyze the dynamic feature of systematic risk based on entropy at different scales. The results indicate that the network structure changes with time, and the important roles of an oil price can be identified. WTI and Brent act as important spillover transmitters, and other prices are important spillover receivers at a scale. With the increase in time scale, both the number of neighbors and the importance of spillovers of Brent and WTI as spillover transmitters show downward trends. The importance for spillovers of China–Shengli and Dubai as spillover receivers shows a downward trend. This paper provides new evidence for explaining WTI and Brent as global benchmark oil prices. In addition, systematic risk is time-varying, and it is smaller at short-term scale than at long-term scale. The trend of systematic risk is also discussed when typical oil-related events occur. This paper provides a new perspective for exploring dynamic spillovers and systematic risk that offers important implications for policymakers and market investors. [ABSTRACT FROM AUTHOR]

The convergence rate for free-distribution functional data analyses is challenging. It requires some advanced pure mathematics functional analysis tools. This paper aims to bring several contributions to the existing functional data analysis literature. First, we prove in this work that Kolmogorov entropy is a fundamental tool in characterizing the convergence rate of the local linear estimation. Precisely, we use this tool to derive the uniform convergence rate of the local linear estimation of the conditional cumulative distribution function and the local linear estimation conditional quantile function. Second, a central limit theorem for the proposed estimators is established. These results are proved under general assumptions, allowing for the incomplete functional time series case to be covered. Specifically, we model the correlation using the ergodic assumption and assume that the response variable is collected with missing at random. Finally, we conduct Monte Carlo simulations to assess the finite sample performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

Chaotic time series are widely present in practice, but due to their characteristics—such as internal randomness, nonlinearity, and long-term unpredictability—it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks. [ABSTRACT FROM AUTHOR]

Currently, sentiment analysis is a research hotspot in many fields such as computer science and statistical science. Topic discovery of the literature in the field of text sentiment analysis aims to provide scholars with a quick and effective understanding of its research trends. In this paper, we propose a new model for the topic discovery analysis of literature. Firstly, the FastText model is applied to calculate the word vector of literature keywords, based on which cosine similarity is applied to calculate keyword similarity, to carry out the merging of synonymous keywords. Secondly, the hierarchical clustering method based on the Jaccard coefficient is used to cluster the domain literature and count the literature volume of each topic. Thirdly, the information gain method is applied to extract the high information gain characteristic words of various topics, based on which the connotation of each topic is condensed. Finally, by conducting a time series analysis of the literature, a four-quadrant matrix of topic distribution is constructed to compare the research trends of each topic within different stages. The 1186 articles in the field of text sentiment analysis from 2012 to 2022 can be divided into 12 categories. By comparing and analyzing the topic distribution matrices of the two phases of 2012 to 2016 and 2017 to 2022, it is found that the various categories of topics have obvious research development changes in different phases. The results show that: ① Among the 12 categories, online opinion analysis of social media comments represented by microblogs is one of the current hot topics. ② The integration and application of methods such as sentiment lexicon, traditional machine learning and deep learning should be enhanced. ③ Semantic disambiguation of aspect-level sentiment analysis is one of the current difficult problems this field faces. ④ Research on multimodal sentiment analysis and cross-modal sentiment analysis should be promoted. [ABSTRACT FROM AUTHOR]

Since its conception, the cryptocurrency market has been frequently described as an immature market, characterized by significant swings in volatility and occasionally described as lacking rhyme or reason. There has been great speculation as to what role it plays in a diversified portfolio. For instance, is cryptocurrency exposure an inflationary hedge or a speculative investment that follows broad market sentiment with amplified beta? We have recently explored similar questions with a clear focus on the equity market. There, our research revealed several noteworthy dynamics such as an increase in the market's collective strength and uniformity during crises, greater diversification benefits across equity sectors (rather than within them), and the existence of a "best value" portfolio of equities. In essence, we can now contrast any potential signatures of maturity we identify in the cryptocurrency market and contrast these with the substantially larger, older and better-established equity market. This paper aims to investigate whether the cryptocurrency market has recently exhibited similar mathematical properties as the equity market. Instead of relying on traditional portfolio theory, which is grounded in the financial dynamics of equity securities, we adjust our experimental focus to capture the presumed behavioral purchasing patterns of retail cryptocurrency investors. Our focus is on collective dynamics and portfolio diversification in the cryptocurrency market, and examining whether previously established results in the equity market hold in the cryptocurrency market and to what extent. The results reveal nuanced signatures of maturity related to the equity market, including the fact that correlations collectively spike around exchange collapses, and identify an ideal portfolio size and spread across different groups of cryptocurrencies. [ABSTRACT FROM AUTHOR]

This paper presents a first-order integer-valued autoregressive time series model featuring observation-driven parameters that may adhere to a particular random distribution. We derive the ergodicity of the model as well as the theoretical properties of point estimation, interval estimation, and parameter testing. The properties are verified through numerical simulations. Lastly, we demonstrate the application of this model using real-world datasets. [ABSTRACT FROM AUTHOR]

Marine background noise (MBN) is the background noise of the marine environment, which can be used to invert the parameters of the marine environment. However, due to the complexity of the marine environment, it is difficult to extract the features of the MBN. In this paper, we study the feature extraction method of MBN based on nonlinear dynamics features, where the nonlinear dynamical features include two main categories: entropy and Lempel–Ziv complexity (LZC). We have performed single feature and multiple feature comparative experiments on feature extraction based on entropy and LZC, respectively: for entropy-based feature extraction experiments, we compared feature extraction methods based on dispersion entropy (DE), permutation entropy (PE), fuzzy entropy (FE), and sample entropy (SE); for LZC-based feature extraction experiments, we compared feature extraction methods based on LZC, dispersion LZC (DLZC) and permutation LZC (PLZC), and dispersion entropy-based LZC (DELZC). The simulation experiments prove that all kinds of nonlinear dynamics features can effectively detect the change of time series complexity, and the actual experimental results show that regardless of the entropy-based feature extraction method or LZC-based feature extraction method, they both present better feature extraction performance for MBN. [ABSTRACT FROM AUTHOR]

As a typical complex system, the stock market has attracted the attention of scholars and investors to comprehensively understand its fractal characteristics and analyze its market efficiency. Firstly, this paper proposes an asymmetric, detrended fluctuation analysis based on overlapping sliding windows (OSW-A-MFDFA). It reduces the generation of fluctuation errors, and the calculation results are more robust and reliable. The advantage of the OSW-A-MFDFA is that it not only can reveal the multifractal characteristics of time series clearly, but also can further accurately analyze the asymmetry of fractal characteristics under different trends. Secondly, this paper focuses on the variation in the width difference and height difference of the multifractal spectrum under different trends. Finally, based on multifractality, this paper proposes a comprehensive indicator MED that can be used to measure market efficiency, which is characterized by traversing all fluctuation orders. The application revealed many interesting findings in style stock indices. Style stock indices have asymmetric multifractal characteristics, and there are significant differences in the fractal spectrum of different style assets. Moreover, the market efficiency of style stock indices is time-varying, which can be reasonably explained from the perspective of the adaptive market hypothesis. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new discrete-time risk model of an insurance portfolio with stochastic premiums, in which the temporal dependence among the premium numbers of consecutive periods is fitted by the first-order integer-valued autoregressive (INAR(1)) process and the temporal dependence among the claim numbers of consecutive periods is described by the integer-valued moving average (INMA(1)) process. To measure the risk of the model quantitatively, we study the explicit expression for a function whose solution is defined as the Lundberg adjustment coefficient and give the Lundberg approximation formula for the infinite-time ruin probability. In the case of heavy-tailed claim sizes, we establish the asymptotic formula for the finite-time ruin probability via the large deviations of the aggregate claims. Two numerical examples are provided in order to illustrate our theoretical findings. [ABSTRACT FROM AUTHOR]

Anticipating and understanding fluctuations in the agri-food market is very important in order to implement policies that can assure fair prices and food availability. In this paper, we contribute to the understanding of this market by exploring its efficiency and whether the local Hurst exponent can help to anticipate its trend or not. We have analyzed the time series of the price for different agri-commodities and classified each day into persistent, anti-persistent, or white-noise. Next, we have studied the probability and speed to mean reversion for several rolling windows. We found that in general mean reversion is more probable and occurs faster during anti-persistent periods. In contrast, for most of the rolling windows we could not find a significant effect of persistence in mean reversion. Hence, we conclude that the Hurst exponent can help to anticipate the future trend and range of the expected prices in this market. [ABSTRACT FROM AUTHOR]

In this paper, the Sun and its behavior are studied by means of complex networks. The complex network was built using the Visibility Graph algorithm. This method maps time series into graphs in which every element of the time series is considered as a node and a visibility criterion is defined in order to connect them. Using this method, we construct complex networks for magnetic field and sunspots time series encompassing four solar cycles, and various measures such as degree, clustering coefficient, mean path length, betweenness centrality, eigenvector centrality and decay exponents were calculated. In order to study the system in several time scales, we perform both a global, where the network contains information on the four solar cycles, and a local analysis, involving moving windows. Some metrics correlate with solar activity, while others do not. Interestingly, those metric which seem to respond to varying levels of solar activity in the global analysis, also do in the moving windows analysis. Our results suggest that complex networks can provide a useful way to follow solar activity, and reveal new features on solar cycles. [ABSTRACT FROM AUTHOR]

Anomaly detection in multivariate time series is an important problem with applications in several domains. However, the key limitation of the approaches that have been proposed so far lies in the lack of a highly parallel model that can fuse temporal and spatial features. In this paper, we propose TDRT, a three-dimensional ResNet and transformer-based anomaly detection method. TDRT can automatically learn the multi-dimensional features of temporal–spatial data to improve the accuracy of anomaly detection. Using the TDRT method, we were able to obtain temporal–spatial correlations from multi-dimensional industrial control temporal–spatial data and quickly mine long-term dependencies. We compared the performance of five state-of-the-art algorithms on three datasets (SWaT, WADI, and BATADAL). TDRT achieves an average anomaly detection F1 score higher than 0.98 and a recall of 0.98, significantly outperforming five state-of-the-art anomaly detection methods. [ABSTRACT FROM AUTHOR]

In this paper, a surjective mapping that satisfies the Li–Yorke chaos in the unit area is constructed and a perturbation algorithm (disturbing its parameters and inputs through another high-dimensional chaos) is proposed to enhance the randomness of the constructed chaotic system and expand its key space. An algorithm for the composition of two systems (combining sequence based on quantum random walks with chaotic system's outputs) is designed to improve the distribution of the system outputs and a compound chaotic system is ultimately obtained. The new compound chaotic system is evaluated using some test methods such as time series complexity, autocorrelation and distribution of output frequency. The test results showed that the new system has complex dynamic behavior such as high randomicity, unpredictability and uniform output distribution. Then, a new scheme for generating pseudorandom numbers is presented utilizing the composite chaotic system. The proposed pseudorandom number generator (PRNG) is evaluated using a series test suites such as NIST sp 800-22 soft and other tools or methods. The results of tests are promising, as the proposed PRNG passed all these tests. Thus, the proposed PRNG can be used in the information security field. [ABSTRACT FROM AUTHOR]

Binomial autoregressive models are frequently used for modeling bounded time series counts. However, they are not well developed for more complex bounded time series counts of the occurrence of n exchangeable and dependent units, which are becoming increasingly common in practice. To fill this gap, this paper first constructs an exchangeable Conway–Maxwell–Poisson-binomial (CMPB) thinning operator and then establishes the Conway–Maxwell–Poisson-binomial AR (CMPBAR) model. We establish its stationarity and ergodicity, discuss the conditional maximum likelihood (CML) estimate of the model's parameters, and establish the asymptotic normality of the CML estimator. In a simulation study, the boxplots illustrate that the CML estimator is consistent and the qqplots show the asymptotic normality of the CML estimator. In the real data example, our model takes a smaller AIC and BIC than its main competitors. [ABSTRACT FROM AUTHOR]

In the actual maintenance of manufacturing enterprises, abnormal changes in after-sale parts demand data often make the inventory strategies unreasonable. Due to the intermittent and small-scale characteristics of demand sequences, it is difficult to accurately identify the anomalies in such sequences using current anomaly detection algorithms. To solve this problem, this paper proposes an unsupervised anomaly detection method for intermittent time series. First, a new abnormal fluctuation similarity matrix is built by calculating the squared coefficient of variation and the maximum information coefficient from the macroscopic granularity. The abnormal fluctuation sequence can then be adaptively screened by using agglomerative hierarchical clustering. Second, the demand change feature and interval feature of the abnormal sequence are constructed and fed into the support vector data description model to perform hypersphere training. Then, the unsupervised abnormal point location detection is realized at the micro-granularity level from the abnormal sequence. Comparative experiments are carried out on the actual demand data of after-sale parts of two large manufacturing enterprises. The results show that, compared with the current representative anomaly detection methods, the proposed approach can effectively identify the abnormal fluctuation position in the intermittent sequence of small samples, and also obtain better detection results. [ABSTRACT FROM AUTHOR]

Slope Entropy (SlpEn) is a very recently proposed entropy calculation method. It is based on the differences between consecutive values in a time series and two new input thresholds to assign a symbol to each resulting difference interval. As the histogram normalisation value, SlpEn uses the actual number of unique patterns found instead of the theoretically expected value. This maximises the information captured by the method but, as a consequence, SlpEn results do not usually fall within the classical [ 0 , 1 ] interval. Although this interval is not necessary at all for time series classification purposes, it is a convenient and common reference framework when entropy analyses take place. This paper describes a method to keep SlpEn results within this interval, and improves the interpretability and comparability of this measure in a similar way as for other methods. It is based on a max–min normalisation scheme, described in two steps. First, an analytic normalisation is proposed using known but very conservative bounds. Afterwards, these bounds are refined using heuristics about the behaviour of the number of patterns found in deterministic and random time series. The results confirm the suitability of the approach proposed, using a mixture of the two methods. [ABSTRACT FROM AUTHOR]

Conventional studies of causal emergence have revealed that stronger causality can be obtained on the macro-level than the micro-level of the same Markovian dynamical systems if an appropriate coarse-graining strategy has been conducted on the micro-states. However, identifying this emergent causality from data is still a difficult problem that has not been solved because the appropriate coarse-graining strategy can not be found easily. This paper proposes a general machine learning framework called Neural Information Squeezer to automatically extract the effective coarse-graining strategy and the macro-level dynamics, as well as identify causal emergence directly from time series data. By using invertible neural network, we can decompose any coarse-graining strategy into two separate procedures: information conversion and information discarding. In this way, we can not only exactly control the width of the information channel, but also can derive some important properties analytically. We also show how our framework can extract the coarse-graining functions and the dynamics on different levels, as well as identify causal emergence from the data on several exampled systems. [ABSTRACT FROM AUTHOR]

As a measure of complexity, information entropy is frequently used to categorize time series, such as machinery failure diagnostics, biological signal identification, etc., and is thought of as a characteristic of dynamic systems. Many entropies, however, are ineffective for multivariate scenarios due to correlations. In this paper, we propose a local structure entropy (LSE) based on the idea of a recurrence network. Given certain tolerance and scales, LSE values can distinguish multivariate chaotic sequences between stochastic signals. Three financial market indices are used to evaluate the proposed LSE. The results show that the L S E F S T E 100 and L S E S & P 500 are higher than L S E S Z I , which indicates that the European and American stock markets are more sophisticated than the Chinese stock market. Additionally, using decision trees as the classifiers, LSE is employed to detect bearing faults. LSE performs higher on recognition accuracy when compared to permutation entropy. [ABSTRACT FROM AUTHOR]

An echo state network (ESN) is an efficient recurrent neural network (RNN) that is widely used in time series prediction tasks due to its simplicity and low training cost. However, the "black-box" nature of reservoirs hinders the development of ESN. Although a large number of studies have concentrated on reservoir interpretability, the perspective of reservoir modeling is relatively single, and the relationship between reservoir richness and reservoir projection capacity has not been effectively established. To tackle this problem, a novel reservoir interpretability framework based on permutation entropy (PE) theory is proposed in this paper. In structure, this framework consists of reservoir state extraction, PE modeling, and PE analysis. Based on these, the instantaneous reservoir states and neuronal time-varying states are extracted, which are followed by phase space reconstruction, sorting, and entropy calculation. Firstly, the obtained instantaneous state entropy (ISE) and global state entropy (GSE) can measure reservoir richness for interpreting good reservoir projection capacity. On the other hand, the multiscale complexity–entropy analysis of global and neuron-level reservoir states is performed to reveal more detailed dynamics. Finally, the relationships between ESN performance and reservoir dynamic are investigated via Pearson correlation, considering different prediction steps and time scales. Experimental evaluations on several benchmarks and real-world datasets demonstrate the effectiveness and superiority of the proposed reservoir interpretability framework. [ABSTRACT FROM AUTHOR]

Fractal properties in time series of human behavior and physiology are quite ubiquitous, and several methods to capture such properties have been proposed in the past decades. Fractal properties are marked by similarities in statistical characteristics over time and space, and it has been suggested that such properties can be well-captured through recurrence quantification analysis. However, no methods to capture fractal fluctuations by means of recurrence-based methods have been developed yet. The present paper takes this suggestion as a point of departure to propose and test several approaches to quantifying fractal fluctuations in synthetic and empirical time-series data using recurrence-based analysis. We show that such measures can be extracted based on recurrence plots, and contrast the different approaches in terms of their accuracy and range of applicability. [ABSTRACT FROM AUTHOR]

Among the existing bearing faults, ball ones are known to be the most difficult to detect and classify. In this work, we propose a diagnosis methodology for these incipient faults' classification using time series of vibration signals and their decomposition. Firstly, the vibration signals were decomposed using empirical mode decomposition (EMD). Time series of intrinsic mode functions (IMFs) were then obtained. Through analysing the energy content and the components' sensitivity to the operating point variation, only the most relevant IMFs were retained. Secondly, a statistical analysis based on statistical moments and the Kullback–Leibler divergence (KLD) was computed allowing the extraction of the most relevant and sensitive features for the fault information. Thirdly, these features were used as inputs for the statistical clustering techniques to perform the classification. In the framework of this paper, the efficiency of several family of techniques were investigated and compared including linear, kernel-based nonlinear, systematic deterministic tree-based, and probabilistic techniques. The methodology's performance was evaluated through the training accuracy rate (TrA), testing accuracy rate (TsA), training time (Trt) and testing time (Tst). The diagnosis methodology has been applied to the Case Western Reserve University (CWRU) dataset. Using our proposed method, the initial EMD decomposition into eighteen IMFs was reduced to four and the most relevant features identified via the IMFs' variance and the KLD were extracted. Classification results showed that the linear classifiers were inefficient, and that kernel or data-mining classifiers achieved 100 % classification rates through the feature fusion. For comparison purposes, our proposed method demonstrated a certain superiority over the multiscale permutation entropy. Finally, the results also showed that the training and testing times for all the classifiers were lower than 2 s, and 0.2 s, respectively, and thus compatible with real-time applications. [ABSTRACT FROM AUTHOR]

This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is called efficient if prices of its assets fully reflect all available information. We show that the degree of market efficiency is significantly low for most of the months from 2012 to 2021. We calculate the degree of market efficiency by (i) filtering out regularities in financial data and (ii) computing the Shannon entropy of the filtered return time series. We developed a simple method for estimating volatility and price staleness in empirical data in order to filter out such regularity patterns from return time series. The resulting financial time series of stock returns are then clustered into different groups according to some entropy measures. In particular, we use the Kullback–Leibler distance and a novel entropy metric capturing the co-movements between pairs of stocks. By using Monte Carlo simulations, we are then able to identify the time periods of market inefficiency for a group of 18 stocks. The inefficiency of the Moscow Stock Exchange that we have detected is a signal of the possibility of devising profitable strategies, net of transaction costs. The deviation from the efficient behavior for a stock strongly depends on the industrial sector that it belongs to. [ABSTRACT FROM AUTHOR]

In this paper, we propose a compression-based anomaly detection method for time series and sequence data using a pattern dictionary. The proposed method is capable of learning complex patterns in a training data sequence, using these learned patterns to detect potentially anomalous patterns in a test data sequence. The proposed pattern dictionary method uses a measure of complexity of the test sequence as an anomaly score that can be used to perform stand-alone anomaly detection. We also show that when combined with a universal source coder, the proposed pattern dictionary yields a powerful atypicality detector that is equally applicable to anomaly detection. The pattern dictionary-based atypicality detector uses an anomaly score defined as the difference between the complexity of the test sequence data encoded by the trained pattern dictionary (typical) encoder and the universal (atypical) encoder, respectively. We consider two complexity measures: the number of parsed phrases in the sequence, and the length of the encoded sequence (codelength). Specializing to a particular type of universal encoder, the Tree-Structured Lempel–Ziv (LZ78), we obtain a novel non-asymptotic upper bound, in terms of the Lambert W function, on the number of distinct phrases resulting from the LZ78 parser. This non-asymptotic bound determines the range of anomaly score. As a concrete application, we illustrate the pattern dictionary framework for constructing a baseline of health against which anomalous deviations can be detected. [ABSTRACT FROM AUTHOR]

The travel time prediction of vehicles is an important part of intelligent expressways. It can not only provide the vehicle distribution trend of each section for the expressway management department to assist the fine management of the expressway, but it can also provide owners with dynamic and accurate travel time prediction services to assist the owners to formulate more reasonable travel plans. However, there are still some problems in the current travel time prediction research (e.g., different types of vehicles are not processed separately, the proximity of the road network is not considered, and the capture of important information in the spatial-temporal perspective is not considered in depth). In this paper, we propose a Multi-View Travel Time Prediction (MVPPT) model. First, the travel times of different types of vehicles of each section in the expressway are analyzed, and the main differences in the travel times of different types of vehicles are obtained. Second, multiple travel time features are constructed, which include a novel spatial proximity feature. On this basis, we use CNN to capture the spatial correlation and the spatial attention mechanism to capture key information, the BiLSTM to capture the time correlation of time series, and the time attention mechanism capture key time information. Experiments on large-scale real traffic data demonstrate the effectiveness of our proposal over state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The green conversion of proton exchange membrane fuel cells (PEMFCs) has received particular attention in both stationary and transportation applications. However, the poor durability of PEMFC represents a major problem that hampers its commercial application since dynamic operating conditions, including physical deterioration, have a serious impact on the cell performance. Under these circumstances, prognosis and health management (PHM) plays an important role in prolonging durability and preventing damage propagation via the accurate planning of a condition-based maintenance (CBM) schedule. In this specific topic, health deterioration modeling with deep learning (DL) is the widely studied representation learning tool due to its adaptation ability to rapid changes in data complexity and drift. In this context, the present paper proposes an investigation of further deeper representations by exposing DL models themselves to recurrent expansion with multiple repeats. Such a recurrent expansion of DL (REDL) allows new, more meaningful representations to be explored by repeatedly using generated feature maps and responses to create new robust models. The proposed REDL, which is designed to be an adaptive learning algorithm, is tested on a PEMFC deterioration dataset and compared to its deep learning baseline version under time series analysis. Using multiple numeric and visual metrics, the results support the REDL learning scheme by showing promising performances. [ABSTRACT FROM AUTHOR]

Various mathematical frameworks play an essential role in understanding the economic systems and the emergence of crises in them. Understanding the relation between the structure of connections between the system's constituents and the emergence of a crisis is of great importance. In this paper, we propose a novel method for the inference of economic systems' structures based on complex networks theory utilizing the time series of prices. Our network is obtained from the correlation matrix between the time series of companies' prices by imposing a threshold on the values of the correlation coefficients. The optimal value of the threshold is determined by comparing the spectral properties of the threshold network and the correlation matrix. We analyze the community structure of the obtained networks and the relation between communities' inter and intra-connectivity as indicators of systemic risk. Our results show how an economic system's behavior is related to its structure and how the crisis is reflected in changes in the structure. We show how regulation and deregulation affect the structure of the system. We demonstrate that our method can identify high systemic risks and measure the impact of the actions taken to increase the system's stability. [ABSTRACT FROM AUTHOR]

In the last decade permutation entropy (PE) has become a popular tool to analyze the degree of randomness within a time series. In typical applications, changes in the dynamics of a source are inferred by observing changes of PE computed on different time series generated by that source. However, most works neglect the crucial question related to the statistical significance of these changes. The main reason probably lies in the difficulty of assessing, out of a single time series, not only the PE value, but also its uncertainty. In this paper we propose a method to overcome this issue by using generation of surrogate time series. The analysis conducted on both synthetic and experimental time series shows the reliability of the approach, which can be promptly implemented by means of widely available numerical tools. The method is computationally affordable for a broad range of users. [ABSTRACT FROM AUTHOR]

Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi's information measure. In particular, we tackle the directional information flow between bivariate time series in terms of Rényi's transfer entropy. We show that by choosing Rényi's parameter α , we can appropriately control information that is transferred only between selected parts of the underlying distributions. This, in turn, is a particularly potent tool for quantifying causal interdependencies in time series, where the knowledge of "black swan" events, such as spikes or sudden jumps, are of key importance. In this connection, we first prove that for Gaussian variables, Granger causality and Rényi transfer entropy are entirely equivalent. Moreover, we also partially extend these results to heavy-tailed α -Gaussian variables. These results allow establishing a connection between autoregressive and Rényi entropy-based information-theoretic approaches to data-driven causal inference. To aid our intuition, we employed the Leonenko et al. entropy estimator and analyzed Rényi's information flow between bivariate time series generated from two unidirectionally coupled Rössler systems. Notably, we find that Rényi's transfer entropy not only allows us to detect a threshold of synchronization but it also provides non-trivial insight into the structure of a transient regime that exists between the region of chaotic correlations and synchronization threshold. In addition, from Rényi's transfer entropy, we could reliably infer the direction of coupling and, hence, causality, only for coupling strengths smaller than the onset value of the transient regime, i.e., when two Rössler systems are coupled but have not yet entered synchronization. [ABSTRACT FROM AUTHOR]

The rolling bearing is a crucial component of the rotating machine, and it is particularly vital to ensure its normal operation. In addition, the selection of different category features will add uncertainty and bias to the classification results. In order to decrease the interference of these factors to fault diagnosis, a new method that automatically learns the features of the data combined with Markov transition field (MTF) and convolutional neural network (CNN) is proposed in this paper, namely MTF-CNN. The MTF contributes to convert the original time series into corresponding figures, and the CNN is used to extract the deep feature information in the figure to complete the fault diagnosis. The effectiveness of the proposed method is verified by two public data sets. The experimental results show that MTF-CNN can classify different types of faults, and the highest accuracy rate can reach 100%. Likewise, the classification accuracy of this method is higher than some existing methods. [ABSTRACT FROM AUTHOR]

Financial and economic time series forecasting has never been an easy task due to its sensibility to political, economic and social factors. For this reason, people who invest in financial markets and currency exchange are usually looking for robust models that can ensure them to maximize their profile and minimize their losses as much as possible. Fortunately, recently, various studies have speculated that a special type of Artificial Neural Networks (ANNs) called Recurrent Neural Networks (RNNs) could improve the predictive accuracy of the behavior of the financial data over time. This paper aims to forecast: (i) the closing price of eight stock market indexes; and (ii) the closing price of six currency exchange rates related to the USD, using the RNNs model and its variants: the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU). The results show that the GRU gives the overall best results, especially for the univariate out-of-sample forecasting for the currency exchange rates and multivariate out-of-sample forecasting for the stock market indexes. [ABSTRACT FROM AUTHOR]

Multivariable time series forecasting is an important topic of machine learning, and it frequently involves a complex mix of inputs, including static covariates and exogenous time series input. A targeted investigation of this input data is critical for improving prediction performance. In this paper, we propose the fusion transformer (FusFormer), a transformer-based model for forecasting time series data, whose framework fuses various computation modules for time series input and static covariates. To be more precise, the model calculation consists of two parallel stages. First, it employs a temporal encoder–decoder framework for extracting dynamic temporal features from time series data input, which analyzes and integrates the relative position information of sequence elements into the attention mechanism. Simultaneously, the static covariates are fed to the static enrichment module, which is inspired by gated linear units, to suppress irrelevant information and control the extent of nonlinear processing. Finally, the prediction results are calculated by fusing the outputs of the above two stages. Using Mooney viscosity forecasting as a case study, we demonstrate considerable forecasting performance improvements over existing methodologies and verify the effectiveness of each component of FusFormer via ablation analysis, and an interpretability use case is conducted to visualize temporal patterns of time series. The experimental results prove that FusFormer can achieve accurate Mooney viscosity prediction and improve the efficiency of the tire production process. [ABSTRACT FROM AUTHOR]

The Granger causality test is essential for detecting lead–lag relationships between time series. Traditionally, one uses a linear version of the test, essentially based on a linear time series regression, itself being based on autocorrelations and cross-correlations of the series. In the present paper, we employ a local Gaussian approach in an empirical investigation of lead–lag and causality relations. The study is carried out for monthly recorded financial indices for ten countries in Europe, North America, Asia and Australia. The local Gaussian approach makes it possible to examine lead–lag relations locally and separately in the tails and in the center of the return distributions of the series. It is shown that this results in a new and much more detailed picture of these relationships. Typically, the dependence is much stronger in the tails than in the center of the return distributions. It is shown that the ensuing nonlinear Granger causality tests may detect causality where traditional linear tests fail. [ABSTRACT FROM AUTHOR]

This paper shows if and how the predictability and complexity of stock market data changed over the last half-century and what influence the M1 money supply has. We use three different machine learning algorithms, i.e., a stochastic gradient descent linear regression, a lasso regression, and an XGBoost tree regression, to test the predictability of two stock market indices, the Dow Jones Industrial Average and the NASDAQ (National Association of Securities Dealers Automated Quotations) Composite. In addition, all data under study are discussed in the context of a variety of measures of signal complexity. The results of this complexity analysis are then linked with the machine learning results to discover trends and correlations between predictability and complexity. Our results show a decrease in predictability and an increase in complexity for more recent years. We find a correlation between approximate entropy, sample entropy, and the predictability of the employed machine learning algorithms on the data under study. This link between the predictability of machine learning algorithms and the mentioned entropy measures has not been shown before. It should be considered when analyzing and predicting complex time series data, e.g., stock market data, to e.g., identify regions of increased predictability. [ABSTRACT FROM AUTHOR]

In order to detect the incipient fault of rolling bearings and to effectively identify fault characteristics, based on amplitude-aware permutation entropy (AAPE), an enhanced method named hierarchical amplitude-aware permutation entropy (HAAPE) is proposed in this paper to solve complex time series in a new dynamic change analysis. Firstly, hierarchical analysis and AAPE are combined to excavate multilevel fault information, both low-frequency and high-frequency components of the abnormal bearing vibration signal. Secondly, from the experimental analysis, it is found that HAAPE is sensitive to the early failure of rolling bearings, which makes it suitable to evaluate the performance degradation of a bearing in its run-to-failure life cycle. Finally, a fault feature selection strategy based on HAAPE is put forward to select the bearing fault characteristics after the application of the least common multiple in singular value decomposition (LCM-SVD) method to the fault vibration signal. Moreover, several other entropy-based methods are also introduced for a comparative analysis of the experimental data, and the results demonstrate that HAAPE can extract fault features more effectively and with a higher accuracy. [ABSTRACT FROM AUTHOR]

The problem is dealt with by applying the penalized empirical risk minimization approach for a convex loss HT ht . The penalized adaptive spline approach is developed in the paper to tackle the data irregularity and is then applied to an unbiased synthetic transformation of HT ht . In [[7]], the authors consider a semiparametric stationary time series model of the form HT ht , where HT ht is a vector of random explanatory variables, HT ht is a temporal covariate, and HT ht is an autoregressive process. [Extracted from the article]