Characteristics Of Time Series Research Articles

Remaining useful life prediction based on time-series features and conformalized quantile regression

Abstract The remaining useful life (RUL) prediction is a key task in the field of prognostics and health management (PHM) and plays a crucial role in preventive maintenance tasks. Traditional prediction methods have mostly focused on point prediction issues, neglecting the uncertain factors in the prediction task, thus failing to ensure the credibility of the prediction. In light of this, this paper focuses on improving the accuracy of point prediction models for RUL and interval prediction issues, proposing the introduction of multi-scale convolutional neural networks (MCNN), decomposed time-sequential linear layers (DL), and conformal quantile regression (CQR) techniques into the RUL prediction task of aero-engines. The aim is to provide timely and accurate failure warnings for aero engines, effectively ensure their reliability and safety, and reduce maintenance costs throughout their life cycle. In response to the limitations of current point prediction models in capturing the temporal features of life data, a MCNN-DL-based RUL prediction model is proposed to capture life data's long-term trends and local variations for precise point predictions. Furthermore, an interval estimation approach for RUL is presented, which integrates the MCNN-DL model with CQR to account for prediction uncertainty. Finally, the method in this paper is verified using the CMAPSS dataset, and the results show that the method has achieved excellent results in both RUL point prediction and interval prediction tasks.

Extraction of Garlic in the North China Plain Using Multi-Feature Combinations from Active and Passive Time Series Data

Garlic constitutes a significant small-scale agricultural commodity in China. A key factor influencing garlic prices is the planted area, which can be accurately and efficiently determined using remote sensing technology. However, the spectral characteristics of garlic and winter wheat are easily confused, and the widespread intercropping of these crops in the study area exacerbates this issue, leading to significant challenges in remote sensing image analysis. Additionally, remote sensing data are often affected by weather conditions, spatial resolution, and revisit frequency, which can result in delayed and inaccurate area extraction. In this study, historical data were utilized to restore Sentinel-2 remote sensing images, aimed at mitigating cloud and rain interference. Feature combinations were devised, incorporating two vegetation indices into a comprehensive time series, along with Sentinel-1 synthetic aperture radar (SAR) time series and other temporal datasets. Multiple classification combinations were employed to extract garlic within the study area, and the accuracy of the classification results was systematically analyzed. First, we used passive satellite imagery to extract winter crops (garlic, winter wheat, and others) with high accuracy. Second, we identified garlic by applying various combinations of time series features derived from both active and passive remote sensing data. Third, we evaluated the classification outcomes of various feature combinations to generate an optimal garlic cultivation distribution map for each region. Fourth, we developed a garlic fragmentation index to assess the impact of landscape fragmentation on garlic extraction accuracy. The findings reveal that: (1) Better results in garlic extraction can be achieved using active–passive time series remote sensing. The performance of the classification model can be further enhanced by incorporating short-wave infrared bands or spliced time series data into the classification features. (2) Examination of garlic cultivation fragmentation using the garlic fragmentation index aids in elucidating variations in accuracy across the study area’s six counties. (3) Comparative analysis with validation samples demonstrated superior garlic extraction outcomes from the six primary garlic-producing counties of the North China Plain in 2021, achieving an overall precision exceeding 90%. This study offers a practical exploration of target crop identification using multi-source remote sensing data in mixed cropping areas. The methodology presented here demonstrates the potential for efficient, cost-effective, and accurate garlic classification, which is crucial for improving garlic production management and optimizing agricultural practices. Moreover, this approach holds promise for broader applications, such as nationwide garlic mapping.

QIGTD: identifying critical genes in the evolution of lung adenocarcinoma with tensor decomposition

BackgroundIdentifying critical genes is important for understanding the pathogenesis of complex diseases. Traditional studies typically comparing the change of biomecules between normal and disease samples or detecting important vertices from a single static biomolecular network, which often overlook the dynamic changes that occur between different disease stages. However, investigating temporal changes in biomolecular networks and identifying critical genes is critical for understanding the occurrence and development of diseases.MethodsA novel method called Quantifying Importance of Genes with Tensor Decomposition (QIGTD) was proposed in this study. It first constructs a time series network by integrating both the intra and inter temporal network information, which preserving connections between networks at adjacent stages according to the local similarities. A tensor is employed to describe the connections of this time series network, and a 3-order tensor decomposition method was proposed to capture both the topological information of each network snapshot and the time series characteristics of the whole network. QIGTD is also a learning-free and efficient method that can be applied to datasets with a small number of samples.ResultsThe effectiveness of QIGTD was evaluated using lung adenocarcinoma (LUAD) datasets and three state-of-the-art methods: T-degree, T-closeness, and T-betweenness were employed as benchmark methods. Numerical experimental results demonstrate that QIGTD outperforms these methods in terms of the indices of both precision and mAP. Notably, out of the top 50 genes, 29 have been verified to be highly related to LUAD according to the DisGeNET Database, and 36 are significantly enriched in LUAD related Gene Ontology (GO) terms, including nuclear division, mitotic nuclear division, chromosome segregation, organelle fission, and mitotic sister chromatid segregation.ConclusionIn conclusion, QIGTD effectively captures the temporal changes in gene networks and identifies critical genes. It provides a valuable tool for studying temporal dynamics in biological networks and can aid in understanding the underlying mechanisms of diseases such as LUAD.

A demand forecasting system of product categories defined by their time series using a hybrid approach of ensemble learning with feature engineering

AbstractRetail companies face major problems in the estimation of their product’s future demand due to the high diversity of sales behavior that each good presents. Different forecasting models are implemented to meet the demand requirements for efficient inventory management. However, in most of the proposed works, a single model approach is applied to forecast all products, ignoring that some methods are better adapted for certain features of the demand time series of each product. The proposed forecasting system addresses this problem, by implementing a two-phase methodology that initially clusters the products with the application of an unsupervised learning approach using the extracted demand features of each good, and then, implements a second phase where, after a feature engineering process, a set of different forecasting methods are evaluated to identify those with best performs for each cluster. Finally, ensemble machine learning models are implemented using the top-performing models of each cluster to carry out the demand estimation. The results indicate that the proposed forecasting system improves the demand estimation over the single forecasting approaches when evaluating the R2, MSE, and MASE quality measures.

Clustering and Interpretation of time-series trajectories of chronic pain using evidential c-means

The most well-known unsupervised classification algorithms allow for the identification of hard or probabilistic partitions. However, when working with complex datasets such as those found in the healthcare domain, it is important to note that these partitions may have limitations, particularly when considering the uncertainty associated with medical data. Indeed, these algorithms do not account for modeling outliers, imprecise, or uncertain observations. In this study, we focused on analyzing time series of barometers attributes related to pain intensity in individuals with chronic pain. Our goal was to identify different typologies of care trajectories, highlighting distinct trajectories of chronic pain through clustering techniques. We propose a soft clustering approach based on feature extraction and selection from sequential data, aiming to improve interpretability and enhance the performance of the clustering procedure. Time series feature extraction and selection effectively handles complex and noisy data, improving interpretability and clustering performance. Evidential soft clustering models data uncertainty and imprecision, providing a better representation of nuances and variations in complex, raw data. The first step involves extracting features from the available time series and selecting the most important attributes. For this purpose, we use a time series feature extractor (Tsfresh) and unsupervised feature selection methods, including unsupervised Random Forest, Laplacian Score, and unsupervised Spectral Feature Selection. The second step involves using the evidential c-means (ECM) clustering algorithm on the extracted attributes. The ECM method, based on belief functions, allows for generating a credal partition that has the ability to model various forms of uncertainty. This partition can then be transformed into a hard partition to study individuals based on this uncertainty criterion. The results reveal the existence of two clusters of chronic pain related to discomfort and well-being, exhibiting excellent separability and compactness. Additionally, an uncertain cluster emerges grouping patients with intermediate characteristics. The interpretability of the determined partitions through descriptive analysis, statistical tests, and repeated measures multinomial regression on clinical and demographic data allowed us to determine the profile of patients in the identified trajectories.

A Study on Historical Big Data Analysis of Surface Ecological Damage in the Coal Mining Area of Lvliang City Based on Two Mining Modes

Coal mining inevitably causes damage to the surface ecological environment. In response to the characteristics of multiple factors, wide scope, and long time series of surface ecological environment damage in coal mining subsidence areas, how to integrate multiple data sources and monitoring methods to achieve monitoring and trend analysis of ecological damage throughout the entire mining cycle still needs to be studied. In addition, the 110 mining method provides an innovative method for underground coal mining to reduce its surface ecological damage, but the differences in surface damage between the two mining modes and the effectiveness of the 110 method in realizing surface ecological damage-reducing mining still need to be studied in depth. Therefore, this study takes the surface ecological damage in the mining area of Lvliang City, a typical resource city in Shanxi Province, China, as the object. It establishes a four-in-one “Satellite–UAV–Ground–Underground” information monitoring method, proposes a historical big data evolution analysis method, constructs three spatial scales of historical big databases, clarifies the current situation and development trend of damage in coal mining areas in Lvliang City and explores the differences in surface ecological environment damage characteristics in coal mining areas based on the 121 and 110 mining methods. The results show that: (1) The existing coal mining subsidence area in Lvliang City is as high as 92,191.47 hectares, and it is expected to continue to increase to 130,739.55 hectares in the future 2035, with a growth rate of 41.812%, which realizes the goals of mapping the current situation, retracing the history and predicting the future of the ecological damage of the surface in Lvliang City. (2) The surface NDVI of the 110 working face is restored to the average level of the mining area faster than that of the 121 working face. The surface crack width, step displacement, length, distribution density, and surface settlement height of the 110 working face are all smaller than those of the 121 working face. It has been verified that the unique top-cutting and swelling filling effect of the 110 methods can effectively reduce the ecological damage caused by coal mining subsidence. And its widespread application can effectively realize the ecological environmental protection of the coal mine area and contribute to the high-quality development of the coal industry in Lvliang City.

Optimal segmentation of non-linear and non-stationary time series based on fractal dimension and Poincare section and its application in solving EEG-signal

Non-linearity and non-stationarity characteristics in physiological and biological time series limit the reliability of conventional analysis. The main challenge in pattern recognition problems is determining the Optimal-Window-Duration (OWD) for segmenting these time series. Our study presents an innovative algorithm, based on Individual-Optimal-Segmentation (IOS), which integrates chaos theory using fractal dimension, and Poincare section into the estimation of the OWD for segmenting time series with non-linear and non-stationary characteristics. In the logistic map case study, the IOS algorithm proved to be effective in detecting cycles in a range of numerical examples, from period-2 to chaotic behavior. So that its performance was superior to previous approaches, especially when it comes to detecting chaotic behaviors. Furthermore, the combination of the IOS algorithm with the Welch signal processing method shows promise in identifying abnormal Power-Spectral-Density (PSD) curves related to Beta and Gamma rhythms in depression diagnosis scenarios. The generated depression diagnosis system attained an accuracy (%) of 99.07±0.35 (with 2-channel) using the Monte Carlo simulation method. These findings suggest a potentially valuable tool for addressing segmentation challenges in time series analysis, particularly in contexts involving complex, dynamic data. While, it is suggested that future research investigate the computational efficiency and robustness of the IOS algorithm when handling large-scale or real-time data and increase its application in various fields in data science and signal processing. Furthermore, expanding the application range of the IOS algorithm for other pattern recognition problems with physiological or biological data can strengthen the generalizability and practical application of the algorithm.

Hierarchical classification for improving parcel-scale crop mapping using time-series Sentinel-1 data

Parcel-scale crop classification utilizing time-series satellite observations is of significant importance in precision agriculture. The prior knowledge that crop types can be organized in a hierarchical tree structure is beneficial for improving crop classification. Moreover, the crop hierarchy aligns with the coarse-to-fine cognitive process of geographic scenes. Based on the crop hierarchy, this study developed a general hierarchical classification framework for enhancing crop mapping using time-series Sentinel-1 data. Central to this method is a deep-learning-based hierarchical classification model that explores and makes use of crop hierarchical knowledge. First, preprocessed Sentinel-1 data were geometrically overlaid onto farmland parcel maps to derive parcel-scale time-series features. Second, we constructed a hierarchical crop type system for study areas based on the crop phenology of labeled crop-type samples. Third, we developed a deep-learning-based hierarchical classification model to identify crop types for each parcel, to generate final crop-type classification maps. The proposed approach was further discussed and verified through the implementation of parcel-scale time-series crop hierarchical classifications in a study area in France with farmland parcel maps and time-series Sentinel-1 data. The classification results, indicating significant improvements greater than 4.0% in overall accuracy and 5.0% in F1 score over comparative methods, demonstrated the effectiveness of the proposed method in learning multi-scale time-series features for hierarchical crop classification utilizing Sentinel-1 data sequences.

Feasibility analysis of using short-term rainfall time series to evaluate rainwater harvesting systems considering climate change

Employing recent short-term historical rainfall data may enhance the performance of rainwater harvesting systems (RWHs) in response to climate change. However, this assumption lacks extensive research, and the evaluation of RWHs currently relies on long-term historical rainfall time series. This study evaluates the feasibility of this assumption and aims to identify the optimal rainfall time series for evaluating RWH performance under climate change. We evaluated RWHs in residential buildings across 16 Japanese cities utilizing historical rainfall time series of varying lengths and 30-year predicted rainfall time series. The minimum rainfall time series length was obtained based on the similarity index between the evaluation results for historical and future periods. The corresponding optimal series can be determined from the distribution of similarity indices in the minimum length. Finally, we introduce supply pressure indices (SPIs) to summarize the rainfall characteristics of these optimal rainfall time series. Our findings highlight that the minimum rainfall time series length increased from 1 year to 30 years as building non-potable water demand rose and city locations varied. Utilizing rainfall time series incorporating recent rainfall data yielded more dependable evaluation results for RWHs under climate change. These optimal rainfall time series share common characteristics with SPIs ranging from 5.37 to 17.87 mm/d, contingent on the local rainfall patterns. Our study concludes that utilizing recent short-term historical rainfall data is feasible to evaluate and design RWHs under climate change.

Learning the feature distribution similarities for online time series anomaly detection

Identifying anomalies in multi-dimensional sequential data is crucial for ensuring optimal performance across various domains and in large-scale systems. Traditional contrastive methods utilize feature similarity between different features extracted from multidimensional raw inputs as an indicator of anomaly severity. However, the complex objective functions and meticulously designed modules of these methods often lead to efficiency issues and a lack of interpretability. Our study introduces a structural framework called SimDetector, which is a Local–Global Multi-Scale Similarity Contrast network. Specifically, the restructured and enhanced GRU module extracts more generalized local features, including long-term cyclical trends. The multi-scale sparse attention module efficiently extracts multi-scale global features with pattern information. Additionally, we modified the KL divergence to suit the characteristics of time series anomaly detection, proposing a symmetric absolute KL divergence that focuses more on overall distribution differences. The proposed method achieves results that surpass or approach the State-of-the-Art (SOTA) on multiple real-world datasets and synthetic datasets, while also significantly reducing Multiply-Accumulate Operations (MACs) and memory usage.

A comparison between machine and deep learning models on high stationarity data

Advances in sensor, computing, and communication technologies are enabling big data analytics by providing time series data. However, conventional models struggle to identify sequence features and forecast accuracy. This paper investigates time series features and shows that some machine learning algorithms can outperform deep learning models. In particular, the problem analyzed concerned predicting the number of vehicles passing through an Italian tollbooth in 2021. The dataset, composed of 8766 rows and 6 columns relating to additional tollbooths, proved to have high stationarity and was treated through machine learning methods such as support vector machine, random forest, and eXtreme gradient boosting (XGBoost), as well as deep learning through recurrent neural networks with long short-term memory (RNN-LSTM) cells. From the comparison of these models, the prediction through the XGBoost algorithm outperforms competing algorithms, particularly in terms of MAE and MSE. The result highlights how a shallower algorithm than a neural network is, in this case, able to obtain a better adaptation to the time series instead of a much deeper model that tends to develop a smoother prediction.

Multifractal characterization of meteorological to agricultural drought propagation over India

Agricultural drought affects the regional food security and thus understanding how meteorological drought propagates to agricultural drought is crucial. This study examines the temporal scaling trends of meteorological and agricultural drought data over 34 Indian meteorological sub-divisions from 1981 to 2020. A maximum Pearson's correlation coefficient (MPCC) derived between multiscale Standardised Precipitation Index (SPI) and monthly Standardised Soil Moisture Index (SSMI) time series was used to assess the seasonal as well as annual drought propagation time (DPT). The multifractal characteristics of the SPI time series at a time scale chosen from propagation analysis as well as the SSMI-1 time series were further examined using Multifractal Detrended Fluctuation Analysis (MF-DFA). Results reveal longer average annual DPT in arid and semi-arid regions like Saurashtra and Kutch (~ 6 months), Madhya Maharashtra (~ 5 months), and Western Rajasthan (~ 6 months), whereas, humid regions like Arunachal Pradesh, Assam and Meghalaya, and Kerala exhibit shorter DPT (~ 2 months). The Hurst Index values greater/less than 0.5 indicates the existence of long/short-term persistence (LTP/STP) in the SPI and SSMI time series. The results of our study highlights the inherent connection among drought propagation time, multifractality, and regional climate variations, and offers insights to enhance drought prediction systems in India.

Time series features and fuzzy memberships combination for time series classification

Time series classification is an increasingly attractive field with the appearance of new problems in an expanding digitalized world. Most of the proposals in the state-of-the-art have focused just on improving the results’ performance, leaving interpretability on a secondary level. The available interpretable proposals do not provide competitive results, which is an issue to be addressed. This paper introduces a new fuzzy feature-based time series classification method, which joins the ability of time series features to capture essential information about the time series with Fuzzy logic. This proposal allows the fuzzy-based approach to incorporate global information about the behavior of time series in the membership calculation with the aim of improving the performance and interpretability of the results by using an interpretable classifier. The proposed method has been evaluated over the 112 state-of-the-art time series classification datasets from the UCR repository, and the results obtained show a better performance. Furthermore, the combination of time series features and fuzzy memberships has also increased the interpretability of final models.

Applying transfer learning to address data scarcity: A case study on LWD gamma ray depth-lag remediation from Volve to another gasfield

In petroleum engineering, obtaining comprehensive subsurface data is challenging due to significant costs and protective regulations. This complexity often restricts the extensive use of data-driven approaches. This study investigates the applicability of deep learning with transfer learning, to tackle this prominent challenges. Grounded in a practical fusion of engineering and geology, we address a specific issue: the depth-lagged measurements of the Logging While Drilling (LWD) tool's Gamma Ray detector, owing to its position meters behind the drill bit. Our approach uniquely integrates real-time drilling engineering parameters with the delayed Gamma time-series features, aiming to predictively correct these lagged measurements.The research extends from the Volve oil field in Norway to a distinct gas field in China, covering a wide geographical range and diverse geological conditions. The results indicated that in environments with limited data, transfer learning could enhance accuracy by up to 13% compared to traditional methods. This transition tests transfer learning's adaptability to various gasfield settings, demonstrating its potential to enhance model accuracy in data-limited environments and advocating for data-driven approaches in petroleum engineering.

Cross-domain diagnosis for polymer electrolyte membrane fuel cell based on digital twins and transfer learning network✰

Existing research on fault diagnosis for polymer electrolyte membrane fuel cells (PEMFC) has advanced significantly, yet performance is hindered by variations in data distributions and the requirement for extensive fault data. In this study, a cross-domain adaptive health diagnosis method for PEMFC is proposed, integrating the digital twin model and transfer convolutional diagnosis model. A physical-based high-fidelity digital twin model is developed to obtain diverse and high-quality datasets for training diagnosis method. To extract long-term time series features from the data, a temporal convolutional network (TCN) is proposed as a pre-trained diagnosis model for the source domain, with feature extraction layers that can be reused to the transfer learning network. It is demonstrated that the proposed pre-trained model can hold the ability to accurately diagnose the various fuel cell faults, including pressure, drying, flow, and flooding faults, with 99.92 % accuracy, through the effective capture of the long-term dependencies in time series data. Finally, a domain adaptive transfer convolutional network (DATCN) is established to improve the diagnosis accuracy across diverse fuel cells by learning domain-invariant features. The results show that the DATCN model, tested on three different target domain devices with adversarial training using only 10 % normal data, can achieve an average accuracy of 98.5 % (30 % improved over traditional diagnosis models). This proposed method provides an effective solution for accurate cross-domain diagnosis of PEMFC devices, significantly reducing the reliance on extensive fault data.

A study of online academic risk prediction based on neural network multivariate time series features

SummaryNeural networks are becoming increasingly widely used in various fields, especially for academic risk forecasts. Academic risk prediction is a hot topic in the field of big data in education that aims to identify and help students who experience great academic difficulties. In recent years, the use of machine learning algorithms and deep learning algorithms to achieve academic risk prediction has garnered increased attention and development. However, most of these studies use nontime series data as features for prediction, which are slightly insufficient in terms of timeliness. Therefore, this article focuses on time series data features that are more expressive of changes in students' learning status and uses multivariate time series data as predictive features. This article proposes a method based on multivariate time series features and a neural network to predict academic risk. The method includes three steps: first, the multivariate time series feature is extracted from the interaction records of the students' online learning platforms; second, the multivariate time series feature transformation model ROCKET is applied to convert the multivariate time series feature into a new feature; third, the new feature is converted into a final prediction result using a linear classification model. Comparative tests show that the proposed method has high effectiveness.

An energy management strategy for fuel cell hybrid electric vehicle based on HHO-BiLSTM-TCN-self attention speed prediction

This research aims to improve the performance and economics of fuel cell hybrid electric vehicles (FCHEVs), validated and established by introducing an innovative energy management strategy (EMS) based on a speed-predictive fusion model. Firstly, a mixed prediction model was built based on BiLSTM, TCN, and Self-attention (SA) mechanism to accurately search, capture and fuse multi-granularity features in time series. Then, Harris-Hawk Optimization (HHO) was used to optimize the dropout rate and model learning rate of the combined BiLSTM-TCN-SA time series model to improve the prediction accuracy and generalization ability of the model. Finally, stochastic model predictive control was combined with BiLSTM-TCN-SA to form SMPC-NSGA III algorithm, which was used for multi-objective optimization of fuel economy, fuel cell durability and battery durability. In this study, the effectiveness of the proposed strategy was verified under the condition of CLTC-P driving cycle. The experimental results showed that RMSE and R2 of HHO-BiLSTM-TCN-SA velocity prediction model are 1.169 and 0.998, respectively. In addition, the output of the model is within the confidence interval of 97.5 % of the real speed, and there is no significant difference, which is statistically significant. Under the SMPC-NSGA III strategy, the average efficiency of the fuel cell was increased by 12 % and 1 % respectively.

Complex Emotion Dynamics Contribute to the Prediction of Depression: A Machine Learning and Time Series Feature Extraction Approach

Complex Emotion Dynamics Contribute to the Prediction of Depression: A Machine Learning and Time Series Feature Extraction Approach

Nonlinearity in affect dynamics persists after accounting for the valence of daily-life events.

In recent years, increased attention has gone to studying nonlinear characteristics of affective time series. An example of such nonlinear features is multimodality-the presence of more than one mode in an affective time series-which might mark the presence of discrete-like transitions between one and another affective state. In an attempt to capture these nonlinear features, Loossens et al. (2020) proposed the Affective Ising Model (AIM) as a model of affect dynamics. This model was validated on daily-life data, but these data did not contain any information on potential environmental factors that might have influenced a participant's affective state. Unfortunately, this omission may have led to erroneously concluding that nonlinearity is a defining characteristic of the affective system, even when it is solely driven by extrinsic influences. To accommodate this limitation, we applied the AIM on daily-life data in which the valence of such external events was measured. Overall, we found that nonlinearity persisted after accounting for the valence of daily-life events, suggesting that nonlinearity is a defining characteristic of affect and should thus be accounted for. Interestingly, this effect was more pronounced for composite compared to single-item measures of affect. While in line with previous research, these results should be replicated in a larger, more representative sample. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

An endogenous evolution mechanism model of asset prices based on time-varying risk aversion coefficient

In the traditional heterogeneous agent model, investors are assumed to be risk averse, and the wealth expected utility function maximization principle is used to form the optimal asset quantity demand. In such models, the risk aversion coefficient of investors is often assumed to be constant. This paper considers that the risk aversion coefficient of investors is time-varying and changes with the change of wealth, and establishes an endogenous evolutionary mechanism model formed by fundamental analysts, technical analysts, and market makers. Compared with the fixed risk aversion coefficient model, this paper analyzes the investor’s behavior, the interaction between investor behaviors, and the influence of different types of investors on the stability of the market. At the same time, we test asset price and asset behavior and conclude that investor behavior affects the stability of the system model. The numerical simulation of the corresponding stochastic model shows that the model can simulate the basic characteristics of financial time series, such as the partial peak and thick tail of asset return series, and the long memory of fluctuations.