Modern methods and tools for working with time series

Time warping finds use in many fields of time series analysis, and it has been effectively implemented in many different application areas. Rather than focusing on a particular application area we approach the general problem definition, and employ principal curves, a powerful machine learning tool, to improve the noise robustness of existing time warping methods. The increasing noise level is the most important problem that leads to unnatural alignments. Therefore, we tested our approach in low signal-to-noise ratio (SNR) signals, and obtained satisfactory results. Moreover, for the signals denoised by principal curve projections we propose a differential equation-based time warping method, which has a comparable performance with lower computational complexity than the existing techniques.

В роботі запропоновано інформаційну технологію класифікації часових рядів, що мають фрактальні властивості, на основі методів машинного навчання. Вибір методу класифікації та відповідного набору ознак ґрунтується на мультифрактальних і самоподібних властивостях часових рядів. Як приклад, на основі запропонованої інформаційної технології проведена бінарна класифікація реалізацій нормальних та атакованих трафіків.

Period detection is one of the most important tasks of time series analysis. Different period detection methods have been proposed for different kind of time series. This paper proposes a period detection method for numerical time series, which is a generalization of the period detection methods for event time series and symbol time series. In the proposed method, fuzzy partition is first carried out on the value domain to build the events, with these events the original time series is then transformed into a multi-event time series; and from this multi-event time series a group of single-event time series are finally built. Period detection is done for each single-event time series. From these detections, the periodicity of the given time series can be asserted. This method can give not only the global period of a time series if the period exists, but also the partial period(s) if the period(s) exist(s). Thus, the proposed period detection method for numerical time series has wider application areas than that for even time series. Experiments on both the synthetic dataset and real dataset showed the effectiveness of the proposed method in this paper.

As science and technology continue to advance, sci-tech journals are developing rapidly, and the quality of these journals affects the development and progress of particular subjects. Whether sci-tech journals can be evaluated and predicted comprehensively and dynamically from multiple angles based on the current qualitative and quantitative evaluations of sci-tech journals is related to a rational adjustment of journal resource allocation and development planning. In this study, we propose a time series analysis task for the comprehensive and dynamic evaluation of sci-tech journals, construct a multivariate short-time multi-series time series dataset that contains 18 journal evaluation metrics, and build models based on machine learning and deep learning methods commonly used in the field of time series analysis to carry out training and testing experiments on the dataset. We compare and analyze the experimental results to confirm the generalizability of these methods for the comprehensive dynamic evaluation of journals and find the LSTM model built on our dataset produced the best performance (MSE: 0.00037, MAE: 0.01238, accuracy based on 80% confidence: 72.442%), laying the foundation for subsequent research on this task. In addition, the dataset constructed in this study can support research on the co-analysis of multiple short time series in the field of time series analysis.

Time series methods in the monitoring of intracranial pressure. Part 1: Problems, suggestions for a monitoring scheme and review of appropriate techniques

The current state of science and technology is characterized by a variety of methods and approaches to solving various tasks, including in the fields of time series analysis and computer vision. This abstract explores a novel approach to the classification of time series based on the analysis of brain activity using recurrent diagrams and deep neural networks. The work begins with an overview of recent achievements in the field of time series analysis and the application of machine learning methods. The importance of time series classification in various domains, including medicine, finance, technology, and others, is em-phasized. Next, the methodology is described, in which time series are transformed into gray-scale images using recurrent diagrams. The key idea is to use recurrent diagrams to visualize the structure of time series and identify their nonlinear properties. This transformed informa-tion serves as input data for deep neural networks. An important aspect of the work is the selection of deep neural networks as classifiers for the obtained images. Specifically, residual neural networks are applied, known for their ability to effectively learn and classify large volumes of data. The structure of such networks and their advantages over other architectures are discussed. The experimental part of the work describes the use of a dataset of brain activity, which includes realizations from different states of a person, including epileptic seizures. The ob-tained visualization and classification methods are applied for binary classification of EEG realizations, where the class of epileptic seizure is compared with the rest. The main evalua-tion metrics for classification are accuracy, precision, recall, and F1-score. The experimental results demonstrate high classification accuracy even for short EEG realizations. The quality metrics of classification indicate the potential effectiveness of this method for automated di-agnosis of epileptic seizures based on the analysis of brain signals. The conclusions highlight the importance of the proposed approach and its potential usefulness in various domains where time series classification based on the analysis of brain activity and recurrent diagrams is required.

Deep learning has become a hot research topic in the field of time series analysis and data mining. Training models often requires balanced and large data sets, but on the one hand, the number of different types of data in time series data sets is often extremely imbalanced, on the other hand, some time series data are often difficult to collect. Therefore, it is necessary to augment the training data before training the deep learning model. SMOTE is a data augmentation method widely used in preprocessing imbalanced data sets, but the classical SMOTE method does not satisfy the characteristics of time series when processing time series, so it is not effective when applied to time series data sets. To address this point, we propose an oversampling data augmentation method based on dynamic time warping—DTW-SMOTE. For the possible phase shifts of time series with the same characteristics, this method uses dynamic time warping to obtain more reasonable similarity between different time series, which improves the classical SMOTE method and achieves data augmentation for time series data. We conducted comparison experiments using two models with different architectures: ResNet and LSTM. The experimental results show that the performance of the above models is significantly improved after training with the DTW-SMOTE method pre-processed dataset.

Access to labeled time series data is often limited in the real world, which constrains the performance of deep learning models in the field of time series analysis. Data augmentation is an effective way to solve the problem of small sample size and imbalance in time series datasets. The two key factors of data augmentation are the distance metric and the choice of interpolation method. SMOTE does not perform well on time series data because it uses a Euclidean distance metric and interpolates directly on the object. Therefore, we propose a DTW-based synthetic minority oversampling technique using siamese encoder for interpolation named DTWSSE. In order to reasonably measure the distance of the time series, DTW, which has been verified to be an effective method forts, is employed as the distance metric. To adapt the DTW metric, we use an autoencoder trained in an unsupervised self-training manner for interpolation. The encoder is a Siamese Neural Network for mapping the time series data from the DTW hidden space to the Euclidean deep feature space, and the decoder is used to map the deep feature space back to the DTW hidden space. We validate the proposed methods on a number of different balanced or unbalanced time series datasets. Experimental results show that the proposed method can lead to better performance of the downstream deep learning model.

On behalf of both the editorial board and the readership of the Journal of Time Series Analysis, I would like to take this opportunity to thank Professor Andrew Harvey for his many years of dedicated service to our journal. Andrew stepped down as a co-editor with effect from 31 May 2018. I am, however, delighted to announce that Andrew has agreed to remain on the editorial board as an advisory editor, as from 1 June 2018. Andrew was first appointed to the editorial board of the Journal of Time Series Analysis in 1989. I have greatly benefitted from his support, help and advice since I took over as editor of the journal. I would like to personally thank Andrew for all he has done for me and for our journal. Shiqing Ling is Professor of at the Hong Kong University of Science and Technology. His research involves change-point problems, empirical processes, financial econometrics, large sample theory, long memory time series, non-stationary time series and nonlinear time series. He is a leading expert in the field of time series analysis and has made a number of fundamental contributions to the area, including asymptotic theory of unit-root GARCH process, inference of GARCH-type models and threshold time series model, and proposed the self-weight estimation method for heavy-tailed time series models.

Whether or not a time series is weakly stationary has long been a question of major interest in the field of time series analysis. Stationary time series can be sufficiently described by means of autoregressive moving average (ARMA) processes. When modelling temporal correlations of GNSS observation noise, the applicability of ARMA processes depends on the stationarity of residual time series from GNSS data analysis. According to the property that stationary processes have homogenous variances, statistical inferences on stationarity can be made by testing for homogeneity of variance (HOV). In addition, considering a time series as a realisation of a stochastic process, stationarity can be assessed by testing for stochastic trends using unit root tests. Based on representative data simulations, this paper analyses the empirical size and power of commonly used HOV and unit root tests. The results show that the performance of the HOV test is strongly affected by serial correlations, whereas the unit root test produces high power without significant size distortions.

This paper gives an overview of time series ideas and methods used in public health and biomedical research. A time series is a sequence of observations made over time. Examples in public health include daily ozone concentrations, weekly admissions to an emergency department, or annual expenditures on health care in the United States. Time series models are most commonly used in regression analysis to describe the dependence of the response at each time on predictor variables including covariates and possibly previous values in the series. For example, Bell et al. ( 2 ) use time series methods to regress daily mortality in U.S. cities on concentrations of particulate air pollution. Time series methods are necessary to make valid inferences from data by accounting for the correlation among repeated responses over time.

The case-crossover design was introduced in epidemiology 15 years ago as a method for studying the effects of a risk factor on a health event using only cases. The idea is to compare a case's exposure immediately prior to or during the case-defining event with that same person's exposure at otherwise similar "reference" times. An alternative approach to the analysis of daily exposure and case-only data is time series analysis. Here, log-linear regression models express the expected total number of events on each day as a function of the exposure level and potential confounding variables. In time series analyses of air pollution, smooth functions of time and weather are the main confounders. Time series and case-crossover methods are often viewed as competing methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for overdispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using standard log-linear model diagnostics.

OBITUARY

Due to the random walk property of the financial time series, it is very difficult to develop a system that solves real financial application problems. However, if we obtain a time series cluster with a high degree of co-movement, it will be very useful for developing financial application systems. This paper proposes a clustering method that finds time series clusters with higher degrees of co-movement than the existing time series clustering algorithms. There is a problem in that clusters generated by the existing time series clustering algorithms contain too much noise with a low degree of co-movement. We propose a clustering method that solves the problem. This method is performed in the following steps. In the Data Preprocessing step, it performs Average Scaling, Weighted Time Series Transformation, Dimension Reduction, and Cluster Diameter Estimation. In the Clustering Step, it performs Preclustering and Refinement. Experiments show that our clustering method has higher performance than the existing time series clustering algorithms in finding clusters with high degree of co-movement.

The existing pattern matching methods of multivariate time series can hardly measure the similarity of multivariate hydrological time series accurately and efficiently. Considering the characteristics of multivariate hydrological time series, the continuity and global features of variables, we proposed a pattern matching method, PP-DTW, which is based on dynamic time warping. In this method, the multivariate time series is firstly segmented, and the average of each segment is used as the feature. Then, PCA is operated on the feature sequence. Finally, the weighted DTW distance is used as the measure of similarity in sequences. Carrying out experiments on the hydrological data of Chu River, we conclude that the pattern matching method can effectively describe the overall characteristics of the multivariate time series, which has a good matching effect on the multivariate hydrological time series.