This article explores the required amount of time series points from a high-speed traffic network to accurately estimate the Hurst exponent. The methodology consists in designing an experiment using estimators that are applied to time series, followed by addressing the minimum amount of points required to obtain accurate estimates of the Hurst exponent in real-time. The methodology addresses the exhaustive analysis of the Hurst exponent considering bias behavior, standard deviation, mean square error, and convergence using fractional gaussian noise signals with stationary increases. Our results show that the Whittle estimator successfully estimates the Hurst exponent in series with few points. Based on the results obtained, a minimum length for the time series is empirically proposed. Finally, to validate the results, the methodology is applied to real traffic captures in a high-speed network based on the IEEE 802.3ab standard.
We propose a three-stage framework for forecasting high-dimensional time-series data. Our method first estimates parameters for each univariate time series. Next, we use these parameters to cluster the time series. These clusters can be viewed as multivariate time series, for which we then compute parameters. The forecasted values of a single time series can depend on the history of other time series in the same cluster, accounting for intra-cluster similarity while minimizing potential noise in predictions by ignoring inter-cluster effects. Our framework -- which we refer to as "cluster-and-conquer" -- is highly general, allowing for any time-series forecasting and clustering method to be used in each step. It is computationally efficient and embarrassingly parallel. We motivate our framework with a theoretical analysis in an idealized mixed linear regression setting, where we provide guarantees on the quality of the estimates. We accompany these guarantees with experimental results that demonstrate the advantages of our framework: when instantiated with simple linear autoregressive models, we are able to achieve state-of-the-art results on several benchmark datasets, sometimes outperforming deep-learning-based approaches.
Time series classification problems exist in many fields and have been explored for a couple of decades. However, they still remain challenging, and their solutions need to be further improved for real-world applications in terms of both accuracy and efficiency. In this paper, we propose a hybrid neural architecture, called Self-Attentive Recurrent Convolutional Networks (SARCoN), to learn multi-faceted representations for univariate time series. SARCoN is the synthesis of long short-term memory networks with self-attentive mechanisms and Fully Convolutional Networks, which work in parallel to learn the representations of univariate time series from different perspectives. The component modules of the proposed architecture are trained jointly in an end-to-end manner and they classify the input time series in a cooperative way. Due to its domain-agnostic nature, SARCoN is able to generalize a diversity of domain tasks. Our experimental results show that, compared to the state-of-the-art approaches for time series classification, the proposed architecture can achieve remarkable improvements for a set of univariate time series benchmarks from the UCR repository. Moreover, the self-attention and the global average pooling in the proposed architecture enable visible interpretability by facilitating the identification of the contribution regions of the original time series. An overall analysis confirms that multi-faceted representations of time series aid in capturing deep temporal corrections within complex time series, which is essential for the improvement of time series classification performance. Our work provides a novel angle that deepens the understanding of time series classification, qualifying our proposed model as an ideal choice for real-world applications.
The paper is focused on the forecasting method for time series groups with the use of algorithms for cluster analysis. $K$-means algorithm is suggested to be a basic one for clustering. The coordinates of the centers of clusters have been put in correspondence with summarizing time series data the centroids of the clusters. A description of time series, the centroids of the clusters, is implemented with the use of forecasting models. They are based on strict binary trees and a modified clonal selection algorithm. With the help of such forecasting models, the possibility of forming analytic dependences is shown. It is suggested to use a common forecasting model, which is constructed for time series the centroid of the cluster, in forecasting the private (individual) time series in the cluster. The promising application of the suggested method for grouped time series forecasting is demonstrated.
Few-shot Time Series Classification (few-shot TSC) is a challenging problem in time series analysis. It is more difficult to classify when time series of the same class are not completely consistent in spectral domain or time series of different classes are partly consistent in spectral domain. To address this problem, we propose a novel method named Spectral Propagation Graph Network (SPGN) to explicitly model and propagate the spectrum-wise relations between different time series with graph network. To the best of our knowledge, SPGN is the first to utilize spectral comparisons in different intervals and involve spectral propagation across all time series with graph networks for few-shot TSC. SPGN first uses bandpass filter to expand time series in spectral domain for calculating spectrum-wise relations between time series. Equipped with graph networks, SPGN then integrates spectral relations with label information to make spectral propagation. The further study conveys the bi-directional effect between spectral relations acquisition and spectral propagation. We conduct extensive experiments on few-shot TSC benchmarks. SPGN outperforms state-of-the-art results by a large margin in $4\% \sim 13\%$. Moreover, SPGN surpasses them by around $12\%$ and $9\%$ under cross-domain and cross-way settings respectively.
We explore the applicability of the causal analysis based on temporally shifted (lagged) Pearson correlation applied to diverse time series of different natures in context of the problem of financial market prediction. Theoretical discussion is followed by description of the practical approach for specific environment of time series data with diverse nature and sparsity, as applied for environments of financial markets. The data involves various financial metrics computable from raw market data such as real-time trades and snapshots of the limit order book as well as metrics determined upon social media news streams such as sentiment and different cognitive distortions. The approach is backed up with presentation of algorithmic framework for data acquisition and analysis, concluded with experimental results, and summary pointing out at the possibility to discriminate causal connections between different sorts of real field market data with further discussion on present issues and possible directions of the following work.
Anomaly detection on multivariate time-series is of great importance in both data mining research and industrial applications. Recent approaches have achieved significant progress in this topic, but there is remaining limitations. One major limitation is that they do not capture the relationships between different time-series explicitly, resulting in inevitable false alarms. In this paper, we propose a novel self-supervised framework for multivariate time-series anomaly detection to address this issue. Our framework considers each univariate time-series as an individual feature and includes two graph attention layers in parallel to learn the complex dependencies of multivariate time-series in both temporal and feature dimensions. In addition, our approach jointly optimizes a forecasting-based model and are construction-based model, obtaining better time-series representations through a combination of single-timestamp prediction and reconstruction of the entire time-series. We demonstrate the efficacy of our model through extensive experiments. The proposed method outperforms other state-of-the-art models on three real-world datasets. Further analysis shows that our method has good interpretability and is useful for anomaly diagnosis.
We developed a new approach for the analysis of physiological time series. An iterative convolution filter is used to decompose the time series into various components. Statistics of these components are extracted as features to characterize the mechanisms underlying the time series. Motivated by the studies that show many normal physiological systems involve irregularity while the decrease of irregularity usually implies the abnormality, the statistics for "outliers" in the components are used as features measuring irregularity. Support vector machines are used to select the most relevant features that are able to differentiate the time series from normal and abnormal systems. This new approach is successfully used in the study of congestive heart failure by heart beat interval time series.
Analyzing better time series with limited human effort is of interest to academia and industry. Driven by business scenarios, we organized the first Automated Time Series Regression challenge (AutoSeries) for the WSDM Cup 2020. We present its design, analysis, and post-hoc experiments. The code submission requirement precluded participants from any manual intervention, testing automated machine learning capabilities of solutions, across many datasets, under hardware and time limitations. We prepared 10 datasets from diverse application domains (sales, power consumption, air quality, traffic, and parking), featuring missing data, mixed continuous and categorical variables, and various sampling rates. Each dataset was split into a training and a test sequence (which was streamed, allowing models to continuously adapt). The setting of time series regression, differs from classical forecasting in that covariates at the present time are known. Great strides were made by participants to tackle this AutoSeries problem, as demonstrated by the jump in performance from the sample submission, and post-hoc comparisons with AutoGluon. Simple yet effective methods were used, based on feature engineering, LightGBM, and random search hyper-parameter tuning, addressing all aspects of the challenge. Our post-hoc analyses revealed that providing additional time did not yield significant improvements. The winners' code was open-sourced https://www.4paradigm.com/competition/autoseries2020.
Irregular sampling occurs in many time series modeling applications where it presents a significant challenge to standard deep learning models. This work is motivated by the analysis of physiological time series data in electronic health records, which are sparse, irregularly sampled, and multivariate. In this paper, we propose a new deep learning framework for this setting that we call Multi-Time Attention Networks. Multi-Time Attention Networks learn an embedding of continuous-time values and use an attention mechanism to produce a fixed-length representation of a time series containing a variable number of observations. We investigate the performance of our framework on interpolation and classification tasks using multiple datasets. Our results show that our approach performs as well or better than a range of baseline and recently proposed models while offering significantly faster training times than current state-of-the-art methods.
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