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"Time Series Analysis": models, code, and papers

Efficient and Consistent Robust Time Series Analysis

Jul 01, 2016
Kush Bhatia, Prateek Jain, Parameswaran Kamalaruban, Purushottam Kar

We study the problem of robust time series analysis under the standard auto-regressive (AR) time series model in the presence of arbitrary outliers. We devise an efficient hard thresholding based algorithm which can obtain a consistent estimate of the optimal AR model despite a large fraction of the time series points being corrupted. Our algorithm alternately estimates the corrupted set of points and the model parameters, and is inspired by recent advances in robust regression and hard-thresholding methods. However, a direct application of existing techniques is hindered by a critical difference in the time-series domain: each point is correlated with all previous points rendering existing tools inapplicable directly. We show how to overcome this hurdle using novel proof techniques. Using our techniques, we are also able to provide the first efficient and provably consistent estimator for the robust regression problem where a standard linear observation model with white additive noise is corrupted arbitrarily. We illustrate our methods on synthetic datasets and show that our methods indeed are able to consistently recover the optimal parameters despite a large fraction of points being corrupted.


Automatic time-series phenotyping using massive feature extraction

Dec 15, 2016
Ben D Fulcher, Nick S Jones

Across a far-reaching diversity of scientific and industrial applications, a general key problem involves relating the structure of time-series data to a meaningful outcome, such as detecting anomalous events from sensor recordings, or diagnosing patients from physiological time-series measurements like heart rate or brain activity. Currently, researchers must devote considerable effort manually devising, or searching for, properties of their time series that are suitable for the particular analysis problem at hand. Addressing this non-systematic and time-consuming procedure, here we introduce a new tool, hctsa, that selects interpretable and useful properties of time series automatically, by comparing implementations over 7700 time-series features drawn from diverse scientific literatures. Using two exemplar biological applications, we show how hctsa allows researchers to leverage decades of time-series research to quantify and understand informative structure in their time-series data.

* Cell Systems 5 (2017) 527 

A fast algorithm for complex discord searches in time series: HOT SAX Time

Jan 26, 2021
Paolo Avogadro, Matteo Alessandro Dominoni

Time series analysis is quickly proceeding towards long and complex tasks. In recent years, fast approximate algorithms for discord search have been proposed in order to compensate for the increasing size of the time series. It is more interesting, however, to find quick exact solutions. In this research, we improved HOT SAX by exploiting two main ideas: the warm-up process, and the similarity between sequences close in time. The resulting algorithm, called HOT SAX Time (HST), has been validated with real and synthetic time series, and successfully compared with HOT SAX, RRA, SCAMP, and DADD. The complexity of a discord search has been evaluated with a new indicator, the cost per sequence (cps), which allows one to compare searches on time series of different lengths. Numerical evidence suggests that two conditions are involved in determining the complexity of a discord search in a non-trivial way: the length of the discords, and the noise/signal ratio. In the case of complex searches, HST can be more than 100 times faster than HOT SAX, thus being at the forefront of the exact discord search.


Traffic Flows Analysis in High-Speed Computer Networks Using Time Series

Mar 05, 2021
G. Millán

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.

* arXiv admin note: substantial text overlap with arXiv:2103.02091 

Cluster-and-Conquer: A Framework For Time-Series Forecasting

Oct 26, 2021
Reese Pathak, Rajat Sen, Nikhil Rao, N. Benjamin Erichson, Michael I. Jordan, Inderjit S. Dhillon

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.

* 25 pages, 3 figures 

Multi-Faceted Representation Learning with Hybrid Architecture for Time Series Classification

Dec 21, 2020
Zhenyu Liu, Jian Cheng

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.


Forecasting Method for Grouped Time Series with the Use of k-Means Algorithm

Sep 15, 2015
N. N. Astakhova, L. A. Demidova, E. V. Nikulchev

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.

* Applied Mathematical Sciences, 2015, 9(97):4813-4830 
* 18 pages 

Spectral Propagation Graph Network for Few-shot Time Series Classification

Feb 08, 2022
Ling Yang, Shenda Hong, Luxia Zhang

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.


Causal Analysis of Generic Time Series Data Applied for Market Prediction

Apr 22, 2022
Anton Kolonin, Ali Raheman, Mukul Vishwas, Ikram Ansari, Juan Pinzon, Alice Ho

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.

* 10 pages, 4 figures, submitted to Artificial General Intelligence 2022 conference 

Multivariate Time-series Anomaly Detection via Graph Attention Network

Sep 04, 2020
Hang Zhao, Yujing Wang, Juanyong Duan, Congrui Huang, Defu Cao, Yunhai Tong, Bixiong Xu, Jing Bai, Jie Tong, Qi Zhang

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.

* Accepted by ICDM 2020. 10 pages