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

Low-Rank Temporal Attention-Augmented Bilinear Network for financial time-series forecasting

Jul 05, 2021
Mostafa Shabani, Alexandros Iosifidis

Financial market analysis, especially the prediction of movements of stock prices, is a challenging problem. The nature of financial time-series data, being non-stationary and nonlinear, is the main cause of these challenges. Deep learning models have led to significant performance improvements in many problems coming from different domains, including prediction problems of financial time-series data. Although the prediction performance is the main goal of such models, dealing with ultra high-frequency data sets restrictions in terms of the number of model parameters and its inference speed. The Temporal Attention-Augmented Bilinear network was recently proposed as an efficient and high-performing model for Limit Order Book time-series forecasting. In this paper, we propose a low-rank tensor approximation of the model to further reduce the number of trainable parameters and increase its speed.

  

Temporal Tensor Transformation Network for Multivariate Time Series Prediction

Jan 04, 2020
Yuya Jeremy Ong, Mu Qiao, Divyesh Jadav

Multivariate time series prediction has applications in a wide variety of domains and is considered to be a very challenging task, especially when the variables have correlations and exhibit complex temporal patterns, such as seasonality and trend. Many existing methods suffer from strong statistical assumptions, numerical issues with high dimensionality, manual feature engineering efforts, and scalability. In this work, we present a novel deep learning architecture, known as Temporal Tensor Transformation Network, which transforms the original multivariate time series into a higher order of tensor through the proposed Temporal-Slicing Stack Transformation. This yields a new representation of the original multivariate time series, which enables the convolution kernel to extract complex and non-linear features as well as variable interactional signals from a relatively large temporal region. Experimental results show that Temporal Tensor Transformation Network outperforms several state-of-the-art methods on window-based predictions across various tasks. The proposed architecture also demonstrates robust prediction performance through an extensive sensitivity analysis.

  

A Study of Graph-Based Approaches for Semi-Supervised Time Series Classification

Apr 16, 2021
Dominik Alfke, Miriam Gondos, Lucile Peroche, Martin Stoll

Time series data play an important role in many applications and their analysis reveals crucial information for understanding the underlying processes. Among the many time series learning tasks of great importance, we here focus on semi-supervised learning which benefits of a graph representation of the data. Two main aspects are involved in this task: A suitable distance measure to evaluate the similarities between time series, and a learning method to make predictions based on these distances. However, the relationship between the two aspects has never been studied systematically. We describe four different distance measures, including (Soft) DTW and Matrix Profile, as well as four successful semi-supervised learning methods, including the graph Allen- Cahn method and a Graph Convolutional Neural Network. We then compare the performance of the algorithms on standard data sets. Our findings show that all measures and methods vary strongly in accuracy between data sets and that there is no clear best combination to employ in all cases.

* 22 pages 
  

Sparse Dynamic Distribution Decomposition: Efficient Integration of Trajectory and Snapshot Time Series Data

Jun 11, 2020
Jake P. Taylor-King, Cristian Regep, Jyothish Soman, Flawnson Tong, Catalina Cangea, Charlie Roberts

Dynamic Distribution Decomposition (DDD) was introduced in Taylor-King et. al. (PLOS Comp Biol, 2020) as a variation on Dynamic Mode Decomposition. In brief, by using basis functions over a continuous state space, DDD allows for the fitting of continuous-time Markov chains over these basis functions and as a result continuously maps between distributions. The number of parameters in DDD scales by the square of the number of basis functions; we reformulate the problem and restrict the method to compact basis functions which leads to the inference of sparse matrices only -- hence reducing the number of parameters. Finally, we demonstrate how DDD is suitable to integrate both trajectory time series (paired between subsequent time points) and snapshot time series (unpaired time points). Methods capable of integrating both scenarios are particularly relevant for the analysis of biomedical data, whereby studies observe population at fixed time points (snapshots) and individual patient journeys with repeated follow ups (trajectories).

* 11 pages, 2 figures 
  

Visual Forecasting of Time Series with Image-to-Image Regression

Nov 18, 2020
Naftali Cohen, Srijan Sood, Zhen Zeng, Tucker Balch, Manuela Veloso

Time series forecasting is essential for agents to make decisions in many domains. Existing models rely on classical statistical methods to predict future values based on previously observed numerical information. Yet, practitioners often rely on visualizations such as charts and plots to reason about their predictions. Inspired by the end-users, we re-imagine the topic by creating a framework to produce visual forecasts, similar to the way humans intuitively do. In this work, we take a novel approach by leveraging advances in deep learning to extend the field of time series forecasting to a visual setting. We do this by transforming the numerical analysis problem into the computer vision domain. Using visualizations of time series data as input, we train a convolutional autoencoder to produce corresponding visual forecasts. We examine various synthetic and real datasets with diverse degrees of complexity. Our experiments show that visual forecasting is effective for cyclic data but somewhat less for irregular data such as stock price. Importantly, we find the proposed visual forecasting method to outperform numerical baselines. We attribute the success of the visual forecasting approach to the fact that we convert the continuous numerical regression problem into a discrete domain with quantization of the continuous target signal into pixel space.

  

Estimation and HAC-based Inference for Machine Learning Time Series Regressions

Dec 13, 2019
Andrii Babii, Eric Ghysels, Jonas Striaukas

Time series regression analysis in econometrics typically involves a framework relying on a set of mixing conditions to establish consistency and asymptotic normality of parameter estimates and HAC-type estimators of the residual long-run variances to conduct proper inference. This article introduces structured machine learning regressions for high-dimensional time series data using the aforementioned commonly used setting. To recognize the time series data structures we rely on the sparse-group LASSO estimator. We derive a new Fuk-Nagaev inequality for a class of $\tau$-dependent processes with heavier than Gaussian tails, nesting $\alpha$-mixing processes as a special case, and establish estimation, prediction, and inferential properties, including convergence rates of the HAC estimator for the long-run variance based on LASSO residuals. An empirical application to nowcasting US GDP growth indicates that the estimator performs favorably compared to other alternatives and that the text data can be a useful addition to more traditional numerical data.

  

Clustering of Time Series Data with Prior Geographical Information

Jul 03, 2021
Reza Asadi, Amelia Regan

Time Series data are broadly studied in various domains of transportation systems. Traffic data area challenging example of spatio-temporal data, as it is multi-variate time series with high correlations in spatial and temporal neighborhoods. Spatio-temporal clustering of traffic flow data find similar patterns in both spatial and temporal domain, where it provides better capability for analyzing a transportation network, and improving related machine learning models, such as traffic flow prediction and anomaly detection. In this paper, we propose a spatio-temporal clustering model, where it clusters time series data based on spatial and temporal contexts. We propose a variation of a Deep Embedded Clustering(DEC) model for finding spatio-temporal clusters. The proposed model Spatial-DEC (S-DEC) use prior geographical information in building latent feature representations. We also define evaluation metrics for spatio-temporal clusters. Not only do the obtained clusters have better temporal similarity when evaluated using DTW distance, but also the clusters better represents spatial connectivity and dis-connectivity. We use traffic flow data obtained by PeMS in our analysis. The results show that the proposed Spatial-DEC can find more desired spatio-temporal clusters.

  

tsrobprep -- an R package for robust preprocessing of time series data

Apr 26, 2021
Michał Narajewski, Jens Kley-Holsteg, Florian Ziel

Data cleaning is a crucial part of every data analysis exercise. Yet, the currently available R packages do not provide fast and robust methods for cleaning and preparation of time series data. The open source package tsrobprep introduces efficient methods for handling missing values and outliers using model based approaches. For data imputation a probabilistic replacement model is proposed, which may consist of autoregressive components and external inputs. For outlier detection a clustering algorithm based on finite mixture modelling is introduced, which considers typical time series related properties as features. By assigning to each observation a probability of being an outlying data point, the degree of outlyingness can be determined. The methods work robust and are fully tunable. Moreover, by providing the auto_data_cleaning function the data preprocessing can be carried out in one cast, without manual tuning and providing suitable results. The primary motivation of the package is the preprocessing of energy system data, however, the package is also suited for other moderate and large sized time series data set. We present application for electricity load, wind and solar power data.

  

Semantic of Cloud Computing services for Time Series workflows

Feb 01, 2022
Manuel Parra-Royón, Francisco Baldan, Ghislain Atemezing, J. M. Benitez

Time series (TS) are present in many fields of knowledge, research, and engineering. The processing and analysis of TS are essential in order to extract knowledge from the data and to tackle forecasting or predictive maintenance tasks among others The modeling of TS is a challenging task, requiring high statistical expertise as well as outstanding knowledge about the application of Data Mining(DM) and Machine Learning (ML) methods. The overall work with TS is not limited to the linear application of several techniques, but is composed of an open workflow of methods and tests. These workflow, developed mainly on programming languages, are complicated to execute and run effectively on different systems, including Cloud Computing (CC) environments. The adoption of CC can facilitate the integration and portability of services allowing to adopt solutions towards services Internet Technologies (IT) industrialization. The definition and description of workflow services for TS open up a new set of possibilities regarding the reduction of complexity in the deployment of this type of issues in CC environments. In this sense, we have designed an effective proposal based on semantic modeling (or vocabulary) that provides the full description of workflow for Time Series modeling as a CC service. Our proposal includes a broad spectrum of the most extended operations, accommodating any workflow applied to classification, regression, or clustering problems for Time Series, as well as including evaluation measures, information, tests, or machine learning algorithms among others.

* 11 pages, 12 figures 
  

Randomized Signature Layers for Signal Extraction in Time Series Data

Jan 02, 2022
Enea Monzio Compagnoni, Luca Biggio, Antonio Orvieto, Thomas Hofmann, Josef Teichmann

Time series analysis is a widespread task in Natural Sciences, Social Sciences, and Engineering. A fundamental problem is finding an expressive yet efficient-to-compute representation of the input time series to use as a starting point to perform arbitrary downstream tasks. In this paper, we build upon recent works that use the Signature of a path as a feature map and investigate a computationally efficient technique to approximate these features based on linear random projections. We present several theoretical results to justify our approach and empirically validate that our random projections can effectively retrieve the underlying Signature of a path. We show the surprising performance of the proposed random features on several tasks, including (1) mapping the controls of stochastic differential equations to the corresponding solutions and (2) using the Randomized Signatures as time series representation for classification tasks. When compared to corresponding truncated Signature approaches, our Randomizes Signatures are more computationally efficient in high dimensions and often lead to better accuracy and faster training. Besides providing a new tool to extract Signatures and further validating the high level of expressiveness of such features, we believe our results provide interesting conceptual links between several existing research areas, suggesting new intriguing directions for future investigations.

  
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