Variables In Multivariate Time Series Research Articles

Efficient semi-supervised clustering with pairwise constraint propagation for multivariate time series

Semi-supervised clustering is an effective method, which improves the clustering performance based on pairwise constraints. However, state-of-the-art methods suffer from two issues: 1) due to the high dimensionality and multiple variables of multivariate time series (MTS) data, the competitive similarity approach DTW is time consuming on large-scale MTS data. 2) Traditional semi-supervised clustering methods could not make full use of pairwise constraints information, which affects clustering performance. To deal with these issues, we propose an efficient semi-supervised clustering with pairwise constraint propagation for MTS data. First, two approximate distance measure methods are designed based on dynamic time warping (DTW) from the perspectives of boundary and dimension reduction, which greatly improve the efficiency of clustering without sacrificing its accuracy. Then, a graph-based clustering method with pairwise constraints propagation (GCPCP) is advanced on multivariate time series data. In GCPCP, the pairwise constraint propagation matrix and the affinity matrix are jointly optimized to exploit the dependence between them, which finally improves the clustering performance. Experimental results on 12 multivariate time series datasets show the effectiveness and efficiency of our proposed method.

Robust anomaly detection for multivariate time series through temporal GCNs and attention-based VAE

Anomaly detection on multivariate time series (MTS) is of great importance in both data mining research and industrial applications. While a handful of anomaly detection models are developed for MTS data, most of them either ignore the potential correlations between different variables or overlook the different importance of variables at each time period in MTS, which leads to poor accuracy in anomaly detection. In this paper, we propose a novel unsupervised MUltivariate Time series ANomaly deTection framework (MUTANT), which simultaneously models the correlations between variables and the importance of variables at each time period. Specifically, we construct a feature graph for variables in each time window and perform graph convolutional network (GCN) to learn embeddings for all variables, which effectively captures the time-varying correlations between variables in MTS. Then, we propose an attention-based reconstruction model to learn robust latent representations to capture normal patterns of MTS by modeling the importance of variables based on time dependencies along with time dimension. Our evaluation experiments are conducted on four real-life datasets from different industrial domains. Experimental results show that MUTANT significantly outperforms state-of-the-art MTS anomaly detection methods, achieving an average anomaly detection F1-score higher than 0.96. The source code is available at https://github.com/Coac-syf/MUTANT.

A novel multivariate time series combination prediction model

This article presents a novel multivariate time series prediction model based on combination model. The input variables of multivariate time series are coupled and correlated. Firstly, kernel principal component analysis is used to preprocess the original multidimensional input variables to determine the principal components that affect the output. Extracting principal components can reduce the complexity of modeling. Then, an improved grey wolf optimization algorithm optimized echo state network is introduced as the prediction model for principal components. Finally, two typical multivariate time series data, air quality index and stock market price, are taken as research objects to verify the performance of the proposed combination prediction model. Compared with other state-of-the-art prediction models, the results clearly reveal that the proposed prediction model is superior to all the considered models herein in terms of both prediction accuracy and performance indicators. As a result, it is concluded that the proposed prediction model can be an efficient and effective technique for multivariate time series prediction.

Dynamic Modeling and Forecasting Data Energy Used and Carbon Dioxide (CO2)

The model of Vector Autoregressive (VAR) with cointegration is able to be modified by Vector Error Correction Model (VECM). Because of its simpilicity and less restrictions the VECM is applied in many studies. The correlation among variables of multivariate time series also can be explained by VECM model, which can explain the effect of a variable or set of variables on others using Granger Causality, Impulse Response Function (IRF), and Forecasting. In this study, the relationship of Energy Used and CO2 will be discussed. The data used here were collected over the year 1971 to 2018. Based on the comparison of some criteria: Akaike Information Criterion Corrected (AICC), Hannan-Quin Information Criterion (HQC), Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC) for some VAR(p) model with p= 1,2,3,4,5, the best model with smallest values of AICC, HQC, AIC and SBC is at lag 2 (p= 2). Then the best model found is VECM (2) and further analysis such as Granger Causality, IRF, and Forecasting will be based on this model.

Hybrid dynamic learning mechanism for multivariate time series segmentation

AbstractTo improve the efficiency of segmentation methods for multivariate time series, a hybrid dynamic learning mechanism for such series' segmentation is proposed. First, an incremental clustering algorithm is used to automatically cluster variables of multivariate time series. Second, common factors are extracted from every cluster by a dynamic factor model as an ensemble description of the system. Third, this common factor series is segmented by dynamic programming. The proposed method can potentially segment multivariate time series and not only performs segmentation better on multivariate time series with a large number of variables but also improves the running accuracy and efficiency of the algorithm, especially when analyzing complex datasets.

Autoregressive forests for multivariate time series modeling

Multivariate Time Series (MTS) modeling has received significant attention in the last decade because of the complex nature of the data. Efficient representations are required to deal with the high dimensionality due to the increase in the number of variables and duration of the time series in different applications. For example, model-based approaches such as Hidden Markov Models (HMM) or autoregressive (AR) models focus on finding a model to represent the series with the model parameters to handle this problem. Both HMM and AR models are known to be very successful in the representation of the time series however most of the HMM approaches assume independence and traditional AR models consider linear dependence between the variables of MTS. As most of the real systems exhibit nonlinear relations, traditional approaches fail to represent the time series. To handle these problems, we propose an autoregressive tree-based ensemble approach that can model the nonlinear behavior embedded in the time series with the help of tree-based learning. Multivariate autoregressive forest, namely mv-ARF, is a nonparametric vector autoregression approach which provides an easy and efficient representation that scales well with large datasets. An error-based representation based on the learned models is the basis of the proposed approach. This is very similar to time series kernels used for multivariate time series classification problems. We test mv-ARF on MTS classification problems and show that mv-ARF provides fast and competitive results on benchmark datasets from several domains. Furthermore, mv-ARF provides a research direction for vector autoregressive models that breaks from the linear dependency models to potentially foster other promising nonlinear approaches.

Graphical modelling of multivariate time series

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependencies. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs each component series is represented by a single vertex and directed edges indicate possible Granger-causal relationships between variables while undirected edges are used to map the contemporaneous dependence structure. We introduce various notions of Granger-causal Markov properties and discuss the relationships among them and to other Markov properties that can be applied in this context.