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This paper contributes multivariate versions of seven commonly used elastic similarity and distance measures for time series data analytics. Elastic similarity and distance measures can compensate for misalignments in the time axis of time series data. We adapt two existing strategies used in a multivariate version of the well-known Dynamic Time Warping (DTW), namely, Independent and Dependent DTW, to these seven measures. While these measures can be applied to various time series analysis tasks, we demonstrate their utility on multivariate time series classification using the nearest neighbor classifier. On 23 well-known datasets, we demonstrate that each of the measures but one achieves the highest accuracy relative to others on at least one dataset, supporting the value of developing a suite of multivariate similarity and distance measures. We also demonstrate that there are datasets for which either the dependent versions of all measures are more accurate than their independent counterparts or vice versa. In addition, we also construct a nearest neighbor-based ensemble of the measures and show that it is competitive to other state-of-the-art single-strategy multivariate time series classifiers.

We develop a statistical model for the analysis and forecasting of football match results which assumes a bivariate Poisson distribution with intensity coefficients that change stochastically over time. The dynamic model is a novelty in the statistical time series analysis of match results in team sports. Our treatment is based on state space and importance sampling methods which are computationally efficient. The out-of-sample performance of our methodology is verified in a betting strategy that is applied to the match outcomes from the 2010–2011 and 2011–2012 seasons of the English football Premier League. We show that our statistical modelling framework can produce a significant positive return over the bookmaker's odds.

Multivariate time series classification has become popular due to its prevalence in many real-world applications. However, most state-of-the-art focuses on improving classification performance, with the best-performing models typically opaque. Interpretable multivariate time series classifiers have been recently introduced, but none can maintain sufficient levels of efficiency and effectiveness together with interpretability. We introduce Z-Time, a novel algorithm for effective and efficient interpretable multivariate time series classification. Z-Time employs temporal abstraction and temporal relations of event intervals to create interpretable features across multiple time series dimensions. In our experimental evaluation on the UEA multivariate time series datasets, Z-Time achieves comparable effectiveness to state-of-the-art non-interpretable multivariate classifiers while being faster than all interpretable multivariate classifiers. We also demonstrate that Z-Time is more robust to missing values and inter-dimensional orders, compared to its interpretable competitors.

Realizing carbon neutral energy generation creates the challenge of accurately predicting time‐series generation data for long‐term capacity planning and for short‐term operational decisions. The key challenges for adopting data‐driven decision‐making, specifically predictive analytics, can be attributed to data volume and velocity. Data volume poses challenges for data storage and retrieval. Data velocity poses challenges for processing the data near real time for operational decisions or for capacity building. This manuscript proposes a novel prediction method to tackle the above two challenges by using an event‐based prediction in place of traditional time series prediction methods. The central concept is to extract meaningful information, denoted by events, from time‐series data and use these events for predictive analysis. These extracted events retain the information required for predictive analytics while significantly reducing the volume of the velocity of data; consequently, a series of events present the information at a glance, effectively enabling data‐driven decision‐making. This method is applied to a data set consisting of six years of historical wind power capacity factor and temperature measurements. Deploying five deep learning models, a comparison is drawn between classical time‐series predictions and series of events predictions based on computational time and several error metrics. The computational analysis results are presented in graphical format and a comparative discussion is drawn on the prediction results. The results indicate that the proposed method obtains the same or better prediction accuracy while significantly reducing computational time and data volume.

Weather forecasting is essential for various applications such as agriculture and transportation, and relies heavily on meteorological sequential data such as multivariate time series collected from weather stations. Traditional numerical weather prediction (NWP) methods applied to multivariate time series forecasting are grounded in statistical principles such as Autoregressive Integrated Moving Average (ARIMA); however, they often struggle with capturing complex nonlinear patterns among meteorological variables and temporal variances. Currently, existing deep learning approaches such as Recurrent Neural Networks (RNNs) and transformers offer remarkable performance in handling complex patterns among meteorological multivariate time series, yet frequently fail to maintain weather-specific physical properties such as strict values constraints, while also incurring the significant computational costs of large parameter scales. In this paper, we present a novel deep learning plug-and-play framework named Post Constraint and Correction (PCC) to address these challenges by incorporating additional constraints and corrections based on weather-specific properties such as multivariant correlations and physical-based strict value constraints into the prediction process. Our method demonstrates notable computational efficiency, delivering significant improvements over existing deep learning time series models and helping to achieve better performance with far fewer parameters. Extensive experiments demonstrate the effectiveness, efficiency, and robustness of our method, highlighting its potential for real-world applications.

Background and Aims Cause‐specific mortality (CSM) count prediction plays a vital role in the context of public health policy. In this study, we introduce a new analytical approach, which is divided into three phases to answer specific questions regarding CSM due to 14 specific causes by computing different simple, compound, and conditional probabilities. Methods A multivariate time series forecasting model was developed using the CDC weekly mortality count data. A binary data matrix was constructed for 14 causes of death (COD) as a function of weeks by combining the observed and forecasted mortalities. We introduced two new concepts: Weekly Exceedance in Mortality Count (WEMC) and Weekly Change in Mortality Indicator (WCMI), which were instrumental in computing various probabilities relating to all the CODs. To test the null hypothesis of no association between the COD and WEMC a chi‐square test of independence was conducted whereas Cramer's V statistic was used to check the strength of the association. Wilcoxon rank sum test, and correlation indices were used to validate the method. Results The results of chi‐square test of independence indicated that there was no statistically significant association between COD and WEMC (p = 0.79). Furthermore, the effect size of this association between COD and WEMC was very small (Cramer's V = 0.055). The results of Wilcoxon rank sum test indicated that there was no statistically significant difference between the observed and forecasted counts (p = 0.11) confirming the consistency of our analytical method. Probabilities associated with WCMIs were also computed as an illustration of the analytical method. Conclusion Utilizing this analytical approach, researchers and policymakers can compute the probabilities of any number of desired events related to different COD which can be helpful for public health interventions, resource allocation, informed decision‐making and risk assessment, by controlling the underlying attributes responsible for the probabilities to surge and plummet.

In IT monitoring systems, anomaly detection plays a vital role in detecting and alerting unexpected behaviors timely to system operators. With the growth of signal data in both volumes and dimensions during operation, unsupervised learning turns out to be a great solution to trigger anomalies thanks to the feasibility of working well with unlabeled data. In recent years, autoencoder, an unsupervised learning technique, has gained much attention because of its robustness. Autoencoder first compresses input data to lower-dimensional latent representation, which obtains normal patterns, then the compressed data are reconstructed back to the input form to detect abnormal data. In this paper, we propose a practical unsupervised learning approach using Multi-Scale Temporal convolutional kernels with Variational AutoEncoder (MST-VAE) for anomaly detection in multivariate time series data. Our key observation is that combining short-scale and long-scale convolutional kernels to extract various temporal information of the time series can enhance the model performance. Extensive empirical studies on five real-world datasets demonstrate that MST-VAE can outperform baseline methods in effectiveness and efficiency.

This paper is about vector autoregressive-moving average models with time-dependent coefficients to represent non-stationary time series. Contrary to other papers in the univariate case, the coefficients depend on time but not on the series' length n. Under appropriate assumptions, it is shown that a Gaussian quasi-maximum likelihood estimator is almost surely consistent and asymptotically normal. The theoretical results are illustrated by means of two examples of bivariate processes. It is shown that the assumptions underlying the theoretical results apply. In the second example, the innovations are marginally heteroscedastic with a correlation ranging from −0.8 to 0.8. In the two examples, the asymptotic information matrix is obtained in the Gaussian case. Finally, the finite-sample behaviour is checked via a Monte Carlo simulation study for n from 25 to 400. The results confirm the validity of the asymptotic properties even for short series and the asymptotic information matrix deduced from the theory.

The Hierarchical Vote Collective of Transformation-based Ensembles (HIVE-COTE) is a heterogeneous meta ensemble for time series classification. HIVE-COTE forms its ensemble from classifiers of multiple domains, including phase-independent shapelets, bag-of-words based dictionaries and phase-dependent intervals. Since it was first proposed in 2016, the algorithm has remained state of the art for accuracy on the UCR time series classification archive. Over time it has been incrementally updated, culminating in its current state, HIVE-COTE 1.0. During this time a number of algorithms have been proposed which match the accuracy of HIVE-COTE. We propose comprehensive changes to the HIVE-COTE algorithm which significantly improve its accuracy and usability, presenting this upgrade as HIVE-COTE 2.0. We introduce two novel classifiers, the Temporal Dictionary Ensemble and Diverse Representation Canonical Interval Forest, which replace existing ensemble members. Additionally, we introduce the Arsenal, an ensemble of ROCKET classifiers as a new HIVE-COTE 2.0 constituent. We demonstrate that HIVE-COTE 2.0 is significantly more accurate on average than the current state of the art on 112 univariate UCR archive datasets and 26 multivariate UEA archive datasets.

Time Series Classification (TSC) involves building predictive models for a discrete target variable from ordered, real valued, attributes. Over recent years, a new set of TSC algorithms have been developed which have made significant improvement over the previous state of the art. The main focus has been on univariate TSC, i.e. the problem where each case has a single series and a class label. In reality, it is more common to encounter multivariate TSC (MTSC) problems where the time series for a single case has multiple dimensions. Despite this, much less consideration has been given to MTSC than the univariate case. The UCR archive has provided a valuable resource for univariate TSC, and the lack of a standard set of test problems may explain why there has been less focus on MTSC. The UEA archive of 30 MTSC problems released in 2018 has made comparison of algorithms easier. We review recently proposed bespoke MTSC algorithms based on deep learning, shapelets and bag of words approaches. If an algorithm cannot naturally handle multivariate data, the simplest approach to adapt a univariate classifier to MTSC is to ensemble it over the multivariate dimensions. We compare the bespoke algorithms to these dimension independent approaches on the 26 of the 30 MTSC archive problems where the data are all of equal length. We demonstrate that four classifiers are significantly more accurate than the benchmark dynamic time warping algorithm and that one of these recently proposed classifiers, ROCKET, achieves significant improvement on the archive datasets in at least an order of magnitude less time than the other three.