A fast LSH-based similarity search method for multivariate time series

The autoregressive analysis of stationary multivariate time series includes construction of a time domain model in the form of a multivariate stochastic difference equation and its transformation into a spectral matrix to study frequency domain properties. The time series is treated as a linear system with one output process and one or several inputs. This approach provides an explicit time domain description of the time series as a function of the past of output and input components. In the bivariate case, the frequency domain results include spectral densities, coherent spectrum, coherence function, and gain and phase factors. The coherence function shows the degree of linear interdependence, the coherent spectrum presents the contribution of the input component to the output, the gain factor consists of amplification coefficients, and the phase factor describes lags between the time series. All these quantities are frequency dependent. The Granger causality concept and feedbacks within the system are discussed as a part of bivariate time and frequency domain analysis. Some comments are given regarding the software for parametric analysis of multivariate time series. The use of cross-correlation coefficient and regression equation for describing dependence between time series or for reconstructing them is shown to be incorrect.

In this paper we study how to efficiently perform similarity join over massive time sequences in parallel using Locality Sensitive Hash and MapReduce. To solve the problem, we proposed a 4-stage approach for time sequences similarity join. Our proposed approach takes as input a set of time sequences, and output pairs of time sequences satisfying a similarity join condition. In our approach, we first map each time sequence into the frequency domain using Discrete Fourier Transform to avoid the dimension curse. Secondly, we find the candidate similar time sequence pairs using the Locality Sensitive Hash, which can ensure an efficient pair-wise similarity computation. Thirdly, we also propose solutions for removing duplicated pairs to avoid repeated computation for similarity pairs that are selected as candidate for more than once. Finally, in order to improve the performance of similarity join over massive time sequences, we use the popular MapReduce framework in each step. The experimental results show that our method is efficient and scalable.

Spectral analysis of multivariate geochemical time series

PurposeThis study aims to examine the relationship between green finance, economic growth, renewable energy consumption (energy efficiency), energy import and CO2 emission in Vietnam using multivariate time series analysis.Design/methodology/approachThe data were collected from 1986 to 2018 since Vietnam initiated the economic reforms, namely “Doi Moi” in 1986. The concept and methods of cointegration, Granger causality and error correction model (ECM) were employed to establish the relationship between the variables of interest.FindingsOur results confirmed the existence of cointegration among the variables. The Granger causality test revealed unidirectional causality running from renewable energy consumption to CO2 emission and green investment to CO2 emission.Originality/valueThis study results confirm the existence of cointegration among the variables. The results of the study imply that policies on economic development impose a significant impact on pollution in Vietnam. This study has described Vietnam, its economic development, green manufacturing practices, its environmental health and level of carbon dioxide emission which was enhanced due to COVID-19.

In this work an algorithm to adjust parameters using a Bayesian method for cumulative rainfall time series forecasting implemented by an ANN-filter is presented. The criterion of adjustment comprises to generate a posterior probability distribution of time series values from forecasted time series, where the structure is changed by considering a Bayesian inference. These are approximated by the ANN based predictor in which a new input is taken in order for changing the structure and parameters of the filter. The proposed technique is based on the prior distribution assumptions. Predictions are obtained by weighting up all possible models and parameter values according to their posterior distribution. Furthermore, if the time series is smooth or rough, the fitting algorithm can be changed to suit, in function of the long or short term stochastic dependence of the time series, an on-line heuristic law to set the training process, modify the NN topology, change the number of patterns and iterations in addition to the Bayesian inference in accordance with Hurst parameter H taking into account that the series forecasted has the same H as the real time series. The performance of the approach is tested over a time series obtained from samples of the Mackey-Glass delay differential equations and cumulative rainfall time series from some geographical points of Cordoba, Argentina.

Multivariate time series analysis is a vital but challenging task, with multidisciplinary applicability, tackling the characterization of multiple interconnected variables over time and their dependencies. Traditional methodologies often adapt univariate approaches or rely on assumptions specific to certain domains or problems, presenting limitations. A recent promising alternative is to map multivariate time series into high-level network structures such as multiplex networks, with past work relying on connecting successive time series components with interconnections between contemporary timestamps. In this work, we first define a novel cross-horizontal visibility mapping between lagged timestamps of different time series and then introduce the concept of multilayer horizontal visibility graphs. This allows describing cross-dimension dependencies via inter-layer edges, leveraging the entire structure of multilayer networks. To this end, a novel parameter-free topological measure is proposed and common measures are extended for the multilayer setting. Our approach is general and applicable to any kind of multivariate time series data. We provide an extensive experimental evaluation with both synthetic and real-world datasets. We first explore the proposed methodology and the data properties highlighted by each measure, showing that inter-layer edges based on cross-horizontal visibility preserve more information than previous mappings, while also complementing the information captured by commonly used intra-layer edges. We then illustrate the applicability and validity of our approach in multivariate time series mining tasks, showcasing its potential for enhanced data analysis and insights.

SUMMARY We propose a method to specify an appropriate yet parsimonious vector autoregressive moving average (ARMA) model for a given multivariate time series. By considering contemporaneous linear transformations of the vector process, we introduce the concept of scalar component models within the vector ARMA framework (a) to reveal possibly hidden simplifying structures of the process, (b) to achieve parsimony in parameterization and (c) to identify the exchangeable models. The simplifying structures are of particular importance in the analysis of multivariate time series because they are often not obvious from the observed data but can be used to gain insights to the process under study. The analytical tool used to search for scalar component models is a canonical correlation analysis of vector processes and the proposed procedures are illustrated via two real examples.

Nowadays, great quantities of data are produced by a large and diverse family of sensors (e.g., remote sensors, biochemical sensors, wearable devices), which typically measure multiple variables over time, resulting in data streams that can be profitably organized as multivariate time-series. In practical scenarios, the speed at which such information is collected often makes the data labeling task uneasy and too expensive, so that limit the use of supervised approaches. For this reason, unsupervised and exploratory methods represent a fundamental tool to deal with the analysis of multivariate time series. In this paper we propose a deep-learning based framework for clustering multivariate time series data with varying lengths. Our framework, namely DeTSEC (Deep Time Series Embedding Clustering), includes two stages: firstly a recurrent autoencoder exploits attention and gating mechanisms to produce a preliminary embedding representation; then, a clustering refinement stage is introduced to stretch the embedding manifold towards the corresponding clusters. Experimental assessment on six real-world benchmarks coming from different domains has highlighted the effectiveness of our proposal.

Much progress has been made in recent years in multivariate time-series analysis. In this paper we summarize some of the methodological developments that are particularly relevant to empirical economics and highlight especially the usefulness of linear transformations in analyzing multivariate time series. The topics considered include vector ARMA models, principal component analysis, scalar component models, canonical correlation analyses, co-integration, and unit-root tests. We illustrate the methods considered by an example using Taiwan’s interest-rate series and provide critiques of these developments.

By extending Takens' embedding theorem [Dynamical Systems and Turbulence, Warwick 1980, edited by D. Rand and L.-S. Young (Springer, Berlin, 1981), pp. 366-381], Deyle and Sugihara [PLoS One 6, 1-8 (2011)] provided a theoretical justification for using parallel measurement time series to reconstruct a system's attractor. Building on Takens' framework, Brunton et al. [Nat. Commun. 8, 19 (2017)] introduced the Hankel alternative view of Koopman (HAVOK) algorithm, a data-driven approach capable of linearizing chaotic systems through delay embeddings. In this work, a modified version of the original algorithm (mHAVOK) is presented, a practical realization of Deyle and Sugihara's generalized embedding theory. mHAVOK extends the original algorithm from one to multiple input time series and introduces a systematic approach to separating linear and nonlinear terms. An R2-informed quality score is introduced and shown to be a reliable guide for the selection of the reduced rank. The algorithm is tested on the familiar Lorenz system, as well as the more sophisticated Sprott system, which features different behaviors depending on the initial conditions. The quality of the reconstructions is assessed with the Chamfer distance, validating how mHAVOK allows for a more accurate reconstruction of the system dynamics. The new methodology generalizes HAVOK by allowing the analysis of multivariate time series, fundamental in real-life data-driven applications.

Inhomogeneous Dependency Modelling with Time Varying Copulae

Time Series: State Space Methods

Results obtained with interindividual techniques in a representative sample of a population are not necessarily generalizable to the individual members of this population. In this article the specific condition is presented that must be satisfied to generalize from the interindividual level to the intraindividual level. A way to investigate whether this condition is satisfied is by means of multivariate time series analysis. More generally, time series analysis can be used to investigate psychological processes situated within individuals. In this article we consider a well established class of multivariate stationary time series models that may be used to study the intraindividual covariance structure. We demonstrate the application of some of these models with an empirical example consisting of state measurements of behavior associated with the Five Factor Model of Personality. We illustrate how one can investigate whether individuals are similar with respect to their intraindividual structure of variation, and whether this structure is similar to the structure of interindividual variation.

Periodic Modeling of Economic Time Series A Multivariate Periodic Unobserved Components Time Series Analysis for Sectoral U.S. Employment Siem Jan Koopman, Marius Ooms, and Irma Hindrayanto Seasonal Heteroskedasticity in Time Series Data: Modeling, Estimation, and Testing Thomas M. Trimbur and William R. Bell Choosing Seasonal Autocovariance Structures: PARMA or SARMA? Robert Lund Estimating Time Series Components with Misspecified Models Specification and Misspecification of Unobserved Components Models Davide Delle Monache and Andrew Harvey The Error in Business Cycle Estimates Obtained From Seasonally Adjusted Data Tucker S. McElroy and Scott H. Holan Frequency Domain Analysis of Seasonal Adjustment Filters Applied To Periodic Labor Force Survey Series Richard B. Tiller Quantifying Error in X-11 Seasonal Adjustments Comparing Mean Squared Errors of X-12-ARIMA and Canonical ARIMA Model-Based Seasonal Adjustments William R. Bell, Yea-Jane Chu, and George C. Tiao Estimating Variance in X-11 Seasonal Adjustment Stuart Scott, Danny Pfeffermann, and Michail Sverchkov Practical Problems in Seasonal Adjustment Asymmetric Filters for Trend-Cycle Estimation Estela Bee Dagum and Alessandra Luati Restoring Accounting Constraints in Time Series: Methods and Software for a Statistical Agency Benoit Quenneville and Susie Fortier Theoretical and Real Trading-Day Frequencies Dominique Ladiray Applying and Interpreting Model-Based Seasonal Adjustment: The Euro-Area Industrial Production Series Agustin Maravall and Domingo Perez Outlier Detection and Modeling Time Series with Extreme Values Additive Outlier Detection in Seasonal ARIMA Models by a Modified Bayesian Information Criterion Pedro Galeano and Daniel Pena Outliers in GARCH Processes Luiz K. Hotta and Ruey S. Tsay Constructing a Credit Default Swap Index and Detecting the Impact of the Financial Crisis Yoko Tanokura, Hiroshi Tsuda, Seisho Sato, and Genshiro Kitagawa Alternative Models for Seasonal and Other Time Series Components Normally Distributed Seasonal Unit Root Tests David A. Dickey Bayesian Seasonal Adjustment of Long-Memory Time Series Scott H. Holan and Tucker S. McElroy Bayesian Stochastic Model Specification Search for Seasonal and Calendar Effects Tommaso Proietti and Stefano Grassi Modeling and Estimation for Nonseasonal Economic Time Series Nonparametric Estimation of the Innovation Variance and Judging the Fit of ARMA Models Priya Kohli and Mohsen Pourahmadi Functional Model Selection for Sparse Binary Time Series with Multiple Inputs Catherine Y. Tu, Dong Song, F. Jay Breidt, Theodore W. Berger, and Haonan Wang Models for High Lead Time Prediction Granville Tunnicliffe-Wilson and John Haywood

Time series mining is a new area of research in temporal data bases. Hitherto various methods have been presented for time series mining which the most of an existing works in different applied areas have been focused on event prediction. Event prediction is one of the main goals of time series mining which can play an effective role for appropriate decision making in different applied areas. Due to the variety and plenty of event prediction methods in time series and lack of a proper context for their systematic introduction, in this paper, a classification is proposed for event prediction methods in time series. Also, event prediction methods in time series are evaluated based on the proposed classification by some proposed measures. Using the proposed classification can be beneficial in selecting the appropriate method and can play an effective role in the analysis of event prediction methods in different application domains.