Multilayer horizontal visibility graphs for multivariate time series analysis

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.

Variable influence on projection (VIP) for OPLS models and its applicability in multivariate time series analysis

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.

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.

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.

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.

To solve the problem of the flashover forecasting of contaminated or polluted insulator, a flashover forecasting model of contaminated insulators based on multivariate nonlinear time series analysis is proposed in the paper. The equivalent salt deposit density (ESDD) is the key of flashover on polluted insulator. The ESDD value of insulator can be forecasted by the method of nonlinear time series analysis of the ESDD time series and a forecasting model of polluted insulator flashover is proposed in the paper. The forecasting model consists of two artificial neural networks that reflect relationship of environment, ESDD and flashover probability. The first is used to estimate the ESDD time series of insulator and the second is employed to calculate the probability of the flashover. A series of artificial pollution tests show that the results of the forecasting model is acceptable.

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: State Space Methods

MultiBEATS: Blocks of eigenvalues algorithm for multivariate time series dimensionality reduction

Sign tests are among the most successful procedures in multivariate nonparametric statistics. In this paper, we consider several testing problems in multivariate analysis, directional statistics and multivariate time series analysis, and we show that, under appropriate symmetry assumptions, the fixed-$p$ multivariate sign tests remain valid in the high-dimensional case. Remarkably, our asymptotic results are universal, in the sense that, unlike in most previous works in high-dimensional statistics, $p$ may go to infinity in an arbitrary way as $n$ does. We conduct simulations that (i) confirm our asymptotic results, (ii) reveal that, even for relatively large $p$, chi-square critical values are to be favoured over the (asymptotically equivalent) Gaussian ones and (iii) show that, for testing i.i.d.-ness against serial dependence in the high-dimensional case, Portmanteau sign tests outperform their competitors in terms of validity-robustness.

Due to the decline in catches of Atlantic salmon at the end of the 1980s, the Natural Heritage Service of the Xunta de Galicia has been obtaining data on the returning adults and the downstream migration of juvenile at the Ximonde fish-trap station since the year 1992 to 2021, as well as on the recapture of marked specimens from artificial restocking. At the same time, and during the same period, catches made by the fishing industry and the recruitment obtained through population censuses of different areas of the basin have been analyzed. A first exploratory analysis of the data indicates that the distribution area and flow regimes did not vary significantly during the study period. Throughout the time series, the number of juveniles stocked in the river changed, and even in some years none were stocked. The multivariate analysis of the time series indicates that the observed variations in the abundance of the population can be predicted based on the type of management carried out during the period studied, and that the methodology used in the Ulla river can potentially be used in other rivers with similar characteristics, especially those located in the southern areas of its natural distribution, affected by dams and with a reduced spawning habitat.

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

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.