Usefulness of Linear Transformations in 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.

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.

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.

A method based on multiple regression, canonical correlation analysis and the Kalman filter is developed with a view to producing a reliable reconstruction of climate from pollen spectra. The study region is the southern France, where traditional analytical techniques are unsatisfactory due to the heavy influence of human activity and the existence of a complex climate. The first stage of the proposed method is the same as the standard techniques in which a spatial network of 36 sites with recent pollen and climate data were analyzed by regression techniques. But since the recent data are frequently subjected to disturbance by such factors as human activity or the particularities of the local vegetations, a second, independent analytical stage was added, in which pairs of fossil sites were compared using ancient data exclusively. In this way a model of the climatic forcing can be obtained, with the above-mentioned factors left out of account. The reconstructions obtained from the first two stages were then compared in the third stage of the method, and the result is a corrected reconstruction, from which it appears that at 14 000 BP annual temperature was 9oC cooler than present, with a 4°C increase between 13 500 and 11 500 BP followed by a 2oC cooling at 10 500 BP. The Holocene temperature maximum occurred between 8000 and 6000 BP. when the temperature was 1°C warmer than present.

In this Part I, there are 7 chapters which focus lies in comprehending the essence of econometrics, ranging from its fundamental principles to its more sophisticated facets. The overarching aim is to equip readers with the understanding needed to effectively apply econometric techniques for prediction and analysis. Through this comprehensive journey, readers will gain the necessary knowledge to harness econometrics as a powerful tool for making informed predictions and conducting thorough analyses.PART I - Introductory and Advanced EconometricsChapter 1       Introduction in EconometricsChapter 2        Regression ModelChapter 3        Univariate Time Series: Linear ModelsChapter 4        Stationarity and Unit Roots TestsChapter 5        Univariate Time Series: Volatility ModelsChapter 6        Multivariate Time Series AnalysisChapter 7        Multivariate GARCH ModelsKeywords: econometrics; regression model; linear models; unit roots tests; volatility models; multivariate time series analysis; multivariate GARCH volatility; hedging. JEL Classification: C01; C53; C58.

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.

Spectral analysis of multivariate geochemical time series

Methods in multivariate statistical analysis are essential for working with large amounts of geophysical data, data from observational arrays, from satellites, or from numerical model output. In classical multivariate statistical analysis, there is a hierarchy of methods, starting with linear regression at the base, followed by principal component analysis (PCA) and finally canonical correlation analysis (CCA). A multivariate time series method, the singular spectrum analysis (SSA), has been a fruitful extension of the PCA technique. The common drawback of these classical methods is that only linear structures can be correctly extracted from the data. Since the late 1980s, neural network methods have become popular for performing nonlinear regression and classification. More recently, neural network methods have been extended to perform nonlinear PCA (NLPCA), nonlinear CCA (NLCCA), and nonlinear SSA (NLSSA). This paper presents a unified view of the NLPCA, NLCCA, and NLSSA techniques and their applications to various data sets of the atmosphere and the ocean (especially for the El Niño‐Southern Oscillation and the stratospheric quasi‐biennial oscillation). These data sets reveal that the linear methods are often too simplistic to describe real‐world systems, with a tendency to scatter a single oscillatory phenomenon into numerous unphysical modes or higher harmonics, which can be largely alleviated in the new nonlinear paradigm.

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.

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.

Exploration of storage and process tolerance of different potato cultivars using principal component and canonical correlation analyses

Time Series: State Space Methods

Chapter 2 used the standard AR model for the inference on unit roots. However, one may contemplate testing for a unit root using different model specifications, and doing so might result in different inferential results. This chapter introduces inferential procedures for a unit root that use model specifications that depart from the standard AR model.

IntroductionRoad traffic fatalities (RTFs) in low-resource settings like Somalia are influenced by a complex interplay of socioeconomic, environmental, and political challenges. This study investigates the impact of climate change (temperature, rainfall), environmental degradation (CO2 emissions), socioeconomic conditions (urban population, foreign aid), and political instability on RTFs in Somalia, aiming to contribute to the limited understanding of these dynamics in fragile states.MethodsA multivariate time series analysis was conducted using data from 1984 to 2021. An Autoregressive Distributed Lag (ARDL) model was employed to examine the short-run and long-run effects of the selected drivers on RTFs. The robustness of the model was confirmed through a series of diagnostic tests.ResultsThe ARDL model revealed significant long-run relationships: increased urbanization, CO2 emissions, and political instability were associated with higher RTFs. Conversely, increased rainfall and foreign aid were associated with lower RTFs in the long run. In the short-run, nuanced effects were observed, with both increased temperature and rainfall exhibiting positive associations with RTFs, suggesting immediate, potentially transitory, impacts.Discussion/ConclusionThese findings challenge simplistic explanations of RTF drivers and highlight the necessity of integrated road safety strategies. Such strategies should address climate change adaptation, environmental protection, socioeconomic development, and the promotion of good governance. This research provides valuable insights for evidence-based policymaking aimed at reducing RTFs and achieving Sustainable Development Goals related to health, infrastructure, and sustainable communities in Somalia and similar contexts.

Factors affecting Internet diffusion in China: A multivariate time series analysis