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Causality Analysis of Climate and Ecosystem Time Series
Published in Vyacheslav Lyubchich, Yulia R. Gel, K. Halimeda Kilbourne, Thomas J. Miller, Nathaniel K. Newlands, Adam B. Smith, Evaluating Climate Change Impacts, 2020
Mohammad Gorji Sefidmazgi, Ali Gorji Sefidmazgi
The linear Granger causality analysis was also extended to P-dimensional multivariate time series, where a linear vector autoregressive model (VAR) is used for modeling purposes: Here, A(l) is the matrix of coefficients that models the effect of the time series with l lags. Usually the minimum value for l is 1. In the case of instantaneous (contemporaneous) causation, l = 0. The instantaneous causation occurs when the length of the measurement interval is too long so that the cause/effect action happens in less time than the length of a single time interval. If all of the l VAR coefficient matrices are lower triangular, then x fails to GC y. This can be tested using Wald or likelihood ration tests.
Bioelectric and Biomagnetic Signal Analysis
Published in Arvind Kumar Bansal, Javed Iqbal Khan, S. Kaisar Alam, Introduction to Computational Health Informatics, 2019
Arvind Kumar Bansal, Javed Iqbal Khan, S. Kaisar Alam
EEG signals are multivariate time-series data associated with some stochastic process. It also has to be compared against MEG, MRI and PET data. After preprocessing the EEG waves, features are extracted in the time-domain and in the frequency-domain. Feature extraction involves identifying the presence or absence of different types of waves, their mean-amplitude and the variance in the amplitude. The presence and absence of different types of waveforms (alpha, beta, gamma, etc.) are ascertained using Fast Fourier Transform that separates the waveforms in the frequency-domain.
Iterated Filtering Methods for Markov Process Epidemic Models
Published in Leonhard Held, Niel Hens, Philip O’Neill, Jacco Wallinga, Handbook of Infectious Disease Data Analysis, 2019
A POMP consists of two model components: (1) an unobserved Markov process , which can be discrete or continuous in time and (2) an observation model which describes how the data collected at discrete points in time , is connected to the transmission model. For notational convenience, we write and . In our application, the process describes the dynamics of the disease spread, e.g., in the case of the simple Markovian SIR model counts the number of susceptible, infectious, and removed individuals at time . Let denote the random variable counting the observations at time which depend on the state of the transmission process at that time (cf. Figure 11.1). Our data, , are then modeled as a realization of this observation process. Depending on how many aspects of the disease dynamics we observe, can be either a univariate or multivariate time series. Assuming that the observable random variable is independent of all other variables given the state of the transmission process , the joint density of the states and the observations is defined as the product of the one-step transmission density, , the observation density, , and the initial density as
Robust estimation using multivariate t innovations for vector autoregressive models via ECM algorithm
Published in Journal of Applied Statistics, 2021
Uchenna C. Nduka, Tobias E. Ugah, Chinyeaka H. Izunobi
Several time series that occur in real life, like economic variables, for example, are best regarded as components of a number of vector-valued (multivariate) time series 3]). Vector autoregressive model of order p, VAR(p), has become a popular tool for analyzing such time series. The increasing popularity of this model can be attributed to the suggestion of Lutkepohl [14] that if observations made sequentially in time are readily available for a variable of interest such that the data from the past carry useful information about the evolution of a variable; then it becomes reasonable to use as forecast some function of the data collected in the past. Here, it is assumed that a p) process: n is the length of the series) and 14] and Tsay [25] provide extensive results on parameter estimation and hypothesis testing for the VAR(p) model with normally distributed innovations.
Multiplex temporal measures reflecting neural underpinnings of brain functional connectivity under cognitive load in Autism Spectrum Disorder
Published in Neurological Research, 2020
The present paper has explored the cognitive task-induced brain reconfigurations and associated neural underpinnings to gain more insights into brain functional dynamics in ASD. The task-activated multivariate-time series has been analyzed using multiplex Visibility Graph (VG) networks. The multiplex VGs can provide both intra- and inter- level analysis by integrating the data into a single structure. The application of VGs to the neuroscience field is in its infancy and has been limited to univariate EEG recordings. The studies exploiting multivariate-time series using VGs are very scarce. Hence, the novelty of the present work is the usage of multiplex VGs to analyze multivariate-time series (i.e., EEG). The intra- and inter-layer properties have been explored using the complex graph parameters- Average weighted degree, clustering coefficient (segregation), global efficiency (integration), and mutual information. The parameter eigenvector centrality has been computed to measure the brain hubs engaged in cognitive functionalities. The paper has also examined whether brain metrics can predict the ASD individual’s performance in the task.
Modeling multivariate cybersecurity risks
Published in Journal of Applied Statistics, 2018
Chen Peng, Maochao Xu, Shouhuai Xu, Taizhong Hu
Since we have a 69-dimensional time series of cyber attack data, we randomly select four of them and plot them in Figure 3. We observe that there exist clusters and extreme attacks in the time series. Furthermore, we observe that there are some time intervals (say the 200th and 400th) during which the numbers of attacks are large for most of the time series. This indicates that there may exist positive dependence among cyber attacks. The experience in studying multivariate time series datasets that exhibit high clusters of volatilities suggests us to use copula-GARCH models to fit the data. Indeed, a preliminary analysis of the residuals obtained after removing the means shows that a GARCH model is preferred for describing the volatilities. Please refer to [4,28,37,39,48] and the references therein for an overview and recent developments in the field of multivariate time series analysis.