Browsing by Subject "time series analysis"

Now showing 1 - 4 of 4
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    Analysis and forecasting of sacral tourism potential of Kazakhstan with the time series analysis
    (2024-03-21) Amina, Uaisova
    The aim of this study is to investigate the effect of tourist resources, conditions and opportunities of sacral tourism in Kazakhstan using panel data (time series and cross-sectional) regression analysis for a sample of 14 regions of Kazakhstan observations over the period from 2004 to 2022. The main focus is on the method of estimating the size and effectiveness of the tourist potential, which reflects the realization and volume of tourist resources and its potential.  
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    Introducing Novel Relationships in Time Series Data
    (2018-12) Agrawal, Saurabh
    In many scientific and engineering domains such as climate, neuroscience, transportation, etc. measurements are collected from sensors installed in different parts of a complex dynamical system over regular intervals of time, resulting in a collection of large volumes of time series data. Automated data-driven approaches that can mine relationships between different time series could potentially lead to discovery of previously unknown physical processes which could further aid in designing policies and solutions to critical problems such as climate change, severe mental disorders, traffic congestion etc. This thesis defines novel relationships and patterns that can be studied in the time series data. In particular, the proposed definitions can capture two new types of relationships: i) multivariate relationships involving more than two time series, and ii) sub-interval relationships, that only exist during certain sub-intervals of time and are absent or occur very feebly during rest of the time. The other major contributions of this thesis include designing new automated data-driven approaches to find most interesting instances of defined relationships from the data in a computationally efficient manner, and proposing empirical approaches to assess the statistical significance of obtained relationships. The proposed approaches were applied to real-world datasets from two scientific domains: i) climate, and ii) neuroscience, and led to discovery of several new instances of relationships. Many of these instances are found to be statistically significant and reproducible in multiple time series datasets that are independent of the original dataset. One such instance led to the discovery of a climate phenomenon that was previously unknown to climate scientists.
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    Network Topology And Causal Structure Recovery In Linear Dynamical Systems
    (2024-04) Shaikh Veedu, Mishfad
    Modeling and representing complex systems by a network of interacting agents provide cost-effective and efficient ways to simulate, design, and test the solutions to real-world problems in science and engineering. Applications such as finance, neuroscience, climate science, power grids, etc. involve modeling the agents and states that interact and evolve dynamically and can contain feedback loops. Most existing literature assumes a static relationship between the agents, which fails to capture the dependencies across time. Learning the interdependency (topology) and cause-and-effect structure among the agents is therefore of importance and having an active interest in the graphical network representation and effective modeling of the dynamical systems. Identifying the unknown interaction structure can in general be classified into active and passive techniques. The active techniques involve intervention in the normal operation of the system by injecting external signals and/or modifying agents in the system. Critical applications in financial markets, power grids, meteorological systems, etc. do not allow active intervention in the system. In such critical applications passive methods, which infer the information from the observed time-series measurements, are applied. In the passive techniques, the evolution of the underlying system is mathematically modeled using a generative model, where the agents are excited with a disturbance signal. In this thesis, we study passive techniques to identify the interdependency and the influence pathways in the dynamical systems, where the agents interact linearly. Further, in practice, it might not be viable to observe all the states in the system. Thus, it is imperative to identify the influence structure (network topology) when the system involves hidden/latent states, which is a challenging problem. In Chapter 2, we provide a novel algorithm to identify the interdependency structure, including the dependency among the latent nodes, when only a subset of the nodes/agents provide the time-series measurements. In many applications, the proposed algorithm retrieves the exact influence pathways, with partial directions, including that of the latent nodes. Another practical issue is that some of the disturbances at the agents themselves can be correlated, which renders the agents' influence structure indistinguishable from passive observations. Examples of such systems are observable in applications such as power grids and stock markets. Learning the network topology in the presence of such correlated disturbances is difficult as it is required to extract the dependency between the disturbances first. In Chapter 3, we show that the correlation between the disturbances is equivalent to the dependency induced by the latent nodes. The network topology only provides the correlation structure of the network of agents. It is well known that correlation is not equivalent to causation and the cause-effect structure contains more information than the correlation structure. In many applications in medicine, biology, and statistics the correlation structure might not be sufficient. Here, it is necessary to know the causal structure of the underlying dynamics. In Chapter 4, we provide an algorithm to learn the causal structure of a linear dynamical system when the agents are excited by identical noise sources. Further, a sample complexity analysis is provided, which finds matching upper and lower bounds on the number of samples required to obtain a given error performance. In general, without intervention and assumptions on the generative models, it is impossible to identify a complete causal structure. The best one can identify without further restriction is an equivalent set of graphs with the same conditional correlation structure, Essential Graphs. In Chapter 5, we provide algorithms to estimate the essential graph in linear dynamical systems using the Wiener filter (WF). The conventional time-domain approach to computing WF is computationally expensive. To speed up the calculation, we propose a fast Fourier transform-based computationally efficient approach to estimate the Wiener filter. The conventional probability notion of CI fails to capture the CI notion in a stochastic process. To tackle this problem, we propose a novel probability notion of CI for stochastic processes in the frequency domain. This notion is used to extend the notions of the front-door and the back-door criterion from static graphical models to linear dynamical systems, where the nodal states are stochastic processes.
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    R Code and Data Supporting: Ecological forecasts reveal limitations of common model selection methods: predicting changes in beaver colony densities
    (2020-04-20) Johnson-Bice, Sean M; Ferguson, Jake M; Erb, John D; Gable, Thomas D; Windels, Steve K; s.johnsonbice@gmail.com; Johnson-Bice, Sean M
    This repository contains the R and JAGS code supporting results reported in: Johnson-Bice, S.M., J.M. Ferguson, J.D. Erb, T.D. Gable, S.K. Windels (2020). Ecological forecasts reveal limitations of common model selection methods: predicting changes in beaver colony densities. Ecological Applications [In Press].