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Cyclic Nonlinear Correlation Analysis for Time Series
IEEE Access, 2022 Principal component analysis (PCA) and kernel PCA allow the decorrelation of data with respect to a basis that is found via variance maximization. However, these techniques are based on pointwise correlations.
Christopher M. A. Bonenberger +3 more
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Stability Conditions for a Nonlinear Time Series Model
International Journal of Mathematics and Mathematical Sciences, 2023 This research aims to determine whether the proposed time series model is stable or not. To achieve this, Ozaki’s approximation method was utilized, where the nonlinear part is a function that approaches zero, similar to Ozaki’s imposed function.
Anas S. Youns, Salim M. Ahmad
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Nonlinear time-series analysis revisited [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015 In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data—typically univariate—via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and ...
Elizabeth Bradley, Holger Kantz
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Time series with tailored nonlinearities [PDF]
Physical Review E, 2015 It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of
Räth, Christoph, Laut, Ingo
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Coupling between Blood Pressure and Subarachnoid Space Width Oscillations during Slow Breathing
Entropy, 2021 The precise mechanisms connecting the cardiovascular system and the cerebrospinal fluid (CSF) are not well understood in detail. This paper investigates the couplings between the cardiac and respiratory components, as extracted from blood pressure (BP ...
Agnieszka Gruszecka +11 more
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Nonlinear Analysis of Financial Time Series [PDF]
Ovidius University Annals: Economic Sciences Series, 2022 One of the axioms of the modern science states that, if one can identify an exact mathematical description of a physical system, then a very detailed understanding of the system’s properties is possible.
Sorin Vlad, Mariana Vlad
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Wavelet analysis for non-stationary, nonlinear time series [PDF]
Nonlinear Processes in Geophysics, 2016 Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the quasi-biennial oscillation (QBO) time series ...
J. A. Schulte
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Mathematics, 2023 Testing for complex serial dependence in economic and financial time series is a crucial task that bears many practical implications. However, the linear paradigm remains pervasive among practitioners as the autocorrelation function, because, despite its
Simone Giannerini, Greta Goracci
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Volatility of linear and nonlinear time series [PDF]
Physical Review E, 2005 Previous studies indicate that nonlinear properties of Gaussian time series with long-range correlations, $u_i$, can be detected and quantified by studying the correlations in the magnitude series $|u_i|$, i.e., the ``volatility''. However, the origin for this empirical observation still remains unclear, and the exact relation between the correlations ...
Tomer Kalisky +2 more
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NoLiTiA: An Open-Source Toolbox for Non-linear Time Series Analysis
Frontiers in Neuroinformatics, 2022 In many scientific fields including neuroscience, climatology or physics, complex relationships can be described most parsimoniously by non-linear mechanics.
Immo Weber +2 more
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