Detecting nonlinearity in multivariate time series

We propose an extension to time series with several simultaneously measured variables of the nonlinearity test, which combines the redundancy -- linear redundancy approach with the surrogate data technique. For several variables various types of the redundancies can be defined, in order to test specific dependence structures between/among (groups of) variables. The null hypothesis of a multivariate linear stochastic process is tested using the multivariate surrogate data. The linear redundancies are used in order to avoid spurious results due to imperfect surrogates. The method is demonstrated using two types of numerically generated multivariate series (linear and nonlinear) and experimental multivariate data from meteorology and physiology.Comment: 11 pages, compressed and uuencoded postscript file, figures included. Also available by anonymous ftp at ftp://ftp.santafe.edu/pub/mp/multi, E-mail: [email protected], [email protected]

Coarse-grained entropy rates for characterization of complex time series

A method for classification of complex time series using coarse-grained entropy rates (CER's) is presented. The CER's, which are computed from information-theoretic functionals -- redundancies, are relative measures of regularity and predictability, and for data generated by dynamical systems they are related to Kolmogorov-Sinai entropy. A deterministic dynamical origin of the data under study, however, is not a necessary condition for the use of the CER's, since the entropy rates can be defined for stochastic processes as well. Sensitivity of the CER's to changes in data dynamics and their robustness with respect to noise are tested by using numerically generated time series resulted from both deterministic -- chaotic and stochastic processes. Potential application of the CER's in analysis of physiological signals or other complex time series is demonstrated by using examples from pharmaco-EEG and tremor classification.Comment: 15 pages, uuencoded compressed postscript file, figures embedded in the text, , <[email protected]

Testing For Nonlinearity Using Redundancies: Quantitative and Qualitative Aspects

A method for testing nonlinearity in time series is described based on information-theoretic functionals -- redundancies, linear and nonlinear forms of which allow either qualitative, or, after incorporating the surrogate data technique, quantitative evaluation of dynamical properties of scrutinized data. An interplay of quantitative and qualitative testing on both the linear and nonlinear levels is analyzed and robustness of this combined approach against spurious nonlinearity detection is demonstrated. Evaluation of redundancies and redundancy-based statistics as functions of time lag and embedding dimension can further enhance insight into dynamics of a system under study.Comment: 32 pages + 1 table in separate postscript files, 12 figures in 12 encapsulated postscript files, all in uuencoded, compressed tar file. Also available by anon. ftp to santafe.edu, in directory pub/Users/mp/qq. To be published in Physica D., [email protected]

Synchronization and Information Flow in EEG of Epileptic Patients

An information-theoretic approach for studying synchronization phenomena in experimental time series is presented and demonstrated in analysis of EEG recordings of an epileptic patients. Two levels of synchronization leading to seizures are quantified and "directions of information flow" (drive-response relationships) are identified

Cross-Scale Interactions and Information Transfer

An information-theoretic approach for detecting interactions and informationtransfer between two systems is extended to interactions between dynamical phenomenaevolving on different time scales of a complex, multiscale process. The approach isdemonstrated in the detection of an information transfer from larger to smaller time scales ina model multifractal process and applied in a study of cross-scale interactions in atmosphericdynamics. Applying a form of the conditional mutual information and a statistical test basedon the Fourier transform and multifractal surrogate data to about a century long recordsof daily mean surface air temperature from various European locations, an informationtransfer from larger to smaller time scales has been observed as the influence of the phaseof slow oscillatory phenomena with the periods around 6–11 years on the amplitudes of thevariability characterized by the smaller temporal scales from a few months to 4–5 years.These directed cross-scale interactions have a non-negligible effect on interannual airtemperature variability in a large area of Europe

Direction of coupling from phases of interacting oscillators: An information-theoretic approach.

A directionality index based on conditional mutual information is proposed for application to the instantaneous phases of weakly coupled oscillators. Its abilities to distinguish unidirectional from bidirectional coupling, as well as to reveal and quantify asymmetry in bidirectional coupling, are demonstrated using numerical examples of quasiperiodic, chaotic, and noisy oscillators, as well as real human cardiorespiratory data

Statistical Modelling of El Niño - Southern Oscillation in Climatology

summary:Pri modelovaní v klimatológii a meteorológii rozlišujeme dva základné druhy modelov — dynamické a štatistické. Dynamické modely majú fyzikálny základ, ktorý pozostáva z diskretizovaných diferenciálnych rovníc a súčasného stavu ako počiatočnej podmienky a následne modelujú stav systému integrovaním týchto rovníc v čase. Štatistické modely sú už v základe odlišné: ich fungovanie sa nezakladá na fyzikálnych mechanizmoch tvoriacich dynamiku modelovaného systému, ale sú odvodené z analýzy chodu počasia v minulosti. V tomto článku opíšeme príklad štatistického modelu, ktorý modeluje atmosféricko-oceánsky jav El Niño - Southern Oscillation. Zvýšenú pozornosť venujeme modelovaniu nelineárnych medziškálových interakcií. Okrem štatistických vlastností modelu sa tiež zaoberáme parametrizáciami šumu. Taktiež zvažujeme možnosť použitia štatistických modelov nízkej komplexity ako surogátnych modelov na generovanie dát za účelom štatistického testovania hypotéz

Statistical Modelling of El Niño - Southern Oscillation in Climatology

summary:Pri modelovaní v klimatológii a meteorológii rozlišujeme dva základné druhy modelov — dynamické a štatistické. Dynamické modely majú fyzikálny základ, ktorý pozostáva z diskretizovaných diferenciálnych rovníc a súčasného stavu ako počiatočnej podmienky a následne modelujú stav systému integrovaním týchto rovníc v čase. Štatistické modely sú už v základe odlišné: ich fungovanie sa nezakladá na fyzikálnych mechanizmoch tvoriacich dynamiku modelovaného systému, ale sú odvodené z analýzy chodu počasia v minulosti. V tomto článku opíšeme príklad štatistického modelu, ktorý modeluje atmosféricko-oceánsky jav El Niño - Southern Oscillation. Zvýšenú pozornosť venujeme modelovaniu nelineárnych medziškálových interakcií. Okrem štatistických vlastností modelu sa tiež zaoberáme parametrizáciami šumu. Taktiež zvažujeme možnosť použitia štatistických modelov nízkej komplexity ako surogátnych modelov na generovanie dát za účelom štatistického testovania hypotéz

Causality in extremes of time series

Consider two stationary time series with heavy-tailed marginal distributions. We aim to detect whether they have a causal relation, that is, if a change in one of them causes a change in the other. Usual methods for causality detection are not well suited if the causal mechanisms only manifest themselves in extremes. This paper aims to detect the causal relations in extremes between time series. We define the so-called causal tail coefficient for time series, which, under some assumptions, correctly detects the asymmetrical causal relations between extremes of the time series. The advantage is that this method works even if nonlinear relations and common ancestors are present. Moreover, we mention how our method can help detect a time delay between the two time series. We describe some of its asymptotic properties and show how it performs on some simulations. Finally, we show how this method works on space-weather and hydro-meteorological data sets.Comment: 54 pages, 10 figures, Submitted to Extreme