Dynamical Analysis of Time Series by Statistical Tests

1997 ◽  
Vol 07 (12) ◽  
pp. 2629-2652 ◽  
Author(s):  
Gustavo Deco ◽  
Christian Schittenkopf ◽  
Bernd Schürmann
Keyword(s):  
Time Series ◽  
Information Flow ◽  
Statistical Tests ◽  
Statistical Test ◽  
Dynamical Analysis ◽  
Fourier Space ◽  
Statistical Framework ◽  
Temporal Structures ◽  
Analysis Of Time Series

In this review we deal with the application of statistical test techniques for the extraction of structures in time series. Two kinds of questions are answered in this statistical framework: Are there any temporal dependences in the data? and Which kind of dynamics generate these temporal dependences? The first question is known as the problem of predictability and also considers the aspect of stationarity. The second question is deeper in the sense that it deals with the dynamical characterization of the detected temporal structures. Central to our approach is a cumulant-based measure of statistical dependences in Fourier space. The dynamical aspects are studied by means of the information flow. The theory is illustrated by artificial and real-world, stochastic and chaotic examples.

Asteroseismic Data Analysis

2017 ◽  
Author(s):  
Sarbani Basu ◽  
William J. Chaplin
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Seismic Data ◽  
Stellar Populations ◽  
Instruction Manual ◽  
Kepler Mission ◽  
Cool Stars ◽  
Internal Properties ◽  
Analysis Of Time Series

Studies of stars and stellar populations, and the discovery and characterization of exoplanets, are being revolutionized by new satellite and telescope observations of unprecedented quality and scope. Some of the most significant advances have been in the field of asteroseismology, the study of stars by observation of their oscillations. This book gives a comprehensive technical introduction to this discipline. It not only helps students and researchers learn about asteroseismology; it also serves as an essential instruction manual for those entering the field. The book presents readers with the foundational techniques used in the analysis and interpretation of asteroseismic data on cool stars that show solar-like oscillations. The techniques have been refined, and in some cases developed, to analyze asteroseismic data collected by the NASA Kepler mission. Topics range from the analysis of time-series observations to extract seismic data for stars to the use of those data to determine global and internal properties of the stars. Reading lists and problem sets are provided, and data necessary for the problem sets are available online.

scholarly journals Simplicial Multivalued Maps and the Witness Complex for Dynamical Analysis of Time Series

2015 ◽  
Vol 14 (3) ◽  
pp. 1278-1307 ◽  
Author(s):  
Zachary Alexander ◽  
Elizabeth Bradley ◽  
James D. Meiss ◽  
Nicole F. Sanderson
Keyword(s):  
Time Series ◽  
Dynamical Analysis ◽  
Multivalued Maps ◽  
Witness Complex ◽  
Analysis Of Time Series

scholarly journals Time-Varying Volatility in Bitcoin Market and Information Flow at Minute-Level Frequency

2021 ◽  
Vol 9 ◽  
Author(s):  
Irena Barjašić ◽  
Nino Antulov-Fantulin
Keyword(s):  
Time Series ◽  
Information Flow ◽  
Statistical Tests ◽  
External Information ◽  
Bid Ask Spread ◽  
Sample Data ◽  
Out Of Sample ◽  
External Signals ◽  
Mixture Of Distribution Hypothesis ◽  
Autoregressive Conditional Heteroscedasticity

In this article, we analyze the time series of minute price returns on the Bitcoin market through the statistical models of the generalized autoregressive conditional heteroscedasticity (GARCH) family. We combine an approach that uses historical values of returns and their volatilities—GARCH family of models, with a so-called Mixture of Distribution Hypothesis, which states that the dynamics of price returns are governed by the information flow about the market. Using time series of Bitcoin-related tweets, the Bitcoin trade volume, and the Bitcoin bid–ask spread, as external information signals, we test for improvement in volatility prediction of several GARCH model variants on a minute-level Bitcoin price time series. Statistical tests show that GARCH(1,1) and cGARCH(1,1) react the best to the addition of external signals to model the volatility process on out-of-sample data.

scholarly journals Statistical analysis of time series with scaling indices

2000 ◽  
Vol 5 (4) ◽  
pp. 297-309
Author(s):  
Harald Atmnaspacher ◽  
Werner Ehm ◽  
Herbert Scheingraber ◽  
Gerda Wiedenmann
Keyword(s):  
Time Series ◽  
Statistical Analysis ◽  
Signal To Noise Ratio ◽  
Statistical Tests ◽  
Statistical Techniques ◽  
Signal To Noise ◽  
Random Components ◽  
Noise Ratio ◽  
Selection Of ◽  
Analysis Of Time Series

Statistical techniques based on scaling indices are applied to detect and investigate patterns in empirically given time series. The key idea is to use the distribution of scaling indices obtained from a delay representation of the empirical time series to distinguish between random and non-random components. Statistical tests for this purpose are designed and applied to specific examples. It is shown that a selection of subseries by scaling indices can significantly enhance the signal-to-noise ratio as compared to that of the total time series.

Correlation in the heart rate data

1998 ◽  
Vol 2 ◽  
pp. 141-148
Author(s):  
J. Ulbikas ◽  
A. Čenys ◽  
D. Žemaitytė ◽  
G. Varoneckas
Keyword(s):  
Nonlinear Dynamics ◽  
Experimental Data ◽  
Heart Rate ◽  
Time Series ◽  
Cardiovascular Function ◽  
Statistical Properties ◽  
Rate Data ◽  
Heart Rate Data ◽  
Dynamical Nature ◽  
Analysis Of Time Series

Variety of methods of nonlinear dynamics have been used for possibility of an analysis of time series in experimental physiology. Dynamical nature of experimental data was checked using specific methods. Statistical properties of the heart rate have been investigated. Correlation between of cardiovascular function and statistical properties of both, heart rate and stroke volume, have been analyzed. Possibility to use a data from correlations in heart rate for monitoring of cardiovascular function was discussed.

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