Estimation of second-order properties from jittered time series

1996 ◽  
Vol 48 (1) ◽  
pp. 29-48 ◽  
Author(s):  
Peter J. Thomson ◽  
Peter M. Robinson
Keyword(s):  
Time Series ◽  
Second Order

HIGHER ORDER COMPLEXITY OF TIME SERIES

2004 ◽  
Vol 14 (08) ◽  
pp. 2979-2990 ◽  
Author(s):  
FANJI GU ◽  
ENHUA SHEN ◽  
XIN MENG ◽  
YANG CAO ◽  
ZHIJIE CAI
Keyword(s):  
Time Series ◽  
Mental Arithmetic ◽  
Higher Order ◽  
Second Order ◽  
Stationary Time Series ◽  
Eeg Signals ◽  
Eyes Closed ◽  
Logistic Mapping ◽  
Original Time ◽  
Different Order

A concept of higher order complexity is proposed in this letter. If a randomness-finding complexity [Rapp & Schmah, 2000] is taken as the complexity measure, the first-order complexity is suggested to be a measure of randomness of the original time series, while the second-order complexity is a measure of its degree of nonstationarity. A different order is associated with each different aspect of complexity. Using logistic mapping repeatedly, some quasi-stationary time series were constructed, the nonstationarity degree of which could be expected theoretically. The estimation of the second-order complexity of these time series shows that the second-order complexities do reflect the degree of nonstationarity and thus can be considered as its indicator. It is also shown that the second-order complexities of the EEG signals from subjects doing mental arithmetic are significantly higher than those from subjects in deep sleep or resting with eyes closed.

scholarly journals Characterizing sand ripples at equilibrium phases

2013 ◽  
Vol 61 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Jie Qin ◽  
Deyu Zhong ◽  
Guangqian Wang
Keyword(s):  
Time Series ◽  
Random Fields ◽  
Morphological Characteristics ◽  
Structure Functions ◽  
Second Order ◽  
Order Structure ◽  
Two Dimensional ◽  
Sand Ripples ◽  
Digital Elevation ◽  
Equilibrium Phases

Abstract Morphological characteristics of ripples are analyzed considering bed surfaces as two dimensional random fields of bed elevations. Two equilibrium phases are analyzed with respect to successive development of ripples based on digital elevation models. The key findings relate to the shape of the two dimensional second-order structure functions and multiscaling behavior revealed by higher-order structure functions. Our results suggest that (1) the two dimensional second-order structure functions can be used to differentiate the two equilibrium phases of ripples; and (2) in contrast to the elevational time series of ripples that exhibit significant multiscaling behavior, the DEMs of ripples at both equilibrium phases do not exhibit multiscaling behavior.

A note on the asymptotic eigenvalues and eigenvectors of the dispersion matrix of a second-order Stationary Process on a d-dimensional Lattice

1986 ◽  
Vol 23 (02) ◽  
pp. 529-535 ◽  
Author(s):  
R. J. Martin
Keyword(s):  
Time Series ◽  
Stationary Process ◽  
Second Order ◽  
Stationary Time Series ◽  
Stationary Processes ◽  
Dispersion Matrix ◽  
Eigenvalues And Eigenvectors ◽  
Dimensional Lattice ◽  
Stationary Time

A sufficiently large finite second-order stationary time series process on a line has approximately the same eigenvalues and eigenvectors of its dispersion matrix as its counterpart on a circle. It is shown here that this result can be extended to second-order stationary processes on a d-dimensional lattice.

Basic Fourier series

1979 ◽  
Vol 369 (1736) ◽  
pp. 115-136 ◽  
Keyword(s):  
Time Series ◽  
Fourier Series ◽  
Stochastic Processes ◽  
Numerical Approximation ◽  
Basic Number ◽  
Second Order ◽  
Orthogonal Functions ◽  
Sturm Liouville

The concept of basic number is applied to the development of a simple analogue of the Sturm–Liouville system of the second order. This is then employed to deduce a family of q -orthogonal functions, which leads to a generalization of the Fourier and Fourier–Bessel expansions. The numerical approximation of basic integrals is discussed and some aspects of the evaluation of C a (q; x) are mentioned. A few of the zeros of this function are listed, and, in conclusion, an indication is given of the possibility of applying the analysis presented in this paper to thé study of stochastic processes and time-series.

Correlation analysis of continuous emotional response to music: Correcting for the effects of serial correlation

2001 ◽  
Vol 5 (1_suppl) ◽  
pp. 213-236 ◽  
Author(s):  
Emery Schubert
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Emotional Response ◽  
Serial Correlation ◽  
Time Series Data ◽  
Second Order ◽  
Series Data ◽  
First Order ◽  
The Relationship ◽  
Pearson Correlations

Publications of research concerning continuous emotional responses to music are increasing. The developing interest brings with it a need to understand the problems associated with the analysis of time series data. This article investigates growing concern in the use of conventional Pearson correlations for comparing time series data. Using continuous data collected in response to selected pieces of music, with two emotional dimensions for each piece, two falsification studies were conducted. The first study consisted of a factor analysis of the individual responses using the original data set and its first-order differenced transformation. The differenced data aligned according to theoretical constraints better than the untransformed data, supporting the use of first-order difference transformations. Using a similar method, the second study specifically investigated the relationship between Pearson correlations, difference transformations and the critical correlation coefficient above which the conventional correlation analysis remains internally valid. A falsification table was formulated and quantified through a hypothesis index function. The study revealed that correlations of undifferenced data must be greater than 0.75 for a valid interpretation of the relationship between bivariate emotional response time series data. First and second-order transformations were also investigated and found to be valid for correlation coefficients as low as 0.24. Of the three version of the data (untransformed, first-order differenced, and second-order differenced), first-order differenced data produced the fewest problems with serial correlation, whilst remaining a simple and meaningful transformation.

Long-Term Area Statistics for Maximum Crest Height Under a Fixed Platform Deck

2018 ◽  
Author(s):  
Øistein Hagen ◽  
Jørn Birknes-Berg ◽  
Ida Håøy Grue ◽  
Gunnar Lian ◽  
Kjersti Bruserud ◽  
...  
Keyword(s):  
Time Series ◽  
North Sea ◽  
Extreme Values ◽  
Second Order ◽  
Irregular Waves ◽  
Scatter Diagram ◽  
Short Term ◽  
Wave Impact ◽  
Crest Height

As offshore reservoirs are depleted, the seabed may subside. Furthermore, the extreme crests estimates are now commonly higher than obtained previously due to improved understanding of statistics of non-linear irregular waves. Consequently, bottom fixed installations which have previously had sufficient clearance between the deck and the sea surface may be in a situation where wave impact with the deck must be considered at relevant probability levels. In the present paper, we investigate the long-term area statistics for maximum crest height under a fixed platform deck for 2nd order short crested and long crested sea based on numerical simulations as a function of platform deck dimension for jackets. The results are for one location in the northern North Sea, but some key results are also reported and verified for a more benign southern North Sea location. Time domain simulations for long crested and short crested waves over a spatial domain with dimension of a platform deck are performed, and relevant statistics for airgap assessment determined. Second order waves are simulated for the different cells in the (Hs, Tp) scatter diagram for Torsethaugen two-peak wave spectrum for long-crested and short-crested sea. A total of 1000 3-hour sea states are generated per cell, and time series generated for 160 spatial points under a platform deck. Short-term and long-term statistics are established for the maximum crest height as function of platform dimension; inline and transverse to the wave direction, and over the area. Results are given for the linear sea and for the second order time series. The annual q-probability estimates for the maximum crest height over area as a function of platform dimension is determined for a location at the Norwegian Continental Shelf by weighting the short-term statistics for the individual cells in the scatter diagram with the long-term probability of occurrence of the sea state. To reduce the number of numerical second order simulations, the effect of excluding cells that have a negligible effect on the long term extreme crest estimate is discussed. The percentiles in the distribution of maximum crest (over area) in design sea states that corresponds to the extreme values obtained from the long-term analysis are determined for long crested and short crested sea. The increase in the extreme crest over an area compared to the point in space estimate is estimated for both linear and second order surface elevation.

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