scholarly journals Testing The Order of Markov Dependence in Error Data of IEEE802.11a Standard

2019 ◽  
pp. 617-625
Author(s):  
Shaghayegh Kordnoori ◽  
Hamidreza Mostafaei ◽  
Mohammad Hassan Behzadi
Keyword(s):  
Time Series ◽  
Sample Size ◽  
Markov Property ◽  
Surrogate Data ◽  
Significance Test ◽  
Uniform Sampling ◽  
Markov Dependence

The Markov order is a crucial measure of the memory of a process and its information is essential for appropriate simulation of aspects of the process. In this paper we suggest a robust and straightforward exact significance test based on generating surrogate data to assess the Markov order of a time series. This method is valid for any sample size and certifies a uniform sampling from the set of sequences that definitely have the nth order characteristics of the observed data. The Markov property and order of IEEE802.11a errors are investigated using this test.

TESTING FOR NONLINEARITY IN SHANGHAI STOCK MARKET

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2720-2724 ◽  
Author(s):  
HAIYAN WANG ◽  
LONGKUN TANG
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Null Hypothesis ◽  
Quantitative Method ◽  
Multivariate Time Series ◽  
Surrogate Data ◽  
Significance Test ◽  
Test Statistic ◽  
Gaussian Random Process ◽  
Linear And Nonlinear

In this paper, we apply IAAFT to generate surrogate time series of measured multivariate time series. A quantitative method to detect nonlinearity in multivariate time series is proposed using the generalized redundancy and linear redundancy as the significance test statistic. The null hypothesis of a multivariate linear Gaussian random process is tested using the multivariate surrogate data. The validity of this method is demonstrated using two types models (linear and nonlinear) and applied to Shanghai stock market.

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

A Significance Test for Time Series

1942 ◽  
Vol 24 (1) ◽  
pp. 366
Author(s):  
Warren C. Waite ◽  
W. Allen Wallis ◽  
Geoffrey H. Moore
Keyword(s):  
Time Series ◽  
Significance Test

scholarly journals Chaotic Patterns in Aeroelastic Signals

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
F. D. Marques ◽  
R. M. G. Vasconcellos
Keyword(s):  
Time Series ◽  
State Space ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Separated Flow ◽  
Direct Analysis ◽  
Surrogate Data ◽  
The State ◽  
Aeroelastic System ◽  
Value Decomposition

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincaré sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

scholarly journals APPLICATION OF CHAOS GAME REPRESENTATION TO NONLINEAR TIME SERIES ANALYSIS

Fractals ◽  
2006 ◽  
Vol 14 (01) ◽  
pp. 27-35 ◽  
Author(s):  
TOMOYA SUZUKI ◽  
TOHRU IKEGUCHI ◽  
MASUO SUZUKI
Keyword(s):  
Time Series ◽  
Real Time ◽  
Dna Sequences ◽  
Surrogate Data ◽  
Nonlinear Time Series Analysis ◽  
Conditional Probabilities ◽  
Fractal Structures ◽  
Chaos Game Representation ◽  
Chaos Game ◽  
Game Representation

Iterative function systems are often used for investigating fractal structures. The method is also referred as Chaos Game Representation (CGR), and is applied for representing characteristic structures of DNA sequences visually. In this paper, we proposed an original way of plotting CGR to easily confirm the property of the temporal evaluation of a time series. We also showed existence of spurious characteristic structures of time series, if we carelessly applied the CGR to real time series. We revealed that the source of spurious identification came from non-uniformity of the frequency histograms of the time series, which is often the case of analyzing real time series. We also showed how to avoid such spurious identification by applying the method of surrogate data and introducing conditional probabilities of the time series.

scholarly journals An ARFIMA-based model for daily precipitation amounts with direct access to fluctuations

2020 ◽  
Vol 34 (10) ◽  
pp. 1487-1505
Author(s):  
Katja Polotzek ◽  
Holger Kantz
Keyword(s):  
Time Series ◽  
Sample Size ◽  
Confidence Intervals ◽  
Daily Precipitation ◽  
Rainfall Simulation ◽  
Direct Access ◽  
Effective Sample Size ◽  
Sample Mean ◽  
Daily Data ◽  
Synthetic Time Series

Abstract Correlations in models for daily precipitation are often generated by elaborate numerics that employ a high number of hidden parameters. We propose a parsimonious and parametric stochastic model for European mid-latitude daily precipitation amounts with focus on the influence of correlations on the statistics. Our method is meta-Gaussian by applying a truncated-Gaussian-power (tGp) transformation to a Gaussian ARFIMA model. The speciality of this approach is that ARFIMA(1, d, 0) processes provide synthetic time series with long- (LRC), meaning the sum of all autocorrelations is infinite, and short-range (SRC) correlations by only one parameter each. Our model requires the fit of only five parameters overall that have a clear interpretation. For model time series of finite length we deduce an effective sample size for the sample mean, whose variance is increased due to correlations. For example the statistical uncertainty of the mean daily amount of 103 years of daily records at the Fichtelberg mountain in Germany equals the one of about 14 years of independent daily data. Our effective sample size approach also yields theoretical confidence intervals for annual total amounts and allows for proper model validation in terms of the empirical mean and fluctuations of annual totals. We evaluate probability plots for the daily amounts, confidence intervals based on the effective sample size for the daily mean and annual totals, and the Mahalanobis distance for the annual maxima distribution. For reproducing annual maxima the way of fitting the marginal distribution is more crucial than the presence of correlations, which is the other way round for annual totals. Our alternative to rainfall simulation proves capable of modeling daily precipitation amounts as the statistics of a random selection of 20 data sets is well reproduced.

scholarly journals Quantifying Statistical Interdependence by Message Passing on Graphs—Part I: One-Dimensional Point Processes

2009 ◽  
Vol 21 (8) ◽  
pp. 2152-2202 ◽  
Author(s):  
J. Dauwels ◽  
F. Vialatte ◽  
T. Weber ◽  
A. Cichocki
Keyword(s):  
Time Series ◽  
Message Passing ◽  
Point Processes ◽  
Pairwise Alignment ◽  
Surrogate Data ◽  
Map Estimation ◽  
One Dimensional ◽  
Novel Approach ◽  
Average Similarity ◽  
Stochastic Event

We present a novel approach to quantify the statistical interdependence of two time series, referred to as stochastic event synchrony (SES). The first step is to extract “events” from the two given time series. The next step is to try to align events from one time series with events from the other. The better the alignment, the more similar the two time series are considered to be. More precisely, the similarity is quantified by the following parameters: time delay, variance of the timing jitter, fraction of noncoincident events, and average similarity of the aligned events. The pairwise alignment and SES parameters are determined by statistical inference. In particular, the SES parameters are computed by maximum a posteriori (MAP) estimation, and the pairwise alignment is obtained by applying the max-product algorithm. This letter deals with one-dimensional point processes; the extension to multidimensional point processes is considered in a companion letter in this issue. By analyzing surrogate data, we demonstrate that SES is able to quantify both timing precision and event reliability more robustly than classical measures can. As an illustration, neuronal spike data generated by the Morris-Lecar neuron model are considered.

A WAVELET BASED SIGNIFICANCE TEST FOR PERIODICITIES IN INDIAN MONSOON RAINFALL

2008 ◽  
Vol 06 (02) ◽  
pp. 291-304 ◽  
Author(s):  
SARITA AZAD ◽  
R. NARASIMHA ◽  
S. K. SETT
Keyword(s):  
Time Series ◽  
Indian Monsoon ◽  
Statistical Significance ◽  
Significance Test ◽  
Rainfall Time Series ◽  
Reference Spectrum ◽  
Power Spectral ◽  
Reconstructed Time Series ◽  
Fourier Spectral Methods ◽  
Stationary Component

This paper is a sequel to a recent study of the authors' that uses a combination of multiresolution analysis (MRA) and classical Fourier spectral methods, to identify 17 peaks in the power spectral density of the Homogeneous Indian Monsoon (HIM) rainfall time series constructed in Ref. 1. Here we propose a new procedure for testing the statistical significance of these peaks. In this procedure, using MRA the stationary component of the rainfall time series is first identified. Then (partially) reconstructed time series are derived over each scale band in the stationary component. For each of these time series an appropriately colored reference spectrum is derived. The significance of the detected peaks is then determined using a χ2 test against the reference spectra, which together represent a noise process spectrally close to rainfall. It is concluded that HIM rainfall exhibits 10 statistically significant periodicities at a confidence level of 99.9%.

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