Generalized spectral coherence for cyclostationary signals with α-stable distribution

2021 ◽  
Vol 159 ◽  
pp. 107737
Author(s):  
Piotr Kruczek ◽  
Radosław Zimroz ◽  
Jerome Antoni ◽  
Agnieszka Wyłomańska
2011 ◽  
Vol 30 (9) ◽  
pp. 2042-2045 ◽  
Author(s):  
Xu-tao Li ◽  
Shou-yong Wang ◽  
Lian-wen Jin

2019 ◽  
Vol 35 (6) ◽  
pp. 1234-1270 ◽  
Author(s):  
Sébastien Fries ◽  
Jean-Michel Zakoian

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.


Author(s):  
Mahnaz Khalafi ◽  
Ahmad Reza Soltani ◽  
Masoud Golalipour ◽  
Farzad Najafiamiri

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.


2019 ◽  
Vol 12 (4) ◽  
pp. 171
Author(s):  
Ashis SenGupta ◽  
Moumita Roy

The aim of this article is to obtain a simple and efficient estimator of the index parameter of symmetric stable distribution that holds universally, i.e., over the entire range of the parameter. We appeal to directional statistics on the classical result on wrapping of a distribution in obtaining the wrapped stable family of distributions. The performance of the estimator obtained is better than the existing estimators in the literature in terms of both consistency and efficiency. The estimator is applied to model some real life financial datasets. A mixture of normal and Cauchy distributions is compared with the stable family of distributions when the estimate of the parameter α lies between 1 and 2. A similar approach can be adopted when α (or its estimate) belongs to (0.5,1). In this case, one may compare with a mixture of Laplace and Cauchy distributions. A new measure of goodness of fit is proposed for the above family of distributions.


2013 ◽  
Vol 14 (4) ◽  
pp. 504-520 ◽  
Author(s):  
Anthony Fiche ◽  
Jean-Christophe Cexus ◽  
Arnaud Martin ◽  
Ali Khenchaf

2003 ◽  
Vol 34 (2) ◽  
pp. 54-69 ◽  
Author(s):  
Frank H. Duffy ◽  
Heidelise Als ◽  
Gloria B. McAnulty

EEG spectral coherence data in quiet sleep of 312 infants were evaluated, at 42 weeks post-menstrual age. All were medically healthy and living at home by time of evaluation. The sample consisted of prematurely born infants with a wide spectrum of underlying risk factors, as well as healthy fullterm infants. Initial 3040 coherence variables were reduced by principal components analysis in an unrestricted manner, which avoided the folding of spectral and spatial information into among-subject variance. One hundred fifty factors explained 90% of the total variance; 40 Varimax rotated factors explained 65% of the variance yielding a 50:1 data reduction. Factor loading patterns ranged from multiple spectral bands for a single electrode pair to multiple electrode pairs for a single spectral band and all intermediate possibilities. Simple left-right and anterior-posterior pairings were not observed within the factor loadings. By multiple regression analysis, the 40 factors significantly predicted gestational age at birth. By canonical correlation, significant relationships were demonstrated between the coherence factors and medical risk factors as well as neurobehavioral factors. Using discriminant analysis, the coherence factors successfully discriminated between infants with high and low medical risk status and between those with the best and worst neurobehavioral status. The two factors accounting for the most variance, and chosen across several analyses, indicated increased left central-temporal coherence from 6–24 Hz, and increased frontal-occipital coherence at 10 Hz, for the infants born closest to term with lowest medical risk factors and best neurobehavioral performance.


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