A CUSUM Tests for Stable Index Changes under Heavy-Tailed Sequences

2018 ◽  
Author(s):  
Hao Jin ◽  
Yanru Yao ◽  
Liping Yang
Keyword(s):  
Index Changes ◽  
Heavy Tailed ◽  
Cusum Tests ◽  
Stable Index

On the Noninvertible Moving Average Time Series with Infinite Variance

1993 ◽  
Vol 9 (4) ◽  
pp. 680-685 ◽  
Author(s):  
Ngai Hang Chan
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Moving Average ◽  
Infinite Variance ◽  
Average Model ◽  
Initial Value ◽  
Least Squares Estimate ◽  
Moving Average Model ◽  
Heavy Tailed ◽  
Stable Index

The limiting distribution of the least squares estimate of the derived process of a noninvertible and nearly noninvertible moving average model with infinite variance innovations is established as a functional of a Lévy process. The form of the limiting law depends on the initial value of the innovation and the stable index α. This result enables one to perform asymptotic testing for the presence of a unit root for a noninvertible moving average model through the constructed derived process under the null hypothesis. It provides not only a parallel analog of its autoregressive counterparts, but also a useful alternative to determine “over-differencing” for time series that exhibit heavy-tailed phenomena.

An Alternative to Cohen's κ

2006 ◽  
Vol 11 (1) ◽  
pp. 12-24 ◽  
Author(s):  
Alexander von Eye
Keyword(s):  
Simulation Study ◽  
Null Hypothesis ◽  
Categorical Variables ◽  
Alternative Measure ◽  
Rater Agreement ◽  
Verbal Processing ◽  
Heavy Tailed ◽  
Applicant Selection

At the level of manifest categorical variables, a large number of coefficients and models for the examination of rater agreement has been proposed and used. The most popular of these is Cohen's κ. In this article, a new coefficient, κ s , is proposed as an alternative measure of rater agreement. Both κ and κ s allow researchers to determine whether agreement in groups of two or more raters is significantly beyond chance. Stouffer's z is used to test the null hypothesis that κ s = 0. The coefficient κ s allows one, in addition to evaluating rater agreement in a fashion parallel to κ, to (1) examine subsets of cells in agreement tables, (2) examine cells that indicate disagreement, (3) consider alternative chance models, (4) take covariates into account, and (5) compare independent samples. Results from a simulation study are reported, which suggest that (a) the four measures of rater agreement, Cohen's κ, Brennan and Prediger's κ n , raw agreement, and κ s are sensitive to the same data characteristics when evaluating rater agreement and (b) both the z-statistic for Cohen's κ and Stouffer's z for κ s are unimodally and symmetrically distributed, but slightly heavy-tailed. Examples use data from verbal processing and applicant selection.

S&P 500 Index Changes and Investor Awareness

CFA Digest ◽  
2007 ◽  
Vol 37 (1) ◽  
pp. 55-57
Author(s):  
Joseph D.V. Vu
Keyword(s):  
Index Changes ◽  
Investor Awareness

New Hierarchically Structured Optical Materials for Dynamic Refractive Index Changes

2003 ◽  
Author(s):  
Bradley F. Chmelka ◽  
Earl Danielson ◽  
Michael D. Wyrsta
Keyword(s):  
Refractive Index ◽  
Optical Materials ◽  
Index Changes

Probability and Random Processes

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Random Processes ◽  
Distribution Functions ◽  
Basic Logic ◽  
Heavy Tailed Distributions ◽  
Random Components ◽  
Classical Distribution ◽  
Heavy Tailed ◽  
Basic Facts ◽  
Stochastic Events ◽  
Stochastic Event

Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.

scholarly journals MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES

2019 ◽  
Vol 35 (6) ◽  
pp. 1234-1270 ◽  
Author(s):  
Sébastien Fries ◽  
Jean-Michel Zakoian
Keyword(s):  
Conditional Distribution ◽  
Stable Distribution ◽  
Financial Time Series ◽  
Domain Of Attraction ◽  
Real Data ◽  
Autoregressive Processes ◽  
Financial Time ◽  
Causal Representation ◽  
Heavy Tailed ◽  
Non Gaussian

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.

scholarly journals Clinical characterization of dysautonomia in long COVID-19 patients

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Nicolas Barizien ◽  
Morgan Le Guen ◽  
Stéphanie Russel ◽  
Pauline Touche ◽  
Florent Huang ◽  
...  
Keyword(s):  
Mixed Models ◽  
Repeated Measures ◽  
Physical Medicine ◽  
Persistent Symptoms ◽  
Index Changes ◽  
Changes Over Time ◽  
And Control ◽  
Testing Group ◽  
Over Time

AbstractIncreasing numbers of COVID-19 patients, continue to experience symptoms months after recovering from mild cases of COVID-19. Amongst these symptoms, several are related to neurological manifestations, including fatigue, anosmia, hypogeusia, headaches and hypoxia. However, the involvement of the autonomic nervous system, expressed by a dysautonomia, which can aggregate all these neurological symptoms has not been prominently reported. Here, we hypothesize that dysautonomia, could occur in secondary COVID-19 infection, also referred to as “long COVID” infection. 39 participants were included from December 2020 to January 2021 for assessment by the Department of physical medicine to enhance their physical capabilities: 12 participants with COVID-19 diagnosis and fatigue, 15 participants with COVID-19 diagnosis without fatigue and 12 control participants without COVID-19 diagnosis and without fatigue. Heart rate variability (HRV) during a change in position is commonly measured to diagnose autonomic dysregulation. In this cohort, to reflect HRV, parasympathetic/sympathetic balance was estimated using the NOL index, a multiparameter artificial intelligence-driven index calculated from extracted physiological signals by the PMD-200 pain monitoring system. Repeated-measures mixed-models testing group effect were performed to analyze NOL index changes over time between groups. A significant NOL index dissociation over time between long COVID-19 participants with fatigue and control participants was observed (p = 0.046). A trend towards significant NOL index dissociation over time was observed between long COVID-19 participants without fatigue and control participants (p = 0.109). No difference over time was observed between the two groups of long COVID-19 participants (p = 0.904). Long COVID-19 participants with fatigue may exhibit a dysautonomia characterized by dysregulation of the HRV, that is reflected by the NOL index measurements, compared to control participants. Dysautonomia may explain the persistent symptoms observed in long COVID-19 patients, such as fatigue and hypoxia. Trial registration: The study was approved by the Foch IRB: IRB00012437 (Approval Number: 20-12-02) on December 16, 2020.

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