Asymptotics for the residual-based bootstrap approximation in nearly nonstationary AR(1) models with possibly heavy-tailed innovations

2013 ◽  
Vol 83 (11) ◽  
pp. 2553-2562 ◽  
Author(s):  
Ke-Ang Fu ◽  
Yuechao Li ◽  
Andrew Cheuk-Yin Ng
Keyword(s):  
Bootstrap Approximation ◽  
Heavy Tailed

scholarly journals Monitoring Persistence Change in Heavy-Tailed Observations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 936
Author(s):  
Dan Wang
Keyword(s):  
Kernel Method ◽  
Alternative Hypothesis ◽  
Null Distribution ◽  
Real Data ◽  
Ratio Test ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Approximation ◽  
Heavy Tailed ◽  
Better Than

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of I(1)-to-I(0) and I(0)-to-I(1). On the basis of residual CUSUM, the test statistic is constructed in a ratio form. I prove the null distribution of the test statistic. The consistency under alternative hypothesis is also discussed. However, the null distribution of the test statistic contains an unknown tail index. To address this challenge, I present a bootstrap approximation method for determining the rejection region of this test. Simulation studies of artificial data are conducted to assess the finite sample performance, which shows that our method is better than the kernel method in all listed cases. The analysis of real data also demonstrates the excellent performance of this method.

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.

Network Selection in Wireless Heterogeneous Environment Based on Available Bandwidth Estimation

2019 ◽  
Vol 12 ◽  
Author(s):  
Kiran Ahuja ◽  
Brahmjit Singh ◽  
Rajesh Khanna
Keyword(s):  
Real Time ◽  
Estimation Error ◽  
Network Selection ◽  
Bandwidth Estimation ◽  
Heterogeneous Environment ◽  
Bootstrap Approximation ◽  
Available Bandwidth ◽  
Internet Connection ◽  
Available Bandwidth Estimation ◽  
Selection Of

Background: With the availability of multiple options in wireless network simultaneously, Always Best Connected (ABC) requires dynamic selection of the best network and access technologies. Objective: In this paper, a novel dynamic access network selection algorithm based on the real time is proposed. The available bandwidth (ABW) of each network is required to be estimated to solve the network selection problem. Method: Proposed algorithm estimates available bandwidth by taking averages, peaks, low points and bootstrap approximation for network selection. It monitors real-time internet connection and resolves the selection issue in internet connection. The proposed algorithm is capable of adapting to prevailing network conditions in heterogeneous environment of 2G, 3G and WLAN networks without user intervention. It is implemented in temporal and spatial domains to check its robustness. Estimation error, overhead, estimation time with the varying size of traffic and reliability are used as the performance metrics. Results: Through numerical results, it is shown that the proposed algorithm’s ABW estimation based on bootstrap approximation gives improved performance in terms of estimation error (less than 20%), overhead (varies from 0.03% to 83%) and reliability (approx. 99%) with respect to existing techniques. Conclusion: Our proposed methodology of network selection criterion estimates the available bandwidth by taking averages, peaks, and low points and bootstrap approximation method (standard deviation) for the selection of network in the wireless heterogeneous environment. It monitors real-time internet connection and resolves internet connections selection issue. All the real-time usage and test results demonstrate the productivity and adequacy of available bandwidth estimation with bootstrap approximation as a practical solution for consistent correspondence among heterogeneous wireless networks by precise network selection for multimedia services.

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.

A novel robust Kalman filter with unknown non-stationary heavy-tailed noise

Automatica ◽  
2021 ◽  
Vol 127 ◽  
pp. 109511
Author(s):  
Hao Zhu ◽  
Guorui Zhang ◽  
Yongfu Li ◽  
Henry Leung
Keyword(s):  
Kalman Filter ◽  
Robust Kalman Filter ◽  
Heavy Tailed
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