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A Bayesian significance test of change for correlated observations

Abdeldjalil Slama (2014)

Discussiones Mathematicae Probability and Statistics

This paper presents a Bayesian significance test for a change in mean when observations are not independent. Using a noninformative prior, a unconditional test based on the highest posterior density credible set is determined. From a Gibbs sampler simulation study the effect of correlation on the performance of the Bayesian significance test derived under the assumption of no correlation is examined. This paper is a generalization of earlier studies by KIM (1991) to not independent observations.

A comparison of cointegration tests

Petr Mariel (1996)

Applications of Mathematics

In this paper some of the cointegration tests applied to a single equation are compared. Many of the existent cointegration tests are simply extensions of the unit root tests applied to the residuals of the cointegrating regression and the habitual H 0 is no cointegration. However, some non residual-based tests and some tests of the opposite null hypothesis have recently appeared in literature. Monte Carlo simulations have been used for the power comparison of the nine selected tests ( A D F , Z ^ α , Z ^ t , D H S ,...

A note on prediction for discrete time series

Gusztáv Morvai, Benjamin Weiss (2012)


Let { X n } be a stationary and ergodic time series taking values from a finite or countably infinite set 𝒳 and that f ( X ) is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times λ n along which we will be able to estimate the conditional expectation E ( f ( X λ n + 1 ) | X 0 , , X λ n ) from the observations ( X 0 , , X λ n ) in a point wise consistent way for a restricted class of stationary and ergodic finite or countably infinite alphabet time series...

A note on the application of integrals involving cyclic products of kernels.

Valery V. Buldygin, Frederic Utzet, Vladimir Zaiats (2002)


In statistics of stochastic processes and random fields, a moment function or a cumulant of an estimate of either the correlation function or the spectral function can often contain an integral involving a cyclic product of kernels. We define and study this class of integrals and prove a Young-Hölder inequality. This inequality further enables us to study asymptotics of the above mentioned integrals in the situation where the kernels depend on a parameter. An application to the problem of estimation...

A sharp analysis on the asymptotic behavior of the Durbin–Watson statistic for the first-order autoregressive process

Bernard Bercu, Frédéric Proïa (2013)

ESAIM: Probability and Statistics

The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin–Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise....

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