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Lecture 13 Time Series: Stationarity, AR(p) & MA(q)

RS –EC2 -Lecture 13 1 1 Lecture 13 Time Series: Stationarity, AR(p) & MA(q) Time Series: Introduction • In the early 1970’s, it was discovered that simple time series models performed better than the complicated multivarate, then popular, 1960s macro models

Asymptotic Palm likelihood theory for stationary point processes

Palm likelihood estimator are simple. Conditions are provided under which the Palm likelihood estimator is strongly consistent and asymptotically normally distributed. Keywords Asymptotic normality · Cluster processes ·Consistency · Neyman–Scott processes · Log Gaussian Cox processes · Palm likelihood · Spatial point process ·Strong mixing


EMPIRICAL PROCESSES OF STATIONARY SEQUENCES 315 as a cumulative weighted prediction measure. It is worthwhile to note that khj(θ,ξ0) − hj(θ,ξ∗0)k has the same order of magnitude as kP0h(θ,ξj)k.

The Equivalence of Ergodicity and Weak Mixing for Infinitely

paper Cambanis et al. [1] have proven the equivalence of ergodicity and weak mixing for all stationary symmetric infinitely divisible processes. Since it is usually much easier to characterize weak mixing than ergodicity, these results are important in obtaining definitive conditions for ergodicity.


A NOTE ON STRONG MIXING By Soutir Bandyopadhyay Department of Statistics Iowa State University April 21, 2006 Abstract The strong mixing property for a sequence of random variables is interesting in its own right. It is discussed that under what conditions the strong mixing property holds for linear stochastic processes and in particular ARMA ...


conditions under which they admit a Dieker{Yakir type representation. Examples for the process W will be general Gaussian processes with stationary increments and L evy processes. In Section3we show that the Dieker{Yakir constant (3) conincides with the constant C F in the intensity of the classical M3 representation (7).

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Basic Properties of Strong Mixing Conditions

R.C. Bradley/Strong mixing conditions 109 with stochastic processes. The \coe cient of information" I(A;B) (along with the related notion of entropy) was developed in papers such as [78] and [146]. The following inequalities give the ranges of possible values

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CENTRAL LIMIT THEOREMFOR STATIONARY PROCESSES M. ROSENBLATT UNIVERSITY OF CALIFORNIA, SAN DIEGO 1. Introduction Adiscussion ofstrong mixing and uniform ergodicity is presented, partly in terms oftheir relation to the central limit problem.

Mittal : A New Mixing Condition for Stationary Gaussian Processes

Weak Convergence for the Maxima of Stationary Gaussian Processes Using Random Normalization McCormick, William P., The Annals of Probability, 1980; Strong Laws for the Maxima of Stationary Gaussian Processes Mittal, Yash and Ylvisaker, Donald, The Annals of Probability, 1976; Rates of Convergence for Conditional Expectations Zabell, Sandy L ...


Kolmogorov, A.N. & Y.A. Rozanov (1960) On the strong mixing conditions for stationary Gaussian sequences. Theory of Probability and Its Applications 5 , 204 – 207 . Künsch , H.R. ( 1989 ) The jacknife and bootstrap for general stationary observations .

Bradley : On the behavior of the covariance matrices in a

Illinois J. Math. Volume 56, Number 3 (2012), 677-704. On the behavior of the covariance matrices in a multivariate central limit theorem under some mixing conditions

Strong mixing conditions - Encyclopedia of Mathematics

Strong Mixing Conditions. Richard C. Bradley Department of Mathematics, Indiana University, Bloomington, Indiana, USA There has been much research on stochastic models that have a well defined, specific structure --- for example, Markov chains, Gaussian processes, or linear models, including ARMA (autoregressive -- moving average) models.

Strong Local Nondeterminism and Sample Path Properties of

relies on the special properties of stationary Gaussian processes. Cuzick and DuPreez (1982, p. 811) point out that it appears to be di–cult to establish conditions under which general Gaussian processes possess the various forms of strong local nondeterminism. There have only been a few known examples of strongly locally nondeterministic

A Note on the Almost Sure Central Limit Theorem for Partial

Let be a strictly stationary sequence of ρ?-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums , where , . The result generalizes and improves the

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nential autoregressive processes among others. The imposed condition on (Xk) is directly related to the data-generating mechanism of the process and hence is easily veriflable. Ad-ditionally, we do not need the summability conditions on joint cumulants and/or strong mixing conditions.

Nonparametric estimation of conditional probability densities and expectations of stationary processes: strong

A.N. Kolmogorov and Yu.A. Rozanov, On strong mixing conditions for stationary Gaussian processes, Theory Probability Appl. 5 (1960) 204-207. [3] E. Masry, Almost sure convergence of recursive density estimators for stationary mixing processes, Statist

A strong mixing condition for second-order stationary random

[11] I. A. Ibragimov and V. N. Solev, A condition for the regularity of a Gaussian stationary process, Soviet Math. Dokl. 10 (1969), 371-375. [12] G. Kallianpur, A. G. Miamee and H. Niemi, On the prediction theory of two-parameter stationary random fields, technical report No. 178, Center for Stochastic Processes, University of North Carolina ...

Introduction to Strong Mixing Conditions

3. Five classic strong mixing conditions 4. Norms and connections with interpolation theory 5. Some other strong mixing conditions 6.Independent pairs of 6-fields 7. Markov chains 8. Second order properties 9. Stationary Gaussian sequences 10. Central limit theorems under the strong mixing condition 11.

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The One‐Sided Barrier Problem for Gaussian Noise

This paper is concerned with the probability, P[T,r(τ)], that a stationary Gaussian process with mean zero and covariance function r(τ) be nonnegative throughout a given interval of duration T. Several strict upper and lower bounds for P are given, along with some comparison theorems that relate P's for different covariance functions.

Tail estimation of the spectral density for a stationary

Under certain regularity conditions on the drift function, ... We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Levy noises. We do not impose any moment condition on the driving Levy process.

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strong mixing conditions - Encyclopedia of Mathematics

erties. That motivated the development of a broad theory of “strong mixing conditions” to handle such situations. This note is a brief description of that theory. The field of strong mixing conditions is a vast area, and a short note such as this cannot even begin to do justice to it. Journal articles (with one exception) will not be

DeepDyve - A Stationary Rho-Mixing Markov Chain

2004/10/20 · Read "A Stationary Rho-Mixing Markov Chain Which Is Not “Interlaced” Rho-Mixing, Journal of Theoretical Probability" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications

Stationary Stochastic Processes : Theory and Applications

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