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This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated...
Many statistical applications require establishing
central limit theorems for sums/integrals
or for quadratic forms , where Xt is a stationary
process. A particularly important case is that of Appell
polynomials h(Xt) = Pm(Xt), h(Xt,Xs) = Pm,n (Xt,Xs), since the “Appell expansion rank" determines typically the
type of central limit theorem satisfied by the functionals
ST(h), QT(h).
We review and extend here to multidimensional
indices, along lines conjectured in [F. Avram and M.S. Taqqu,...
An iterative procedure for computation of stationary density of autoregressive processes is proposed. On an example with exponentially distributed white noise it is demonstrated that the procedure converges geometrically fast. The AR(1) and AR(2) models are analyzed in detail.
A linear moving average model with random coefficients (RCMA) is proposed as more general alternative to usual linear MA models. The basic properties of this model are obtained. Although some model properties are similar to linear case the RCMA model class is too general to find general invertibility conditions. The invertibility of some special examples of RCMA(1) model are investigated in this paper.
In a 1987 paper, Cambanis, Hardin and Weron defined doubly stationary stable processes as those stable processes which have a spectral representation which is itself stationary, and they gave an example of a stationary symmetric stable process which they claimed was not doubly stationary. Here we show that their process actually had a moving average representation, and hence was doubly stationary. We also characterize doubly stationary processes in terms of measure-preserving regular set isomorphisms...
The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.
The irregularity coefficient is one of the numerical characteristics of the spectral bandwith of a stationary random process. Its basic properties are investigated and the application to the dichotomic classification of a process into narrow-band and wide-band ones is given. Further, its behaviour is analyzed for sufficiently wide classes of stationary processes whose spectral densities frequently appear both in theory and applications.
We investigate the estimation of a multidimensional regression function from observations of an -mixing process , where , represents the design and the noise. We concentrate on wavelet methods. In most papers considering this problem, either the proposed wavelet estimator is not adaptive (i.e., it depends on the knowledge of the smoothness of in its construction) or it is supposed that is bounded or/and has a known distribution. In this paper, we go far beyond this classical framework....
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