In this paper, we prove the validity of the Edgeworth expansion of the Discrete Fourier transforms of some linear time series. This result is applied to approach moments of non-linear functionals of the periodogram. As an illustration, we give an expression of the mean square error of the...

A new sufficient condition for the existence of a stationary causal solution of an equation is provided. This condition allows us to consider coefficients with power-law decay, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved.

There exists a wide literature on parametrically or semi-parametrically modelling strongly dependent time series using a long-memory parameter d, including more recent work on wavelet estimation. As a generalization of these latter approaches, in this work we allow the long-memory parameter d to...

In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in [A. Ayache, F. Roueff, Y. Xiao, Local and asymptotic properties of linear fractional stable sheets, C.R. Acad. Sci. Paris Ser. I. 344 (6) (2007)...

Multiple-try methods are extensions of the Metropolis algorithm in which the next state of the Markov chain is selected among a pool of proposals. These techniques have witnessed a recent surge of interest because they lend themselves easily to parallel implementations. We consider extended...

We consider semiparametric fractional exponential (FEXP) estimators of the memory parameter d for a potentially non-stationary linear long-memory time series with additive polynomial trend. We use differencing to annihilate the polynomial trend, followed by tapering to handle the potential...

We obtain limit theorems for a class of nonlinear discrete-time processes X(n) called the kth order Volterra processes of order k. These are moving average kth order polynomial forms: X(n)=∑0i1,…,ik∞a(i1,…,ik)ϵn−i1…ϵn−ik, where {ϵi} is i.i.d. with Eϵi=0, Eϵi2=1, where a(⋅)...

Consider the sum Z=∑n=1∞λn(ηn−Eηn), where ηn are independent gamma random variables with shape parameters rn0, and the λn’s are predetermined weights. We study the asymptotic behavior of the tail ∑n=M∞λn(ηn−Eηn), which is asymptotically normal under certain conditions. We...

We introduce a broad class of self-similar processes {Z(t),t≥0} called generalized Hermite processes. They have stationary increments, are defined on a Wiener chaos with Hurst index H∈(1/2,1), and include Hermite processes as a special case. They are defined through a homogeneous kernel g,...

Suppose that f is a deterministic function, is a sequence of random variables with long-range dependence and BH is a fractional Brownian motion (fBm) with index . In this work, we provide sufficient conditions for the convergencein distribution, as m--[infinity]. We also consider two examples....