The aggregation procedure when a sample of length N is divided into blocks of length m=o(N), m--[infinity] and observations in each block are replaced by their sample mean, is widely used in statistical inference. Taqqu et al. (1995, Fractals, 3, 785-798), and Teverovsky and Taqqu (1997, J. Time...

We discuss the covariance structure and long-memory properties of stationary solutions of the bilinear equation Xt=[zeta]tAt+Bt,(*), where are standard i.i.d. r.v.'s, and At,Bt are moving averages in Xs, st. Stationary solution of (*) is obtained as an orthogonal Volterra expansion. In the case...

In Puplinskaitė and Surgailis (2014) we introduced the notion of scaling transition for stationary random fields X on Z2 in terms of partial sums limits, or scaling limits, of X over rectangles whose sides grow at possibly different rate. The present paper establishes the existence of scaling...

A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a multidimensional central limit theorem for this estimator are...

This paper discusses the consistency and limiting distributions of a class of M-estimators in two-phase random design linear regression models where the regression function is discontinuous at the change-point with a fixed jump size. The consistency rate of an M-estimator for the change-point...

The paper obtains a functional limit theorem for the empirical process of a stationary moving average process Xt with i.i.d. innovations belonging to the domain of attraction of a symmetric [alpha]-stable law, 1[alpha]2, with weights bj decaying as j-[beta], 1[beta]2/[alpha]. We show that the...

Extending the recent work of Philippe et al. [A. Philippe, D. Surgailis, M.-C. Viano, Invariance principle for a class of non stationary processes with long memory, C. R. Acad. Sci. Paris, Ser. 1. 342 (2006) 269-274; A. Philippe, D. Surgailis, M.-C. Viano, Time varying fractionally integrated...

This paper obtains a uniform reduction principle for the empirical process of a stationary moving average time series {Xt} with long memory and independent and identically distributed innovations belonging to the domain of attraction of symmetric [alpha]-stable laws, 1[alpha]2. As a consequence,...

We discuss joint temporal and contemporaneous aggregation of N independent copies of AR(1) process with random-coefficient a∈[0,1) when N and time scale n increase at different rate. Assuming that a has a density, regularly varying at a=1 with exponent −1β1, different joint limits of...

This paper establishes the consistency and the root-n asymptotic normality of the exact maximum likelihood estimator of the dependence parameter in linear regression models where the errors are a nondecreasing function of a long-range-dependent stationary Gaussian process. The spectral density...