A general moment bound for sums of products of Gaussian vector’s functions extending the moment bound in Taqqu (1977, Lemma 4.5) [28] is established. A general central limit theorem for triangular arrays of nonlinear functionals of multidimensional non-stationary Gaussian sequences is proved....

We consider the estimation of the location of the pole and memory parameter, λ0 and α respectively, of covariance stationary linear processes whose spectral density function f(λ) satisfies f(λ) ∼ C|λ − λ0|−α in a neighbourhood of λ0. We define a consistent estimator of λ0 and...

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density f(λ) can be written as f(λ)=|λ|−2dg(|λ|), where 0d1/2 (resp., −1/2d0), and g is continuous and positive. We propose a novel Bayesian nonparametric approach for the estimation...

The sieve bootstrap is a resampling technique that uses autoregressive approximations of order p to model invertible linear time series, where p is allowed to go to infinity with sample size n. The asymptotic properties of sieve bootstrap prediction intervals for stationary invertible linear...

We establish the validity of an Edgeworth expansion to the distribution of the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The result covers ARFIMA type models, including fractional Gaussian noise. The method of proof consists of three...

We investigate the asymptotic behavior of the maxima of a general class of deterministic chaotic processes –including the Tent map and the Logistic map -, of noisy chaotic processes, and of the Gaussian long memory k-factor Genebauer processes.

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a...