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...

We consider two multivariate long-memory ARCH models, which extend the univariate long-memory ARCH models, we first consider a long-memory extension of the restricted constant conditional correlations (CCC) model introduced by Bollerslev (1990), and we propose a new unrestricted conditional...

We consider two multivariate long-memory ARCH models, which extend the univariate long-memory ARCH models, we first consider a long-memory extension of the restricted constant conditional correlations (CCC) model introduced by Bollerslev (1990), and we propose a new unrestricted conditional...

We use a new method of studying the Hurst exponent with time and scale dependency. This new approach allows us to recover the major events affecting worldwide markets (such as the September 11th terrorist attack) and analyze the way those effects propagate through the different scales. The...

Recently, there has been an upsurge of interest in the possibility of confusing long memory and structural changes in level. Many studies have shown that when a stationary short memory process is contaminated by level shifts the estimate of the fractional differencing parameter is biased away...