Parametric Estimation for Gaussian Long-Range Dependent Processes Based on the Log-Periodogram

Log-periodogram Regression of Time Series with Long Range Dependence

This paper discusses the use of fractional exponential models (Robinson (1990), Beran (1994)) to model the spectral density f(x) of a covariance stationary process when f(x) may be decomposed as f(x) = x ?2d f (x), where f (x) is bounded and bounded away from zero. A form of log-periodogram regression technique is presented both in the parametric context (i.e. f (x) is a nite order exponential ...

Filtered Log-periodogram Regression of long memory processes

Filtered log-periodogram regression estimation of the fractional differencing parameter d is considered. Asymptotic properties are derived and the effect of filtering on d̂ is investigated. It is shown that the estimator by Geweke and Porter-Hudak (1983) can be improved significantly using a simple family of filters. The essential improvement is based on a binary decision that is asymptotically ...

Log-periodogram regression in asymmetric long memory

Nonlinear Log-periodogram Regression for Perturbed Fractional Processes

This paper studies fractional processes that may be perturbed by weakly dependent time series. The model for a perturbed fractional process has a components framework in which there may be components of both long and short memory. All commonly used estimates of the long memory parameter (such as log periodogram (LP) regression) may be used in a components model where the data are affected by we...

The Rate of Entropy for Gaussian Processes

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...