We consider a parametric spectral density with power-law behaviour about a fractional pole at the unknown frequency !. The case of known !, especially ! = 0, is standard in the long memory literature. When ! is unknown, asymptotic distribution theory for estimates of parameters, including the...

The behavior of averaged periodograms and cross-periodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones. The cross-periodogram can involve two...

This paper studies taper-based estimates of the spectral density utilizing a fixed bandwidth ratio asymptotic framework, and makes several theoretical contributions: (i) we treat multiple frequencies jointly, (ii) we allow for long-range dependence or anti-persistence at differing frequencies,...

We establish a maximal moment inequality for the weighted sum of a long- range dependent process. An extension to H$\acute{a}$jek-R$\acute{e}$ny and Chow's type inequality is then obtained. It enables us to deduce a strong law for the weighted sum of a stationary long-range dependent time...

Several features may be present in rainfall data, and sophisticated time series procedures are needed for the analysis. These features are that of seasonality, long range dependency of observations and time trend as observed in the climatological series. This paper therefore considered the...

Several features may be present in rainfall data, and sophisticated time series procedures are needed for the analysis. These features are that of seasonality, long range dependency of observations and time trend as observed in the climatological series. This paper therefore considered the...

We present the results of a simulation study into the properties of 12 different estimators of the Hurst parameter, H, or the fractional integration parameter, d, in long memory time series which are available in R packages. We compare and contrast their performance on simulated Fractional...

We present the results of a simulation study into the properties of 12 different estimators of the Hurst parameter, H, or the fractional integration parameter, d, in long memory time series. We compare and contrast their performance on simulated Fractional Gaussian Noises and fractionally...

We consider semiparametric estimation in time series regression in the presence of long range dependence in both the errors and the stochastic regressors. A central limit theorem is established for a class of semiparametric frequency domain weighted least squares estimates, which includes both...

In this paper we give the theoretical basis of a possible explanation for two stylized facts observed in long log-return series: the long range dependence (LRD) in volatility and the integrated GARCH (IGARCH). Both these effects can be theoretically explained if one assumes that the data is...