We consider semiparametric fractional exponential (FEXP) estimators of the memory parameter d for a potentially non-stationary linear long-memory time series with additive polynomial trend. We use differencing to annihilate the polynomial trend, followed by tapering to handle the potential...

This paper describes the limiting behaviour of tail empirical processes associated with long memory stochastic volatility models. We show that such a process has dichotomous behaviour, according to an interplay between the Hurst parameter and the tail index. On the other hand, the tail empirical...

A new sufficient condition for the existence of a stationary causal solution of an equation is provided. This condition allows us to consider coefficients with power-law decay, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved.

Periodogram ordinates of a Gaussian white-noise computed at Fourier frequencies are well known to form an i.i.d. sequence. This is no longer true in the non-Gaussian case. In this paper, we develop a full theory for weighted sums of non-linear functionals of the periodogram of an i.i.d....

We consider a general long memory time series, assumed stationary and linear, but not necessarily Gaussian or generated by a finite-parameter model. For such a process, we derive the asymptotic joint distribution of the normalized periodogram at a fixed, finite collection of Fourier frequencies....