Long-memory, or more generally fractal, processes are known to play an important role in
many scientific disciplines and applied fields such as physics, geophysics, hydrology …

Stationary long memory processes have been extensively studied over the past decades.
When we deal with financial, economic, or environmental data, seasonality and time-varying …

A unified asymptotic theory for nearly unstable higher order autoregressive processes and
their least squares estimates is established. A novel version of Jordan's canonical …

In this paper, we recall some concepts on seasonal long memory, we review the diverse
fractionally integrated seasonal time series models and we discuss their statistical …

Traveling phenomena are prevalent in a variety of fields, from atmospheric science to
seismography and oceanography. However, there are two main shortcomings in the current …

This thesis examines issues of seasonality in ARMA processes, comparing and contrasting
Box-Jenkins seasonality with Gegenbauer seasonality, and the SGAR or seasonal GAR …

In this thesis, we consider two classes of long memory processes: the stationary long
memory processes and the non-stationary long memory processes. We are devoted to the …

Business surveys are an important element in the analysis of the short-term economic
situation because of the timeliness and nature of the information they convey. Especially …

In this paper, we study, by a Monte Carlo simulation, the effect of the order p of “Zhurbenko-
Kolmogorov” taper on the asymptotic properties of semiparametric estimators. We show that …

This chapter deals with statistical inference for long-range dependent linear and
subordinated processes. Some of the tools will also be used in Chaps. 6 and 7 when we …