Stochastic processes are widely used for model building in the social, physical, engineering
and life sciences as well as in financial economics. In model building, statistical inference for …

We generalize the Wiener-Khinchin theorem. A full generalization is presented where both
the autocorrelation function and power spectral density are defined in terms of a general …

We introduce a new stylized fact: the hump-shaped behavior of slopes and coefficients of
determination as a function of the aggregation horizon when running (forward/backward) …

Lamperti's transformation, an isometry between self-similar and stationary processes, is
used to solve some problems of linear estimation of continuous-time, self-similar processes …

Forecasting non-stationary stochastic time series represents a rather complex problem. The
reason is that such temporal series are not only self-similar but also exhibit a Long-Range …

Axiomatic design (AD) provides a framework to describe design objects and a set of axioms
to evaluate relations between intended functions and means by which they are achieved. It …

Springer Cham Heidelberg New York Dordrecht London are believed to be true and
accurate at the date of publication. Neither the publisher nor the authors or the editors give a …

The Lamperti transformation defines a one-to-one correspondence between stationary
processes on the real line and self-similar processes on the real half-line. Although dating …

This article suggests the contributions with two highlights. One is to propose a novel model
of sea level fluctuations (sea level for short), which is called the generalized Cauchy (GC) …

Scale-invariant processes, and hereafter processes with broken versions of this symmetry,
are studied by means of the Lamperti transformation, a one-to-one transformation linking …