Suppose that f is a deterministic function, is a sequence of random variables with long-range dependence and BH is a fractional Brownian motion (fBm) with index . In this work, we provide sufficient conditions for the convergencein distribution, as m--[infinity]. We also consider two examples....

It is known that Hermite processes have a finite-time interval representation. For fractional Brownian motion, the representation has been well known and plays a fundamental role in developing stochastic calculus for the process. For the Rosenblatt process, the finite-time interval...

Let 0<[alpha][less-than-or-equals, slant]2 and let . Let {X(t),t[set membership, variant]T} be a linear fractional [alpha]-stable (0<[alpha][less-than-or-equals, slant]2) motion with scaling index H (0<H<1) and with symmetric [alpha]-stable random measure. Suppose that [psi] is a bounded real function with compact support [a,b] and at least one null moment. Let the sequence of the discrete wavelet coefficients of the process X beWe use a stochastic integral representation of the process X to describe the wavelet coefficients as [alpha]-stable integrals when H-1/[alpha]>-1. This stochastic representation is used to prove that the stochastic process of wavelet coefficients , with fixed scale index , is strictly stationary. Furthermore, a property of self-similarity of the wavelet coefficients of X is proved. This property has been the motivation of several...</[alpha][less-than-or-equals,>

Community shared bicycle systems, such as the Vélo'v program launched in Lyon in May 2005, are public transportation programs that can be studied as a complex system composed of interconnected stations that exchange bicycles. They generate digital footprints that reveal the activity in the city...

type="main" xml:id="jtsa12086-abs-0001"The notion of multivariate long-range dependence is reexamined here from the perspectives of time and spectral domains. The role of the so-called phase parameters is clarified and stressed throughout. In particular, examples of causal (one-sided)...

In an influential work by Diebold and Inoue (2001), the Markov switching model was shown to exhibit long memory, in terms of the behavior of the second moments of partial sums. The relationship between the Markov switching model and long memory is reexamined here. Common estimators of the long...

In a multivariate varying-coefficient model, the response vectors <bold>Y</bold> are regressed on known functions <bold>v</bold>(<bold>X</bold>) of some explanatory variables <bold>X</bold> and the coefficients in an unknown regression matrix <bold> <italic>θ</italic> </bold>(<bold>Z</bold>) depend on another set of explanatory variables <bold>Z</bold>. We provide statistical tests, called local and...

New criteria are provided for determining whether an integral representation of a stable process is minimal. These criteria are based on various nonminimal sets and their projections, and have several advantages over and shed light on already available criteria. In particular, they naturally...