Long range dependence or long memory is a feature of many processes in the natural world, which provides important insights on the underlying mechanisms that generate the observed data. The usual tools available to characterize the phenomenon are mostly based on second order correlations. However, the long memory effects may not be evident at the level of second order correlations and may requi...

This paper revisits three important concepts in fractal type network traffic, namely, self-similarity (SS), long-range dependence (LRD), and local self-similarity (LSS). Based on those concepts, we address the reason why the local properties of fractional Gaussian noise (fGn) are contained in the global properties of fGn and vice versa, which may be a limitation of fGn in data traffic modeling....

With the availability of intra-daily price data, researchers have focused more attention on market microstructure issues to understand and help formulate strategies for the timing of trades. The purpose of this article is to provide a brief survey of the research employing intra-daily price data. Specifically, we review stylized facts of intra-daily data, econometric issues of data analysis, ap...

This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov modulated process based on an infinite Markov chain is described. The work described is motivated by applications in telecommunications where LRD is a known property of time series measured on the Internet. The process can generate a time series exhibit...

Various classes of arrival processes in telecommunication traffic modeling based on heavy-tailed interarrival time distributions exhibit long-range dependence. This includes arrival rate processes of Anick-MitraSondhi (AMS) type where the rate process is an on/off-process with heavy-tailed on-period distribution and/or off-period distribution, as well as generalized Kosten type models (infinite...

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This paper studies the dynamics of Brazilian interest rates for short-term maturities. The paper employs developed techniques in the econophysics literature and tests for long-range dependence in the term structure of these interest rates for the last decade. Empirical results suggest that the degree of long-range dependence has changed over time due to changes in monetary policy, specially in ...

We address the problem of detecting slow-moving targets using space-time adaptive processing (STAP) radar. Determining the optimum weights at each range requires data snapshots at neighboring ranges. However, in virtually all configurations, snapshot statistics are range dependent, meaning that snapshots are nonstationary with respect to range. This results in poor performance. In this paper, w...

This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in (1/2,1). Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional Brownian motion. Résumé. Ce papier a pour but d’établir ...