The assumption of independence is often only an approximation to the real correlation structure. Models with short-range memory are well known and often used in practice. However even for supposedly i.i.d. high~uality data slowly decaying correlations may occur. If not taken into account, they have disastrous effects on tests and confidence intervals. Stationary processes with a pole of the spe...

Based on ours and other studies, it is becoming evident that Internet traffic is often nonstationary. Since such traffic is generally found to be long-range dependent as well, and the two properties can get confused, it is important to have a method for separately characterizing them. This paper proposes such a methodology aimed specifically for traffic scenarios where nonstationarity comes int...

Over the last ten years, long-range dependence (LRD) has become a key concept in modeling networking phenomena. The research community has undergone a mental shift from Poisson and memoryless processes to LRD and bursty processes. Despite its popularity, LRD analysis is hindered by two main problems: a) it cannot be used by nonexperts easily, and b) the identification of LRD is often questioned...

There is mounting experimental evidence that network traff c processes exhibit ubiquitous properties of self-similarity and long range dependence (LRD), i.e. of correlations over a wide range of time scales. However, there is still considerable debate about how to model such processes and about their impact on network and application performance. In this paper, we argue that much recent modelin...

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...