The notions of self-similarity, scaling, fractional processes and long range dependence have been repeatedly used to describe properties of financial time series: stock prices, foreign exchange rates, market indices and commodity prices. We discuss the relevance of these concepts in the context of financial modelling, their relation with the basic principles of financial theory and possible eco...

The Long Range Dependence (LRD) property of actual traffic in today’s network applications has been shown to have significant impact on network performance. In this paper we consider the problem of optimally dimensioning token bucket parameters for LRD traffic. We first empirically illustrate the different behavior of token buckets when acting on LRD vs. SRD traffic with identical average and p...

Abstract. We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H > 1/2 as a typical example. We establish infinite and finite past prediction formulas for the processes in which the predictor coefficients are given explicitly in terms of the MA(∞) and AR(∞) coefficients. We a...

Consider a single server queue with unit service rate fed by an arrival process of the following form: sessions arrive at the times of a Poisson process of rate λ, with each session lasting for an independent integer time τ > 1, where P (τ = k) = pk with pk ∼ αk−(1+α)L(k), where 1 < α < 2 and L(·) is a slowly varying function. Each session brings in work at unit rate while it is active. Thus th...

In this paper, we propose an -stable 2D extension of the 1D fractional Gaussian noise. The considered model exhibits long-range dependence properties, while its stability index allows us to control the degree of spikyness of the synthesized fields. A least square method for the estimation of the three parameters of this model is also described and its performances are evaluated by a Monte Carlo...

Recent measurements of various types of network traac have shown evidence consistent with long-range dependence and self-similarity. However, an alternative explanation for these measurements is non-stationarity in the data. Standard estimators of LRD parameters such as the Hurst parameter H assume stationarity and are susceptible to bias when this assumption does not hold. Hence LRD may be ind...

♣ This research was sponsored by WorldCom, Inc. Abstract—We report the first statistical analysis of Internet backbone traffic, based on traces with levels of aggregation 10 times larger and timestamp accuracy 1000 times better than in previous studies. We analyze the first three moments, marginal distributions and correlation structures of packet size, packet inter-arrival time, byte count and...