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99
Analysis, Modeling and Generation of SelfSimilar VBR Video Traffic
, 1994
"... We present a detailed statistical analysis of a 2hour long empirical sample of VBR video. The sample was obtained by applying a simple intraframe video compression code to an action movie. The main findings of our analysis are (1) the tail behavior of the marginal bandwidth distribution can be accu ..."
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Cited by 548 (6 self)
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We present a detailed statistical analysis of a 2hour long empirical sample of VBR video. The sample was obtained by applying a simple intraframe video compression code to an action movie. The main findings of our analysis are (1) the tail behavior of the marginal bandwidth distribution can be accurately described using "heavytailed" distributions (e.g., Pareto); (2) the autocorrelation of the VBR video sequence decays hyperbolically (equivalent to longrange dependence) and can be modeled using selfsimilar processes. We combine our findings in a new (nonMarkovian) source model for VBR video and present an algorithm for generating synthetic traffic. Tracedriven simulations show that statistical multiplexing results in significant bandwidth efficiency even when longrange dependence is present. Simulations of our source model show longrange dependence and heavytailed marginals to be important components which are not accounted for in currently used VBR video traffic models. 1 I...
Long memory processes and fractional integration in Econometrics
 JOURNAL OF NOMETRI ELSEVIER JOURNAL OF ECONOMETRICS 73{1996) 5 59
, 1996
"... This paper provides a survey and review of the major econometric work on long memory processes, fractional integration, and their applications in economics and finance. Some of the definitions of long memory are reviewed, together with previous work in other disciplines. Section 3 describes the popu ..."
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Cited by 377 (0 self)
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This paper provides a survey and review of the major econometric work on long memory processes, fractional integration, and their applications in economics and finance. Some of the definitions of long memory are reviewed, together with previous work in other disciplines. Section 3 describes the population characteristics of various long memory processes in the mean, including ARFIMA. Section 4 is concerned with estimation and examines emiparametric procedures in both *he frequency and time domain, and also the properties of various regression based and maximum likelihood techniques. Long memory volatility processes are discussed in Section 5, while Section 6 discusses applications in economics and finance. The paper also has a concluding section.
Estimators for LongRange Dependence: An Empirical Study
, 1995
"... Various methods for estimating the selfsimilarity parameter and/or the intensity of longrange dependence in a time series are available. Some are more reliable than others. To discover the ones that work best, we apply the different methods to simulated sequences of fractional Gaussian noise and f ..."
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Cited by 157 (6 self)
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Various methods for estimating the selfsimilarity parameter and/or the intensity of longrange dependence in a time series are available. Some are more reliable than others. To discover the ones that work best, we apply the different methods to simulated sequences of fractional Gaussian noise and fractional ARIMA(0, d, 0). We also provide here a theoretical justification for the method of residuals of regression.
Traffic Models in Broadband Networks
, 1997
"... Traffic models are at the heart of any performance evaluation of telecommunications networks. An accurate estimation of network performance is critical for the success of broadband networks. Such networks need to guarantee an acceptable quality of service (QoS) level to the users. Therefore, traff ..."
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Cited by 104 (0 self)
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Traffic models are at the heart of any performance evaluation of telecommunications networks. An accurate estimation of network performance is critical for the success of broadband networks. Such networks need to guarantee an acceptable quality of service (QoS) level to the users. Therefore, traffic models need to be accurate and able to capture the statistical characteristics of the actual traffic. In this article we survey and examine traffic models that are currently used in the literature. Traditional shortrange and nontraditional longrange dependent traffic models are presented. Number of parameters needed, parameter estimation, analytical tractability, and ability of traffic models to capture marginal distribution and autocorrelation structure of actual traffic are discussed. n Figure 1. Finite state model for voice. This research was supported in part by the National Science Foundation under grant NCR9396299. This article is based on Georgia Tech technical report G...
OnChip Traffic Modeling and Synthesis for MPEG2 Video Applications
, 2004
"... The objective of this paper is to introduce selfsimilarity as a fundamental property exhibited by the bursty traffic between onchip modules in typical MPEG2 video applications. Statistical tests performed on relevant traces extracted from common video clips establish unequivocally the existence ..."
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Cited by 73 (10 self)
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The objective of this paper is to introduce selfsimilarity as a fundamental property exhibited by the bursty traffic between onchip modules in typical MPEG2 video applications. Statistical tests performed on relevant traces extracted from common video clips establish unequivocally the existence of selfsimilarity in video traffic. Using a generic tilebased communication architecture, we discuss the implications of our findings on onchip buffer space allocation and present quantitative evaluations for typical video streams. We also describe a technique for synthetically generating traces having statistical properties similar to those obtained from real video clips. Our proposed technique speeds up buffer simulations, allows media system designers to explore architectures rapidly and use large media data benchmarks more efficiently. We believe that our findings open new directions of research with deep implications on some fundamental issues in onchip networks design for multimedia applications.
Microeconomic Models for LongMemory in the Volatility of Financial Time Series
"... We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991, 1993), can replicate the empirical longmemory properties of the two first conditional moments of financial time series. The essence of these models is that the forecasts and thus the desired ..."
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Cited by 61 (2 self)
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We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991, 1993), can replicate the empirical longmemory properties of the two first conditional moments of financial time series. The essence of these models is that the forecasts and thus the desired trades of the individuals in the markets are influenced, directly, or indirectly by those of the other participants. These "field effects" generate "herding" behaviour which affects the structure of the asset price dynamics. The series of returns generated by these models display the same empirical properties as financial returns: returns are I(0), the series of absolute and squared returns display strong dependence, while the series of absolute returns do not display a trend. Furthermore, this class of models is able to replicate the common longmemory properties in the volatility and covolatility of financial time series, revealed by Teyssière (1997, 1998a). These properties are investigated by using various model independent tests and estimators, i.e., semiparametric and nonparametric, introduced by Lo (1991), Kwiatkowski, Phillips, Schmidt and Shin (1992), Robinson (1995), Lobato and Robinson (1998), Giraitis, Kokoszka Leipus and Teyssière (2000, 2001). The relative performance of these tests and estimators for longmemory in a nonstandard data generating process is then assessed.
On Resource Management and QoS Guarantees For Long Range Dependent Traffic
 in Proc. IEEE INFOCOM '95
, 1994
"... It has been known for several years now that variablebitrate video sources are strongly autocorrelated. Recently, several studies have indicated that the resulting stochastic processes exhibit longrange dependence properties. This implies that large buffers at intermediate switching points may n ..."
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Cited by 57 (10 self)
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It has been known for several years now that variablebitrate video sources are strongly autocorrelated. Recently, several studies have indicated that the resulting stochastic processes exhibit longrange dependence properties. This implies that large buffers at intermediate switching points may not provide adequate delay performance for such classes of traffic in Broadband packetswitched networks (such as ATM). In this paper, we study the effect of longmemory processes on queue length statistics of a single queue system through a controlled fractionally differenced ARIMA(1; d; 0) input process. This process has two parameters OE 1 (0 OE 1 1) and d (0 d ! 1=2) representing an autoregressive component and a longrange dependent component, respectively. Results show that the queue length statistics studied (mean, variance and the 0:999 quantile) are proportional to e c1 OE 1 e c2 d ; where (c 1 ; c 2 ) are positive constants, and c 2 ? c 1 : The effect of the autocorrelation...
SelfSimilarity in File Systems
, 1998
"... We demonstrate that highlevel file system events exhibit selfsimilar behaviour, but only for shortterm time scales of approximately under a day. We do so through the analysis of four sets of traces that span time scales of milliseconds through months, and that differ in the trace collection metho ..."
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Cited by 45 (0 self)
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We demonstrate that highlevel file system events exhibit selfsimilar behaviour, but only for shortterm time scales of approximately under a day. We do so through the analysis of four sets of traces that span time scales of milliseconds through months, and that differ in the trace collection method, the file systems being traced, and the chronological times of the tracing. Two sets of detailed, shortterm file system trace data are analyzed; both are shown to have selfsimilar like behaviour, with consistent Hurst parameters (a measure of selfsimilarity) for all file system traffic as well as individual classes of file system events. Longterm file system trace data is then analyzed, and we discover that the traces' high variability and selfsimilar behaviour does not persist across time scales of days, weeks, and months. Using the shortterm trace data, weshow that sources of file system traffic exhibit ON/OFF source behaviour, which is characterized by highly variably lengthed bursts of activity, followed by similarly variably lengthed periods of inactivity. This ON/OFF behaviour is used to motivate a simple technique for synthesizing a stream of events that exhibit the same selfsimilar shortterm behaviour as was observed in the file system traces.
Stock market prices and longrange dependence, Finance Stoch. 3
, 1999
"... Abstract. Using the CRSP (Center for Research in Security Prices) daily stock return data, we revisit the question of whether or not actual stock market prices exhibit longrange dependence. Our study is based on an empirical investigation reported in Teverovsky, Taqqu and Willinger [33] of the mo ..."
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Cited by 44 (0 self)
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Abstract. Using the CRSP (Center for Research in Security Prices) daily stock return data, we revisit the question of whether or not actual stock market prices exhibit longrange dependence. Our study is based on an empirical investigation reported in Teverovsky, Taqqu and Willinger [33] of the modified rescaled adjusted range or R/S statistic that was proposed by Lo [17] as a test for longrange dependence with good robustness properties under "extra" shortrange dependence. Our main conclusion is that because the modified R/S statistic shows a strong preference for accepting the null hypothesis of no longrange dependence, irrespective of whether longrange dependence is present in the data or not, Lo's acceptance of the hypothesis for the CRSP data (i.e., no longrange dependence in stock market prices) is less conclusive than is usually regarded in the econometrics literature. In fact, upon further analysis of the data, we find empirical evidence of longrange dependence in stock price returns, but because the corresponding degree of longrange dependence (measured via the Hurst parameter H ) is typically very low (i.e., H values around 0.60), the evidence is not absolutely conclusive.
The Hurst Phenomenon and Fractional Gaussian Noise Made Easy
 Hydrological Sciences Journal
, 2002
"... Abstract The Hurst phenomenon, which characterizes hydrological and other geophysical time series, is formulated and studied in an easy manner in terms of the variance and autocorrelation of a stochastic process on multiple temporal scales. In addition, a simple explanation of the Hurst phenomenon b ..."
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Cited by 44 (17 self)
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Abstract The Hurst phenomenon, which characterizes hydrological and other geophysical time series, is formulated and studied in an easy manner in terms of the variance and autocorrelation of a stochastic process on multiple temporal scales. In addition, a simple explanation of the Hurst phenomenon based on the fluctuation of a hydrological process upon different temporal scales is presented. The stochastic process that was devised to represent the Hurst phenomenon, i.e. the fractional Gaussian noise, is also studied on the same grounds. Based on its studied properties, three simple and fast methods to generate fractional Gaussian noise, or good approximations of it, are proposed. Key words Hurst phenomenon; fractional Gaussian noise; persistence; climate change Le phénomène de Hurst et le bruit fractionnel gaussien rendus faciles dans leur utilisation Résumé On formule et étudie d'une manière simple le phénomène de Hurst, qui caractérise des séries chronologiques en hydrologie et en géophysique, en termes de variance et d'autocorrélation d'un processus stochastique considéré selon des échelles temporelles multiples. De plus, on présente une explication simple du phénomène de Hurst sur la base de la fluctuation d'un processus hydrologique dans des échelles temporelles multiples. On étudie également d'une manière analogue le bruit fractionnel gaussien qui constitue le processus stochastique construit pour représenter le phénomène de Hurst. En se basant sur les propriétés étudiées de ce processus, on propose trois méthodes simples et rapides pour générer du bruit fractionnel gaussien, voire une bonne approximation. Mots clefs phénomène de Hurst; bruit fractionnel gaussien; persistance; changement climatique