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185
On the Selfsimilar Nature of Ethernet Traffic (Extended Version)
, 1994
"... We demonstrate that Ethernet LAN traffic is statistically selfsimilar, that none of the commonly used traffic models is able to capture this fractallike behavior, that such behavior has serious implications for the design, control, and analysis of highspeed, cellbased networks, and that aggrega ..."
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Cited by 2213 (46 self)
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We demonstrate that Ethernet LAN traffic is statistically selfsimilar, that none of the commonly used traffic models is able to capture this fractallike behavior, that such behavior has serious implications for the design, control, and analysis of highspeed, cellbased networks, and that aggregating streams of such traffic typically intensifies the selfsimilarity (“burstiness”) instead of smoothing it. Our conclusions are supported by a rigorous statistical analysis of hundreds of millions of high quality Ethernet traffic measurements collected between 1989 and 1992, coupled with a discussion of the underlying mathematical and statistical properties of selfsimilarity and their relationship with actual network behavior. We also present traffic models based on selfsimilar stochastic processes that provide simple, accurate, and realistic descriptions of traffic scenarios expected during BISDN deployment.
On the Detection and Estimation of Long Memory in Stochastic Volatility
, 1995
"... Recent studies have suggested that stock markets' volatility has a type of longrange dependence that is not appropriately described by the usual Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential GARCH (EGARCH) models. In this paper, different models for describing ..."
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Cited by 214 (6 self)
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Recent studies have suggested that stock markets' volatility has a type of longrange dependence that is not appropriately described by the usual Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential GARCH (EGARCH) models. In this paper, different models for describing this longrange dependence are examined and the properties of a LongMemory Stochastic Volatility (LMSV) model, constructed by incorporating an Autoregressive Fractionally Integrated Moving Average (ARFIMA) process in a stochastic volatility scheme, are discussed. Strongly consistent estimators for the parameters of this LMSV model are obtained by maximizing the spectral likelihood. The distribution of the estimators is analyzed by means of a Monte Carlo study. The LMSV is applied to daily stock market returns providing an improved description of the volatility behavior. In order to assess the empirical relevance of this approach, tests for longmemory volatility are described and applied to an e...
Functionalcoefficient Regression Models for Nonlinear Time Series
 Journal of the American Statistical Association
, 1998
"... We apply the local linear regression technique for estimation of functionalcoefficient regression models for time series data. The models include threshold autoregressive models (Tong 1990) and functionalcoefficient autoregressive models (Chen and Tsay 1993) as special cases but with the added adv ..."
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Cited by 82 (15 self)
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We apply the local linear regression technique for estimation of functionalcoefficient regression models for time series data. The models include threshold autoregressive models (Tong 1990) and functionalcoefficient autoregressive models (Chen and Tsay 1993) as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better postsample forecasting performance. We have also proposed a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined crossvalidatory estimation for the expected forecasting errors. The proposed methodology is dataanalytic and is of appreciable flexibility to analyze complex and multivariate nonlinear structures without suffering from the "curse of dimensionality". The asymptotic properties of the proposed estimators are investigated under the ffmixing condition. Both simulated and real data examples are used for illustration. Key Words: ffmixing; Asymptotic normali...
LogPeriodogram Regression Of Time Series With Long Range Dependence
 ANNALS OF STATISTICS
, 1999
"... This paper discusses the use of fractional exponential models (Robinson (1990), Beran (1994)) to model the spectral density f(x) of a covariance stationary process when f(x) may be decomposed as f(x) = x \Gamma2d f (x), where f (x) is bounded and bounded away from zero. A form of logperiodogram ..."
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Cited by 58 (1 self)
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This paper discusses the use of fractional exponential models (Robinson (1990), Beran (1994)) to model the spectral density f(x) of a covariance stationary process when f(x) may be decomposed as f(x) = x \Gamma2d f (x), where f (x) is bounded and bounded away from zero. A form of logperiodogram regression technique is presented both in the parametric context (i.e. f (x) is a finite order exponential model in the sense of Bloomfield (1973)) and the semiparametric context (f (x) is regarded as a nuisance parameter). Assuming gaussianity and additional conditions on the regularity of f (x) which seem mild, asymptotic normality of the parameter estimates in the parametric and the semiparametric context is established. As a byproduct, some improvements over the results presented by Robinson (1994) have been obtained for the large sample distribution of logperiodogram ordinates for Gaussian processes.
On the spectral density of the wavelet coefficients of long memory time series with application to the logregression estimation of the memory parameter
, 2006
"... Abstract. In the recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semiparametric asymptotic theory, comparable to the one developed for Fourier methods, is still missing. In this con ..."
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Cited by 38 (13 self)
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Abstract. In the recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semiparametric asymptotic theory, comparable to the one developed for Fourier methods, is still missing. In this contribution, we adapt the classical semiparametric framework introduced by Robinson and his coauthors for estimating the memory parameter of a (possibly) nonstationary process. As an application, we obtain minimax upper bounds for the logscale regression estimator of the memory parameter for a Gaussian process and we derive an explicit expression of its variance.
Estimation of the Hurst Parameter of Long Range Dependent Time Series, Research Report,
, 1996
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LongRange Dependence and Data Network Traffic
, 2001
"... This is an overview of a relatively recent application of longrange dependence (LRD) to the area of communication networks, in particular to problems concerned with the dynamic nature of packet flows in highspeed data networks such as the Internet. We demonstrate that this new application area off ..."
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Cited by 35 (1 self)
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This is an overview of a relatively recent application of longrange dependence (LRD) to the area of communication networks, in particular to problems concerned with the dynamic nature of packet flows in highspeed data networks such as the Internet. We demonstrate that this new application area offers unique opportunities for significantly advancing our understanding of LRD and related phenomena. These advances are made possible by moving beyond the conventional approaches associated with the widespread "blackbox" perspective of traditional time series analysis and exploiting instead the physical mechanisms that exist in the networking context and that are intimately tied to the observed characteristics of measured network traffic. In order to describe this complexity we provide a basic understanding of the design, architecture and operations of data networks, including a description of the TCP/IP protocols used in today's Internet. LRD is observed in the large scale behavior of the data traffic and we provide a physical explanation for its presence. LRD tends to be caused by user and application characteristics and has little to do with the network itself. The network affects mostly small time scales, and this is why a rudimentary understanding of the main protocols is important. We illustrate why multifractals may be relevant for describing some aspects of the highly irregular traffic behavior over small time scales. We distinguish between a timedomain and waveletdomain approach to analyzing the small time scale dynamics and discuss why the waveletdomain approach appears to be better suited than the timedomain approach for identifying features in measured traffic (e.g., relatively regular traffic patterns over certain time scales) that have a direct networking interpretation (e....
The Long Range Dependence Paradigm for Macroeconomics and Finance
, 2002
"... The long range dependence paradigm appears to be a suitable description of the data generating process for many observed economic time series. This is mainly due to the fact that it naturally characterizes time series displaying a high degree of persistence, in the form of a long lasting effect of ..."
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Cited by 35 (1 self)
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The long range dependence paradigm appears to be a suitable description of the data generating process for many observed economic time series. This is mainly due to the fact that it naturally characterizes time series displaying a high degree of persistence, in the form of a long lasting effect of unanticipated shocks, yet exhibiting mean reversion. Whereas linear long range dependent time series models have been extensively used in macroeconomics, empirical evidence from financial time series prompted the development of nonlinear long range dependent time series models, in particular models of changing volatility. We discuss empirical evidence of long range dependence as well as the theoretical issues, both for economics and econometrics, such evidence has stimulated.
The Effects of Systematic Sampling and Temporal Aggregation on Discrete Time Long Memory Processes and Their Finite Sample Properties
 ECONOMETRIC THEORY
, 1999
"... This study investigates the effects of varying sampling intervals on the long memory characteristics of certain stochastic processes. We find that although different sampling intervals do not affect the decay rate of discrete time long memory autocorrelation functions in large lags, the autocorrela ..."
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Cited by 30 (5 self)
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This study investigates the effects of varying sampling intervals on the long memory characteristics of certain stochastic processes. We find that although different sampling intervals do not affect the decay rate of discrete time long memory autocorrelation functions in large lags, the autocorrelation functions in short lags are affected significantly. The level of the autocorrelation functions moves upward for temporally aggregated processes and downward for systematically sampled processes, and these effects result in a bias in the long memory parameter. For the ARFIMA(0,d,0) process, the absolute magnitude of the long memory parameter, d, of the temporally aggregated process is greater than the d  of the true process, which is greater than the d  of the systematically sampled process. We also find that the true long memory parameter can be obtained if we use a decay rate that is not affected by different sampling intervals.
Parameter Estimation for Infinite Variance Fractional ARIMA
 ARIMA, Annals of Statistics
, 1996
"... Consider the fractional ARIMA time series with innovations that have infinite variance. This is a finite parameter model which exhibits both longrange dependence (long memory) and high variability. We prove the consistency of an estimator of the unknown parameters which is based on the periodogram ..."
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Cited by 29 (5 self)
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Consider the fractional ARIMA time series with innovations that have infinite variance. This is a finite parameter model which exhibits both longrange dependence (long memory) and high variability. We prove the consistency of an estimator of the unknown parameters which is based on the periodogram and derive its asymptotic distribution. This shows that the results of Mikosch, Gadrich, Kluppelberg and Adler (1995) for ARMA time series remain valid for fractional ARIMA with longrange dependence. We also extend the limit theorem for sample autocovariances of infinite variance moving averages developed in Davis and Resnick (1985) to moving averages whose coefficients are not absolutely summable. 1 Introduction and main results This paper is concerned with the estimation of the parameters of the fractional ARIMA time series fX n g defined by the equations \Phi(B)X n = \Theta(B )\Delta \Gammad Z n ; (1.1) where the innovations Z n have infinite variance and where d is a positive fracti...