Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. We evaluate 24 wide-area traces, investigating a number of wide-area TCP arrival processes (session and connection arrivals, FTP data connection arrivals within FTP sessions, and TELNET packet arrivals) to determine the error introduced by modeling them using Poisson processes. We find that user-initiated TCP session arrivals, such as remotelogin and file-transfer, are well-modeled as Poisson processes with fixed hourly rates, but that other connection arrivals deviate considerably from Poisson; that modeling TELNET packet interarrivals as exponential grievously underestimates the burstiness of TELNET traffic, but using the empirical Tcplib [Danzig et al, 1992] interarrivals preserves burstiness over many time scales; and that FTP data connection arrivals within FTP sessions come bunched into “connection bursts,” the largest of which are so large that they completely dominate FTP data traffic. Finally, we offer some results regarding how our findings relate to the possible self-similarity of widearea traffic.

Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94a, PF94]. One difficulty in dealing with selfsimilar models is how to efficiently synthesize traces (sample paths) corresponding to self-similar traffic. We present a fast Fourier transform method for synthesizing approximate selfsimilar sample paths and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate a closer approximation to true self-similar sample paths than the other known fast method (Random Midpoint Displacement). We then discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittle's estimator for H, the Hurst parameter giving the strength of long-range dependence present in a self-similar time s...

Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94, PF95]. One difficulty in dealing with selfsimilar models is how to efficiently synthesize traces (sample paths) corresponding to self-similar traffic. We present a fast Fourier transform method for synthesizing approximate self-similar sample paths for one type of self-similar process, Fractional Gaussian Noise, and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate close approximations to true self-similar sample paths. We also discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittle's estimator for H, the Hurst parameter giving the strength of long-range dependence present in a self-similar time series.

Based on simple time series plots and periodic sample autocorrelations, we document that monthly river flow data display long memory, in addition to pronounced seasonality. In fact, it appears that the long memory characteristics vary with the season. To describe these two properties jointly, we propose a seasonal periodic long memory model and fit it to the well-known Fraser river data (to be obtained from Statlib at http://lib.stat.cmu.edu/datasets/). We provide a statistical analysis and provide impulse response functions to show that shocks in certain months of the year have a longer lasting impact than those in other months. Keywords Seasonal difference, Periodic model, Long Memory, PARFIMA, SPARFIMA 1 Introduction It is well known since the early work by Hurst on Nile data that river flows show persistent fluctuations which may be characterized by long memory. Additional to long memory, most river flow data display pronounced seasonality, both in mean and in variance. ...

(required signature)

We present a goodness of ¯t test for time series models based on the discrete spectral average estimator. Unlike current tests of goodness of ¯t, the asymptotic distribution of our test statistic allows the null hypothesis to be either a short or long range dependence model. Our test is in the frequency domain, is easy to compute and does not require the calculation of residuals from the ¯tted model. This is especially advantageous when the ¯tted model is not a ¯nite order autoregressive model. The test statistic is a frequency domain analogue of the test by Hong (1996) which is a generalization of the Box-Pierce (1970) test statistic. A simulation study shows that our test has power comparable to that of Hong's test and superior to that of another frequency domain test by Milhoj (1981).

We present the results of a simulation study into the properties of 12 different estimators of the Hurst parameter, H, or the fractional integration parameter, d, in long memory time series. We compare and contrast their performance on simulated Fractional Gaussian Noises and fractionally integrated series with lengths between 100 and 10,000 data points and H values between 0.55 and 0.90 or d values between 0.05 and 0.40. We apply all 12 estimators to the Campito Mountain data and estimate the accuracy of their estimates using the Beran goodness of fit test for long memory time series.

We fit structural change and long-memory models to examine the quarterly structure of the U.S. ex-post real interest rate. The results are of substantial importance and indicate that the series shows real breaks since the structural change effect is not totally due to the long-memory property. On the other hand, it shows spurious long-memory since this feature is totally explained by the presence of breaks in the series rather than an I (d) process. Our results partially contradict those of Boutahar and Jouini (2004) who find that the U.S. inflation rate shows real breaks and long-memory. Specification tests and maximum likelihood estimates support the fitted models.

This thesis describes methods of analysis and synthesis of long memory processes. Long memory processes are those which exhibit correlations between events separated by a long period of time. This phenomenon is characterized in the frequency domain by a sharp peak in the spectral density function as the frequency approaches zero. This characteristic is observed in many physical time series, including those in the fields of geophysics, astronomy and finance. A class of models that captures such long memory behaviour are fractionally differenced processes, the simplest of these processes is obtained by differencing white noise a fractional number of times. We employ two methods of analyzing such processes: Multitaper spectral estimation and Wavelet analysis. Multitaper spectral analysis uses the average of several direct spectral estimators evaluated using orthogonal tapers. We look at two sets of tapers: the discrete prolate spheroidal sequences and sinusoidal tapers. This method of s...

This paper introduces a version of empirical likelihood based on the periodogram and spectral estimating equations. This formulation handles dependent data through a data transformation (i.e., a Fourier transform) and is developed in terms of the spectral distribution rather than a time domain probability distribution. The asymptotic properties of frequency domain empirical likelihood are studied for linear time processes exhibiting both short- and long-range dependence. The method results in likelihood ratios which can be used to build nonparametric, asymptotically correct confidence regions for a class of normalized (or ratio) spectral parameters, including autocorrelations. Maximum empirical likelihood estimators are possible, as well as tests of spectral moment conditions. The methodology can be applied to several inference problems such as Whittle estimation and goodness-of-fit testing. 1. Introduction. The