This paper presents an overview of the existing traffic models for data, voice and video sources in ATM. The first paragraph is devoted to bursty traffic of constant throughput, based on classical ON/OFF model. Obviously the superposition of several independent sources gives the method for modelling the variable rate streams. Possible solutions for voice traffic are offered by Markov-Modulated ...

In this paper we consider an autoregressive Pareto process which can be used as an alternative to heavy tailed MARMA. We focus on the tail behavior and prove that the tail empirical quantile function can be approximated by a Gaussian process. This result allows to derive a class of consistent and asymptotically normal estimators for the shape parameter. We will see through simulation that the u...

We investigate autoregressive approximations of multiple frequency I(1) processes, of which I(1) processes are a special class. The underlying data generating process is assumed to allow for an infinite order autoregressive representation where the coefficients of the Wold representation of the suitably filtered process satisfy mild summability constraints. An important special case of this pro...

Abstract. Definitions from the theory of point processes are recalled. Models of intensity function paramaterization and maximum likelihood estimation from data are explored. Closed-form log-likelihood expressions are given for the Hawkes (unidimensional andmultidimensional)process, Autoregressive Conditional Duration(ACD), and Log-ACD models. The Autoregressive Conditional Intensity model is a...

Abstract. Definitions from the theory of point processes are recalled. Models of intensity function paramaterization and maximum likelihood estimation from data are explored. Closed-form log-likelihood expressions are given for the Hawkes process, Autoregressive Conditional Duration(ACD), and Log-ACD models. The Autoregressive Conditional Intensity model is also discussed. Data from the symbol ...

Abstract. This paper deals with the problem of testing a change in variance of the p-th order autoregressive process, AR(p), at an unknown change point τ . We propose a test based on maximum likelihood principle for detecting such type of change, find asymptotic distribution of the test statistic and compare it with the tests for detecting changes in both variance and autoregressive parameters ...