There are many situations in which indicators of changes or anomalies in communication networks can be helpful, e.g. in the identification of faults. A dynamic communication network is characterised as a series of graphs with vertices representing IP addresses and edges representing information exchange between these entities weighted by packets sent. Ten graph distance metrics are used to crea...

The purpose of this paper is to analyze in bivariate vector autoregression the relationship between feedback in stochastic systems, Granger causality and a measure of dissimilarity between ARMA models. In particular, we consider a bivariate vector autoregressive processes of order p (a bivariate VAR(p) process) and we prove if the distance between the univariate ARMA models implied by the VAR r...

Long intermediate AR models are used in Durbin's algorithms for ARMA estimation. The order of that long AR model is infinite in the asymptotical theory, but very high AR orders are known to give inaccurate ARMA models in practice. A theoretical derivation is given for two different finite AR orders, as a function of the sample size. The first is the AR order optimal for prediction with a purely...

Abstrac t . Some simple models are introduced which may be used for modelling or generating sequences of dependent discrete random variables with generalized Poisson marginal distribution. Our approach for building these models is similar to that of the Poisson ARMA processes considered by Al-Osh and Alzaid (1987, J. Time Ser. Anal., 8, 261-275; 1988, Statist. Hefte, 29, 281-300) and McKenzie (...

We discuss theoretical properties and estimation of continuous-time ARMA (CARMA) processes, which are driven by a stable Lévy process. Such processes are very useful in a continuous-time linear stationary set-up: they have a similar structure as the widely used ARMA models, and provide all advantages of a continuous-time model. As an application we consider data from a deregulated electricity m...

The impact of fast moving items, modeled by auto-regressive moving average (ARMA) type processes, on the bullwhip effect is well known. However, slow moving items that can be modeled using integer ARMA processes have received little attention. Herein, we measure the impact of bullwhip effect under a first order integer auto-regressive, INAR(1), demand process. We consider a simple two-stage sup...

The class of multivariate Lévy-driven autoregressive moving average (MCARMA) processes, the continuous-time analogs of the classical vector ARMA processes, is shown to be equivalent to the class of continuous-time state space models. The linear innovations of the weak ARMA process arising from sampling an MCARMA process at an equidistant grid are proved to be exponentially completely regular (β...

We address the problem of estimating changes in fractional integrated ARMA (FARIMA) processes. These changes may be in the Long Range Dependence (LRD) parameter or the ARMA parameters. The signal is divided into “elementary” segments: the objective is then to estimate the segments in which the changes occur. This estimation is achieved by minimizing a penalized least-squares criterion based on ...