This note establishes stationarity of a number of stochastic processes of interest in the study of Transport Protocols. For many of the processes studied in this note stationarity had been established before, but for one class the result is new. For that class, it was counterintuitive that stationarity was hard to prove. This note also explains why that class offered such stiff resistance. The ...

Recent analyses have claimed the possible presence of non-stationarity, produced by the presence of either trend or long-term climatic fluctuations, in some historical hydrometeorological records observed in Europe as well as in other countries. Such non-stationarity might exert a remarkable effect on the estimation of the frequency distribution of the extreme events. However, it is well known ...

Economic integration, globalization and financial crises represent examples of processes whose understanding requires the analysis of the underlying network structure. Of particular interest is establishing whether a real economic network is in a state of (quasi) stationary equilibrium, i.e. characterized by smooth structural changes rather than abrupt transitions. While in the former case the ...

Careful statistical analyses indicate that the measured traffic traces from live packet networks often contain non-stationary effects like level shifts or polynomial trends. In these cases several popular tests for long-range dependence can result in wrong conclusions and unreliable estimate of the Hurst parameter. In this paper both analytical and simulation investigations of the implications ...

We analyze in this paper the asymptotic behavior of the specification test of Aït-Sahalia (1996) for the stationary density of a diffusion process, but when the diffusion is not stationary. We consider integrated and explosive processes, as well as nearly integrated ones in the spirit of the local to unity analysis in classical unit root theory. We find that the behavior of the test predicted b...

Hypothesis testing on point processes has several applications such as model fitting, plasticity detection, and non-stationarity detection. Standard tools for hypothesis testing include tests on mean firing rate and time varying rate function. However, these statistics do not fully describe a point process, and therefore, the conclusions drawn by these tests can be misleading. In this paper, we...

The possibility that a series can contain an unknown number of smooth breaks raises two distinct problems. First, even if the breaks are sharp, the number of breaks and the break dates themselves are generally unknown and need to be estimated along with the other parameters of the model. Second, even if the number of breaks is known, the possibility of a smooth break means that the functional f...

Our results complement the recent ̄ndings of real exchange rates as stationary processes. The standard procedure of applying a battery of unit root tests can be problematic since the tests are sensitive to the speci ̄cs of the time series process. The novelty of the approach we apply is in emphasizing the information content of the data in distinguishing between the competing processes. Stationa...

An important problem in the implementation of Markov Chain Monte Carlo algorithms is to determine the convergence time, or the number of iterations before the chain is close to stationarity. For many Markov chains used in practice this time is not known. Even in cases where the convergence time is known to be polynomial, the theoretical bounds are often too crude to be practical. Thus, practiti...