We prove some heavy-traffic limit theorems for some nonstationary linear processes which encompass the fractionally differentiated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a non-Gaussian stable distribution. The results are based on an...

We prove some heavy-traffic limit theorems for processes which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a non-Gaussian stable distribution.

Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F. The expansion is based on an expansion for the right...

Cramér's theorem provides an estimate for the tail probability of the maximum of a random walk with negative drift and increments having a moment generating function finite in a neighborhood of the origin. The class of (g,F)-processes generalizes in a natural way random walks and fractional...

Bifurcating autoregressive processes are used to model each line of descent in a binary tree as a standard AR(p) process, allowing for correlations between nodes which share the same parent. Limit distributions of the least-squares estimators of the model parameters for a pth-order bifurcating...

Models for time-dependent contingency tables are presented. Multinomial-logit, conditional exponential family, Markov chain and multinomial-Dirichlet models are discussed for bivariate binary time series. The models are applied to two real data sets.

Models for Markov processes indexed by a branching process are presented. The new class of models is referred to as the branching Markov process (BMP). The law of large numbers and a central limit theorem for the BMP are established. Bifurcating autoregressive processes (BAR) are special cases...

Parameter estimation based on the differences of two positive exponential family random variables is studied. Waiting time data, adjusted for idle times when necessary, are used for estimating the parameters in GI/G/1 queues. The sampling plan presented uses incomplete information on the...

Critical random coefficient AR(1) processes are investigated where the random coefficient is binary, taking values -1 and 1. Asymptotic behavior of least squares estimator for the mean of the random coefficient is discussed. Ordinary least squares estimator is shown to be consistent. Weighted...

Observation-driven state space models are presented for categorical time series as an alternative to the regression type models which are commonly used in the literature. As an application to multi-categorical time series, we present a DNA data analysis and demonstrate the advantages of using...