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...

This article is concerned with explosive AR(1) processes generated by conditionally heteroscedastic errors. Conditional least squares as well as generalized least squares estimation for autoregressive parameter are discussed and relevant limiting distributions are expressed as products of...

Multivariate tree-indexed Markov processes are discussed with applications. A Galton-Watson super-critical branching process is used to model the random tree-indexed process. Martingale estimating functions are used as a basic framework to discuss asymptotic properties and optimality of...

Godambe (1985) introduced a class of optimum estimating functions which can be regarded as a generalization of quasilikelihood score functions. The "optimality" established by Godambe (1985) within a certain class is for estimating functions and it is based on finite samples. The question that...

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.

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...

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...

This paper is concerned with a general approach for sequential estimation for dependent observations, and an application to a non-standard first order autoregressive process having Weibull errors. The natural estimator of the autoregressive parameter when the errors are non negative turns out to...

Multi-casting autoregression (MCAR, for short) is suggested as a natural extension of the bifurcating autoregressive (BAR) model (cf. [Cowan, R., Staudte, R.G., 1986. The bifurcating autoregression model in cell lineage studies. Biometrics 42, 769-783]) in order to analyze multi-splitting...