Threshold models in the context of conditionally heteroscedastic time series have been found to be useful in analyzing asymmetric volatilities. While the effect of current volatility on the future volatility decreases to zero at an exponential rate for standard-threshold-GARCH (TGARCH)...

The threshold-asymmetric GARCH (TGARCH, for short) models have been useful for analyzing asymmetric volatilities arising mainly from financial time series. Most of the research on TGARCH has been directed to the stationary case. In this article, motivated by unstable features in recent time...

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...

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...

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...

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 a broad class of explosive AR(1) models. Allowing stationary dependence on the error process, we do not restrict ourselves to independent and identically distributed errors. The model accommodates, as special cases, GARCH errors, AR(1) errors and Gaussian ARMA...

A class of asymmetric GARCH models is proposed by combining threshold effect and bilinear structure. The class is referred to as threshold-bilinear GARCH processes. A simulation study demonstrates that the class exhibits diverse asymmetries in volatilities, accommodating existing asymmetric...

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...