Explore the vast range of titles available.

This article studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a two-regime structure according to the magnitude of the lagged observations. Generalized from the Poisson autoregression, it allows more flexible, and even negative correlation, in the observations, which cannot be produced by the single-regime model. Classical Markov chain theory and Lyapunov's method are used to derive the conditions under which the process has a unique invariant probability measure and to show a strong law of large numbers of the intensity process. Moreover, the asymptotic theory of the maximum likelihood estimates of the parameters is established. A simulation study and a real-data application are considered, where the model is applied to the number of major earthquakes in the world. Supplementary materials for this article are available online.

Possible asymmetric behaviour of stock prices during bear and bull markets are studied by using a threshold type non-linear time series model with conditional heteroscedastic variance. Using Hong Kong data it is demonstrated that the return series could have a conditional mean structure which depends on the rise and fall of the market on a previous day. The findings also shed some light on why it could be difficult to reject the efficient market hypothesis. The threshold model with conditional changing variance is also of interest in other financial applications.