For modeling count time series data, one class of models is generalized integer autoregressive of order p based on thinning operators. It is shown how numerical maximum likelihood estimation is possible by inverting the probability generating function of the conditional distribution of an...

We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor's 500...

In this paper we propose a test for a set of linear restrictions in a Vector Autoregressive Moving Average (VARMA) model. This test is based on the autoregressive metric, a notion of distance between two univariate ARMA models, M0 and M1, introduced by Piccolo in 1990. In particular, we show...

We generalize the Gaussian Mixture Autoregressive (GMAR) model to the Fisher's z Mixture Autoregressive (ZMAR) model for modeling nonlinear time series. The model consists of a mixture of K-component Fisher's z autoregressive models with the mixing proportions changing over time. This model can...

The paper is concerned with estimation and application of a special stationary integer autoregressive model where multiple binomial thinnings are not independent of one another. Parameter estimation in such models has hitherto been accomplished using method of moments, or nonlinear least...