This note studies the geometric ergodicity of nonlinear autoregressive models with conditionally heteroskedastic errors. A nonlinear autoregression of order p (AR(p)) with the conditional variance specified as the conventional linear autoregressive conditional heteroskedasticity model of order q...

This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a general nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized...

This paper studies the stability of nonlinear autoregressive models with conditionality heteroskedastic errors. We consider a nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a nonlinear first order generalized autoregressive conditional heteroskedasticity...

This paper studies a class of Markov models which consist of two components. Typically, one of the components is observable and the other is unobservable or `hidden`. Conditions under which geometric ergodicity of the unobservable component is inherited by the joint process formed of the two...

This paper proposes neural network based measures of predictability in conditional mean, and then uses them to construct nonlinear analogues to autocorrelograms and partial autocorrelograms. In contrast to other measures of nonlinear dependence that rely on nonparametric estimation of densities...

Bivariate time series data often show strong relationships between the two components, while both individual variables can be approximated by random walks in the short run andare obviously bounded in the long run. Three model classes are considered for a time-series model selection problem:...

Given that it is quite impractical to use standard model selection criteria in a nonlinear modeling context, the builders of nonlinear models often choose lag length by setting it equal to the lag length chosen for a linear autoregression of the data. This paper studies the performance of this...

A two-regime self-exciting threshold autoregressive process is estimated for quarterly aggregate GDP of the fifteen countries that compose the European Union, and the forecasts from this nonlinear model are compared, by means of a Monte Carlo simulation, with those from a simple autoregressive...