This paper studies a class of Markov models that 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...

type="main" xml:id="jtsa12108-abs-0001"The Gaussian mixture autoregressive model studied in this article belongs to the family of mixture autoregressive models, but it differs from its previous alternatives in several advantageous ways. A major theoretical advantage is that, by the definition of...

This edited collection concerns nonlinear economic relations that involve time. It is divided into four broad themes that all reflect the work and methodology of Professor Timo Terasvirta, one of the leading scholars in the field of nonlinear time series econometrics. The themes are: Testing for...

We develop tests for predictability in a first-order ARMA model often suggested for stock returns. Instead of the conventional ARMA model, we consider its non-Gaussian and noninvertible counterpart that has identical autocorrelation properties but allows for conditional heteroskedasticity...

We consider maximum likelihood estimation of a particular noninvertible ARMA model with autoregressive conditionally heteroskedastic (ARCH) errors. The model can be seen as an extension to so-called all-pass models in that it allows for autocorrelation and for more fl exible forms of conditional...

This paper studies the stability of nonlinear autoregressive models with conditionally 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 article studies the stability of nonlinear autoregressive models with conditionally 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 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...

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

We develop likelihood-based tests for autocorrelation and predictability in a first order non- Gaussian and noninvertible ARMA model. Tests based on a special case of the general model, referred to as an all-pass model, are also obtained. Data generated by an all-pass process are uncorrelated...