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 (a form of) geometric ergodicity of the unobservable component is inherited by the joint process formed of...

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...

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...

This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. In these models, future errors are predictable, indicating that they can be used to empirically approach rational expectations models with nonfundamental solutions. In...

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 (a form of) geometric ergodicity of the unobservable component is inherited by the joint process formed of...

This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. We argue that noncausal autoregressive models are especially well suited for modeling expectations. Unlike conventional causal autoregressive models, they explicitly...

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...

In this paper, we propose a simulation-based method for computing point and density forecasts for univariate noncausal and non-Gaussian autoregressive processes. Numerical methods are needed to forecast such time series because the prediction problem is generally nonlinear and no analytic...

Lagged variables are often used as instruments when the generalized method of moments (GMM) is applied to time series data. We show that if these variables follow noncausal autoregressive processes, their lags are not valid instruments and the GMM estimator is inconsistent. Moreover, in this...