This paper develops methods of investigating the existence and extent of cointegration in fractionally integrated systems. We focus on stationary series, with some discussion of extension to nonstationarity. The setting is semiparametric, so that modelling is effectively confined to a...

Efficient semiparametric and parametric estimates are developed for a spatial autoregressive model, containing nonstochastic explanatory variables and innovations suspected to be non-normal. The main stress is on the case of distribution of unknown, nonparametric, form, where series...

This paper derives the asymptotic distribution of nonparametric neural network estimator of the Lyapunov exponent in a noisy system proposed by Nychka et al (1992) and others. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for...

We consider a cointegrated system generated by processes that may be fractionally integrated, and by additive polynomial and generalized polynomial trends. In view of the consequent competition between stochastic and deterministic trends, we consider various estimates of the cointegrating vector...

This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the...

Cointegrated bivariate nonstationary time series are considered in fractional context, without allowance for deterministic trends. Both the observable series and the cointegrating error can be fractional processes. The familiar situation in which the respective integration orders are 1 and 0 is...