A limit theory is established for autoregressive time series that smooths the transition between local and moderate deviations from unity and provides a transitional form that links conventional unit root distributions and the standard normal. Edgeworth expansions of the limit theory are given....

This paper aims at improved accuracy in testing for long-run predictability in noisy series, such as stock market returns. Long-horizon regressions have previously been the dominant approach in this area. We suggest an alternative method that yields more accurate results. We find evidence of...

This paper considers integer-valued autoregressive processes where the autoregression parameter is close to unity.We consider the asymptotics of this `near unit root' situation.The local asymptotic structure of the likelihood ratios of the model is obtained, showing that the limit experiment is...