This paper proposes simple Hausman-type tests to check for bias in the log-periodogram regression of a time series believed to be long memory. The statistics are asymptotically standard normal on the null hypothesis that no bias is present, and the tests are consistent.

We study the empirical behaviour of semi-parametric estimation for long-memory models when the true data generating process exhibits a change in persistence. Evidence for long memory is likely to be found. Procedures for discrimination between different models are proposed.

Linearity testing against smooth transition autoregressive (STAR) models when deterministic trends are potentially present in the data is considered in this work. Our findings show, in contrast to results recently reported in Zhang (2012), that linearity tests against STAR models lead to useful...