The so-called type I and type II fractional Brownian motions are limit distributions associated with the fractional integration model in which pre-sample shocks are either included in the lag structure, or suppressed. There can be substantial differences between the distributions of these two...

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.

This paper surveys the extensive recent literature on the problems of deciding what is meant by an I(0) process, and then deciding how to test for the property. A formidable difficulty exists in the construction of consistent and asymptotically correctly sized tests for the I(0) hypothesis, and...

This paper considers tests for cointegration with allowance for structural breaks, using the extrema of residual-based tests over subsamples of the data. One motivation for the approach is to formalize the practice of data snooping by practitioners, who may examine subsamples after failing to...

This paper considers the asymptotic distribution of the covariance of a nonstationary fractionally integrated process with the stationary increments of another such process - possibly, itself. Questions of interest include the relationship between the harmonic representation of these random...

This paper proposes a consistent model speci?cation test that can be applied to a wide class of models and estimators, including all variants of quasi-maximum likelihood and generalized method of moments. Our framework is independent of the form of the model and generalizes Bierens?(1982, 1990)...