For a fractional time series model integrated of order d we derive two results. First, it is obtained how a change in d affects the coefficients of the integration filter. For long memory (d0), the effect is always positive; in the case of anti-persistence (d0) the effect may be positive or...

Consider two independent random walks. By chance, there will be spells of association between them where the two processes move in the same direction, or in opposite direction. We compute the probabilities of the length of the longest spell of such random association for a given sample size, and...

We suggest a model for long memory in time series that amounts to harmonically weighting short memory processes, ∑ _j ^x t − j / ( j 1). A nonstandard rate of convergence is required to establish a Gaussian functional central limit theorem. Further, we study the asymptotic least squares theory...

We consider a class of panel tests covering tests for the null hypothesis of no cointegration as well as cointegration. All tests under investigation rely on single-equations estimated by ordinary least squares, and they may be residual-based or not. We focus on test statistics computed from...

We propose a class of ratio tests that is applicable whenever a cumulation (of transformed) data is asymptotically normal upon appropriate normalization. All it requires is the orthonormal expansion using the Karhunen-Loeve [KL] theorem, which is employed to compute weighted averages of the...