We provide a fast algorithm for calculating the fractional difference of a time series. In standard implementations, the calculation speed (complexity) is of order T 2, where T is the length of the time series. Our algorithm allows calculation speed of order T log2 T . For moderate and large...

We suggest improved tests for cointegration rank in the vector au- toregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but of course the asymptotic results apply more generally....

In this paper we apply the recently developed fractionally cointegrated vector autoregressive (FCVAR) model to analyze price discovery in the spot and futures markets for five non-ferrous metals (aluminium, copper, lead, nickel, and zinc). The FCVAR model allows for long memory (fractional...