The concept of cointegration has principally been developed under the assumption that the raw data vector zt is I(1) and the cointegrating residual et is I(0), but is also of interest in more general, including fractional, circumstances, where zt is stationary with long memory and et is...

Empirical evidence has emerged of the possibility of fractional cointegration such that thegap, ß, between the integration order d of observable time series, and the integrationorder ? of cointegrating errors, is less than 0.5. This includes circumstances whenobservables are stationary or...

Asset returns are frequently assumed to be determined by one or more commonfactors. We consider a bivariate factor model, where the unobservable commonfactor and idiosyncratic errors are stationary and serially uncorrelated, but havestrong dependence in higher moments. Stochastic volatility...

We consider a cointegrated system generated by processes that may be fractionally integrated, and by additive polynomial and generalized polynomial trends. In view of the consequent competition between stochastic and deterministic trends, we consider various estimates of the cointegrating vector...

Nonlinear functions of multivariate financial time series can exhibit longmemory and fractional cointegration. However, tools for analysingthese phenomena have principally been justified under assumptionsthat are invalid in this setting. Determination of asymptotic theoryunder more plausible...

A semiparametric bivariate fractionally cointegrated system is considered, integrationorders possibly being unknown and I (0) unobservable inputs having nonparametricspectral density. Two kinds of estimate of the cointegrating parameter ? are considered,one involving inverse spectral weighting...

This paper develops methods of investigating the existence and extent of cointegration in fractionally integrated systems. We focus on stationary series, with some discussion of extension to nonstationarity. The setting is semiparametric, so that modelling is effectively confined to a...

The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be...

Empirical evidence has emerged of the possibility of fractional cointegration such that the gap, ß, between the integration order d of observable time series, and the integration order ? of cointegrating errors, is less than 0.5. This includes circumstances when observables are stationary or...

We develop a sequence of tests for specifying the cointegrating rank of, possiblyfractional, multiple time series. Memory parameters of observables are treated asunknown, as are those of possible cointegrating errors. The individual test statisticshave standard null asymptotics, and are related...