Cointegration imposes restrictions on the frequency domain behavior of a time series at the zero-frequency. We derive these restrictions for a multivariate fractionally cointegrated system. In particular, we consider a p-vector time series integrated of order d with r cointegrating relations,...

We propose a Lagrange Multiplier (LM) test of the null hypothesis of cointegration in fractionally cointegrated models. The test statistic utilizes fully modified residuals to cancel the endogeneity and serial correlation biases, and we show that standard asymptotics apply. With i.i.d. Gaussian...

We consider statistical inference for multivariate fractionally integrated time series models using a computationally simple conditional likelihood procedure which has recently been shown to be efficient in the univariate case. We show that those results generalize to the present multivariate...

We derive a functional central limit theorem for the empirical spectral measure or discretely averaged (integrated) periodogram of a multivariate long range dependent stochastic process in a degenerating neighborhood of the origin. We show that, under certain restrictions on the memory...

We introduce a multivariate Lagrange Multiplier (LM) test for fractional integration. We derive and analyze the LM statistic and show that it is asymptotically chi-squared distributed under local alternatives, and that, under Gaussianity, the LM test is asymptotically efficient against local...

It is well known that in standard I(1) cointegration, the timing of variables in the cointegrating relation does not interfere with the cointegration property, whereas in an I(2) framework, it may. We show that, in a general (fractional) CI(d,b) model, it is the reduction in integration orders,...

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X_{t} to be fractional of order d and cofractional of order d-b; that is, there exist vectors β for which...

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X(t) to be fractional of order d and cofractional of order d-b; that is, there exist vectors β for which...

We calculate numerically the asymptotic distribution functions of likelihood ratio tests for fractional unit roots and cointegration rank. Because these distributions depend on a real-valued parameter, b, which must be estimated, simple tabulation is not feasible. Partly due to the presence of...

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X_{t} to be fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which...