In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive uni ed treatment of deterministic terms in the additive model Xt = γZt + Yt, where Zt belongs to a large class of...

We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and make two distinct contributions. First, in their con- sistency proof, Johansen and Nielsen (2012a) imposed moment conditions on the errors that depend on the parameter space, such that...

We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and show that the test statistic for the ususal CVAR model is asymptotically chi-squared distributed. Because the usual CVAR model lies on the boundary of the parameter space for the...

We consider the nonstationary fractional model Δ^{d}X_{t}=ε_{t} with ε_{t} i.i.d.(0,σ²) and d1/2. We derive an analytical expression for the main term of the asymptotic bias of the maximum likelihood estimator of d conditional on initial values, and we discuss the role of the initial values...

We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of <italic>x</italic> = Δ⁻ <italic>u</italic>, where <inline-graphic>null</inline-graphic> is the fractional integration parameter and <italic>u</italic> is weakly dependent. The classical condition is existence of <italic>q</italic> ≥ 2 and <inline-graphic>null</inline-graphic> moments of the innovation sequence....