We investigate vector autoregressive processes and find the condition under which the processes are <italic>I</italic>(2). A representation theorem forsuch processes is proved and the interpretation of the AR model as an error correction model is discussed.

This paper discusses inference for I(2) variables in a VAR model. The estimation procedure suggested consists of two reduced rank regressions. The asymptotic distribution of the proposed estimators of the cointegrating coefficients is mixed Gaussian, which implies that asymptotic inference can...

Based on an idea of Granger (1986, <italic>Oxford Bulletin of Economics and Statistics</italic> 48, 213–228), we analyze a new vector autoregressive model defined from the fractional lag operator 1 − (1 − <italic>L</italic>)^null. We first derive conditions in terms of the coefficients for the model to generate processes...

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....