Statistical analysis of hypotheses on the cointegrating relations in the I(2) model

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Representation of Cointegrated Autoregressive Processes with Application to Fractional Processes (2008, unknown): “…̄′̇C1 = 0, because (14) and (15) show that ′C0 + ̄′̇C1 = −Ir + ̄′ C2 ̄ − ̄′̇C2̇̄ = −Ir + ̄′ C2 ̄ − ̄′ C2 ̄ = −Ir For I (2) processes we usually apply the error correction model (18), where satisfies ′⊥ ⊥ = ′ Inference can be found in Boswijk (2000), Johansen (1997, 2006), and Paruolo (1996, 2000).”
Testing hypotheses in an I(2) model with piecewise linear trends. An analysis of the persistent long swings in the Dmk/$ rate (2010, methodology): “Treating the process as I(1) is likely to yield unreliable inference (see Johansen, 2006b and Juselius, 2008) as one (or two) very persistent components in the data would be treated as stationary.”