Likelihood inference for a nonstationary fractional autoregressive model

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NUMERICAL DISTRIBUTION FUNCTIONS OF FRACTIONAL UNIT ROOT AND COINTEGRATION TESTS (2010, unknown): “Email: jgm@econ.queensu.ca Johansen and Nielsen (2010a, 2010b), henceforth JN.”
Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model (2010, methodology): “Zit = (∆ d+ib −∆)β0⊥Xt, Zkt = ∆β0⊥Xt, Wjt = (∆ d+jb −∆)β0Xt, Wkt = ∆β0Xt, (17)”
Nonparametric cointegration analysis of fractional systems with unknown integration orders (2010, background): “Robinson & Hualde (2003), if there is no strong a priori reason to pick any particular integration orders it is important to make only minimal assumptions on their values and possibly allow them to be estimated as part of the procedure.”
THE ROLE OF INITIAL VALUES IN CONDITIONAL SUM-OF-SQUARES ESTIMATION OF NONSTATIONARY FRACTIONAL TIME SERIES MODELS (2015, background): “We thus insert the expressions (75), (76), and (77) into the expansion (17) and find T (d̂− d0) = − A0 + T A1 B0 + T−1/2B1 − 1 2 T−1/2( A0 + T A1 B0 + T−1/2B1 )(2) C0 B0 + T−1/2B1 + oP (T −1/2), which, using the expansion 1/(1 + z) = 1− z + z(2) + .”