Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model

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THE ROLE OF INITIAL VALUES IN CONDITIONAL SUM-OF-SQUARES ESTIMATION OF NONSTATIONARY FRACTIONAL TIME SERIES MODELS (2015, background): “From (18) we find η0t(1) = ∑0 n=−N0+1 1(t−n=1)(Xn − μ0) = 1(t=1)(X0 − μ0), whereas η1t(1) is non-zero only for t ≥ 2 because otherwise the summation over k in (19) is empty.”
NUMERICAL DISTRIBUTION FUNCTIONS OF FRACTIONAL UNIT ROOT AND COINTEGRATION TESTS (2010, methodology): “In MacKinnon (1996) and other previous work on numerical distribution functions, informal model selection procedures were used to choose the best model and value of N for each set of 221 estimated quantiles.”
Long Memory Interdependency and Inefficiency in Bitcoin Markets (2018, background): “The coefficients that characterize this long-run equilibrium are normalized and presented in equations (10-12), with the constant term given by β̂ ′ μ.”