Residual Log-Periodogram Inference for Long-Run-Relationships

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Semiparametric Estimation in Time‐Series Regression with Long‐Range Dependence (2005, unknown): “Hassler et al. (2000) and Velasco (2003) provide some evidence that the logperiodogram and Gaussian semiparametric procedures of Robinson (1995a,b), with carefully chosen bandwidth parameters, satisfy Assumption 6 with d̂p dp ¼ Opðm 1=2Þ. Denote the feasible estimate b̂d̂p ;m.”
Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach (2007, methodology): “Since Pm 1 νj = 0, (20) is, apart from op (1) terms, pX a=1 ηa 2m−1/2 Gaa mX j=1 νj (Iua (λj)−Gaa) = pX a=1 ηa 2 m1/2 mX j=1 νj Gaa (Ca (λj) Iε (λj)Ca (λj) ∗ −Gaa) = pX a=1 ηa 2 m1/2 mX j=1 νj Gaa Ã Ca (λj) 1 2πn nX t=1 εtε 0 tCa (λj) ∗ −Gaa !”
Local Whittle Analysis of Stationary Fractional Cointegration and the Implied–Realized Volatility Relation (2007, background): “Although this may indeed be a valid course of action, see Velasco (2003) and Hassler, Marmol, and Velasco (2006) for the nonstationary case, a joint estimation method for the integration orders and the cointegration vector would be preferable.”