Local Whittle Analysis of Stationary Fractional Cointegration and the Implied–Realized Volatility Relation

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Volatility in Equilibrium: Asymmetries and Dynamic Dependencies (2009, background): “…as does the empirical evidence of fractional co-integration between implied and realized volatility presented by, e.g., Bandi and Perron (2006) and Nielsen (2007).6 Next, in order to highlight the aforemention return-volatility asymmetry, the first panel in Figure 2 plots the cross-correlations…”
Nonparametric cointegration analysis of fractional systems with unknown integration orders (2010, methodology): “This version of the test is analyzed in detail by Nielsen (2005). The test is constructed as a ratio of variances of the observed series and its fractional partial sum, thereby canceling nuisance parameters from the limiting distribution.”
Exact local Whittle estimation of fractionally cointegrated systems (2012, background): “Nielsen (2007) considers joint estimation of δ1, δ2 and the cointegrating vector under the assumption 0 ≤ δ1, δ2 1/2, but derives its asymptotic distribution only under the long-run exogeneity between the stochastic trend and equilibrium error.”
Multiple Local Whittle Estimation in Stationary Systems (2008, unknown): “In both cases the estimates of β0, δ01, δ02, after correct centering and normalization as in Theorem 4, converge to independent zero-mean normal variates, whose variances can be deduced from the formulae in Σ in the latter case (which the CLT of [24] addresses).”