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Detection of non-constant long memory parameter

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Academic year: 2021

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Figure 1: Representation of the ratio q I [I] (0.05, d)/q [II] I (0.05, d) as function of d, with the choice τ = 0.1 and τ = 0.9.
Figure 2: The upper 5% quantile of I(B d+.5 I ) as a function of d, for τ = .05 (solid graph); τ = .1 (solid graph with points); τ = .2 (dashed graph)
Figure 3: Sample paths simulated from model (2.4) with θ ∗ = 1/2 for different values of d 1 and d 2 : d 1 = .1, d 2 = .4 (top); d 1 = .3, d 2 = .6 (middle); d 1 = .8, d 2 = 1.1 (bottom)
Figure 4: Sample paths simulated from models (5.13) (top) and (5.17) (bottom) with d(τ ) = .2 + .6τ , θ = 0 and θ = 1.
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