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Adaptive wavelet based estimator of the memory parameter for stationary Gaussian processes

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Academic year: 2021

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Figure 1: Log-log graphs for different samples of X (D,D ′ ) with D = 0.5 and D ′ = 1 when N = 10 3 (up and left, Dbb N ≃ 1.04), N = 10 4 (up and right, Dbb N ≃ 0.66), N = 10 5 (down and left, Dbb N ≃ 0.62) and N = 10 6 (down and right, Dbb N ≃ 0.54).
Figure 2: Histograms of D bb N and D ˜ N for 100 samples of FARIMA(1, d, 1) with D = 0.5 for N = 10 5 .
Table 1: Consistency of estimators D bb N , D ˜ N , α b N , α ˜ N following ℓ from simulations of the different long-memory processes of the benchmark
Table 2: Estimation of the memory parameter from 100 independent samples in case of short memory (D ≤ 0).
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