For a Gaussian long-memory process sampled at Poisson times, the periodogram converges to a weighted chi-square limit with explicit d-dependent constants, and the local Whittle estimator of the memory parameter remains consistent.
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Inference for continuous-time long memory randomly sampled processes
For a Gaussian long-memory process sampled at Poisson times, the periodogram converges to a weighted chi-square limit with explicit d-dependent constants, and the local Whittle estimator of the memory parameter remains consistent.