Unverified50% confidenceFactExact time
The autocovariance of long-memory linear processes (such as FARIMA) decays slowly as a power law |k|^{2β−1}, with memory parameter β∈(1/2,1); in this case the sample mean converges at rate n^{β−1/2}, and the limiting process is the integral of fractional Brownian motion with Hurst index H=β+1/2>1/2.
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10/14/2026
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