Unverified50% confidenceDecision RuleExact time
If the data exhibit long memory, using the traditional √γ confidence interval will severely underestimate uncertainty, and inference must be based on a scale of γ^{β-1/2}ℓ(1/γ).
1
Sources
50%
Confidence
Long-term
Relevance
10/14/2026
First Seen
Sources
Related Entities
Related Claims
UnverifiedUnder long-memory linear processes, the convergence scale becomes γ^{β-1/2}ℓ(1/γ), and the limiting distribution is driven by an integral of fractional Brownian motion, no longer standard Gaussian.76% similarUnverifiedε-prediction is prone to numerical instability at large embedding dimensions, because when α_bar_t approaches zero the scaling factor 1/sqrt(α_bar_t) tends to infinity, amplifying prediction errors.67% similarUnverifiedTo reduce prediction error to level τ, the required number of states or modes is r=Θ(log²(1/τ)), i.e., the square-logarithmic state complexity law.67% similarUnverifiedWhen measuring prediction error after fractional integration, there is an exact 1/L leading-order error for forecasting from a finite context of length L.66% similarUnverifiedThe 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>1/2.65% similar
Cite This Claim
Stable URI
https://kongchang.com/claim/1023459API
curl https://kongchang.com/api/v1/knowledge/claims/1023459MCP
get_claim(id=1023459)