Design Feasibility and Identification of Local Covariance Paths

ABSTRACT Overlapping local covariance estimates can share the same population information. We characterize the information in their retained moments, distinguishing full‐line Gaussian systems from compact empirical designs. Smooth diffusion constructions give different covariance paths with identical finite sampled‐price laws. Within a declared path approximation, row‐space calculations identify the targets that can be recovered; recovery weights separate moment error, unresolved directions, and approximation bias. A Gaussian covariance envelope turns a stated path bound into an upper risk bound that accounts for overlap. For deterministic compact spectral designs, we establish feasible joint covariance and correlation limits with positive Gaussian level noise, locally Hölder exogenous covariance, bounded adapted drift, and finite price jumps away from the evaluation points. Simulations examine finite‐sample studentization, rough drivers, leverage, and covariance jumps. Fifteen BTC/ETH minute‐close refits vary bandwidth, spacing, filtering, noise assumptions, and unavailable observations. Two designs share the same count index although one leaves an event covariance average unidentified. Recovery and regularization calculations translate a target tolerance into a moment‐error budget. Identification, stable recovery, and statistical precision therefore lead to different design decisions.