Independent onset of persistent discrepancy

Read the equation

The event time is the first eligible window in the full observation record whose persistence indicator is one. Because the search does not start at the declaration time, it can detect a change that precedes, coincides with, or follows a declaration. Eligibility T_W must specify missing-data handling and whether a complete future window is available.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

For tolerance ϵ≥0 and a window of W consecutive updates, let TW contain every candidate starting time for which the required measurements are available. Eligibility is determined without reference to declaration time. Define

Pt(ϵ,W)=1{min0≤j<Wδt+j>ϵ},

tΔ(ϵ,W)=inf{t∈TW:Pt(ϵ,W)=1}.

(2.4)

This locates the first observed qualifying window in the eligible record. When both event times are observed, their difference is

ℓ=tΔ−tD.

{t}_{\Delta }(ϵ,W)=inf{t\in {T}_{W}:{P}_{t}(ϵ,W)=1}.

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