Tracking signal

A forecast-monitoring statistic comparing cumulative error with a scale estimate to flag sustained directional bias beyond ordinary variation.

Version

v1 · 2026-09-08 · History

Domain-specific #

7190

Origin domain

forecast control

Subdomain

forecast control

Core Idea

A common tracking signal divides running sum of forecast errors by mean absolute deviation, with alternative CUSUM and smoothed forms requiring explicit sign, initialization, and threshold conventions. Errors update a signed cumulative numerator while a scale denominator normalizes typical magnitude; persistent one-sided misses push the ratio across a control threshold and trigger review. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application

Tracking signal belongs to forecast control and is useful where the analyst can specify the typed forecast control carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate forecast target, horizon, error sign, update frequency, numerator, scale denominator, initialization, threshold, missing data, interventions, and false-alarm policy are explicit. The scope is broad within that domain but bounded by the need for forecast target, horizon, error sign, update frequency, numerator, scale denominator, initialization, threshold, missing data, interventions, and false-alarm policy are explicit. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity

The abstraction clarifies a crowded vocabulary by making forecast target, horizon, error sign, update frequency, numerator, scale denominator, initialization, threshold, missing data, interventions, and false-alarm policy are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Tracking signal can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Tracking signal. Tracking signal compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: the typed forecast control carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express forecast target, horizon, error sign, update frequency, numerator, scale denominator, initialization, threshold, missing data, interventions, and false-alarm policy are explicit independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of forecast control because they reuse the typed forecast control carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Errors update a signed cumulative numerator while a scale denominator normalizes typical magnitude; persistent one-sided misses push the ratio across a control threshold and trigger review., and type the carrier, state every parameter and convention in the definition, test that forecast target, horizon, error sign, update frequency, numerator, scale denominator, initialization, threshold, missing data, interventions, and false-alarm policy are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Tracking signal Domain-specific

Parents (1) — more general patterns this builds on

• Tracking signal is a kind of Feedback Prime

  The proposed strict upward parent is prime:feedback.

Hierarchy path (1) — routes to 1 parentless root

• Tracking signal → Feedback

Neighborhood in Abstraction Space

Tracking signal sits in a crowded region of the domain-specific corpus (26^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Model Estimation & Numerical Diagnostics (15 abstractions)

Nearest neighbors

• Forecast skill — 0.94
• Mean absolute scaled error — 0.92
• Meteorological intelligence — 0.91
• Control variates — 0.91
• Moving horizon estimation — 0.91

Computed from structural-signature embeddings · 2026-09-08