Mean absolute scaled error¶
A scale-free forecast-accuracy measure dividing mean absolute forecast error by the in-sample mean absolute error of a specified naive benchmark.
Core Idea¶
The denominator changes for seasonal series and can be zero or unstable, the training and evaluation samples must be separated and values compare performance only relative to the declared naive forecast. Absolute errors on the forecast horizon are averaged and normalized by average one-step naive errors from training data, so values below one indicate improvement over that benchmark across series scales. 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¶
Mean absolute scaled error belongs to forecasting and is useful where the analyst can specify the typed forecasting carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the observed and forecast series, training and evaluation ranges, forecast horizon, absolute-error numerator, naive or seasonal-naive benchmark and lag, scaling denominator, zero-denominator handling, aggregation convention and interpretation around one are explicit. The scope is broad within that domain but bounded by the need for the observed and forecast series, training and evaluation ranges, forecast horizon, absolute-error numerator, naive or seasonal-naive benchmark and lag, scaling denominator, zero-denominator handling, aggregation convention and interpretation around one are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the observed and forecast series, training and evaluation ranges, forecast horizon, absolute-error numerator, naive or seasonal-naive benchmark and lag, scaling denominator, zero-denominator handling, aggregation convention and interpretation around one 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.
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 Mean absolute scaled error. Mean absolute scaled error 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¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed forecasting carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the observed and forecast series, training and evaluation ranges, forecast horizon, absolute-error numerator, naive or seasonal-naive benchmark and lag, scaling denominator, zero-denominator handling, aggregation convention and interpretation around one are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of forecasting because they reuse the typed forecasting carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Absolute errors on the forecast horizon are averaged and normalized by average one-step naive errors from training data, so values below one indicate improvement over that benchmark across series scales., and type the carrier, state every parameter and convention in the definition, test that the observed and forecast series, training and evaluation ranges, forecast horizon, absolute-error numerator, naive or seasonal-naive benchmark and lag, scaling denominator, zero-denominator handling, aggregation convention and interpretation around one are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Mean absolute scaled error Domain-specific
Parents (1) — more general patterns this builds on
-
Mean absolute scaled error is a kind of Measurement Prime
The proposed strict upward parent is
prime:measurement.
Hierarchy path (1) — routes to 1 parentless root
- Mean absolute scaled error → Measurement
Neighborhood in Abstraction Space¶
Mean absolute scaled error sits in a crowded region of the domain-specific corpus (35th 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 — 0.93
- Tracking signal — 0.92
- Mean absolute error — 0.90
- Meteorological intelligence — 0.90
- Directional symmetry (time series) — 0.89
Computed from structural-signature embeddings · 2026-09-08