Directional symmetry (time series)¶

A forecast-accuracy statistic equal to the percentage of successive periods in which predicted and observed changes have the same sign.

Version: v1 · 2026-09-08 · History
Domain-specific #: 4193
Origin domain: forecast evaluation
Subdomain: directional accuracy

Core Idea¶

Directional symmetry measures how often a model correctly predicts whether a time series rises or falls from one period to the next. Each adjacent pair is converted to observed and predicted direction signs, agreement receives one, and the mean agreement is expressed as a proportion or percentage. 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.

The load-bearing residual is not the broad topic of forecast evaluation. It is sign-only time-series accuracy independent of change magnitude. That residual remains recognizable when examples, notation, scale, or implementation change, but it disappears if the carrier is mistyped, the condition that forecast alignment, horizon, tie rule and missing-data treatment are fixed and no future observation enters forecast construction fails, a neighboring object is substituted, or notation and topical resemblance replace the constitutive test.

Scope of Application¶

Directional symmetry (time series) belongs to forecast evaluation and is useful where the analyst can specify an observed time series, aligned forecasts, successive observed differences, successive predicted differences, sign-matching indicator, treatment of ties and an aggregation interval, then evaluate forecast alignment, horizon, tie rule and missing-data treatment are fixed and no future observation enters forecast construction. The scope is broad within that domain but bounded by the need for forecast alignment, horizon, tie rule and missing-data treatment are fixed and no future observation enters forecast construction. 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 alignment, horizon, tie rule and missing-data treatment are fixed and no future observation enters forecast construction 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 Directional symmetry (time series) 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 Directional symmetry (time series). Directional symmetry (time series) 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: an observed time series, aligned forecasts, successive observed differences, successive predicted differences, sign-matching indicator, treatment of ties and an aggregation interval. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express forecast alignment, horizon, tie rule and missing-data treatment are fixed and no future observation enters forecast construction independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of forecast evaluation because they reuse an observed time series, aligned forecasts, successive observed differences, successive predicted differences, sign-matching indicator, treatment of ties and an aggregation interval, Each adjacent pair is converted to observed and predicted direction signs, agreement receives one, and the mean agreement is expressed as a proportion or percentage., and type the carrier, state every parameter and convention in the definition, test that forecast alignment, horizon, tie rule and missing-data treatment are fixed and no future observation enters forecast construction, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Directional symmetry (time series) Domain-specific

Parents (1) — more general patterns this builds on

Directional symmetry (time series) is a kind of Measurement Prime

The proposed strict upward parent is prime:measurement.

Hierarchy path (1) — routes to 1 parentless root

Directional symmetry (time series) → Measurement

Neighborhood in Abstraction Space¶

Directional symmetry (time series) sits in a moderately populated region (45^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Longitudinal Models & Time-Series Structure (8 abstractions)

Nearest neighbors

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