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: v2 · 2026-09-19 · History
Domain-specific #: 4193
Domain group: Formal Sciences
Origin domain: Experimental Design & Statistics
Subdomains: Forecast Evaluation, Directional Accuracy → Experimental Design & Statistics

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.

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Up-or-Down Guess Score

Imagine guessing each day whether tomorrow will be warmer or colder than today. Directional symmetry is a score for how often your up-or-down guesses were right. It doesn't care how much warmer or colder, just which way.

Right-Direction Forecast Score

When people predict something that changes over time, like prices or temperatures, one way to grade them is directional symmetry. For each step, you ask: did the real value go up or down, and did the prediction say up or down? A match gets one point. The score is the share of steps where the guess got the direction right, often given as a percentage. It ignores how big the change was, so a prediction can get the direction right while being far off in size.

Sign-Only Forecast Accuracy

Directional symmetry is a forecast accuracy measure for time series that counts how often a model correctly predicts whether the series will rise or fall from one period to the next. For each pair of neighboring time points, you turn both the actual change and the predicted change into a sign, up or down. If the signs match, that step scores 1; if not, 0. The average of those scores, as a proportion or percentage, is the directional symmetry. It ignores the size of the changes entirely, so a model can score well even if its predicted amounts are far off. To be fair, you must fix how forecasts line up with actual values, the forecast horizon, what to do with ties (no change), and how to handle missing data, and forecasts must not use any future information.

Directional symmetry (DS) is a sign-only accuracy measure for time-series forecasts: for each adjacent pair of periods, the observed change and the predicted change are converted to direction signs, a match scores 1 and a mismatch 0, and DS is the mean agreement expressed as a proportion or percentage. Because only signs enter, it is invariant to the magnitude of changes and complements magnitude-based error measures. Its value is well defined only once forecast alignment, horizon, the rule for ties (zero changes), and missing-data treatment are fixed. Validity also requires that no future observation enters forecast construction, since look-ahead leakage would inflate directional agreement. It answers a different question from error measures like mean squared error: whether the model gets the direction of movement right.

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.
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) — outgoing typed relations

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

The statistic measures directional forecast agreement.

Hierarchy path (1) — routes to 1 parentless root

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

Neighborhood in Abstraction Space¶

Directional symmetry (time series) sits in a crowded region of the domain-specific corpus (29^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Forecast Accuracy & Climate Measures (5 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-25