Breusch–Godfrey test¶
A regression diagnostic testing residual serial correlation through an auxiliary regression that permits higher-order autocorrelation and lagged dependent regressors.
Core Idea¶
The LM statistic is asymptotically chi-square under regularity conditions; lag order, deterministic terms, heteroskedasticity and small-sample F variants affect interpretation. Residuals from the original model are regressed on its regressors and selected residual lags, and the auxiliary explained variation measures whether lagged errors add systematic predictive power. 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 econometrics. It is the domain-specific identity determined by the fitted model and time ordering, null correlation orders, lag choice, auxiliary regression and included regressors, LM or F statistic, reference distribution, sample adjustment, significance and residual assumptions are explicit.
Scope of Application¶
Breusch–Godfrey test belongs to econometrics and is useful where the analyst can specify the typed econometrics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the fitted model and time ordering, null correlation orders, lag choice, auxiliary regression and included regressors, LM or F statistic, reference distribution, sample adjustment, significance and residual assumptions are explicit. The scope is broad within that domain but bounded by the need for the fitted model and time ordering, null correlation orders, lag choice, auxiliary regression and included regressors, LM or F statistic, reference distribution, sample adjustment, significance and residual assumptions are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the fitted model and time ordering, null correlation orders, lag choice, auxiliary regression and included regressors, LM or F statistic, reference distribution, sample adjustment, significance and residual assumptions 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 Breusch–Godfrey test. Breusch–Godfrey test 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 econometrics 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 the fitted model and time ordering, null correlation orders, lag choice, auxiliary regression and included regressors, LM or F statistic, reference distribution, sample adjustment, significance and residual assumptions are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of econometrics because they reuse the typed econometrics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Residuals from the original model are regressed on its regressors and selected residual lags, and the auxiliary explained variation measures whether lagged errors add systematic predictive power., and type the carrier, state every parameter and convention in the definition, test that the fitted model and time ordering, null correlation orders, lag choice, auxiliary regression and included regressors, LM or F statistic, reference distribution, sample adjustment, significance and residual assumptions are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Breusch–Godfrey test Domain-specific
Parents (1) — more general patterns this builds on
-
Breusch–Godfrey test is a kind of Statistical Inference Prime
The proposed strict upward parent is
prime:statistical_inference.
Hierarchy paths (4) — routes to 4 parentless roots
- Breusch–Godfrey test → Statistical Inference → Inductive Reasoning
- Breusch–Godfrey test → Statistical Inference → Uncertainty
- Breusch–Godfrey test → Statistical Inference → Probability → Measure → Set and Membership
- Breusch–Godfrey test → Statistical Inference → Probability → Measure → Aggregation → Micro Macro Linkage
Neighborhood in Abstraction Space¶
Breusch–Godfrey test sits in a moderately populated region (44th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Welfare, Production & Economic Choice (45 abstractions)
Nearest neighbors
- KPSS test — 0.91
- Pareto index — 0.90
- Polytomous choice — 0.89
- Full employment — 0.89
- Ecological regression — 0.89
Computed from structural-signature embeddings · 2026-09-08