Optimal Tests of Noncorrelation Between Multivariate Time Series
Bibliographic record
Abstract
The problem of testing noncorrelation between two multivariate time series is considered. Assuming that the global process admits a joint vector autoregressive (VAR) representation, noncorrelation between the two component series is equivalent to the hypothesis that all off-diagonal blocks in the matrix coefficients and the innovation covariance of the joint VAR representation are zero. We establish an adequate local asymptotic normality (LAN) property for this VAR model in the vicinity of noncorrelation. This LAN structure allows construction of optimal pseudo-Gaussian tests—that is, tests that are locally and asymptotically optimal under Gaussian innovations, but remain valid under non-Gaussian ones—for the null hypothesis of noncorrelation and for comparing their local asymptotic powers with those of the heuristic tests (Haugh–El Himdi–Roy and Koch–Yang–Hallin–Saidi) proposed in the literature.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".