ROBUST OPTIMAL TESTS FOR CAUSALITY IN MULTIVARIATE TIME SERIES
Bibliographic record
Abstract
Here, we derive optimal rank-based tests for noncausality in the sense of Granger between two multivariate time series. Assuming that the global process admits a joint stationary vector autoregressive (VAR) representation with an elliptically symmetric innovation density, both no feedback and one direction causality hypotheses are tested. Using the characterization of noncausality in the VAR context, the local asymptotic normality (LAN) theory described in Le Cam (1986,Asymptotic Methods in Statistical Decision Theory) allows for constructing locally and asymptotically optimal tests for the null hypothesis of noncausality in one or both directions. These tests are based on multivariate residual ranks and signs (Hallin and Paindaveine, 2004a,Annals of Statistics32, 2642–2678) and are shown to be asymptotically distribution free under elliptically symmetric innovation densities and invariant with respect to some affine transformations. Local powers and asymptotic relative efficiencies are also derived. The level, power, and robustness (to outliers) of the resulting tests are studied by simulation and are compared to those of the Wald test. Finally, the new tests are applied to Canadian money and income data.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.022 | 0.149 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".