Nonparametric Copula-Based Test for Conditional Independence with Applications to Granger Causality
Bibliographic record
Abstract
This article proposes a new nonparametric test for conditional independence that can directly be applied to test for Granger causality. Based on the comparison of copula densities, the test is easy to implement because it does not involve a weighting function in the test statistic, and it can be applied in general settings since there is no restriction on the dimension of the time series data. In fact, to apply the test, only a bandwidth is needed for the nonparametric copula. We prove that the test statistic is asymptotically pivotal under the null hypothesis, establishes local power properties, and motivates the validity of the bootstrap technique that we use in finite sample settings. A simulation study illustrates the size and power properties of the test. We illustrate the practical relevance of our test by considering two empirical applications where we examine the Granger noncausality between financial variables. In a first application and contrary to the general findings in the literature, we provide evidence on two alternative mechanisms of nonlinear interaction between returns and volatilities: nonlinear leverage and volatility feedback effects. This can help better understand the well known asymmetric volatility phenomenon. In a second application, we investigate the Granger causality between stock index returns and trading volume. We find convincing evidence of linear and nonlinear feedback effects from stock returns to volume, but a weak evidence of nonlinear feedback effect from volume to stock returns.
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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 | 0.016 | 0.140 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 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".