On testing for independence between the innovations of several time series
Bibliographic record
Abstract
Abstract Test statistics for checking the independence between the innovations of several time series are developed. The time series models considered allow for general specifications for the conditional mean and variance functions that could depend on common explanatory variables. In testing for independence between more than two time series, checking pairwise independence does not lead to consistent procedures. Thus a finite family of empirical processes relying on multivariate lagged residuals are constructed, and we derive their asymptotic distributions. In order to obtain simple asymptotic covariance structures, Möbius transformations of the empirical processes are studied, and simplifications occur. Under the null hypothesis of independence, we show that these transformed processes are asymptotically Gaussian, independent, and with tractable covariance functions not depending on the estimated parameters. Various procedures are discussed, including Cramér–von Mises test statistics and tests based on non‐parametric measures. The ranks of the residuals are considered in the new methods, giving test statistics which are asymptotically margin‐free. Generalized cross‐correlations are introduced, extending the concept of cross‐correlation to an arbitrary number of time series; portmanteau procedures based on them are discussed. In order to detect the dependence visually, graphical devices are proposed. Simulations are conducted to explore the finite sample properties of the methodology, which is found to be powerful against various types of alternatives when the independence is tested between two and three time series. An application is considered, using the daily log‐returns of Apple, Intel and Hewlett‐Packard traded on the Nasdaq financial market. The Canadian Journal of Statistics 40: 447–479; 2012 © 2012 Statistical Society of Canada
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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 | 0.001 | 0.002 |
| 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".