On Testing for Serial Correlation of Unknown Form Using Wavelet Thresholding
Bibliographic record
Abstract
Omnibus procedures for testing serial correlation are developed, using spectral density estimation and wavelet shrinkage. The asymptotic distributions of the wavelet coefficients under the null hypothesis of no serial correlation are derived. Under some general conditions on the wavelet basis, the wavelet coefficients asymptotically follow a normal distribution. Furthermore, they are asymptotically uncorrelated. Adopting a spectral approach and using results on wavelet shrinkage, new one-sided test statistics are proposed. As a spatially adaptive estimation method, wavelets can effectively detect fine features in the spectral density, such as sharp peaks and high frequency alternations. Using an appropriate thresholding parameter, shrinkage rules are applied to the empirical wavelet coefficients, resulting in a non-linear wavelet-based spectral density estimator. Consequently, the advocated approach avoids the need to select the finest scale J, since the noise in the wavelet coefficients is naturally suppressed. Simple data-dependent threshold parameters are also considered. In general, the convergence of the spectral test statistics toward their respective asymptotic distributions appears to be relatively slow. In view of that, Monte Carlo methods are investigated. In a small simulation study, several spectral test statistics are compared, with respect to level and power, including versions of these test statistics using Monte Carlo simulations.
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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 | 0.054 | 0.272 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.007 | 0.005 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".