Testing for Multivariate Autoregressive Conditional Heteroskedasticity Using Wavelets
Bibliographic record
Abstract
Test statistics for autoregressive conditional heteroskedasticity (ARCH) in the residuals from a possibly nonlinear and dynamic multivariate regression model are considered. The new approach is based on estimation of the multivariate spectral density of squared and cross-residuals. A simple wavelet-based spectral density estimator is advocated, which is a particularly suitable analytic tool when the spectral density exhibits peaks or kinks that may arise from strong cross-dependence, seasonal patterns and other forms of periodic behaviors. In several circumstances, the spectral density may have peaks at various frequencies, such as seasonal frequencies, and the wavelet method may capture them effectively. Compared to kernel-based test statistics for multivariate ARCH effects, the weighting scheme offered by the new wavelet-based test statistics differs in several important aspects. An asymptotic analysis under the null hypothesis of no ARCH effects shows that the wavelet-based test statistic converges in distribution to a convenient standard normal distribution. Under fixed alternatives, the consistency of the wavelet-based test statistics is established in a class of static regression models with uncorrelated but dependent errors. In a Monte Carlo study comparisons are made under various alternatives between the proposed wavelet-based test statistics, the kernel-based test statistics for ARCH effects, and several popular portmanteau test statistics for ARCH effects available in the literature.
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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 | 0.021 | 0.129 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".