Diagnostic Checking in ARMA Models With Uncorrelated Errors
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Bibliographic record
Abstract
We consider tests for lack of fit in ARMA models with nonindependent innovations. In this framework, the standard Box–Pierce and Ljung–Box portmanteau tests can perform poorly. Specifically, the usual text book formulas for asymptotic distributions are based on strong assumptions and should not be applied without careful consideration. In this article we derive the asymptotic covariance matrix of a vector of autocorrelations for residuals of ARMA models under weak assumptions on the noise. The asymptotic distribution of the portmanteau statistics follows. A consistent estimator of , and a modification of the portmanteau tests are proposed. This allows us to construct valid asymptotic significance limits for the residual autocorrelations, and (asymptotically) valid goodness-of-fit tests, when the underlying noise process is assumed to be noncorrelated rather than independent or a martingale difference. A set of Monte Carlo experiments, and an application to the Standard & Poor 500 returns, illustrate the practical relevance of our theoretical results.
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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 | 0.007 | 0.071 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it