Local Whittle Analysis of Stationary Fractional Cointegration
Bibliographic record
Abstract
We consider a local Whittle analysis of a stationary fractionally cointegrated model. A two step estimator equivalent to the local Whittle QMLE is proposed to jointly estimate the integration orders of the regressors, the integration order of the errors, and the cointegration vector. The estimator is semiparametric in the sense that it employs local assumptions on the joint spectral density matrix of the regressors and the errors near the zero frequency. We show that, for the entire stationary region of the integration orders, the estimator is asymptotically normal with block diagonal covariance matrix. Thus, the estimates of the integration orders are asymptotically independent of the estimate of the cointegration vector. Furthermore, our estimator of the cointegrating vector is asymptotically normal for a wider range of integration orders than the narrow band frequency domain least squares estimator and is superior with respect to asymptotic variance. An application to financial volatility series is offered.
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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 | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".