Unit Root Tests and Structural Change when the Initial Observation is Drawn from its unconditional Distribution
Bibliographic record
Abstract
Following Elliott (1999) and Perron and Rodríguez (2003), we develop unit root tests in the context of structural change models using GLS detrended data (Elliott, Rothenberg and Stock, 1996) when the initial observation is drawn from its unconditional distribution. We derive the limiting distributions of the M-tests (Stock, 1999; Perron, and Ng, 1996), the ADF statistic and a feasible optimal point test from which we derive the power envelope. Asymptotic power functions are calculated and compared with the case where the initial condition is not random. Finite sample size and power simulations under various forms of error processes are performed using different lag selection methods and two different methods to select the break point. Empirical applications are also provided. / Suivant Elliott (1999) et Perron et Rodríguez (2003), nous dérivons des tests pour racine unitaire dans le cas où la fonction de tendance peut avoir une rupture à une date inconnue. Ces tests utilisent la méthode des moindres carrés généralisés (MCG) pour éliminer les composantes déterministes, tel que proposé par Elliott, Rothenberg et Stock (1996). Nous considérons le cas où la condition initielle est obtenue à partir de sa distribution non conditionnelle. Nous dérivons les distributions asymptotiques de M-tests (Stock, 1999; Perron and Ng, 1996), du test ADF et celle d’une version réalisable du test optimal en un point. Ce test nous permet de dériver l’enveloppe de puissance. Nous calculons les fonctions de puissance asymptotique et nous les comparons au cas où la condition initielle n’est pas aléatoire. En utilisant des simulations, nous évaluons le niveau et la puissance des tests en échantillon finis et nous étudions plusieurs méthodes pour sélectionner le retard nécessaire pour calculer l’estimateur de la densité spectrale, ainsi que deux méthodes pour sélectionner le point de rupture. Une application à des séries des salaires réels et aux prix des actions ordinaires aux Etats-Unis est aussi considérée à la fin.
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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 | 0.137 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 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".