Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties
Bibliographic record
Abstract
Many unit root tests have distorted sizes when the root of the error process is close to the unit circle. This paper analyses the properties of the Phillips-Perron tests and some of their variants in the problematic parameter space. We use local asymptotic analyses to explain why the Phillips-Perron tests suffer from severe size distortions regardless of the choice of the spectral density estimator but that the modified statistics show dramatic improvements in size when used in conjunction with a particular formulation of an autoregressive spectral density estimator. We explain why kernel based spectral density estimators aggravate the size problem in the Phillips-Perron tests and yield no size improvement to the modified statistics. The local asymptotic power of the modified statistics are also evaluated. These modified statistics are recommended as being useful in empirical work since they are free of. the size problems which have plagued many unit root tests, and they retain respectable power. Copyright 1996 by The Review of Economic Studies Limited.
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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 | 0.034 | 0.285 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.007 | 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".