Threshold Autoregressive Moving-Average models: probabilistic structure, statistical aspects and applications
Bibliographic record
Abstract
The thesis analyses threshold autoregressive moving-average models (TARMA). They are an extension of threshold autoregressive models (TAR) as to allow serially dependent noise. TARMA models describe parsimoniously many non-linear phenomena. The systematic study of TARMA models presents several challenges. The thesis solves the probabilistic problems for the first order TARMA models enabling their practical application. The results allow to develop a powerful unit root test for both linear and non-linear processes. Most unit root tests are affected by size distortion in presence of dependent errors, especially of the moving-average kind. The proposals that address such problem do not consider non-linear alternatives. On the other hand, tests that have a non-linear specification in the alternative hypothesis do not deal with the size issue. We use TARMA models to develop a novel unit root test based upon Lagrange multipliers that does not suffer from size distortions and, at the same time, allows for a wide and flexible non-linear alternative. We prove that our supLM test is consistent, it is similar and it is nuisance-parameters free. In addition to the asymptotic version of the test we propose a wild bootstrap version with very good properties in terms of size and power. The final part of the thesis is devoted to a preliminary empirical investigation regarding the parsimony of TARMA models. Moreover, we use TARMA models to analyse the Canadian lynx time series.
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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 | 0.006 | 0.033 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 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".