On AR(1) versus MA(1) models for Non-stationary time series of Poisson counts: part I (theory)
Bibliographic record
Abstract
Abstract: Analysis of time series of counts is an important research topic in many bio-medical and socio-economic sectors. For example, analyzing the yearly number of patients of a particular disease in a country is an important problem for health economics. Similarly, analyzing the monthly number of tourists for a city/country and the yearly number of patents awarded to a firm are important economic problems. Unlike in the Gaussian time series case, the analysis of this type of count data is, however, not easy due to the difficulty of modelling the correlated count data recorded over a long period of time. The problem becomes much more difficult if the counts are non-stationary over time, which is likely to be the case in many practical situations. Recently, some authors have developed Gaussian type non-stationary AR(1) (auto-regressive of order 1) models to fit the time series of count data. But, as in practice, there may be situations where Gaussian type moving average (MA) models may fit the count data better than the AR models, this paper develops a non-stationary MA(1) model and compare its basic properties with those of the AR(1) model. For the purpose of statistical inference, the parameters of the proposed models are estimated through an efficient quasi-likelihood (QL) approach.
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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 | 0.027 | 0.059 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.004 | 0.004 |
| 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".