Inference on autoregressive moving average models for count data
Bibliographic record
Abstract
In the analysis of count time series at equally spaced intervals with covariate information, Poisson Autoregressive (AR) or Integer-Valued Autoregressive (INAR) models have been widely discussed in the literature, with their fundamental properties and estimation methods thoroughly explored. However, when time series data exhibits both long-term dependencies (autocorrelation) and moving average effects, capturing both of these elements is essential for more effective modeling and forecasting. To address this, we introduce autoregressive moving average (ARMA) models of order (1,1) for count time series. We first consider the case where the offspring random variable follows a Bernoulli distribution, meaning that each individual in the population at time t - 1 can produce only one or zero offspring at time t. Additionally, we extend this model to incorporate the possibility of any individual producing multiple offspring at a given time point, resulting in a binomial offspring random variable. We derive the key properties of these models, present methods for parameter estimation and forecasting function. The performance of the proposed methods are assessed through simulation studies.
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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 | 0.016 | 0.058 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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".