Regularization and selection in Gaussian mixture of autoregressive models
Bibliographic record
Abstract
Abstract Gaussian mixtures of autoregressive models can be adopted to explain heterogeneous behaviour in mean, volatility, and multi‐modality of the conditional or marginal distributions of time series. One important task is to infer the number of autoregressive regimes and the autoregressive orders. Information‐theoretic criteria such asaicorbicare commonly used for such inference, and typically evaluate each regime/autoregressive combination separately in order to choose an optimal model. However the number of combinations can be so large that such an approach is computationally infeasible. In this article we first develop a computationally efficient regularization method for simultaneous autoregressive‐order and parameter estimation when the number of autoregressive regimes is pre‐determined. We then propose a regularized Bayesian information criterion (rbic) to select the number of regimes. We study asymptotic properties of the proposed methods, and investigate their finite sample performance via simulations. We show that asymptotically therbicdoes not underestimate the number of autoregressive regimes, and provide a discussion on the current challenges in investigating whether and under what conditions therbicprovides a consistent estimator of the number of regimes. We finally analyze U.S. gross domestic product growth and unemployment rate data to demonstrate the proposed methods.The Canadian Journal of Statistics45: 356–374; 2017 © 2017 Statistical Society of Canada
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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 | 0.013 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".