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 as aic or bic are 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 the rbic does not underestimate the number of autoregressive regimes, and provide a discussion on the current challenges in investigating whether and under what conditions the rbic provides 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 Statistics 45: 356–374; 2017 © 2017 Statistical Society of Canada
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".