Time Series Clustering of GARCH (1,1) Model Using Modified Piccolo Distance
Bibliographic record
Abstract
As investors select stocks more efficiently to form portfolios that meet their objectives, they should be grouped based on their time-varying risk levels.One of the clustering approaches is time series clustering with a model-based approach using hierarchical and K-means clustering algorithms.The distance calculation is based on the estimated parameters of the model used; in this case, the GARCH (1,1) model is used.This paper proposes a modified Piccolo distance that uses the absolute value between two GARCH (1,1) models, which is a development of the Manhattan distance.The modified Piccolo distance improves robustness to outliers and simplifies calculations, resulting in more accurate and efficient time series cluster analysis.Applying hierarchical and K-means clustering with modified Piccolo distance will be compared with other model-based distance modifications for clustering applied to simulated data and case studies using stock data incorporated in the Indonesia Stock Exchange.A measure of cluster validity is calculated using the C index.From the simulated data and case studies, it is found that clustering with Piccolo distance modification and other distance modifications between two GARCH (1,1) models produce clusters with a small C index, both for simulated data and case studies.A small C index value in the clustering results indicates good clustering quality, where the clusters formed have high similarity and are well separated from others.Furthermore, the clusters formed will be considered in making a good portfolio, so it is expected to reduce the risk in the stock portfolio.
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".