Diagnostic for Volatility and Local Influence Analysis for the Vasicek Model
Bibliographic record
Abstract
The Ornstein–Uhlenbeck process is widely used in modeling biological systems and, in financial engineering, is commonly employed to describe the dynamics of interest rates, currency exchange rates, and asset price volatilities. As in any stochastic model, influential observations, such as outliers, can significantly influence the accuracy of statistical analysis and the conclusions we draw from it. Identifying atypical data is, therefore, an essential step in any statistical analysis. In this work, we explore a set of methods called local influence, which helps us understand how small changes in the data or model can affect an analysis. We focus on deriving local influence methods for models that predict interest or currency exchange rates, specifically the stochastic model called the Vasicek model. We develop and implement local influence diagnostic techniques based on likelihood displacement, assessing the impact of the perturbation of the variance and the response. We also introduce a novel and simple way to test whether the model’s variability stays constant over time based on the Gradient test. The purpose of these methods is to identify potential risks of reaching incorrect conclusions from the model, such as the inaccurate prediction of future interest rates. Finally, we illustrate the methodology using the monthly exchange rate between the US dollar and the Swiss franc over a period exceeding 20 years and assess the performance through a simulation study.
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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 | 0.005 | 0.032 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| 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".