Absolute and relative measures for evaluating the forecasting performance of time series models for daily streamflows
Bibliographic record
Abstract
Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) are widely used measures for evaluating the forecasting performance of time series models. Although these absolute measures can be used to compare the performance of competing models, one needs a reference to judge the goodness of the forecasts. In this paper, two relative measures, coefficient of efficiency (E) and index of agreement (d), and their modified versions (EM, EMP, dM and dMP) with desired values of closer to one are presented. These measures are illustrated by comparing the modeling ability and validation forecasting performance of a Nonlinear Additive Autoregressive with Exogenous variables (NAARX), Nested Threshold Autoregressive (NeTAR), and Multiple Nonlinear Inputs Transfer Function (MNITF) models developed for the Jökulsá eystri daily streamflow data. The results suggest that NeTAR describes the system best, and gives better 1- and 2-day ahead validation forecasts. MNITF gives better forecasts for 3-day ahead, and NeTAR and NAARX give comparable performance for 4- and 5-day ahead forecasting. The values of E and d were larger than those of the modified versions, giving a false sense of model performance, and unlike the modified versions, they decreased as forecast lead times increased. Differences among the values of these six relative measures can reveal the sensitiveness of competing models to outliers, and their potential for long-term forecasting. Accordingly, NeTAR was the least sensitive to outliers and NAARX was the most sensitive, with MNITF in between; and NAARX showed the most potential for long-term streamflow forecasting.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.025 | 0.077 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.007 | 0.007 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".