Interaction between deterministic trend and autoregressive process
Bibliographic record
Abstract
When both an autoregressive (AR) process (stochastic trend) and a deterministic trend (systematic changes over mean) exist within a time series, there may be some interactions between them. This study investigates whether these two components interact with each other. Only time series consisting of a linear trend and a lag 1 autoregressive AR(1) process are explored, which are commonly used in hydrology. Results indicate that (1) the presence of a deterministic trend will overestimate positive serial correlation and underestimate negative serial correlation, while (2) the existence of an AR(1) process does not affect the estimate of the magnitude of the deterministic trend. However, a positive AR(1) will inflate the variance of the trend and a negative AR(1) will shrink the variance of the trend. For a time series with a deterministic trend the trend has to be removed in order to correctly model the stochastic properties of the time series. In the literature, both differencing and detrending have been proposed to fulfill such a task. Their applicability is based on the assumption that they cannot distort the residual series. However, no evidence has been provided to certify whether this assumption is appropriate. This study examines this issue and it indicates that differencing can remove a deterministic trend from a time series but it can seriously damage the existing AR(1) process. In contrast to differencing, detrending can remove a deterministic trend without distorting the existing AR process.
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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 | 0.004 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 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".