The Effect of Spectral Line Components on Coefficients in Time Series Regression Models
Bibliographic record
Abstract
Inference on the fitted parameters from two time series regressions can be improved by considering their correlation structure. We investigate the performance of an estimator of covariance between two time series regressions in which the responses are correlated, which is based on the multitaper method (MTM) cross-spectral estimator for the response series. We compare the MTM-based covariance estimator to the "standard" one based on the Bartlett estimate of the cross-covariance function of the two response series. A simulation study is used to evaluate performance using realizations of bivariate autoregressive processes with different characterizations of their cross-covariance function, and the effect of embedding a common deterministic line component in the response and predictor is examined. \n \nWe find that the presence of a deterministic sinusoidal component has an effect on the estimated covariance between the two regressions, and greatly increases the bias of both estimators. When common line components are detected and removed using tools within the MTM framework, covariance estimates with lower estimated mean squared errors are produced. In all cases, the MTM-based covariance estimator is found to have greater efficiency than the Bartlett-based estimator. \n \nIn an application to hourly electricity demand and price data for the province of Ontario, Canada, a linear regression model is fit in overlapping time segments in which price is designated as the response variable, and a vector of regression coefficients is obtained. Using our MTM-based covariance estimator, a covariance matrix for the coefficient vector is estimated, and more informative confidence intervals for each coefficient are obtained.
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 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 | 0.001 | 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".