Adaptive inference in heteroskedastic fractional time series models
Bibliographic record
Abstract
We consider estimation and inference in fractionally integrated time series models driven by shocks which can display conditional and unconditional heteroskedasticity of unknown form. Although the standard conditional sum-of-squares (CSS) estimator remains consistent and asymptotically normal in such cases, unconditional heteroskedasticity inflates its variance matrix by a scalar quantity, lambda>1, thereby inducing a loss in efficiency relative to the unconditionally homoskedastic case, lambda=1. We propose an adaptive version of the CSS estimator, based on non-parametric kernel-based estimation of the unconditional variance process. This eliminates the factor lambda from the variance matrix, thereby delivering the same asymptotic efficiency as that attained by the standard CSS estimator in the unconditionally homoskedastic case and, hence, asymptotic efficiency under Gaussianity. The asymptotic variance matrices of both the standard and adaptive CSS estimators depend on any conditional heteroskedasticity and/or weak parametric autocorrelation present in the shocks. Consequently, asymptotically pivotal inference can be achieved through the development of confidence regions or hypothesis tests using either heteroskedasticity robust standard errors and/or a wild bootstrap. Monte Carlo simulations and empirical applications are included to illustrate the practical usefulness of the methods proposed.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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; both teacher heads agree on what is shown here.
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".