Bootstrap Score Tests for Fractional Integration in Heteroskedastic ARFIMA Models, with an Application to Price Dynamics in Commodity Spot and Futures Markets
Bibliographic record
Abstract
We propose bootstrap implementations of the asymptotic Wald, likelihood ratio and Lagrange multiplier tests for the order of integration of a fractionally integrated time series. Our main purpose in doing so is to develop tests which are robust to both conditional and unconditional heteroskedasticity of a quite general and unknown form in the shocks. We show that neither the asymptotic tests nor the analogues of these which obtain from using a standard i.i.d. bootstrap admit pivotal asymptotic null distributions in the presence of heteroskedasticity, but that the corresponding tests based on the wild bootstrap principle do. An heteroskedasticity-robust Wald test, based around a sandwich estimator of the variance, is also shown to deliver asymptotically pivotal inference under the null, and we show that it can be successfully bootstrapped using either i.i.d. resampling or the wild bootstrap. We quantify the dependence of the asymptotic size and local power of the asymptotic tests on the degree of heteroskedasticity present. An extensive Monte Carlo simulation study demonstrates that signi.cant improvements in .nite sample behaviour can be obtained by the bootstrap vis-à-vis the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments. The results also suggest that a bootstrap algorithm based on model estimates obtained under the null hypothesis is preferable to one which uses unrestricted model estimates.
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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 | 0.011 | 0.054 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".