BIVARIATE ARCH MODELS: FINITE-SAMPLE PROPERTIES OF QML ESTIMATORS AND AN APPLICATION TO AN LM-TYPE TEST
Bibliographic record
Abstract
This paper provides two main new results: the first shows theoretically that large biases and variances can arise when the quasi-maximum likelihood (QML) estimation method is employed in a simple bivariate structure under the assumption of conditional heteroskedasticity; and the second demonstrates how these analytical theoretical results can be used to improve the finite-sample performance of a test for multivariate autoregressive conditional heteroskedastic (ARCH) effects, suggesting an alternative to a traditional Bartlett-type correction. We analyze two models: one proposed in Wong and Li (1997, Biometrika 84, 111–123) and another proposed by Engle and Kroner (1995, Econometric Theory 11, 122–150) and Liu and Polasek (1999, Modelling and Decisions in Economics; 2000, working paper, University of Basel). We prove theoretically that a relatively large difference between the intercepts in the two conditional variance equations, which leads to the two series having correspondingly different volatilities in the restricted case, may produce very large variances in some QML estimators in the first model and very severe biases in some QML estimators in the second. Later we use our bias expressions to propose an LM-type test of multivariate ARCH effects and show through simulations that small-sample improvements are possible, especially in relation to the size, when we bias correct the estimators and use the expected hessian version of the test.Both authors thank H. Wong for providing us with the Gauss program to simulate the Wong and Li (1997) model. We also thank three anonymous referees for extremely helpful comments, and we are grateful for the comments received at seminars given at Cardiff University, Michigan State University, Queen Mary London, University of Exeter, and University of Montreal. We acknowledge gratefully also the financial support from an ESRC grant (award number T026 27 1238). A previous version of this paper appeared as IVIE Working paper 2004-09.
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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 | 0.031 | 0.189 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 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".