Consistent Inference for Predictive Regressions in Persistent VAR Economies
Bibliographic record
Abstract
This paper studies the properties of standard predictive regressions in model economies, characterized through persistent vector autoregressive dynamics for the state variables and the associated series of interest. In particular, we consider a setting where all, or a subset, of the variables may be fractionally integrated, and note that this induces a spurious regression problem. We then propose a new inference and testing procedure - the local spectrum (LCM) approach - for the joint significance of the regressors, which is robust against the variables having different integration orders. The LCM procedure is based on (semi-)parametric fractional-filtering and band spectrum regression using a suitably selected set of frequency ordinates. We establish the asymptotic properties and explain how they differ from and extend existing procedures. Using these new inference and testing techniques, we explore the implications of assuming VAR dynamics in predictive regressions for the realized return variation. Standard least squares predictive regressions indicate that popular financial and macroeconomic variables carry valuable information about return volatility. In contrast, we find no significant evidence using our robust LCM procedure, indicating that prior conclusions may be premature. In fact, if anything, our results suggest the reverse causality, i.e., rising volatility predates adverse innovations to key macroeconomic variables. Simulations are employed to illustrate the relevance of the theoretical arguments for finite-sample inference.
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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 | 0.025 | 0.168 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| 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".