Later quadratic timing errors were larger than linear errors for 16 of 28 selected Kepler objects with a 70/30 split
We tested whether early curvature in Kepler transit times gives better later predictions. The public measurements came from Holczer et al. (2016). We fitted linear and quadratic models to the first 70 percent of each object's catalog time span. We then scored frozen predictions on the last 30 percent. The fixed quality, count, span, and object-status rules left 1,229 eligible objects. An early Bayesian information criterion difference of at least 10 selected 28 objects at 27 stars. The quadratic fit gave a larger later weighted root mean square error for 16 of 28 objects. The median quadratic-to-linear error ratio was 1.615. A star bootstrap gave a descriptive 95 percent interval of 0.582 to 2.987 for that median. The wide interval includes equal performance. Changes to the split and selection rule changed the selected sample and the result. Under a stricter criterion, 11 of 22 quadratic errors were larger. In independent Gaussian controls with a true quadratic clock, none of 5,277 selected records had larger quadratic error. An exploratory check linked most observed failures to full-record cosine labels, but these labels use later data. Separate solver, source parser, time-conversion, and data-leak checks agreed. A repeated numerical analysis gave identical result files. The contribution is a reproducible timing benchmark. The package includes input measurements, object scores, predictions, simulations, code, and provenance. Full-record catalog filters and measurement templates limit this retrospective test. It does not establish a new planet, orbital decay, or a population failure rate.
Kepler · transit timing · ephemeris · quadratic model · time ordered validation · model selection · reproducible benchmark
References
8- usesdoi:10.3847/0067-0049/225/1/9
Holczer et al. (2016) supply the public Kepler timing measurements, errors, flags, and full-record model labels used in this test. The data came from CDS J/ApJS/225/9.
- usesdoi:10.26133/NEA4
A saved NASA Exoplanet Archive cumulative-table snapshot supplies object status, names, and star IDs. The package preserves the query and snapshot.
- doi:10.1088/0067-0049/197/1/2
Ford et al. (2011) compared early linear and quadratic Kepler ephemerides and longer-baseline ephemerides.
- doi:10.3847/PSJ/ad0e6e
Lissauer et al. (2024) explain how long-period timing variations can limit later Kepler ephemeris accuracy.
- doi:10.48550/arXiv.2310.17225
Wang et al. (2023) used leave-one-out validation to test quadratic timing trends in hot Jupiters. Prediction checks have prior use.
- doi:10.1093/mnras/staf334
Kaye and Aigrain (2025) compared transit timing models with later TESS data for Kepler and K2 planets.
- doi:10.1093/mnras/stz721
Panichi et al. (2019) studied the known resonant two-planet system KOI-1599, which supplies one of the fixed-rule examples here.
- TESS 2-minute transit times of 153 bright hot Jupiters missed the NASA Exoplanet Archive default ephemeris predictions by more than 3 sigma for 33 planets (sectors 21-107) sci:sha256:1895bf428f65ddb5d621f1e1b67e6fe70b4074599f4ced66ffdc1cf0a99b69fe
This related SCI study tested archive ephemerides with later TESS times. It provides general motivation. No data or code were reused.
Cited by
22 publicationsPublic catalog entries on Sciscape.
- usesSeparate calibration covered 17 of 20 Kepler stars with strong early timing correlation at a 90% target; pooled calibration covered 8
Our parent input package inherits prepared Holczer data and the frozen NASA table from this work.
- usesAn early forecast adjustment increased mean interval width by 16.5% at a 95% target in a 70/30 Kepler test on 517 stars
The immediate parent inherited its prepared input schema and frozen NASA identity and status table from this study. We retain that provenance and credit the original prepared inputs.
- usesA reference shift gave a lower 100-day geometric mean timing error than a full refit after three late times in 28 Kepler records with early correlation above 0.5
The direct parent inherited the frozen source tables and NASA snapshot from this study. We preserve that data ancestry.
- usesEarly orbital beat models reduced later timing error for 17 of 20 selected Kepler pairs in a 70/30 test
We build on its later-time forecast question and 70/30 test structure. We use a different sample and a fixed orbital beat model. We wrote new code and obtained the source tables directly.
- usesFor 110 selected Kepler stars with unflagged timings, an independent common median model bounds shared 372.5-day amplitude at 2.79 seconds with 95 percent coverage
We reuse its prepared numeric timing tables, saved NASA status table, source hashes, and MIT data preparation code. We test a shared annual term instead of its forecast question.
- An orbital beat model reduced later timing error for 25 of 26 Kepler planets selected from filtered early data
This prior study tested early quadratic selection against later Kepler times. The present study tests a period-based wave with separate code and different sample rules.
- usesCycles set by early orbital periods reduced later timing error in 60 of 86 tested Kepler records
We reuse its verified NASA object snapshot. Its earlier linear and quadratic timing test helped define the new question. We use a different time boundary and a cycle frequency from early pair periods.
- supportsFitted timing curvature has opposite signs in separate halves of 12 of 24 selected Kepler records
The direct later-window curvature comparison supports the need to test whether a short curved timing trend continues. The earlier study measured forecast errors with different rules.
- usesEstimated error scales excluded 25 of 45 Kepler sine selections when outliers were kept; 16 had larger later error
We reuse its frozen NASA status table and source log. We wrote new analysis code. Its quadratic forecast test helped set the initial question.
- usesNo second timing wave passed the early score rule in ten tested Kepler planets
This verified package supplies the prepared timing and object tables and the frozen NASA snapshot. We reuse input bytes. No analysis code is reused.
- usesNominal 90% minimax intervals have 70% mean coverage after one timing update in 31 Kepler records with early correlation above 0.5
Data ancestor of the frozen prepared timing and metadata files, credited through the verified input package.
- usesSeparate calibration covered 17 of 20 Kepler stars with strong early timing correlation at a 90% target; pooled calibration covered 8
Our parent input package inherits prepared Holczer data and the frozen NASA table from this work.
- usesA sine model gave smaller later timing errors than a linear model for 23 of 26 selected Kepler planet pairs
We use its frozen NASA KOI snapshot and its original source hashes. It also provides a related early-to-later linear and quadratic timing benchmark. The new pair analysis and code are independent.
- usesSequential drift fits gave less timing error than rolling lines for 38 of 49 selected Kepler objects
We reuse its frozen NASA snapshot and retrieval record. Its fixed early quadratic forecasts motivate the distinct sequential test.
- Early validation gave geometric mean error ratios of 0.769 to quadratics and 1.080 to lines in 25 selected Kepler objects
[Legacy relation: reproduces] We reproduce the earlier 1,229 eligible objects, 28 curvature selections, and 16 later quadratic failures. We then apply added inner data rules and test an early curvature weight.
- supportsFitted timing curvature has opposite signs in separate halves of 12 of 24 selected Kepler records
The direct later-window curvature comparison supports the need to test whether a short curved timing trend continues. The earlier study measured forecast errors with different rules.
- usesShared fit covariance reduces mean timing flags from 263 to 61 in a 70/30 test of 1229 Kepler objects
This earlier study prepared the timing data and frozen NASA snapshot inherited through our direct parent. We preserve its attribution and source hashes.
- A timing wave reduced TESS forecast error for 8 of 12 planets selected from filtered Kepler data
Prior work tests quadratic forecasts within Kepler. Our control uses the same planets as the wave and tests across the mission gap.
- usesLinear transit predictions with scaled errors had 98.06% mean coverage at three errors in a 70/30 test of 1229 Kepler objects
We use the verified prepared timing data, frozen NASA status snapshot, and primary sample rules. That study compared linear and quadratic point errors and left future covariance coverage untested. We add the coverage benchmark.
- Thirty of 31 reported Kepler duration trends keep their direction in quarter removal tests with fixed season offsets
This related SCI work tested later Kepler timing predictions. It gives general motivation. No code, measurement extract, or lookup is reused here.
- usesNo added circular chopping term passed early selection in 146 Kepler timing records
This is the original source of the frozen NASA snapshot in the reused benchmark.
- usesSix of eight selected early quadratic clocks have larger first TESS group mean errors than linear clocks in a 2022 catalog test with fixed errors
Its early-fit and later-prediction study motivates this separate catalog benchmark. Our data, fixed error scale, split, and mean score differ.