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arxiv: 2405.12324 · v2 · submitted 2024-05-20 · 🌌 astro-ph.IM

Robust 1-norm periodograms for analysis of noisy non-Gaussian time series with irregular cadences: Application to VLBI astrometry of quasars

Valeri V. Makarov , S\'ebastien Lambert , Phil Cigan , Christopher DiLullo , David Gordon This is my paper

Pith reviewed 2026-05-24 01:28 UTC · model grok-4.3

classification 🌌 astro-ph.IM
keywords periodogramrobust statisticsVLBI astrometryquasarstime seriesirregular samplingnon-Gaussian noiseICRF3
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The pith

The robust 1-norm periodogram resists outliers better than Lomb-Scargle and flags 49 quasars with quasi-periodic position changes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a periodogram that minimizes the sum of absolute residuals instead of squared residuals to fit test sinusoids to irregularly sampled data. This change makes the statistic more stable when measurements contain outliers or follow heavy-tailed distributions rather than Gaussian errors. The authors test the approach on one quasar in detail and then apply it uniformly to 259 ICRF3 sources that each have more than 200 VLBI epochs, recovering 49 objects above a 3σ threshold. The result matters because many astronomical time series suffer from occasional bad points caused by instrumental or atmospheric effects that can distort conventional least-squares periodograms.

Core claim

The robust 1-norm periodogram technique can be implemented in weighted or unweighted options and is less easily corrupted by a subset of statistical outliers or an intrinsically non-Gaussian population than the standard Lomb-Scargle periodogram; its uniform application to 259 ICRF3 quasars yields 49 objects with quasi-periodic position changes above the 3σ level.

What carries the argument

The 1-norm periodogram, which finds the best-fitting sinusoid at each test frequency by minimizing the sum of absolute deviations rather than the sum of squared deviations.

If this is right

  • The weighted form of the method allows measurement uncertainties to be incorporated directly into the fit.
  • The 49 flagged quasars become candidates for follow-up studies of possible periodic motion.
  • The technique extends to any other astronomical time series that combine irregular cadences with non-Gaussian errors.
  • Direct comparison on the same data set shows where the classical Lomb-Scargle method produces misleading peaks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Re-processing earlier VLBI campaigns with this statistic could change which sources are classified as variable.
  • Confirmed periodic position changes would point toward binary supermassive black holes or other dynamical mechanisms in quasars.
  • Applying the same 1-norm approach to optical or Gaia time series of active galactic nuclei would test whether the detected fraction is instrument-specific.

Load-bearing premise

The distribution of the 1-norm periodogram statistic under the null hypothesis of no periodicity is sufficiently well-behaved in the presence of the actual VLBI noise and sampling to allow a simple 3σ threshold to be interpreted as a reliable false-alarm probability without additional calibration or multiple-testing correction.

What would settle it

A Monte Carlo simulation that draws many noise-only realizations using the real VLBI observation times and the observed residual distribution, then measures the fraction of trials in which the maximum 1-norm periodogram power exceeds the 3σ threshold.

Figures

Figures reproduced from arXiv: 2405.12324 by Christopher DiLullo, David Gordon, Phil Cigan, S\'ebastien Lambert, Valeri V. Makarov.

Figure 1
Figure 1. Figure 1: Astrometric offsets from the mean position of the ICRF3 source IERS B0642+449 measured by VLBI over 30 years. Left plot: right ascension tangential component (x) in mas. Right plot: declination tangential components (y) in mas. Each data point is shown with its formal ±1σ error bar. 0 500 1000 1500 2000 2500 3000 3500 0.00 0.02 0.04 0.06 0.08 0.10 0.12 period days x amplitude mas RA OFFSET 2-NORM 0 500 100… view at source ↗
Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Distribution of standardized astrometric deviations for the data set shown in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Periodograms calculated for the astrometric time series shown in [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

Astronomical time series often have non-uniform sampling in time, or irregular cadences, with long gaps separating clusters of observations. Some of these data sets are also explicitly non-Gaussian with respect to the expected model fit, or the simple mean. The standard Lomb-Scargle periodogram is based on the least squares solution for a set of test periods and, therefore, is easily corrupted by a subset of statistical outliers or an intrinsically non-Gaussian population. It can produce completely misleading results for heavy-tailed distribution of residuals. We propose a robust 1-norm periodogram technique, which is based on the principles of robust statistical estimation. This technique can be implemented in weighted or unweighted options. The method is described in detail and compared with the classical least squares periodogram on a set of astrometric VLBI measurements of the ICRF quasar IERS B0642+449. It is uniformly applied to a collection of 259 ICRF3 quasars each with more than 200 epoch VLBI measurements, resulting in a list of 49 objects with quasi-periodic position changes above the $3\sigma$ level, which warrant further investigation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a robust 1-norm periodogram based on L1 minimization for detecting periodic signals in irregularly sampled, non-Gaussian astronomical time series. It compares the method to the standard Lomb-Scargle periodogram on VLBI astrometric measurements of quasar IERS B0642+449 and applies it uniformly to 259 ICRF3 quasars (each with >200 epochs), reporting 49 objects with quasi-periodic position changes above the 3σ level.

Significance. A well-validated robust periodogram would be a useful addition to the toolkit for VLBI and other outlier-prone time-series analyses. The uniform application to a large, homogeneous sample of 259 objects is a positive feature. However, the headline claim of 49 detections rests on an uncalibrated 3σ threshold whose false-alarm properties under realistic VLBI cadence and heavy-tailed residuals are not demonstrated, limiting the immediate scientific impact.

major comments (2)
  1. [Abstract] Abstract: the claim that the method is 'described in detail' is not supported by the provided text, which contains no equations for the 1-norm periodogram, no derivation of its null distribution, and no quantitative performance metrics or error-bar methodology. The 3σ detections reported for 259 objects therefore depend on unshown statistical machinery.
  2. [Application to 259 ICRF3 quasars] Application section (259 quasars): the identification of 49 objects above a fixed 3σ level treats the 1-norm periodogram statistic as having a known, well-behaved null distribution under the actual VLBI sampling, non-Gaussian residuals, and multi-frequency search. No analytic derivation or Monte-Carlo calibration of the false-alarm probability is supplied, nor is any correction for 259 independent searches or the look-elsewhere effect across trial frequencies.
minor comments (1)
  1. [Abstract] The abstract states that weighted and unweighted implementations exist but does not specify how weights are chosen or validated for VLBI position residuals.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments correctly identify areas where the manuscript would benefit from additional mathematical detail and statistical validation. We address each point below and will incorporate the necessary revisions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the method is 'described in detail' is not supported by the provided text, which contains no equations for the 1-norm periodogram, no derivation of its null distribution, and no quantitative performance metrics or error-bar methodology. The 3σ detections reported for 259 objects therefore depend on unshown statistical machinery.

    Authors: We agree that the current manuscript does not include explicit equations for the 1-norm periodogram, a derivation of its null distribution, or quantitative performance metrics. The abstract's statement that the method is 'described in detail' is therefore not fully supported by the text. We will revise the manuscript to add the mathematical formulation based on L1 minimization (both weighted and unweighted), any analytic results on the statistic's distribution, simulation-based performance metrics, and the error-bar methodology used for the 3σ threshold. revision: yes

  2. Referee: [Application to 259 ICRF3 quasars] Application section (259 quasars): the identification of 49 objects above a fixed 3σ level treats the 1-norm periodogram statistic as having a known, well-behaved null distribution under the actual VLBI sampling, non-Gaussian residuals, and multi-frequency search. No analytic derivation or Monte-Carlo calibration of the false-alarm probability is supplied, nor is any correction for 259 independent searches or the look-elsewhere effect across trial frequencies.

    Authors: The referee is correct that no Monte Carlo calibration of the false-alarm probability is provided for the specific VLBI sampling, non-Gaussian residuals, or multi-frequency search, and that no correction for multiple testing across 259 objects or the look-elsewhere effect is applied. We will add a dedicated section with Monte Carlo simulations that replicate the observed cadences and residual distributions to calibrate the 3σ threshold and false-alarm rates. We will also incorporate a discussion and, where feasible, a correction for the multiple searches performed. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper introduces the 1-norm periodogram as a direct application of standard L1-norm robust estimation principles to replace least-squares in the Lomb-Scargle framework. The 3σ threshold is presented as a conventional significance cut applied uniformly after the method is defined; no parameter is fitted to a data subset and then reused as a detection criterion, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled in. The central claim (49 detections out of 259) therefore rests on an independent statistical procedure rather than reducing to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are identifiable. The 3σ threshold is a chosen cutoff whose statistical justification is not provided.

pith-pipeline@v0.9.0 · 5765 in / 1286 out tokens · 32806 ms · 2026-05-24T01:28:52.946783+00:00 · methodology

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