pqc.detect.step_changes

Detect achromatic and DM-like step changes in timing residuals.

This module fits single changepoint step models using weighted two-segment means and a likelihood-ratio-style statistic expressed as \(\Delta\chi^2\). It supports:

• achromatic steps (constant amplitude after t0), and

• DM-like chromatic steps scaling as \(1/f^2\).

Notes

Statistic

For a split at index \(i\), let weighted means before/after be \(\mu_1, \mu_2\) with variances \(1/W_1, 1/W_2\). The step contrast is \(\delta=\mu_2-\mu_1\) and score is \(\Delta\chi^2 = \delta^2/(1/W_1+1/W_2)\).

Why used here

Step discontinuities are common signatures of timing-model offsets or abrupt propagation/instrument changes.

Assumptions

• One dominant changepoint in the tested series.

• Gaussian errors with known/estimated sigma.

• Sorted times and enough points on each side of split.

References

[1]

Lorimer, D. R., & Kramer, M. (2005), Handbook of Pulsar Astronomy.

[2]

Edwards, R. T., Hobbs, G. B., & Manchester, R. N. (2006), MNRAS 372.

[3]

Killick, R., Fearnhead, P., & Eckley, I. A. (2012), JASA 107(500), 1590-1598.

Functions

detect_dm_step(df, *[, mjd_col, resid_col, ...])	Detect chromatic step offsets consistent with DM-like scaling.
detect_step(df, *[, mjd_col, resid_col, ...])	Detect a single achromatic step-like offset and annotate rows.