Rolling Correlation — Did the Relationship Between Two Channels Change?

Pro

One correlation over a whole record is an average over everything that happened, and it is the wrong answer whenever something happened. Pick two channels and get the coefficient window by window: the shipped example is a tunnel crack that tracked temperature at −0.9 until it was grouted and has not since — a record whose whole-record coefficient is 0.01, which reads as no relationship at all. Windows without enough overlapping readings are left blank rather than plotted.

Your data

This tool is showing its sample dataset.

Everything in the figure is real output computed in your browser. Loading a file of your own is part of Pro.

Synthetic 36-day hourly record from a tunnel lining: air temperature and the width of a monitored crack. For the first 18 days the crack breathes with the temperature — it opens as the lining cools, so the two are strongly inverse at about r = −0.9. The crack is then grouted and the relationship stops — over the whole record r is 0.01, which is the finding this tool recovers and a single coefficient destroys. The gauge also drops out for 26 hours on day 28, so several windows are left blank rather than plotted. Not measured data.

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Figure title

Options

Series

First channel (x)

Both channels are averaged onto one grid first, then correlated inside each window.

Second channel (y)

Align onto

A window is a number of grid steps, so the two channels are put on one regular grid before anything is windowed.

Coefficient

The same two coefficients as the correlation matrix, computed the same way — Spearman is Pearson on the ranks, with tied readings sharing their average rank.

Lag (grid steps)

Correlate the first channel at t+lag against the second at t — the cross-correlation tool’s convention, so a lag it reported can be typed straight in here. A positive lag means the second channel leads.

Window

Window length

Short windows find changes sooner and invent more of them; long windows are steadier and smear a real change across their own length. Automatic takes about a twelfth of the record.

Move the window by

Consecutive windows overlap, so their coefficients are not independent of each other — a smaller step draws a smoother line, not a more informative one.

Plot each window at

Middle is what a report figure wants: a change shows up under where it happened. The right-hand edge is what a monitoring dashboard wants, where only readings up to now may be used.

Minimum coverage of a window

A window with fewer than this share of its steps holding both readings is left blank rather than plotted. A coefficient from the surviving quarter of a window is not comparable with one from a full window.

Figure

Show the whole-record rShade the sampling rangeHow far the windows would wander from the whole-record r on sampling alone, at this window size — wide enough to hold all of them 95% of the time, not just one, because one window in twenty leaves a plain 95% band by definition. It assumes independent readings inside a window, which sensor readings are not, so it is a floor on the wobble rather than a confidence interval.Show pairs per windowGridlines

All of that was worked out in this browser tab. Your file was not uploaded, and no request goes out while you work — open the network panel and watch, if you like.

The figure above is this tool's sample dataset, and everything in it is real output — every option works and every number is computed here in your browser. Running Rolling correlation on a file of your own is part of Pro.