Change Point Detector Calculator

Calculator

Series data

Tip: You can paste values separated by commas, spaces, or new lines. For two-column data, select “Two-column CSV”.

Input format

Two-column CSV uses the last column as the value.

Detection method

SSE is strongest for mean shifts under noise.

Minimum segment length

Prevents tiny segments and unstable split points.

Detect multiple change points (SSE only)

Uses greedy binary segmentation with your stopping rule.

Max change points

Higher values can over-segment short series.

Stopping rule

Used only when multiple change points are enabled.

Improvement threshold (0–1)

Example: 0.10 means ≥10% SSE drop.

BIC delta (≥0)

Higher values demand stronger evidence to split.

Estimate p-value via resampling

Uses permutation to test against random order.

Resampling iterations

More iterations improve stability but run slower.

Reference alpha

Used as a guide when reading p-values.

If you want to test quickly, paste the example values from the table below.

Example data table

t	x
1	10.10
2	9.80
3	10.40
4	9.90
5	10.20
6	10.00
7	13.20
8	12.80
9	13.50
10	13.10
11	12.90
12	13.40

This series has a visible upward shift around t=7.

Formula used

Least-Squares Split (SSE)

For each candidate split k, compute segment means and total error:

SSE(k) = Σ_i≤k(xᵢ − μ₁)² + Σ_i>k(xᵢ − μ₂)²

The selected change point minimizes SSE(k). Improvement is:

Improvement = (SSE₀ − SSE*) / SSE₀

We also report ΔBIC to balance fit and complexity.

Pettitt and CUSUM

Pettitt uses ranks to detect a distributional shift without assuming normality. CUSUM tracks cumulative deviations from the global mean and finds the largest excursion.

Resampling (permutation) estimates how often a random ordering produces a score at least as extreme as the observed score.

p ≈ (count(score ≥ observed) + 1) / (iters + 1)

How to use this calculator

Paste your numeric series into the input box. Use one value per line for clarity.
Choose a method. Use SSE for mean shifts, Pettitt for rank-based shifts, and CUSUM for abrupt drift.
Set a minimum segment length so the algorithm avoids tiny segments.
Enable resampling if you want a reference p-value, then pick iterations.
Click “Detect Change Points” to show results above the form.
Download CSV or PDF to share results with others.

Series requirements and sampling stability

Reliable change detection starts with clean inputs. Use at least 30 observations when possible, and keep the minimum segment length above 5 to reduce false splits in production settings. Replace missing values consistently. If your data are seasonal, detrend first, because repeated cycles can mimic breaks. The calculator accepts values, two‑column files, or JSON arrays, and it ignores nonnumeric headers so you can paste directly from spreadsheets.

Method selection and assumptions

The least‑squares split minimizes total squared error and performs best when the main shift is a change in mean under roughly constant variance. It also supports multiple breakpoints with a controlled stopping rule. Pettitt’s rank test is distribution‑free and is useful when the scale is skewed, heavy‑tailed, or contains outliers. CUSUM highlights abrupt drifts by accumulating deviations from the overall mean, making it effective for process monitoring and sensor streams.

Tuning sensitivity with stopping rules

Multiple change points are found using binary segmentation, which repeatedly splits the segment with the strongest evidence. Select BIC improvement to penalize extra splits and avoid overfitting; increasing the BIC delta demands stronger support before a cut is accepted. If you need an operational rule, use an SSE improvement threshold such as 0.10, meaning each split must reduce error by at least 10 percent.

Interpreting segment statistics

After detection, compare segment means and variances rather than relying on the index alone. A practical effect size is the mean difference divided by the pooled standard deviation; values near 0.2 are small, 0.5 moderate, and 0.8 large. Also report percent change between adjacent means to communicate impact. When variance rises after the change, the “shift” may reflect instability, not a stable new level, and you should review domain drivers.

Reporting, exporting, and validation

Use resampling to estimate a reference p‑value by permutation; larger iteration counts improve stability and reduce Monte Carlo noise. Exported CSV files include the method, detected points, score, and per‑segment summaries, which supports peer review and reproducible analysis. The PDF report is designed for audits and sharing, so you can attach results to incident tickets, QA notes, or experiment logs. Save parameters alongside data to recreate outcomes later.

FAQs

1) What is a change point?

A change point is an index where the series behavior shifts, such as a new mean level, a drift, or a distribution change. It separates the data into more stable segments for analysis and decisions.

2) Which method should I use?

Use SSE for mean shifts with stable noise, Pettitt when you want a rank‑based, distribution‑free test, and CUSUM when you monitor abrupt drift in streaming or operational signals.

3) How do I set the minimum segment length?

Start with 5–10% of your series length, then increase if you see too many tiny segments. Larger minimums reduce false positives but can miss short regime changes.

4) What does ΔBIC tell me?

ΔBIC compares a single‑segment model against a split model while penalizing added complexity. Positive values favor a split; larger values suggest stronger evidence that the change is not just noise.

5) Why is the p-value missing sometimes?

The calculator shows a p‑value only when resampling is enabled. Permutation resampling estimates how often random orderings produce an equal or larger score, giving a practical reference for significance.

6) What do the CSV and PDF exports include?

Exports contain the selected method, detected change points, score, optional p‑value, and per‑segment summaries (start, end, n, mean, variance). This supports sharing, audits, and reproducible reporting.