The annual flow of the Nile at Aswan from 1871 to 1970 is one of the classic series in statistics: a hundred numbers that every time-series textbook seems to use. It is famous for one feature, a drop in the level around the turn of the century. I wanted to find that break properly, put an uncertainty on it, and then ask a practical question: how much does a forecaster actually gain from knowing about it?

Three methods, one answer

The data is the series published by Durbin and Koopman (2001), available as datasets::Nile in R: 100 annual values in units of 10⁸ m³.

Method Break after Mean before → after

Binary segmentation, one break ( ruptures ) 1900 1,078 → 851

PELT, penalty picks the number of breaks (it found one) 1900 1,078 → 851

Two-mean scan with a 2,000-draw bootstrap 1898 (95% CI 1896–1902) 1,098 → 850

Three methods built on different ideas land within two years of each other, and the bootstrap interval covers all of them.…