Ask a default changepoint detector about the Canadian lynx trapping record, 1821 to 1934, and it finds 23 level changes. There are none: the numbers swing on a ten-year cycle. The yearly sunspot count does the same, 46 steps in 289 years.
We checked four setups on both series. A longer minimum segment only thins the false steps (3 and 7). Allowing for lag-1 autocorrelation (--ar1) or using the bootstrapped mean-and-variance penalty leaves none. The catch: zero is also what a detector that sees nothing would say, and we have not measured power on a real step hidden inside a cycle. The numbers and code are in the changepoint-detector README.