The AR(1) option that does keep a step inside a cycle

Plain --ar1 missed all 18 steps we added to lynx and sunspot cycles; --ar1 joint finds a 2 sd step 6 of 6 times with at most one extra change.

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changepoint-detectorevaluationtime-series

Our last note on the changepoint detector said --ar1 removes the false steps a cycle produces but also hides real ones: 0 of 18 steps added to the lynx and sunspot series were found. We had not tried the other autocorrelation setting, --ar1 joint, which fits the step and the persistence together instead of widening the noise scale.

We ran it on the same 18 inserted steps. A 2 standard deviation step was found in 6 of 6 cases, the same as the bootstrapped meanvar penalty. A 1 sd step was found in 3 of 6 (the bootstrap: 2 of 6). A 0.5 sd step was mostly missed (1 of 6). With no step inserted it reports no false change on lynx and one on sunspots.

So the advice changes: on a series with a visible cycle, plain --ar1 is a filter, and --ar1 joint can also confirm a large break. Each cell is 3 trials on two series, and a step added to real data is not a real step; the next test is a series with a documented break inside a cycle. Numbers, script and test are in the README.

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