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Testing CUSUM Breakpoint Detection Against Theoretical False-Alarm Rates

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Summary

The article evaluates a two-sided CUSUM indicator that accumulates standardized log returns and flags a breakpoint when either accumulator crosses a threshold. It tests the Siegmund average run length formula, commonly used to estimate the spacing of false alarms under stationary returns, against the indicator’s observed behavior across six instruments and three timeframes. With the tested default settings, empirical detections occur about five times as often as the formula predicts. The excess is concentrated in volatile periods, while quiet periods are somewhat more conservative than theory suggests.

The article also examines what detected breaks correspond to by comparing the 200 bars before and after each event with variance and mean tests. About half of detections align with variance shifts, while mean shifts are uncommon. Detection latency is usually low but can lengthen with more conservative thresholds, particularly for gradual changes. These findings characterize this implementation as a detector of volatility regime changes more than mean shifts. The results come from a finite test battery and specific indicator settings; the article concludes that false-alarm behavior should be calibrated empirically for each instrument rather than inferred from the theoretical formula alone.

Key ideas

  • The indicator flags changes when either of two CUSUM accumulators crosses a threshold applied to standardized log returns.
  • In the reported tests, detections occur about five times as often as the Siegmund formula predicts.
  • The excess false alarms are concentrated in volatile periods, while quiet periods are slightly more conservative than theory predicts.
  • About half of detected breaks coincide with variance shifts, whereas mean shifts are rare.
  • Higher thresholds can reduce detections but increase latency, especially for gradual transitions.

Tags

StatisticsVolatilityMachine learningBacktesting

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.