Interrupted Time Series in Crime Analysis
Also known as: Crime Intervention Analysis, ITS Crime Evaluation, Quasi-Experimental Time Series for Crime, Pre-Post Crime Trend Analysis
Interrupted time series (ITS) analysis evaluates whether a law, policy, or intervention changed the course of a crime series. By modeling the level and slope of crime before and after a dated 'interruption' — a gun-control law, a policing crackdown, a sentencing reform — it tests whether the series jumped or bent at that moment relative to its prior trend. Box and Tiao formalized intervention analysis in 1975, and McDowall, McCleary, and colleagues brought the method to criminology in their widely used 1980 monograph.
Key highlights
- Estimates a policy's effect from aggregate administrative data without needing a randomized experiment.
- Separates an immediate level change from a longer-run slope change, matching how policies actually act on crime.
- Builds an explicit counterfactual from the pre-intervention trend, making the comparison transparent and visual.
- Properly models autocorrelation through ARIMA, avoiding the false significance that plagues naive pre-post tests.
- Extends to multiple interventions, comparison series, and gradual or temporary effects within one framework.
Intuition
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How it works
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When to use it
Use ITS when a policy, law, or program took effect at a known date and you have a long crime series measured consistently before and after it, and you want to know whether the series changed beyond its prior trajectory. It is well suited to evaluating gun laws, policing operations, sentencing or decriminalization reforms, and bans or crackdowns at the population level. It is weaker when the pre-period is short or unstable, when other events occur near the same time (history threats) that could explain a change, when the intervention date is fuzzy or phased in gradually, or when the series is too short or noisy to model the autocorrelation. Adding a comparison series (controlled ITS) or pairing with a synthetic-control or difference-in-differences design strengthens causal claims.
Strengths & limitations
- Estimates a policy's effect from aggregate administrative data without needing a randomized experiment.
- Separates an immediate level change from a longer-run slope change, matching how policies actually act on crime.
- Builds an explicit counterfactual from the pre-intervention trend, making the comparison transparent and visual.
- Properly models autocorrelation through ARIMA, avoiding the false significance that plagues naive pre-post tests.
- Extends to multiple interventions, comparison series, and gradual or temporary effects within one framework.
- Cannot rule out coincident events (history threats) that change crime at the same time as the intervention.
- Requires a long, stable pre-intervention series; short or erratic baselines give an unreliable counterfactual.
- Effects are sensitive to how the intervention is specified — abrupt versus gradual, permanent versus temporary.
- Identifying the correct ARIMA noise model is technical and somewhat subjective, and misspecification biases inference.
- A single interrupted series has no untreated comparison, so secular national trends can be mistaken for local effects.
Common pitfalls
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Applications
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Frequently asked
What is the difference between a level change and a slope change?
A level change is an immediate, sustained jump or drop in crime right at the intervention (the series shifts up or down by a fixed amount). A slope change is a change in the trend — the rate at which crime rises or falls — that accumulates over time after the intervention. A policy can produce one, both, or neither, and distinguishing them matters: a one-time deterrent shock looks like a level change, while a gradual program rollout often appears as a slope change.
Why is ARIMA modeling necessary instead of ordinary regression?
Crime counts are serially correlated — adjacent periods move together and the series may trend or have seasonality — which violates the independence assumption of ordinary regression and makes its standard errors far too small, so almost any intervention looks significant. ARIMA models the autocorrelation, trend, and seasonality in the noise explicitly, so the intervention coefficients are estimated against a realistic error structure and the significance tests are valid.
How can ITS results be made more credible?
The strongest threat to ITS is a coincident event that changed crime at the same time as the intervention. Adding an untreated comparison series (a controlled or comparative ITS), or a synthetic-control or difference-in-differences design, lets the comparison absorb shared national trends so the effect is identified from the difference between treated and control series. Pre-specifying the intervention date and functional form, and testing placebo dates, further guards against fishing.
Sources
- 1.McDowall, D., McCleary, R., Meidinger, E. E., & Hay, R. A. (1980). Interrupted Time Series Analysis. Sage Publications.ISBN 9780803914933
- 2.Box, G. E. P., & Tiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems. Journal of the American Statistical Association, 70(349), 70–79.
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Cite this page
ScholarGate. (2026, June 22). Interrupted Time Series in Crime Analysis. ScholarGate. https://scholargate.app/criminology/interrupted-time-series-crime