Causal Impact Analysis

📊 Causal Impact Analysis

Causal Impact is a Bayesian structural time-series method used to evaluate the effect of an intervention when randomization is not feasible.

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🧪 Simulate Pre/Post Intervention Time Series

set.seed(101)
n <- 100
pre_period <- 1:70
post_period <- 71:100

x <- arima.sim(model = list(order = c(1, 0, 0), ar = 0.8), n = n)
y <- x + rnorm(n, 0, 0.5)

# Add treatment effect in post period
y[post_period] <- y[post_period] + 2

data_ts <- cbind(y, x)

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📈 Run Causal Impact

impact <- CausalImpact(data_ts, pre.period = c(1, 70), post.period = c(71, 100))
summary(impact)

## Posterior inference {CausalImpact}
## 
##                          Average             Cumulative       
## Actual                   2                   60               
## Prediction (s.d.)        -0.092 (0.16)       -2.771 (4.87)    
## 95% CI                   [-0.41, 0.2]        [-12.43, 6.1]    
##                                                               
## Absolute effect (s.d.)   2.1 (0.16)          62.9 (4.87)      
## 95% CI                   [1.8, 2.4]          [53.9, 72.5]     
##                                                               
## Relative effect (s.d.)   -625% (32539%)      -625% (32539%)   
## 95% CI                   [-16020%, 13361%]   [-16020%, 13361%]
## 
## Posterior tail-area probability p:   0.00101
## Posterior prob. of a causal effect:  99.8993%
## 
## For more details, type: summary(impact, "report")

plot(impact)

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✅ Interpretation

• CausalImpact estimates the counterfactual (what would’ve happened without intervention).
• The difference between observed and predicted is the estimated effect.

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📚 References

• Brodersen et al. (2015). Inferring causal impact using Bayesian structural time-series models. Annals of Applied Statistics.