# Can a permutation test be used on time series to quantify an effect of the marketing campaign?

I am trying to accept or reject a hypothesis that a marketing campaign had positive effect on sales of some product. I am working with time series of monthly sales. The series is not stationary (it has positive linear trend).

I would like to use permutation test as I find it simpler to explain in comparison with t-test, however I wonder if my approach below is correct:

1. Remove the trend from the series and make it stationary.

2. State the significance level $$\alpha = 0.05$$

3. $$\mu_b=$$ mean of sales before campaign

$$\mu_a=$$ mean of sales after campaign

4. State the null hypothesis $$H_0: \mu_a - \mu_b = 0$$

5. State the alternative hypothesis $$H_a: \mu_a - \mu_b > 0$$

6. Compute empirical difference of means: $$\mu_e = \mu_a - \mu_b$$

7. Generate large number of permutation replicates

8. Compute the probability (p-value) of obtaining $$\mu >= \mu_e$$ from permutation replicates

9. Compare the p-value to $$\alpha$$

Is this method valid on time series, or do I need to use t-test?

• Commented Jun 21, 2020 at 1:32