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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?

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