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I have a data on counts of images submitted with requests overtime. I would like to test the null hypothesis of no trend vs alternative hypothesis that there is a downward trend.

My data is a sequence of numbers [2,3,5,6,2,4,5...], where every number represents number of images submitted with request. Order is chronological.

There are two things I am concerned about.

First how can I check for no serial dependence? Data is discrete not continuous - I ma not to sure how to test for serial dependence in this case. Is simple ACF/PACF plot good test?

Second I have around 200 observations but the range of possible values is small, X is form 1 to 8, hence I have a lot of tied groups. Is this a problem for Mann-Kendall trend test?

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So for the Mann-Kendall test, there are three things you need to consider:

  1. Your data is collected consistently, and not seasonally (there can be season effects in the data but it must be collected regularly)
  2. Your data does not have covariates (such as scheduling problems, etc.)
  3. You only have one data point per time point

For reference, look here.

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