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[0,1,0,2,4,1,0,1,5,1,4,2,1,3,1,1,1,1,0,1,1,0,2,0,2,0,0,1,0,1,2,2,1,2,4,1,4,1,0,0,4,1,0,1,0,1,1,2,1,1,0,0] What is the best way to convince myself that these data are correlated? that no univariate discrete distribution would approximate them well? that a time series model is necessary to better estimate the future distribution of counts? |
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You could just plot the ACF and check if the first coefficient is inside the critical values. The critical values are ok for non-Gaussian time series (at least asymptotically). Alternatively, fit a simple count time series model such as the INAR(1) and see if the coefficient is significantly different from zero. |
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Immediately, a runs test comes to mind. That is, if this is an ordered set and you are interested in knowing if the ordered observations are independent. It tests whether the sequence is likely due to randomness rather than systematic variation. Without more detail, that's the best I can come up with. |
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There's a clear time trend (decreasing average count). Hence (unless you condition on that trend) they're dependent (values close together in time will be more alike than values further apart in time). |
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