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IrishStat
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There is a very clear pattern in the data as shown here enter image description here . Your 20 values are adequately descRibed by a hybrid model using an AR(1) and a step/level shift along with 3 pulses . enter image description here and here enter image description here and here enter image description here

The tools (approaches) that you were considering are presumptive in form whereas your data has it's own message. This data has not only a strong memory but has been affected by external activity causing the step.level shift and the 3 pulses.

The method used here to form the model is called Intervention Detection . Search SE for "INTERVENTION DETECTION"

IrishStat
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