I'm getting odd results with time-series data and I'm trying to interpret them to find seasonality. Using latest Stata, Win 10.

I'm working with a dataset using monthly count data with 17 years' worth of data on number of prisoners in a state prison system and a univariate time series. There is a positive upward trend for 15 years and then it decreases rapidly. I've attached this below.

My problem is this - I've concluded that using a differenced correlogram in tandem with a differenced periodogram is a good method for my data to find seasonal highs in prisoner counts. I've attached both below. The correlogram seems to indicate that I have seasonality at 1 year, 1.5 years, 2 years, and further harmonics on this 6 month cycle (2.5, 3, etc). The periodogram (I've added xlines) also seems to indicate this cycle as well at 1/0.83 , 1/.166 , 1/.25 , 1/.33 , etc, but this periodogram also has a strange dip at .22, .31, and .48.
Syntax used: -pergram D.docaverage- and -ac D.docaverage-

Now I'm fairly new to these analyses so maybe this isn't an issue but I'm not sure how to interpret those dips in the periodogram. What do they mean? Overall these two seem to indicate seasonality, but it isn't as clear as I would like

Secondary question- When I run the function -estat sbknown- and pick a date (any date) in my time series it invariably finds a structural break (significant result), even at points in the data where the function -estat sbsingle- does not. I am running this function on non-differenced data. Do these functions work differently or use different math? What could explain this result?






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