Dear all:

I'm a newbie and an amateur seeking help with forecasting the next in a non-stationary time series, with constraints of 1 (low) and 27 (high) applicable to all. 

What I need help with is the solution concept. The series has 439 observations as of last week. I'd like to analyze obs 1 - 30 (which are historical and therefore invariate), to solve for 31.

The history:
Obs 1        2
2                1
3                1
4                16
5                9
6                6
7                7
8                11
9                11
 10                1
11                12
12                14
13                13
14                2
15                4
16                5
17                14
18                6
19                4
20                7
21                5
22                8
23                7
24                15
25                11
26                3
27                4
28                6
29                8
30                4                             
31                ?? (a known)

For backtesting of forecasting accuracy, I can use either a sliding window ( 1 - 30 to solve for 31, 2 - 31 to solve for 32, 3 - 32 to solve for 33, etc.) OR a cumulative window (1 - 30 to solve for 31, 1 - 31 to solve for 32, 1 - 32 to solve for 33, etc.), whichever works better. I can also supply different windows if deemed  appropriate, e.g., 50 or 75 or 100 obs, whatever, in either configuration.

The 30 obs window is selected for this list query only so as not to take up too much message space.

Query: How would you solve for ob 31 in the above series, with the constraints stated? (If you need a longer history, say, 50 obs or more, I can supply it off-list.) I've tried all the relevant Excel functions with no success, and suspect that the solution lies in some combination of them. Here I defer to the collective wisdom of you all. 

Once the correct concept is established, I can proceed to set it up in R for this and other similar series.

Many TIA and regards,
Perry E. Gary
Tokyo
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