all the averages, diff to diff, running averages, serial second derivitive? head spinning!!!
If your data is all coming in the same then there would be no difference between data points, right?
If the data is getting larger then the difference between data points, the last one subtracted from the one before, would be more than zero.
data: difference, difference-of-difference
1 ............ no data before this to subtract from this so no difference or difference-of-difference
2: 1 ......... we see the data is increasing by 1. but no difference before this so no difference-of-difference
4: 2, 1 ...... we see the data increasing by 2 and we see that the increase is increasing by 1
7: 3, 1
12: 5, 2 ..... we see the increase is increasing by 2
16: 4, -1 .... we see the data increasing by 2 but now that increase is getting to be less
19: 3, -1 .... data still increasing but not as fast as before
21: 2, -1 .... if we drew a curve of the data it would still be going up but starting to 'hilltop'.
22: 1, -1
22: 0, -1 .... and here the data curve would be level
20: -2, -2 ... then it's going down
The difference is like rate of change of the data, +values are increasing and -values are decreasing.
The difference-of-difference is like the rate that the difference itself is changing.
If the data is not chaotic then the diff-of-diff (just abbreviating!) will tell you the trend farther ahead than just the difference will do.
By using the difference and difference-of-difference you can detect two levels of change to spot trends. You can take that as many levels as you want btw, but remember that the time between data points needs to be (at least close to) even for it to work.
Sorry about the terms, they aren't exactly standard and the approach is a bit rough. I just took an idea from calculus and applied it to data, have done so before to good ends even though it's not precisely calculus.