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For example in this set of data (in ascending order of time)

[ 100, 98, 105, 91, 108, 106, 110, 109]

It is clearly the trend is rising but i would like to know how to determine the rate of change, so that actually the rising trend is slowing. For example here, if 110 is local max, then the rate of change form there is going from positive to negative.

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    $\begingroup$ What about taking the difference of your data? For example, if you had a series $[1,3,3,2,1]$, the differenced series would be $[3-1,3-3,2-3,1-2]= \color{blue}{[2,0,-1,-1]}$. The signs in the difference tell you if your series is moving up, or down. $\endgroup$ – Minus One-Twelfth Mar 15 at 19:39
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    $\begingroup$ There are many ways. You can weight each year exactly the same and just go for $9/7$. You can also put weights that put more emphasis on the most recent years so take the difference of each year and have $-1*(7/28)$ + $4*(6/28)$ + $-2*(5/28)$ + ... Your data your model. $\endgroup$ – Matthew Liu Mar 15 at 19:43
  • $\begingroup$ @MatthewLiu what do you mean by 9/7? Will discounting the further data affect the timing for catching "turning point", for example the data [ 100, 98, 105, 91, 108, 106, 110, 109], and respective changes [-2,7,-6,17,-2,4,1], multiplying by 1/7 to 7/7, the change will be discounted, and less sensitive to determine change of trend? $\endgroup$ – Edison Lo Mar 16 at 10:29

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