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Re: [ferret_users] Re: running trend



Hi Saurabh,

On Fri, May 17, 2019 at 8:58 PM saurabh rathore <rohitsrb2020@xxxxxxxxx> wrote:
From a quite long time I am fascinated to compute running trend in ferret (I hope we can do it in ferret). Lets say I have monthly data and and I like to compute 10 year running trend with a sliding window of 12 months. Please help me out in this regard because I am completely blank in doing this in ferret. I strongly want to say that this type of statistic is very useful for many of us. I am attaching a netcdf file as a test data. I hope I will get an elegant solution like we did in running "correlation" case. 

I'm not 100% sure, but I have the feeling that you can do it.

I'm too lazy.  So, you, or somebody else, please figure it out. I just outline my idea.

Our model is y = a x + b.

Problem: Find a and b that minimize:

   J = sum_i (Y_i - y_i)^2

where y_i = a x_i + b and Y_i are the original data points.  (Hint: take partial derivatives of J with respect to a and to b and equate them to zero.)  Then, you'll find that a and b are each a function of sum_i (x_i)^2, sum_i x_i, sum_i Y_i, etc.

As we saw in the running correlation case, these sums can be calculated in the "sliding way".  Therefore we can calculate a and b in the sliding way.

I may be totally wrong.  Just try.

Cheers,
Ryo

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