[Thread Prev][Thread Next][Index]

Re: [ferret_users] 21 yr running correlation

Hi Ferret users,

On Wed, Aug 29, 2018 at 11:57 AM Ryo Furue <furue@xxxxxxxxxx> wrote:
Your method utilizes the identity

mean{ [a - mean(a)]^2}
= mean(a^2) - [mean(a)]^2

so that the operation mean() is applied only once in each term.  That's elegant.

Currently, I need a "running skewness", which I think I can calculate applying your method.

For a record, I describe how one can calculate it.

To extend Andrew's method, we first need a formula to calculate the third moment without nested applications of mean(). The formula is

mean{ [a - mean(a)]^3 }
 = mean{ a^3 - 3 a^2 mean(a) + 3 a [mean(a)]^2 - [mean(a)]^3 }
 = mean(a^3) - 3 mean(a^2) mean(a) + 3 mean(a) [mean(a)]^2 - [mean(a)]^3
 = mean(a^3) - 3 mean(a^2) mean(a) + 2 [mean(a)]^3

So, my Ferret code looks like:

[Thread Prev][Thread Next][Index]