Cyclic autoregression with Python

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I have an histogram looking like a Poisson law. X is the day of lunar cycle (so periodic, Xfirst comes after Xlast).

I would like to define an autoregressive model in Python to fit the histogram such as :

y(x+1) = F(y(x),sin(x)) so that Xfirst is estimated with Xlast and forcing is periodic.

But I cant' figure out how to do so far ... Any suggestion ?

Thanks !

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