Sampling: simple stable Autoregressive

I want to try out the convex hull inclusivity tester on data that is less random. One way to get such data is to sample a stable ARMA process. In fourier space, an ARMA can be expressed as a quotient of two polynomials:



P contains the poles, and Q contains the zeroes, or nills. In this post, I use only Q = 1.
The criterion for stability is that all roots of P is in the unit circle. To get a uniform sampling from the unit circle, we can sample an angle from a uniform distribution, and an absolute value from a triangle distribution (since the density must increase linearly with the absolute value). The code:

This output format fits perfectly into the ArmaProcess object from statsmodels.

Random stable AR process from 5 pairs of poles.