# Is there an equivalent model to the Hidden Markov Model for continuous hidden variables?

I understand that Hidden Markov Models are used to learn about hidden variables $$z_i$$ with the help of observable variables $$\xi_i$$. On Wikipedia, I read that while the $$\xi_i$$'s can be continuous (say Gaussian), the $$z_i$$'s are discrete. Is this necessary, and why? Are there ways in which I could extend this to continuous domains?