  We analyze the current and the shot-noise of an electron interferometer made
of the helical edge states of a two-dimensional topological insulator within
the framework of non-equilibrium Green's functions formalism. We study in
detail setups with a single and with two quantum point contacts inducing
scattering between the different edge states. We consider processes preserving
the spin as well as the effect of spin-flip scattering. In the case of a single
quantum point contact, a simple test based on the shot-noise measurement is
proposed to quantify the strength of the spin-flip scattering. In the case of
two single point contacts with the additional ingredient of gate voltages
applied within a finite-size region at the top and bottom edges of the sample,
we identify two type of interference processes in the behavior of the currents
and the noise. One of such processes is analogous to that taking place in a
Fabry-P\'erot interferometer, while the second one corresponds to a
configuration similar to a Mach-Zehnder interferometer. In the helical
interferometer these two processes compete.
