Here we present an in-depth analysis of the periodicity of the continua and broad emission lines of a quasar E1821+643. We applied non-parametric composite models, the linear sum of stationary and non-stationary Gaussian processes, and quantified contribution of their periodic parts. We found important qualitative differences among the three periodic signals. Periods of $∼ 2200$ and $∼ 4500$ days appear in both continua 5100 Å \, and 4200 Å \,, as well as in the H$γ$ emission line. Their integer ratio is nearly harmonic $∼ \frac{1}{2}$, suggesting the same physical origin. We discuss the nature of these periods, proposing that the system of two objects in dynamically interaction can be origin of two largest periods. ; Comment: accepted for publication in Astrophysics and Space Science,13 pages, 6 figures