The Lorenz system is a system of ordinary differential equations $$\begin{aligned}{\frac {\mathrm {d} x}{\mathrm {d} t}}&=\sigma (y-x),\\{\frac {\mathrm {d} y}{\mathrm {d} t}}&=x(\rho -z)-y,\\{\frac {\mathrm {d} z}{\mathrm {d} t}}&=xy-\beta z.\end{aligned}$$ It is notable for having chaotic solutions for certain parameter values and initial conditions. My question is, although it is a deterministic system (because consists of three deterministic ODE), can it shows locally stochastic behavior?
Many tools have been introduced to distinguish between deterministic and stochastic behavior. For example, according to RQA (recurrence quantification analysis) there exists a measure (DET) which is called determinism and is related with the predictability of the dynamical system. If DET$=1$ (or $=0$) the system is purely deterministic (or stochastic).
Although Lorenz system shows DET near to 1, can it shows locally stochastic behavior?