By far, the most interesting stochastic process used in financial economics is Brownian motion. The role of Brownian motion in stochastic processes is similar to that of Normal random variables in elementary statistics. The concept of a random walk, the discrete counterpart of the (continuous time) Brownian motion, is well known among students of economics, since most macroeconomic time series behave in a similar fashion (A random walk is a special case of what is known as unit root process or I(1) process). The plot given below shows trajectories (realizations) of a random walk process.
I agree, it is a statistical process that continues to interest me. My question is when trying to distinguish between a stationary and a non-stationary process: what is the difference between a permanent innovation and a structural break? And how can we distinguish between the two?