When we deal with observed data, we are usually interested in a few things:
Are we observing a certain constant that simply has some random noisy data? In this case, we check for stationarity (the mean value of the sample does not depend on time).
Will the process characteristics repeat again after a certain time (invertible processes)?
Is the observation data dependent on the previous data? Is the seasonality possible (process autocorrelation)?
Let's consider each of these tests in practice.
Here we'll check whether the process is weakly stationary. A random process, proc,
is weakly stationary if its mean function is independent of time and its covariance function is independent of time translation. This check is done using the WeakStationarity
function with the random process as its only parameter: