The autocovariance function of stochastic process is pretty powerful tool to determine some property of the process -- mean square continuity, Riemann integrability and partially weakly stationarity and existence of the spectral density.
So I am wonder if we can make equivalence classes on the space of stochastic processes with finite second moment (maybe for simplicity only weakly stationary processes) such that two processes are equivalent if their autocovariance function is the same.
Is this space even relevant? If so, where/when it could be useful.
