Multidimensional autoregression

PREDICTION-ERROR FILTER OUTPUT IS WHITE

In Chapter we learned that least squares residuals should be IID (Independent, Identically Distributed) which in practical terms means in both Fourier space and physical space they should have a uniform variance. Further, not only should residuals have the IID property, but we should choose a preconditioning transformation so that our unknowns have the same IID nature. It is easy enough to achieve flattening in physical space by means of weighting functions. Here we see that Prediction-error filters (PEFs) enable us to flatten in fourier space.

PEFs transform signals and images to whiteness. Residuals and preconditioned models should be white.