Need PSD-based methods of fitting models

[joefowler]

We need PSD-based methods for fitting models with frequency-specific weighting. See branch:model_fitting for progress. I've been working for a few months on this, but not quite done. To complete, we need:

• Fix cases where the model_psd(...) spectrum is rescaled by some number. Example: ARMA(4,6) for load(111, "20170629"). Aha! This is a case where adding a constant to keep zeros off [-1,+1] ruins the model. Need a new way to fix illegal roots?
• Fix cases where the model spectrum approaches zero at high frequency. This boosts high freq noise too much when whitening. Maybe we want a lower bound on the spectral model, or a max ratio of high/low frequency spectrum. Example: ARMA(6,8) for the same data.
• Understand (fix?) cases where the ARMA model whitening is good but toeplitz_whiten(...) is bad. Example: ARMA(5,5) for the same data.

[joefowler]

This set of bugs ("bugs"?) is in good shape. Now what we need is to try this PSD-based fitter on real data and see if that uncovers any new problems, or if we are close enough to done.