Here's how I'm interpreting it (graphic attached). If only the yellow line is prediction vs. actual, that's only 3 days (8/3 to 8/6?). Whereby, actual data is green bars and prediction is light blue (cyan) line. Am I interpreting that as you intend?
Also, signal definition of a cycle is pk to pk, or trough to trough (like one sine wave).
But looking back at your definition (pk to trough), that is about a half cycle in basic signal terminology. Although, as you mentioned the data and predictions are aperiodic, the standard zero crossing or pk to pk terminology should still apply IMO.
"So, in the picture, more than 1 cycle is shown, not a quarter cycle, but I consider that the projection is only "accurate" enough for 2 cycles at most."
More than 1 is shown, but how much is actual data overlaid on prediction. From what I outlined in yellow, (only place where green bars and cyan overlap), that's only 1 cycle (per your def) of actual data vs. prediction. It does look like prediction matched actual for the cycle attached. Was the cyan portion predicted before the real data was overlaid? If so, do you see this occur more often than not?
If you get a strong correlation, even to 1 cycle (per your def), that may well be very useful (I'm doubting a strong correlation, but you did much more work on it than me
)
You mentioned your fft is calibrated somewhat? How far does it deviate from the ideal fft on a window of data?
(for instance, do snr or fundamental tones track?). How long a length of data (days?) do you sample to create your projected waveform?
Again, interesting work. Assuming you created your predicted waveform BEFORE you overlaid the actual data, it's worth investigating. I like it better than the curve fit approach I've seen others post.