The Living Thing / Notebooks :

Cepstral transforms and harmonic identification

See also machine listening, system identification.

Just as you can generalise linear models for i.i.d observations you can do it with time series. You can also do it for the power-spectral representation of the time series, which includes as a special case the cepstral representation of the series.

I haven’t actually read the foundational literature here, just used some algorithms; but it seems to be mostly a hack for rapid identification of correlation lags where said lags are long.

Harmonic regression

A random thing I saw mentioned - I wonder if this is just another smoother for regressions?

Estimating the magnitude of individual cyclic components in a signal, e.g.

Rather than count peaks to guess the period or frequency […] fit regressions at many frequencies to find hidden sinusoids. Use the estimated amplitude at these frequencies to locate hidden periodic components. It is particularly easy to estimate the amplitude at a grid of evenly spaced frequencies from 0 to 1/2.