Genuinely curious -- how do you create predictive time-series models in the frequency domain?

(background: control systems)

speech recognition immediately jumps to mind

Speech recognition is generally not considered a time series problem though.

what about speech is nontemporal?

Time series problems are indeed temporal, but not all temporal problems are time series problems. Time series deals with time-specific features of a discrete sequence like autocorrelation, trends, seasonality, etc. whereas frequency domain methods deal with, well, frequency.

Support you’re are looking at sales patterns over a long period of time, which has certain patterns. FFTs are unlikely to tell you much that is useful or predict much whereas time series methods can reveal patterns where the t is the independent variable.

In the spirit of the article, how can frequency domain representation be used for prediction / forecasting? Any examples you could share?

+1. FFT is under appreciated.

What do you mean? It's one of the most used algorithm in the history of mankind.

Under appreciated by people just now getting into time series regression, who may be really excited about throwing deep learning at the problem.

Edit: literally saw this happen two weeks ago by a PhD in electrical engineering.

So much that! Also under appreciated: plots and OLS.

Start plotting before firing up the GPUs, then compare to standard OLS - like in this article!

Suggested reading if you don't know OLS: ML from scratch.

Well to be fair if you use a convolutional recurrent architecture, you're doing it without realizing it.

Is that true? I would think that would be more like a wavelet transform where the wavelets are learned?

Yeah, that's true.

and not a single DS/ML person seems to have ever heard of it.

Because most folks in DS/ML are working on predicting likelihood to press a button. You don’t need Fourier transforms for that.

CNN is essentially a FT with learnable kernels.

well, it’s certainly usually convolution. Hardly anyone knows why or how that connects to the FT though.

you do, depending on your feature preprocessing.

Most DS/ML people are useless chimps.

FWIIW I've used it all the time, along with wavelets, cepstrums, lifters and Hilbert transforms. For timeseries with nonlinearities and lots of data points, it's the way to go. 9/10 times I'd rather hire a EE with signal processing background than a statistician or data scientist for time series work.

Can you give an example pls?

“bandpass with a butterworth then plot the FFT and phase”

If you would indulge me, what sorts of insights would this get you? (genuinely curious)

All I can think of is identification of frequency modes.