I am interested in knowing where do regression models of the form:
$$
\phi(x,A,B,C)=A\sin(kx+B)+C
$$
for a given $k\in\mathbb{R}$ are applied in domains such as engineering and science. What example are there that requires the use of this model?
I had encountered this model recently on math stack exchange. I would suspect the use of this model would be in a domain that heavily requires the use of signal processing but I can't seem to find any answer on the web of any application of sine regression.
These questions on MATHSE are mainly about how to transform the nonlinear sine model to a linear one via substitution in order to be solved numerically (such as using the normal system)
https://math.stackexchange.com/questions/3926007/least-squares-regression-of-sine-wave
Best Answer
Forecasting a process with seasonalities, i.e., recurring patterns. Sinusoidals, or higher Fourier terms, are especially useful if you have seasonalities with long periods, e.g., for daily or weekly data with yearly seasonalities, or for minutely data with daily seasonalities. My answer to Linear regression with “hour of the day” gives a few examples. Alternatively, take a look at the TBATS model for forecasting data with "complex" seasonalities, where the "T" stands for "trigonometric". A literature reference is given in the "multiple-seasonalities" tag wiki.