Greetings,
If this is not the appropriate place to post this question please let me
know where
to post it.
I have a package under development which fits models of the form
$$
f(t)=\sum_i B_iG_i(t,\omega)
$$
depending on a parameter vector $\omega$ of arbitrary dimension to
data (one dimensional time series) in the general framework of the
data = deterministic signal + Gaussian noise
in the spirit of
Bretthorst, G. Larry, 1988, "Bayesian Spectrum Analysis and Parameter
Estimation,"
Lecture Notes in Statistics, vol. 48, Springer-Verlag, New York.
The basic parametric model
$$
G_i(t,\omega)=cos(\omega_i t), sin(\omega_i t)
$$
corresponds to classical spectral analysis, however the model can (at least
in principle)
be completely general. The problem is that the models cannot be defined by
the user but
have to be hard coded (in C++ since the computations are substantial).
I plan to include the ability to modify each model by the action of further
parameters as:
time changes: t -> t+omega, t -> omega*t, t -> t^omega
model function change: G(t) -> sign(G(t))*|G(t)|^omega
I plan to include models that can be generated by these actions from trig
functions,
some piecewise linear functions, monomials, and exponential function.
My question is: what further parametric models are of sufficiently general
interest to be
included?
Many thanks,
Michael Meyer
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