Parameter estimation for a process with multiplicative noise via regression

Question

Tamas Bodai 2021-7-13

0
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https://ww2.mathworks.cn/matlabcentral/answers/877268-parameter-estimation-for-a-process-with-multiplicative-noise-via-regression

Hello All,

I have a process featuring a so-called CAM (correlated addtive and multiplicative) noise:

.

I would like to estimate the parameters

I have alternative ways of doing it that work in this simple case, but i wonder if it can be done via nonlinear regression. My attempt was to express -- upon discretisation by Euler-Maruyama -- the noise increment, and apply Matlab's lsqnonlin, or, just use 'fminsreach' to minimise a the sum of squared noise increments. However, they do not find the right parameter values. If I provide the location parameter b, then c is estimated with a very big bias still. I get to wonder that the regression problem is not even well posed. In the wiki article they do mention that the noise is assumed to be additive, unlike, it appears, the help page of lsqnonlin. The help page of fitnlm also explicitly mentions what type of noise it can deal with. The 'ErrorModel' 'combined' seems something like in my equation. However, it's too restrictive and actually doesn't apply in my case. I wonder why it's so restrictive, why is the absolute value

imposed?

Any help or clue, paper or book reference, would be much appreciated.

Tamas