> The ad hoc method of parameter estimation used here needs some explaining
I tried to imitate a "least squares regression" actually. I confess I wasn't sure if this was the most appropriate approach. I will run the analysis again using the more standard technique you suggested and compare the results.
> Since the author uses mean for the estimate and sample sd in the other code I'm confused why this isn't used as the estimate for the variance in the guassian?
The mean value from the density estimate was used for fitting both the Gaussian and Cauchy models because they are symmetric functions, in an attempt to reduce this one-dimensional (single variable) fitting error.
Later on the mean is removed when estimating prices since I was assuming a driftless stochastic process for the underlying stock.
> The ad hoc method of parameter estimation used here needs some explaining
I tried to imitate a "least squares regression" actually. I confess I wasn't sure if this was the most appropriate approach. I will run the analysis again using the more standard technique you suggested and compare the results.
> Since the author uses mean for the estimate and sample sd in the other code I'm confused why this isn't used as the estimate for the variance in the guassian?
The mean value from the density estimate was used for fitting both the Gaussian and Cauchy models because they are symmetric functions, in an attempt to reduce this one-dimensional (single variable) fitting error.
Later on the mean is removed when estimating prices since I was assuming a driftless stochastic process for the underlying stock.