Given some real-valued empirical data (time series), I could convert it to a histogram to have an (non-parametric) empirical distribution of the data, but histograms are blocky and jagged.
Instead, I would like to identify the best-fitting parametric distribution from the scipy
or scipy.stats
libraries of distribution functions, so that I can artificially generate a parametric distribution that closely fits the empirical distribution of my real data and is continuous.
If the empirical data are monthly returns of empirical AAPL stock returns, for example, I know that the parametric Johnson-SU distribution resembles, and can mimic, stock return distributions because of its customizable skew. However, the Johnson SU distribution in scipy
requires four input parameters to be calibrated. How can I search for the best parameter settings of this parametric distribution from scipy
that fits to the empirical distribution of my sample of AAPL returns?
scipy
has MLE built-in which also makes it more convenient. Matching the Johnson parameters, on the other hand, to the target levels of skewness, kurtosis, etc might involve method of moments though, with some help from known closed-form solutions that were derived to show this particular distribution's moments being functions of its parameters. $\endgroup$