I have a price series. The natural logarithm of the price shows good normality. As shown in the standardized normal probability plot below:
However, by viewing the standardized normal probability plot, the returns (or say, change of the price), do not show good normality.
My questions are why the price is log-normal, yet the return can be non-normal? And given the situation, what can be the feasible model to describe the price process?
Thank you in advance.