January 7th, 2014, 3:02 pm
Your implied premise is problematic. Say your data is a return series [$]\{r_i\}[$] Initially, people explored the notion that the [$]r_i[$] were best described as IID draws from some univariate density [$]p(r)[$].In that context, your question makes sense -- you want to know the best distribution.But I'd say this approach was generally abandoned by the late 60's, as it failed to account for things like volatility clustering.However, if you want to catch up to the 60's try this classic by FamaNowdays, people tend to look at multivariate process models, often in continuous-time, often with hidden states that must be estimated.So they don't start with a distribution, but a parameterized process. Parameters and hidden statesare estimated (ideally and normatively) by maximum likelihood or good approximations. With the voluminous time series data in finance, such inference rarely depends on priors. p.s. I will add that priors play a strong role in the following sense. People tend to fall in love with classes of favorite processes.So, results from a particular researcher or group tend to always be from their favorite class. Given the vagaries of the whole(academic) notion that a stochastic process actually describes financial returns, and the zillions of possibleprocesses, this is inevitable.
Last edited by
Alan on January 6th, 2014, 11:00 pm, edited 1 time in total.