Taking a simple alpha-stable distribution, the Normal Inverse Gaussian distribution for example, how would one derive the likelihood function provided non-i.i.d. data, e.g. a price series?
Asked
Active
Viewed 472 times
1
-
3*Writing* the likelihood is trivial--it's no different for one continuous distribution than for another (it's just the product of the values of the PDF evaluated at the data, assuming they are iid). Is your problem really one of *computing* the likelihood? – whuber Jun 11 '12 at 19:48
-
@whuber, I suppose I really should be asking about a good reference on writing likelihood functions for non-iid data. Prior question: http://stats.stackexchange.com/questions/29190/does-mle-require-i-i-d-data-or-just-independent-parameters – Felix Jun 11 '12 at 20:59
-
2Are you modifying this question then? As it stands, it suggests you are thinking of iid data. BTW, although the likelihood expression may become more complicated with non-iid data, conceptually it's no different: you write the probability of the data. That's all there is to it. Because you're being explicit, the probability of course displays its dependence on any parameters involved in the (now multivariate) distribution. Calling this probability a "likelihood" merely indicates you are considering it to be a function of the parameters; the data are treated as constants. – whuber Jun 11 '12 at 21:05