I am trying to calculate the probability of stock return to be greater than X in next 28 days, using the skewed t-distribution as it fits the best to the distribution of the returns. I have estimated the mean, sd, nu and xi using the historical data. Now, assuming that the returns are Normally distributed and i.i.d if I want to get the probability of return greater than 0.1 in next 28 days would be:

pnorm(0.1, mean = -0.000148 * 28, sd = 0.0238 * 28, lower.tail=FALSE)

But the returns are not Normally distributed but rather skewed t-distributed, so if I want to calculate similar probability how do I do that? Below is what I'm doing but I'm not sure if it is correct:


1 - psstd(0.1, mean = 28*sstd_fit$estimate[[1]], sd = 28*sstd_fit$estimate[[2]], 
           nu = sstd_fit$estimate[[3]], xi = sstd_fit$estimate[[4]]) ### Returns = 0.2570

I'm not multiplying 28 to the parameters nu and xi because as they are shape parameters and should not be affected. Please let me know if this is the correct way of doing it or if there is better correct way of solving this problem. Thanks a lot in advance.



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