I have a panel data for 20000 stocks over a sample period from 1950 to 2018. What I need to do is to compute for each of this stocks a moving skewness and kurtosis over the previous 5 year. My data is on a monthly basis, therefore what it should be done is to compute those measures based on the first 60 observations of a given stock, then with a step of 12 month compute it again using the previous 5 years, and so on as long as the data is still available. Then it should be repeated for each stock.
Any idea on how to do this? I got stack in this problem since a while and have no idea ho to go on.

Ps. I'm still a beginner in Stata and for unknown reason I cannot download any external package. Would appreciate if you can present me any possible solution without those packages