Calculating rolling 6-month skewness from daily returns

[xplosive111]

I have data of daily returns for several stocks. This is what my data looks like (simplified):

PERMNO	DATE	RETURN
10078	2010JAN02	0.0500
10104	2010JAN02	-0.0190
10107	2010JAN02	0.0020
10078	2010JAN03	0.0040
10104	2010JAN03	-0.0400
10107	2010JAN03	0.0500
...	...	...
10078	2015JAN02	-0.0190
10104	2015JAN02	0.0100
10107	2015JAN02	0.0700
10078	2015JAN05	0.0500
10104	2010JAN03	-0.0190
10107	2010JAN03	0.0020

PERMNO identifies a stock, DATE identifies a date (yyyymmmdd), RETURN is the daily stock return.

I have simplified this example for only three stocks (10078, 10104, 10107).

Goal: I am trying to calculate rolling skewness for each stock i in a given month t.

I want to calculate the monthly skewness measure for each stock using the previous 6 months (i.e. months t-6 to t-1) of daily returns data. Therefore, for a stock in e.g. July 2010, I want the skewness measure for that month to be based on its daily returns from January 2010 to June 2010.

I want the output data to include PERMNO, month ID, and the monthly skewness measure (based on prior 6 months of data) for that month. Here is a a picture to illustrate the desired output I want:

PERMNO	DATE	6MONTH_SKEWNESS
10078	2010JUL30	0.7257
10104	2010JUL30	-0.7056
10107	2010JUL30	-0.6781
10078	2010AUG31	0.9999
10104	2010AUG31	-0.6719
10107	2010AUG31	-0.7056
...	...	...
10078	2015JUL30	-0.1651
10104	2015JUL30	0.1056
10107	2015JUL30	0.6181
10078	2015AUG31	-0.8886
10104	2015AUG31	0.6119
10107	2015AUG31	0.1056

I have searched the web extensively and tried this myself, but I feel really stuck on this problem. Thank you in advance for anyone who is able to help in any way.

[Reeza]

If your data is continuous you can use something like the following:

https://gist.github.com/statgeek/07a3708dee1225ceb9d4aa75daab2c52

If you don't have continuous data or PROC EXPAND here is another method:

https://communities.sas.com/t5/SAS-Statistical-Procedures/Moving-Average-with-Multiple-Observations/...

You'll have to modify either for skewness, but that doesn't even have a standard definition so make sure the ones in SAS are what you want. 

[mkeintz]

data want;
  set have;
  by permno ;
  obs+1;
  if first.permno then obs=1;
  
  array ret_hist{0:59} _temporary_;
  if obs>=61 then do;
    sk=skewness(of ret_hist{*});
    output;
  end;
  ret_hist{mod(obs,60)}=return;
 run;

This calculates lagged skewness for every window of size 60, by applying the skewness function against a 60-element history of returns.  The array RET_HIST contains returns for date{i-60} through date{i-1}.  Only after skewness is calculated is the history updated with returns for date{i} (replacing returns of date{i-60}).  This establishes an array for dates{i-59} through date{i}, ready for the next incoming obs.

The program is slightly inefficient since each skewness is calculated from scratch.   One could calculate skewness of a window from (a) skewness of the previous windows and the returns from the (b) new return in the window (actually the return for date{i-1}) and the (c) dropped return (for date{I-61}).  Come back to us if you need that efficiency, although I doubt it would make that much difference.