topic Re: calculate SKEWNESS of residual in a rolling window regression in SAS Programming

calculate SKEWNESS of residual in a rolling window regression

Nieves — Tue, 26 Dec 2023 03:58:07 GMT

Hi SAS expert, I'm trying to calculate idiosyncratic skewness of residual in a rolling regression using past 6 months data. The regression is regress individaul stock return on market return:

reg ret mktret

For each month t, I run the regression using t-1 to t-6 data, and get the residual and calculate skewness of residual

Re: calculate SKEWNESS of residual in a rolling window regression

mkeintz — Tue, 26 Dec 2023 23:23:51 GMT

Please show a sample of the data, in the form of a working data step - so that proposed code can be tested.

In particular, how are you constructing data to be submitted for rolling window regressions?

Re: calculate SKEWNESS of residual in a rolling window regression

Rick_SAS — Wed, 27 Dec 2023 11:53:33 GMT

1. Are you using forward, backward, or centered windows?

2. For the regression, do you want a least-squares regression for k=6 time points, or do you want a moving average?

3. Do you have access to SAS IML software?

You can review common moving-window statistics by reading the article, "Compute a moving average in SAS."
Since the skewness of residuals for a moving regression is not built into any SAS procedure, I suggest you program it yourself in the SAS IML Language. The basic ideas are shown in the article, "Rolling Statistics in SAS/IML". A second article on rolling medians shows how to extract the data from a rolling window.

I would tackle this problem in two steps:

Extract the data from the rolling window, solve the normal equations to get the parameter estimates, and construct the residuals (which gives you a NEW series!).
Compute the rolling skewness of the residuals.