Parameter Stability - 2

My previous post (Parameter Stability-1) showed the betas and r-squares obtained from 366 rolling 36 month regressions of IBM against the Fama French market factor. I was surprised to see how unstable the regression parameters were. I suspected data outliers were the problem, but some preliminary testing showed that the sharp jumps in the parameters were not completely due to extreme returns. I decided to expand this study by looking at both HP and IBM, and regressing against both the S&P 500 Index as well as the FF market factors. I excluded stock returns that were more than 4 standard deviations from the stock's long term mean.

The results can be seen below. The upper four graphs show results for IBM; the lower four ones for HP. The graphs on the left show regressions against the Fama French data; the ones on the right are against the S&P 500. The graphs are paired: beta above and r-squared below. Click the image for a better view.

I was surprised at the results, but was somewhat comforted by the fact that they were pretty much the same for both stocks and against either index. However, just as I was writing this post, it occurred to me I hadn't grasped the implication of using the whole 36 year period as a basis for excluding returns. I should have exclude outliers based on the returns in each 36 month period. I'll do that next. But even though it's clear that I made a methodological error, comments would be appreciated.