My previous post (Parameter Stability-2) showed that even when I excluded outlying returns from the regression of IBM's and HP's monthly returns against the S&P 500 Index and the Fama French market factor, I still got sharp jumps in estimated beta as I moved across 36 years of history. But, as I realized while making the post, I didn't do the exclusion correctly. I should have re-estimated the mean and standard deviation for each sub-period. I redid the study, this time against the S&P 500 Index because it was convenient and because all I care about for the moment are methodological requirements for parameter stability. The estimation period is 36 months long. I excluded returns that were more than 2.9 standard deviations away from the mean for each period. No returns were excluded for most periods; one or two returns were excluded about 15% of the time; three returns were excluded in about 0.5% of the periods. Although the r-squares jump around a lot, the betas are a lot more stable now.
Data for IBM is on the left below; HP is on the right. The Mathematica code shown produced the two plots on the left. I pasted the ones on the right later.
Procedurally, the code gets lists of IBM, HP and the S&P returns from Wolfram Research, transposes two lists into a single list of paired values for the regression, and then 396 regressions, recalculating the sample mean and standard deviation for each, filtering the returns subset for outliers, running regression, adding the regression values for beta and r-squared to the end of the list {params}, and finally, plotting the values in the list. Pretty neat, huh? Click the image for a better view.
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