By way of footnotes...

Actually, the matter of the iPod regression analysis is over and done with. The paper's been written, turned in, graded (much to my chagrin) and shelved. But for those interested in a bit more:

The original intention was to do something (anything!) involving CAPM. That didn't quite turn out as expected, so I settled on the index model. I've given it a lot of thought (but not much since), and I think the equation is fairly accurate vis-a-vis the theory it's based on.

Also, just to clarify: I never used actual sales. I just used whether they were sold or not as a dummy variable. I wanted to do the former, but there was only annual data; and since the iPod's only been around since 2001 that means very few observations. Further, using "announcement of new iPod models" as a dummy variable did cross my mind. At the time, I was enthusiastically moving in that direction...until I realized that there's been a new iPod model every year, not to mention in some cases more than one a year. I then tried to work on using "number of new iPod models" as independent variables, but at some point just fell back on the simplest possible thing to do. And there you have it.

The random walk idea is something to think about. But perhaps within the context of another theoretical model. Depending on how you look at it, the random walk is already implied in the index model. I still need to further study CAPM, index models and arbitrage pricing theory models, but the one I used was a cross between these last two, and the whole idea behind these is that if you employ as many macro-level factors as independent variables you should be able to diversify away market-level risk and be left with firm-specific determinants of a stock price (where the random walk will apply). To some extent, this is captured by the &beta₀ value, which is why it's defined as the stock price's "expected value". As a random walk, if expected equals actual, the value is zero.

At least that's what I think about it.

Anyway, a data quirk you might be interested in. There were over 250 observations in my sample and since it was a time series, I knew to correct for autocorrelation. How many lags? 43! The odd thing is that when I corrected for around 41, the results would be significant at a 0.01 level of significance, but not at a 0.05 level. I still haven't figured out why that is.

JAZ called it. I am a nerd.