Forgive me if my questions seem very basic. Don’t worry, I’m not studying for this upcoming test. I’m just going over the curriculum videos and essentially skimming the material so that when I do the real studying for June 2015 I will recognize things and catch on quicker.
In the videos the regression coefficients are often referred to as beta1, beta2 etc… My understanding was that these betas were the same as the Betas we learned about in Level I (systematic risk)
However, in Time Series I just learned that we can’t analyze betas with unit or explosive root (so b >= 1)…yet half of systematic risk betas are greater than 1, so this doesn’t make intuitive sense to me. Where am I mistaken?
The beta we covered in Level I was the slope coefficient for a security’s return vs. the market’s return. The betas we talk about in Level II are also slope coefficients, but the independent variable(s) needn’t be the market’s return and the dependent variable needn’t be a particular security’s return. The Level I beta was a specific example of a slope coefficient; in Level II we look at more general applications of slope coefficients. But the underlying idea is identical.
Your comment about time series’ betas applies to formulae where the independent variable is a lagged value of the dependent variable; in that case, you have to worry about unit and explosive roots. For general regression analysis – where the independent and dependent variables measure different quantities, not lagged versions of the same quantity – those worries don’t apply.
Ah of course, that makes perfect sense now. Betas can be greater than 1 without issue in general regression because we aren’t comparing lagged versions of the same values, but in Time Series this would cause an issue because a slope coefficient greater than one would be “explosive” growth.