Hello, Goodbye Linear Regression

Summer is the time to visit family. Kids get some grandma and grandpa time, parents get to spend some time with siblings and their parents or in-laws. It's a grand time of the year. For some, these summer relationships are a little "quote" -- complicated. "Well it's good to see things are going well." Ten minutes pass. "I think we'd better go to the airport a little early since there is so much traffic and with the new security issues and all." Hello, goodbye is a common meme.

I decided to pick up a book on statistics this past week to help pass some time during these hot days. I can't remember when we started a relationship, but I know it's been a long time. And often frustrating. After pondering how linear regression modeling can help me with building trading models, I decided that it can't. These statistical techniques have too much baggage and I don't have time to deal with it. Everything has to be perfect for them. Zero mean of disturbances, constant variance of errors (homoscedasticity, if you prefer six-syllable words),  non-stochastic predictor variables. Really?  People live like this? In what universe if you don't mind me asking?

I've also changed through the years, so maybe I shouldn't be too hard on linear regression. These days, I much prefer questions that are framed where the dependent variable is dichotomous. This is asking too much from linear regression modeling. Sure they try with dummy variables, but then they suffer from nonsense predictions given the nature of boundary problems. They try to compensate for this with truncating regression lines at boundaries, but then they're saying that predictor variables have no influence at these points, which is troublesome as I'm sure you'd agree. By the time they start modifying their straight line predictions to an S-shaped curve, which is more appropriate, we have our last vestige of hope that this relationship can be meaningful dashed. You see, once you start curving a linear regression model to accommodate for a boundary, you've violated just about every assumption that linear regression has. There is probably a warrant out for your arrest. Not to mention that you're saying sayonara to making sense of additivity with this approach.

There is a statistical technique related to linear regression called non-linear regression. If you familiarize yourself with her it will remind you of when you first got married and pondered how such a lovely person could come from such people who have so little in common with you.