This past year was the first year I made two models. That’s because my youngest son has joined his older brother in Cub Scouts and the annual ritual of Pinewood Derby Car building became twice the fun. I’ve been “quote” — helping — my oldest for two years now, so I’ve got some experience. I’ve learned quite a bit from watching how others have built their cars. I look at both winners and losers to form my theories on how a model should be constructed. Losers typically have some piece of Lego attached to it, creating a pretty car with catastrophic drag. The winners tend to be modestly built (not over-engineered, mind you) and properly weighted.
This year as I had both models resting on a table near my kitchen, my neighbor came over and decided to make some comments. This is the neighbor who takes great pleasure in contradicting everything I say. I could say “the sky is blue” and he would invariably respond with “the sky is not blue.” I call him Null Hypothesis. I take pleasure in watching his silly comments laid waste, but sometimes it takes more effort than I’m willing to expend at the moment. This year he proclaimed “those cars will lose, they are too simple.” I could not prove him wrong on the spot, but the die was cast. I responded “they will not lose, but you will lose. These cars will win first place!” It would take racing day results to reject my neighbor’s proclamation. I couldn’t wait.
While it’s true that I’m a Cub-Scout Pinewood Derby car-builder dad by day, I’m also a algorithm trading model builder by night. I’ve got the Bumblebee, Gnat, Monkey, Pelican and a whole host of others sitting on the shelf. These vary in construction from simple trading-rule algos to more sophisticated predictors that implement radial-basis function support vector machines. I do suffer from an ambitious curiosity as to how others are building their models though, so I tend to look around and survey the landscape often. I’ve lately glanced over to a group of builders called Econometricians. No, not electricians. I mean practitioners of the black art of Econometrics.
Econometrics is the science, art and voodoo of building financial models. They are typically frequentists so I found it important to familiarize myself with their methods and terms. When they build their models, they save the wood chips for analysis. Yes, they are indeed a serious group.
One of their favorite modeling techniques is called regression. All types including simple linear regression, polynomial and multiple linear regressions. Regression is basically the process of fitting a line or curve to describe the relationship between a dependent variable and an independent variable or variables. Kind of like the return tomorrow of the S&P 500 will have a relationship with the return of the range of the VIX today. Something like that.
Building the model is not the difficult part. It’s analyzing the model and the wood chips (commonly referred to as disturbances) where things can get a little complicated. If the wood chips are too cozy with each other, as in they are serially correlated, there’s a problem. If the goodness of fit (R-squared) is low, there’s a problem. If the F-statistic isn’t large enough or the p-value isn’t small enough, there’s a problem. You spend most of the time trying to prove that the opposite of what you’re trying to show is false. I can sort of relate to this, with my neighbor being who he is. But I know what my neighbor looks like, a 50-something male with kids already out of the house. They don’t tell you up front who their pesky neighbor is so you need to listen carefully. Actually, you don’t have to listen because I’ll just tell you. It’s the hypothesis that there is no relationship, or that the slope of the regression is zero.
It isn’t good enough to reject this null hypothesis of course, but that’s the minimum. I’m going to take a shot soon at this wily art and build myself my own model or two. I’m expecting the first few attempts to fail miserably because this process includes a laundry list of assumptions that I can’t keep track of ranging from expected mean of errors is zero to explanatory variables must be non-stochastic. I really can’t tell you if anyone ever races one of these models though, so I can’t tell you how well they will perform.
You have to race your model eventually, and on race day back at Cub Scouts I was able to prove my neighbor Null Hypothesis wrong. My boys’ cars didn’t lose. They won a couple of heats. I wasn’t really right to say they would win first place because they didn’t (silly dad forgot to sand off the burrs on the nail axles!), but at least my neighbor Null Hypothesis was rejected. Next year, the Den Leaders have agreed that dads will be able to build their own dad-only cars for a special race. The only rules are no thermonuclear powered devices. I can’t wait.