I just love brownies, chocolate fudge cake and the like. As a result of eating too many of those –so my dietician told me- I have gained weight over the past years. According to my dietician, somebody’s body weight depends on the ratio of their caloric input and output (i.e. someone’s personal ‘energy balance’). I also believed that. Until recently.
Here’s a graph of my body weight over the past 32 years:
As you can see from this graph, I’ve been on quite a few diets. But often, as soon as I had lost a few pounds, they came back when I lost my appetite in carrots and hunted down the chocolate aisle again. In the nineties, I did quite a bit of sports, which prevented my weight from increasing too much. I’ve stopped since; it just makes me tired.
Over the past 8 years, despite the yo-yo effect of sometimes losing as much as 5 kg over the course of a few months, my weight has increased. My dietician told me that unless I change my eating and sporting habits in a sustainable way, my weight will probably keep yo-yo-ing up.
I was gonna go back to drinking carrot juice again, but then somebody pointed out that my weight increase had nothing to do with my eating too much chocolate or anything like that. Huh?
He pointed out to me that the timeseries of my weight versus time (as shown in the graph above) contains a unit root! No, that’s not a consequence of eating too much carrots; it’s a characteristic of the time series. So what, you my ask? Well,
According to this theory, my body weight just varies stochastically, e.g. between the blue lines in the graph below:
As you can see, the theory is valid: My weight has indeed remained between the blue lines. And for the next few years, my weight will be between 55 and 105 kg, irrespective of what I eat and how much I sport! After all, that would be deterministic, wouldn’t it? (i.e. my eating and other habits determining my weight)
Wow, if that’s the case, then I’ll stop my carrot juice diet right now and run to the corner store for a box of mars bars!! And I’ll cancel further consultations with my dietician. Energy balance… such nonsense. Never thought I’d be so happy with a root!
PS: This post is not meant to ridicule the arguments made in favor of a unit root. It is meant to draw attention to the fact that the physical (or biological in this case) context of the quantity we’re investigating is very important. If someone is riding a bike downhill, I could wonder if the bike could have gotten to where it is all by itself, and conclude that I cannot possibly predict when the bike will reach the valley. But that ignores the (deterministic) effect of the guy who is riding the bike. Share your favorite analogy in the comments!
[Some typos edited]