Thread by @LilyWrites4

I don't know who needs to hear this today, but if you have two time series that both increase over time, they will especially visually show spurious correlation. This should be intuitive. Imagine I was looking at number of CS graduate students versus the number of arcades open.

So I fit a model to both, because that makes sense. In this example it shouldn't really matter if I take the totals of each, because we can obviously surmise both the total and rate of CS graduate students is increasing over time. We can't obviously say the same about arcades

without some data to back us up, but we can guess it probably is also increasing at a rate related to urbanization and normal population increase (arcades per capita, essentially). Here's what our graph looks like.

Fuck, that r^2 is sexy. Can I predict anything with this? Certainly not. Correlation doesn't imply causation, and statistically if you look hard enough to find random correlations you will find them. A commenter mentioned on my shared threads the same thing occurs when you

look at time series that have natural covariance - a good example is number of Bitcoin wallets (or rate) and price of a Bitcoin (or rate). Naturally over time we expect two things. As the price of Bitcoin goes up, more people will open Bitcoin wallets to capitalize on it.

Similarly, as the rate of Bitcoin price increase goes up, we expect that the rate of people looking to join the Bitcoin network should *also* go up. In this case, we really have two variables, x1 and x2, that depend on a latent variable x3 -- the popularity of Bitcoin itself.

That said, unlike our prior example (CS grads vs arcades open), it's also incorrect to say there isn't a real correlation here. It's quite likely the size of the network (Metcalfe's law) has some explanatory power on the current price of the Bitcoin, just perhaps less than

what basic linear regression would imply. A general rule of thumb I have with financial time series is except for obvious tautologies (e.g. VX and vs spot VIX, for ex.), if you see an r^2 > .5 or so, you're probably doing something wrong. There's a heavy noise component, and

r^2 of course is a simple linear model. How often do you see strong linear trends in real world data? Not very often, unless it is causative. It doesn't mean such models (Bitcoin network vs price) are useless or even wrong, it just is a good example of *lying with statistics*.

Be careful around charts, because the beautiful thing is a skilled data technician can tell you any story you want to hear. Without proper hypotheses, data is simply a quantitative way to lie to you. Fin.