Exploring The "Number Go Up" Model Of BTC Price Forecasting

Just about everyone in the crypto space has heard of the Stock-t0-Flow (S2F) model of bitcoin price forecasting, developed by PlanB. S2F models bitcoin's price over time using scarcity, which is significantly impacted by halving events.

But there's a new model in town, and it's gaining attention for its uncanny ability to predict bitcoin's price from the simplest of parameters: Time, and time alone.

Number Go Up

It's called the "Number Go Up" model (NGU), and it was developed by mathematician Allen Farrington.

You can read how it works in the linked article, but Farrington keeps things simple, using just one variable (time) to predict bitcoin's price. The result is staggeringly accurate, with an R-squared value of 0.97. This means that 97% of the variability in bitcoin's price can be explained by changes in time.

At this point, it's important to give the disclaimers that:

1) All models are wrong, some are useful

2) NGU describes the past, and the past may not predict the future

Nonetheless, the correlation is remarkable. Farrington tweets: "I think the reason the NGU model is so breathtakingly accurate is that, unlike some others, it captures ***both supply and demand*** inside just a few assumptions that are extremely simple and obviously true."

How Does It Work?

While the broad strokes are simple, the detail is a little more complicated, since although bitcoin price rises in the long run, the model also tries to take into account bitcoin's periodic crashes.

It starts with a logarithmic regression of bitcoin's price history, which actually has a surprisingly high R-squared of 0.87, just to kick things off. That alone suggests that bitcoin's price is reliant on some fairly fundamental laws of the universe (the passage of time), with a few kinks thrown in to keep things interesting.

Next, bung in a sinusoidal component to model bitcoin's periodic crashes. Here, you're basically modelling human emotion and the market's tendency to get a little overexcited from time to time, and then run screaming for the exit. Add another function to compress and stretch that sine wave, to take into account the fact that the spikes are hard and fast, and the bear markets take a little longer to play out. Add a decay term to dampen the growth over time, since it can't possibly go up exponentially forever. Finally, add a "wibble wobble" wave, to model the shorter-term fluctuations. Result?

With these simple, logical, and reasonable assumptions in mind, let’s put together a model that captures all of the above. This will take the form:

Where r is the regression coefficient derived from Figure 1, the f(t)’s are the monotonic dampening of this coefficient and the sinusoidal modulations, as captured in Figure 8, g(t) parameterizes how we input “time” such that the amplitude, frequency, shift, and so on, of the sinusoidal functions are suitable for this domain, and h(t) makes it all wibbly wobbly.

So How Good Is It?

An R-squared of 0.97 is pretty remarkable. Against that, we have to weigh the mathematical gymnastics required to fit the curve to the data, and generally show some skepticism about the ability to model bitcoin's price development from first principles (being wedded to any mathematical model or trading strategy is a bad idea). Still, it's impressive.

Extrapolate that into the future, and you get some eye-watering numbers—though not the $100k BTC in 2024 that many analysts are predicting.

Will the NGU model prove more useful, or wrong? Only time, and time alone, will tell.

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