**The Rise of Bitcoin**

Bitcoin is in the news again as it hits $10,000 a coin – the online crypto-currency has seen huge growth over the past 1 1/2 years, and there are now reports that hedge funds are now investing part of their portfolios in the currency. So let’s have a look at some regression techniques to predict the future price of the currency.

Here the graph has been inserted into Desmos and the scales aligned. 1 on the y axis corresponds to $1000 and 1 on the x axis corresponds to 6 months. 2013 is aligned with (0,0).

Next, I plot some points to fit the curve through.

Next, we use Desmos’ regression for y = ae^{bx}+d. This gives the line above with equation:

y = 5.10 x 10^{-7 }e^{1.67x }+ 0.432.

I included the vertical translation (d) because without it the graph didn’t fit the early data points well.

So, If I want to predict what the price will be in December 2019, I use x = 12

y = 5.10 x 10^{-7 }e^{1.67(12) }+ 0.432 = 258

and as my scale has 1 unit on the y axis equal to $1000, this is equal to $258,000.

So what does this show? Well it shows that Bitcoin is currently in a very steep exponential growth curve – which if sustained even over the next 12 months would result in astronomical returns. However we also know that exponential growth models are very poor at predicting long term trends – as they become unfeasibly large very quickly. The two most likely scenarios are:

- continued growth following a polynomial rather than exponential model
- a price crash

Predicting which of these 2 outcomes are most likely is probably best left to the experts! If you do choose to buy bitcoins you should be prepared for significant price fluctuations – which could be down as well as up. I’ll revisit this post in a few months and see what has happened.

If you are interested in some more of the maths behind Bitcoin, you can read about the method that is used to encrypt these currencies (a method called elliptical curve cryptography).

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