Thread by @DeFi_initiate

How is the projection line of the #bitcoin DPC model built? I'm glad you asked.

For starters, it would be helpful to check the latest update:

https://twitter.com/DeFi_initiate/status/1489939862274789376

For model background, see this post:

https://twitter.com/DeFi_initiate/status/1487837760324964354

Building the DPC Model, Part I - 🧵 8

1. To recap, the DPC model consists of two fundamental components (power law + halving cycle) and two refinements (daily price adjustment + cycle fading):

https://twitter.com/DeFi_initiate/status/1487837803249815552?s=20&t=HFkDpFdwT8C_iIQUUs2i-A

Context to power law:

https://twitter.com/DeFi_initiate/status/1487837806298742787?s=20&t=HFkDpFdwT8C_iIQUUs2i-A

Halving cycle explained: investopedia.com/bitcoin-halvin…

2. We start with the power law, which is shown as a green line on this monthly #bitcoin chart (blue candles indicate prices). To build this line, we need to compute linear regression (i.e., straight line estimation, a trendline) for the logarithm of both price and time.

3. The equation is y = mx + b, where y = log(price) and x = log(time). We are trying to find values for parameters m (slope) and b (intercept) such that the fit of the line to actual prices is the best possible. The goodness of fit can be measured and optimized using #math.

4. Why is the green line not straight if this is linear regression (straight line estimation)? It is because the vertical scale of price is logarithmic but the horizontal scale of time is linear (it's called a semilog chart). This line will look straight on a true log-log chart.

5. To avoid backfitting and to make the model dynamic, we will not just compute the two regression parameters once at a random point in time, but will do this every day. The chart below shows how slope (orange linie) and intercept (purple line) have changed over the years.

6. Following a violent period of the initial few years, the parameters settled down quickly and are now showing strong stability. Observe how the green power law line is not as smooth as on the previous chart, which is due to its rapidly changing parameters in the beginning.

7. This chart demonstrates how well the power law fits the behavior of #bitcoin's price in the long run. In case you still doubt that this is the best possible long-term model to build on, a recent comparison of approaches should put your mind at ease:

https://twitter.com/DeFi_initiate/status/1479897909890105346

8. To be continued with a look at modeling #bitcoin's block subsidy (miner reward) halving cycle (Part II of Building the DPC Model)

Part II is here:

https://twitter.com/DeFi_initiate/status/1490195229504200705

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