I've been diving deep into the swampy depths of Bitcoin's historical price movements, and I always have been a fan of the well-known "rainbow" chart. One day, while sipping my third can of caffeine and trying to get a decent workout in, I thought, "Why not take a stab at this myself?" So here I am, sharing my homemade flavor of crypto analysis with you all. The goal is to explore not just how Bitcoin's price has behaved over time, but also to understand potential future trajectories using statistical models.
First up, we'll take a look at the Logarithmic Regression Model. This approach captures the non-linear growth of Bitcoin’s price over time, highlighting a general upward trend. The model uses a logarithmic scale for price (jumping from $1 to $10 to $100), which evens out exponential growth to a more linear progression, making it easier to spot trends.
This model boasts an impressive R-squared value of 0.933, indicating that the logarithmic time scale explains a significant portion of the variance in Bitcoin's price. For the non-statisticians amongst us; think of the R-squared value as a score that tells us how well our model, like a detective, is at explaining the mystery of Bitcoin’s price changes over time. A score of 0.933 out of 1 is like saying the detective has found clues that explain 93.3% of the mystery (which is rather impressive). The logarithmic scale is like a magnifying glass that helps the detective see the clues better by making the huge leaps in Bitcoin's price easier to compare. So, in very simple terms, the R-squared score tells us that we've got a pretty good summary of the story so far.
Moving on to the star of this little show - the Quantile Regression Model. This is where things get colorful (literally, check out the image below).
Unlike the average trend line of our logarithmic model, quantile regression allows us to see different potential pathways that Bitcoin's price could take, based on historical behavior. We're talking about a range of outcomes from the 1st percentile (pessimistic) to the 99th percentile (optimistic) scenarios. Theoretically, IF the bitcoin price decides to move in patterns generally resembling historical precedents, this method of analysis should be a "robust" way to forecast, while accommodating outliers and the asymmetric volatility that's characteristic of BTC's price movement. Okay, if you just heard a bunch of statistical mumbo-jumbo, this is an ELI5:
This chart paints a picture of what could happen, ranging from "Oh no, my wallet!" to "I'm buying a yacht!", based on BTC doing its usual BTC thing (no guarantees).
The historical accuracy of this method is illuminated when we apply the model to past data, truncating the dataset at various points in time to simulate the model's performance. In the images below, I have indicated where I "limited" the data included in the model. You can either look at the dashed purple line, and/or look at the chart title to see where the data was limited. You can then compare how these models would have performed from that point onward.
These snapshots provide back-testing evidence, showing how the bands would have predicted future prices at different times in Bitcoin's history.
The current price position within the bands based on the current data can tell us about Bitcoin's relative strength or weakness. I will repeat the full quantile regression image here again, the title contains the current price position within the bands.
For instance, if the current price is hovering around the 50th percentile, it's following the median path of historical growth. If it's near the 90th percentile, we're in a relatively bullish phase compared to historical data. As you can see, the price seems to be around the 35th percentile band right now.
So, what can we potentially learn from all this? While past performance is not indicative of future results, this analysis could provide insight in the various ranges the BTC price could potentially move it. It presents a spectrum of probable outcomes, not just a single line of best fit.
Remember, this is a statistical view, devoid of investment advice. Treat these models as tools made by a non-financial expert, using statistics for fun, not crystal balls for fortune-telling.
I'm very curious to hear your thoughts and interpretations! Do you agree/disagree with my approach? Should I have used more crayons?
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