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Sign in Already have an account? Sign In Now. Go To Topic Listing. Let's take a look at the raw value of closing prices. As you can see, we can sense the trend of each coin's price but a comparison is difficult due to different scales.
While there are several ways to conduct correlation analysis, I am going to use the Pearson correlation coefficient as it is a simple and well-known method. The coefficient tells whether two time series are correlated or not. The value ranges from 1 to 1. A value close to 1 means that two data sets have a positive relationship, whereas a value close to 1, implies a negative relationship.
Since the price data has a trend, first-order differences are used to calculate the coefficient. As a rule of thumb, we say that two variables have a strong positive relationship when their coefficient is 0.
The strong positive relationship indicates that when the price of BTC goes up, so will the price of ETH with a great likelihood. We can conclude that all three coins have a strong positive relationship one to another. The previous correlation was done for whole data.
But if we can determine the correlations on shorter time scales and track that correlation it will offer more insight into the correlation. Let's compute the correlation again with a rolling window.
A rolling window means that sub-datasets of the full data set are used. As you can see, the average Pearson coefficient is "0. The average Pearson coefficient is "0. It is a high number. This is the same result compared to the previous one. Here is a small conclusion. Before moving forward, let me make one thing very clear: correlation does not tell us about the order.
In other words, it does not tell us which one would move first. Knowing correlation is good, but that's not enough. Think about when you are driving with your GPS. If your GPS tells you only the list of turns left or right without when to take those turns, it would be of no use. It is the same with the correlation data. To make the data practical and relevant for investment and portfolio management, we need to add the chronological dimension.
We can supplement that piece of information with differenced time-series data. Differenced time-series data could help us extrapolate chronological information from the data set by telling us the exact relationship between the time series data. In layman's terms, this can tell us more information on which one moves first. But since it has changed. Suppose the differenced data show a pattern, then we can derive a mathematical function from the pattern and utilize that as a tool to manage the portfolio.
Let's check it. We can model a function to understand the relationship between two coins. If the model explains the movement of differenced data, we can use it to decide when to sell or buy, and what to sell or buy. The red line is a fitted model function. It seems to be a good fit. To know how much the fitted function can explain the residual data set, I calculated the r2 score to be "0.
R-squared R2 score is a statistical measure that tells you how well the model fits the data.