Cryptocurrency exchange rates appear to be correlated with one another, let’s take a look at two popular ones BTC and LTC, and check the correlation coefficient.

The correlation coefficient of random variables X and Y is:
cryptocorrelations_1.png)

Where the covariance, cov(X,Y) is defined as:
cov(X,Y) = E[(X-E[X])(Y-E[Y])]

where E[.] is the expected value, in this case it’s equivalent to the mean.

Hypothesis: The correlation coefficient between BTC/USD and ETH/USD is at least 0.7
(0 is uncorrelated, 1 is completely positively correlated, and -1 is completely negatively correlated).

cryptocorrelations_2.gif

cryptocorrelations_3.gif

cryptocorrelations_4.png

cryptocorrelations_5.gif

cryptocorrelations_6.png

cryptocorrelations_7.png

cryptocorrelations_8.png

cryptocorrelations_9.gif

Now we have joined on “date”, and can compute the correlation between the USD exchange rate for BTC and LTC

cryptocorrelations_10.png

cryptocorrelations_11.png

That is much higher than I expected, that’s almost perfectly correlated.

Created with the Wolfram Language