"Well, not all victories at once"

"Well, not all victories at once" (Pekhov V. "Under the Sign of the Manticore"), referring to the previous note. It is clear that we need to change the model being tested. Here, a model with a linear trend is used, the third in the "Cointegration" section of Magnus' econometrics book. In this case, the Engle-Granger test results for the BTC and ETH series are as follows:

Test 10pct 5pct 1pct

r≤1 2.11 10.49 12.25 16.26

r=0 17.33 16.85 18.96 23.65

At the 5% significance level, we cannot reject the null hypothesis r≤1 (accepting r=0 does not contradict the hypothesis r≤0, as they are nested hypotheses). The cointegration relationship is:

1⋅BTC−0.9417562⋅ETH+−0.0005700729⋅t

The ADF test gives the following results:

Dickey-Fuller = -6.8882e+14

Lag order = 6

p-value = 0.01

Alternative hypothesis: stationary

This fully corresponds to the theory. Additionally, the spread oscillates around the zero value (striped line), so it can be assumed that the BTC and ETH time series may exhibit similar behavior in the long term.