import numpy as np
import scipy
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns
import json
from datetime import timedelta

You can find and save yourself the data thanks to the cryptocompare API. Here, I select the pair BTC/USD (first link) and a daily aggregate (&aggregate=1&e=CCCAGG). I do the same for the ETH/USD pair.

data_BTC = []
with open('BTCUSD.json') as f:
    for line in f:
        data_BTC.append(json.loads(line))
        
data_ETH = []
with open('ETHUSD.json') as f:
    for line in f:
        data_ETH.append(json.loads(line))
        
histo_BTC = pd.DataFrame(data_BTC)
histo_ETH = pd.DataFrame(data_ETH)

histo_ETH['time'] = pd.to_datetime(histo_ETH['time'],unit='s')
histo_BTC['time'] = pd.to_datetime(histo_BTC['time'],unit='s')

histo_ETH.index = histo_ETH['time']
histo_BTC.index = histo_BTC['time']

histo_ETH.tail()
close high low open time volumefrom volumeto
time
2017-08-18 292.62 306.52 287.17 300.30 2017-08-18 523133.90 1.553331e+08
2017-08-19 293.02 298.79 283.65 292.62 2017-08-19 458296.55 1.333319e+08
2017-08-20 298.20 298.78 288.48 293.02 2017-08-20 293661.68 8.621471e+07
2017-08-21 321.85 345.44 294.93 298.20 2017-08-21 1147950.71 3.713201e+08
2017-08-22 315.09 329.39 293.09 321.85 2017-08-22 728103.98 2.256794e+08

We compute the log returns from the prices:

returns_BTC = pd.DataFrame(np.diff(np.log(histo_BTC['close'].get_values()),axis=0))
returns_BTC.index = histo_BTC.index[1:]
returns_BTC.columns = ['returns']

returns_ETH = pd.DataFrame(np.diff(np.log(histo_ETH['close'].get_values()),axis=0))
returns_ETH.index = histo_ETH.index[1:]
returns_ETH.columns = ['returns']

plt.figure(figsize=(20,10))
plt.plot(returns_BTC)
plt.plot(returns_ETH)
plt.show()

Then, we are going to compute the correlation on a rolling window of 60 consecutive days:

start_date = returns_BTC.index[0]
window_length = timedelta(days=60)
step_length = timedelta(days=1)

correls = []
start_window = start_date
while start_window + window_length <= histo_BTC.index[-1]:
    end_window = start_window + window_length
    
    window_returns_BTC = returns_BTC.loc[start_window:end_window]
    window_returns_ETH = returns_ETH.loc[start_window:end_window]
    
    correl = np.corrcoef(window_returns_BTC.values.flatten(),
                         window_returns_ETH.values.flatten(),
                         "spearman")[0,1]
    correls.append(correl)
    start_window += step_length
    
correl_df = pd.DataFrame(correls,index=returns_BTC.loc[start_date+window_length:].index,columns=['corr'])

plt.figure(figsize=(25,10))
ax = plt.gca()
ax2 = ax.twinx()
plt.axis('normal')
ax.plot(histo_ETH['close'])
ax.plot(histo_BTC['close'])
ax2.plot(correl_df,color='red')
ax.set_ylabel("crypto rates",fontsize=14,color='blue')
ax2.set_ylabel("correlation",fontsize=14,color='blue')
ax.grid(True)
plt.title("ETH/USD and BTC/USD rates and their correlation", fontsize=20,color='black')
ax.set_xlabel('time', fontsize=14, color='b')
ax.legend(['ETH/USD','BTC/USD'],loc='best')
ax2.legend(['correl(BTC,ETH)'],loc='upper right')
plt.show()

Here is the result:

Correlation between the two pairs is nearly at an all time high!