analysis/random_walk.py at main · doubletrends/analysis · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
# -*- coding: utf-8 -*-
"""
@author: chengmarc
@github: https://github.com/chengmarc

"""
import os
script_path = os.path.dirname(os.path.realpath(__file__))
os.chdir(script_path)

import numpy as np
import scipy.stats as stats
import matplotlib.pyplot as plt
plt.style.use('seaborn-v0_8-darkgrid')

from tqdm import tqdm
import warnings
warnings.filterwarnings("ignore")


# %%
from datahelper import cmc_get
df = cmc_get('btc', cutoff='2014-09-22')


# %% Histogram for observations
observations = df['pct_change'].tolist()[1:]

print("Mean:", np.mean(observations))
print("Standard Deviation:", np.std(observations))

plt.figure(figsize=(8, 8))
plt.hist(observations, bins=60, range=(0.7, 1.3), edgecolor='black')
plt.title('Histogram of Observed Daily Returns')
plt.xlabel('Daily Return Percentage %')
plt.ylabel('Frequency')
plt.show()


# %% Fit distribution for observations


def fit_dist(rv_list):

    distributions = [stats.norm, stats.cauchy, stats.t, stats.f,
                     stats.alpha, stats.beta, stats.gamma,
                     stats.chi, stats.chi2]

    best_fit = None
    best_params = None
    best_ks_stat = np.inf

    for distribution in distributions:

        params = distribution.fit(rv_list)
        ks_stat, _ = stats.kstest(rv_list, distribution.cdf, args=params)
        # Perform the Kolmogorov-Smirnov test

        if ks_stat < best_ks_stat:
            best_fit = distribution
            best_params = params
            best_ks_stat = ks_stat

    print("Best fit distribution:", best_fit.name)
    print("Best fit parameters:", best_params)
    print("Kolmogorov-Smirnov statistic:", best_ks_stat)

    return best_fit, best_params


dist, params = fit_dist(observations)


# %% Histogram for fitted distribution
plt.figure(figsize=(8, 8))
plt.hist(dist.rvs(*params, size=10000), bins=60, range=(0.7, 1.3), edgecolor='black')
plt.title('Histogram of Simulated Daily Returns')
plt.xlabel('Daily Return Percentage %')
plt.ylabel('Frequency')
plt.show()


# %% Function for simulation


def simulate_market(dist, params, starting_price, depth):

    price = starting_price
    simulations = [starting_price]
    for i in range(depth):
        change = -1
        while change < 0 or change > 1.5:
            change = dist.rvs(*params)
        price = price * change
        simulations.append(price)

    return simulations


# %% Run simulation

historical_data = df['PriceUSD'].to_list()[-365*4:-1]  # Last 4 years of data
simulated_data = simulate_market(dist, params, df['PriceUSD'].to_list()[-1], 365*2)


plt.figure(figsize=(12, 8))

plt.plot(historical_data, label='Historical Data', color='blue')
plt.plot(range(len(historical_data), len(historical_data) + len(simulated_data)),
         simulated_data, label='Simulated Data', color='red')
plt.title('Simulated XRP Price Using Markov Process')
plt.xlabel('Days Past')
plt.ylabel('Price (USD)')
plt.legend() or plt.show()


# %% Simulate 100 times
simulations = []
plt.figure(figsize=(15, 5))
for i in tqdm(range(100)):
    simulations.append(simulate_market(dist, params, df['PriceUSD'].to_list()[-1], 365*2))

for series in simulations:
    plt.plot(series, color='black', alpha=0.1)

plt.title('Multiple Series Plot of XRP Price Simulation')
plt.xlabel('Days Past')
plt.ylabel('Price (USD)')
plt.ylim(0, 600000)
plt.show()