3 min read

Random Walk Examples in Python

2019/02/19 
library(reticulate)
## Warning: package 'reticulate' was built under R version 3.5.2

Random Walk Examples in Python

import numpy as np
import matplotlib.pyplot as plt
plt.rc('figure', figsize=(10, 6))
import seaborn as sns
import pandas as pd
np.random.seed(12345)
nwalks = 5000
nsteps = 1000
draws = np.random.randint(0, 2, size=(nwalks, nsteps)) # 0 or 1
steps = np.where(draws > 0, 1, -1)
walks = steps.cumsum(1)
walks
array([[  1,   0,  -1, ...,  -6,  -7,  -6],
       [  1,   0,   1, ...,  46,  45,  46],
       [ -1,  -2,  -3, ..., -46, -47, -48],
       ...,
       [ -1,   0,  -1, ...,   0,   1,   0],
       [  1,   0,   1, ..., 104, 105, 104],
       [  1,   2,   3, ...,  14,  15,  16]], dtype=int32)
walks.shape
(5000, 1000)
hits30 = (np.abs(walks) >= 30).any(1)
hits30
hits30.sum() # Number that hit 30 or -30
3352
crossing_times = (np.abs(walks[hits30]) >= 30).argmax(1)
crossing_times.mean()
502.1700477326969
steps = np.random.normal(loc=0, scale=0.25,
                         size=(nwalks, nsteps))
steps.shape
(5000, 1000)
plt.figure()
plt.plot(walks[0]);
png1

png1

df = pd.DataFrame(walks.T); df.head()
0 1 2 3 4 5 6 7 8 9 … 4990 4991 4992 4993 4994 4995 4996 4997 4998 4999
0 1 1 -1 -1 1 1 1 -1 -1 -1 … 1 1 1 1 1 -1 -1 -1 1 1
1 0 0 -2 0 2 0 2 0 0 0 … 0 0 2 2 0 -2 0 0 0 2
2 -1 1 -3 1 3 -1 1 1 1 1 … -1 -1 3 1 1 -1 -1 -1 1 3
3 0 0 -4 0 4 -2 2 0 0 0 … 0 0 4 2 0 0 0 -2 0 4
4 1 1 -3 -1 5 -3 1 -1 -1 -1 … -1 -1 5 1 -1 1 1 -3 1 5

5 rows × 5000 columns 

plt.figure()
plt.plot(df[0]);
df.shape

(5000, 1000)

test = df.iloc[:, :100]
test.reset_index(level=0, inplace=True); test.head()
index 0 1 2 3 4 5 6 7 8 … 90 91 92 93 94 95 96 97 98 99
0 0 1 1 -1 -1 1 1 1 -1 -1 … 1 -1 -1 1 1 1 1 -1 -1 1
1 1 0 0 -2 0 2 0 2 0 0 … 0 -2 0 0 0 0 0 -2 -2 2
2 2 -1 1 -3 1 3 -1 1 1 1 … -1 -3 1 -1 1 1 -1 -1 -1 1
3 3 0 0 -4 0 4 -2 2 0 0 … -2 -2 0 -2 2 0 0 -2 -2 2
4 4 1 1 -3 -1 5 -3 1 -1 -1 … -3 -1 1 -1 3 -1 1 -1 -1 3

5 rows × 101 columns 

test2 = pd.melt(test, id_vars= ['index'])
test2['variable'] = test2['variable'].astype('category')
sns.lineplot(x = 'index', y= 'value',  hue= 'variable', data = test2, legend = False, palette = "Blues");
png2

png2

Histograms

test2[test2.variable == 999]
index variable value 
sns.distplot(test2[test2['index'] == 999].value);
png3

png3