第3章 ランダムウォーク

In [14]:

import yfinance as yf
import pandas_datareader.data as web
import numpy as np
from statsmodels.tsa.stattools import adfuller
from statsmodels.graphics.tsaplots import plot_acf
from sklearn.metrics import mean_squared_error
import matplotlib.pyplot as plt
import pandas as pd

yf.pdr_override()

import yfinance as yf import pandas_datareader.data as web import numpy as np from statsmodels.tsa.stattools import adfuller from statsmodels.graphics.tsaplots import plot_acf from sklearn.metrics import mean_squared_error import matplotlib.pyplot as plt import pandas as pd yf.pdr_override()

In [6]:

ser_google = web.get_data_yahoo(tickers='GOOGL', start='2020-04-27', end='2021-04-27')['Close']
ser_google.plot()

ser_google = web.get_data_yahoo(tickers='GOOGL', start='2020-04-27', end='2021-04-27')['Close'] ser_google.plot()

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Out[6]:

<Axes: xlabel='Date'>

In [7]:

stationary = np.empty(400)
stationary[0] = 0
non_stationary = np.empty(400)
non_stationary[0] = 10
np.random.seed(42)
steps = np.random.standard_normal(400)

for i in range(1, 400):
    stationary[i] = 0.5 * stationary[i-1] + steps[i]
    non_stationary[i] = non_stationary[i-1] + steps[i]

mean_stationary = [stationary[:i].mean() for i in range(1, 400)]
mean_non_stationary = [non_stationary[:i].mean() for i in range(1, 400)]

var_stationary = [stationary[:i].var() for i in range(1, 400)]
var_non_stationary = [non_stationary[:i].var() for i in range(1, 400)]

fig, axes = plt.subplots(1, 3, figsize=[15, 4])

axes[0].set_xlabel('Timestep')
axes[0].set_ylabel('Value')
axes[0].plot(stationary, label='stationary')
axes[0].plot(non_stationary, label='non-stationary', ls='dashed')
axes[0].legend()

axes[1].set_xlabel('Timestep')
axes[1].set_ylabel('Mean')
axes[1].plot(mean_stationary, label='stationary')
axes[1].plot(mean_non_stationary, label='non-stationary', ls='dashed')
axes[1].legend()

axes[2].set_xlabel('Timestep')
axes[2].set_ylabel('Variance')
axes[2].plot(var_stationary, label='stationary')
axes[2].plot(var_non_stationary, label='non-stationary', ls='dashed')
axes[2].legend()

stationary = np.empty(400) stationary[0] = 0 non_stationary = np.empty(400) non_stationary[0] = 10 np.random.seed(42) steps = np.random.standard_normal(400) for i in range(1, 400): stationary[i] = 0.5 * stationary[i-1] + steps[i] non_stationary[i] = non_stationary[i-1] + steps[i] mean_stationary = [stationary[:i].mean() for i in range(1, 400)] mean_non_stationary = [non_stationary[:i].mean() for i in range(1, 400)] var_stationary = [stationary[:i].var() for i in range(1, 400)] var_non_stationary = [non_stationary[:i].var() for i in range(1, 400)] fig, axes = plt.subplots(1, 3, figsize=[15, 4]) axes[0].set_xlabel('Timestep') axes[0].set_ylabel('Value') axes[0].plot(stationary, label='stationary') axes[0].plot(non_stationary, label='non-stationary', ls='dashed') axes[0].legend() axes[1].set_xlabel('Timestep') axes[1].set_ylabel('Mean') axes[1].plot(mean_stationary, label='stationary') axes[1].plot(mean_non_stationary, label='non-stationary', ls='dashed') axes[1].legend() axes[2].set_xlabel('Timestep') axes[2].set_ylabel('Variance') axes[2].plot(var_stationary, label='stationary') axes[2].plot(var_non_stationary, label='non-stationary', ls='dashed') axes[2].legend()

Out[7]:

<matplotlib.legend.Legend at 0x7fcfcd0d67a0>

In [8]:

np.random.seed(42)
steps = np.random.standard_normal(1000)
steps[0] = 0
random_walk = steps.cumsum()

ADF_result = adfuller(random_walk)
print(f'ADF Statics: {ADF_result[0]:.3f}')
print(f'p-value: {ADF_result[1]:.3f}')

fig, axes = plt.subplots(1, 2, figsize=[12, 4])
axes[0].plot(random_walk)
axes[0].set_xlabel('Timestep')
axes[0].set_ylabel('Value')
plot_acf(random_walk, ax=axes[1], lags=20, auto_ylims=True)
plt.show()

np.random.seed(42) steps = np.random.standard_normal(1000) steps[0] = 0 random_walk = steps.cumsum() ADF_result = adfuller(random_walk) print(f'ADF Statics: {ADF_result[0]:.3f}') print(f'p-value: {ADF_result[1]:.3f}') fig, axes = plt.subplots(1, 2, figsize=[12, 4]) axes[0].plot(random_walk) axes[0].set_xlabel('Timestep') axes[0].set_ylabel('Value') plot_acf(random_walk, ax=axes[1], lags=20, auto_ylims=True) plt.show()

ADF Statics: -0.966
p-value: 0.765

In [9]:

diff_random_walk = np.diff(random_walk)
ADF_result = adfuller(diff_random_walk)
print(f'ADF Statics: {ADF_result[0]:.3f}')
print(f'p-value: {ADF_result[1]:.3f}')

fig, axes = plt.subplots(1, 2, figsize=[12, 4])
axes[0].plot(diff_random_walk)
axes[0].set_xlabel('Timestep')
axes[0].set_ylabel('Value')
plot_acf(diff_random_walk, ax=axes[1], lags=20, auto_ylims=True)
plt.show()

diff_random_walk = np.diff(random_walk) ADF_result = adfuller(diff_random_walk) print(f'ADF Statics: {ADF_result[0]:.3f}') print(f'p-value: {ADF_result[1]:.3f}') fig, axes = plt.subplots(1, 2, figsize=[12, 4]) axes[0].plot(diff_random_walk) axes[0].set_xlabel('Timestep') axes[0].set_ylabel('Value') plot_acf(diff_random_walk, ax=axes[1], lags=20, auto_ylims=True) plt.show()

ADF Statics: -31.789
p-value: 0.000

In [10]:

ADF_google_result = adfuller(ser_google)
print(f'ADF Statics: {ADF_google_result[0]:.3f}')
print(f'p-value: {ADF_google_result[1]:.3f}')

ADF_google_result = adfuller(ser_google) print(f'ADF Statics: {ADF_google_result[0]:.3f}') print(f'p-value: {ADF_google_result[1]:.3f}')

ADF Statics: 0.318
p-value: 0.978

In [11]:

ser_google_diff = ser_google.diff().dropna()
ADF_google_result = adfuller(ser_google_diff)
print(f'ADF Statics: {ADF_google_result[0]:.3f}')
print(f'p-value: {ADF_google_result[1]:.3f}')

plot_acf(ser_google_diff, lags=20, auto_ylims=True)
plt.show()

ser_google_diff = ser_google.diff().dropna() ADF_google_result = adfuller(ser_google_diff) print(f'ADF Statics: {ADF_google_result[0]:.3f}') print(f'p-value: {ADF_google_result[1]:.3f}') plot_acf(ser_google_diff, lags=20, auto_ylims=True) plt.show()

ADF Statics: -5.263
p-value: 0.000

In [15]:

df = pd.DataFrame({'value': random_walk})
train = df[:800]
test = df[800:]

df = pd.DataFrame({'value': random_walk}) train = df[:800] test = df[800:]

In [16]:

test.loc[:, 'pred_mean'] = train.mean().value
test.loc[:, 'pred_last'] = train.iloc[-1].value
drift = (train['value'].iloc[-1] - train['value'].iloc[0]) / (train.index[-1] - train.index[0])
test.loc[:, 'pred_drift'] = np.arange(801, 1001) * drift
test.loc[:, 'pred_shift'] = df['value'].shift()[800:]

plt.xlabel('Timestep')
plt.ylabel('Value')
plt.plot(train.index, train['value'], label='Train')
plt.plot(test.index, test['value'], label='Test')
plt.plot(test.index, test['pred_mean'], ls='dashed', label='Mean')
plt.plot(test.index, test['pred_last'], ls='dashed', label='Last Value')
plt.plot(test.index, test['pred_drift'], ls='dashed', label='Drift')
plt.plot(test.index, test['pred_shift'], ls='dashed', label='Shift')
plt.axvspan(test.index[0], test.index[-1], alpha=0.2, color='gray')

plt.legend()

test.loc[:, 'pred_mean'] = train.mean().value test.loc[:, 'pred_last'] = train.iloc[-1].value drift = (train['value'].iloc[-1] - train['value'].iloc[0]) / (train.index[-1] - train.index[0]) test.loc[:, 'pred_drift'] = np.arange(801, 1001) * drift test.loc[:, 'pred_shift'] = df['value'].shift()[800:] plt.xlabel('Timestep') plt.ylabel('Value') plt.plot(train.index, train['value'], label='Train') plt.plot(test.index, test['value'], label='Test') plt.plot(test.index, test['pred_mean'], ls='dashed', label='Mean') plt.plot(test.index, test['pred_last'], ls='dashed', label='Last Value') plt.plot(test.index, test['pred_drift'], ls='dashed', label='Drift') plt.plot(test.index, test['pred_shift'], ls='dashed', label='Shift') plt.axvspan(test.index[0], test.index[-1], alpha=0.2, color='gray') plt.legend()

/tmp/ipykernel_13890/1854262779.py:1: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  test.loc[:, 'pred_mean'] = train.mean().value
/tmp/ipykernel_13890/1854262779.py:2: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  test.loc[:, 'pred_last'] = train.iloc[-1].value
/tmp/ipykernel_13890/1854262779.py:4: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  test.loc[:, 'pred_drift'] = np.arange(801, 1001) * drift
/tmp/ipykernel_13890/1854262779.py:5: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  test.loc[:, 'pred_shift'] = df['value'].shift()[800:]

Out[16]:

<matplotlib.legend.Legend at 0x7fcfcbc89720>

In [17]:

xs = ['pred_mean', 'pred_last', 'pred_drift', 'pred_shift']
ys = [mean_squared_error(test['value'], test[x]) for x in xs]

plt.bar(xs, ys)
plt.xlabel('Methods')
plt.ylabel('MSE')

xs = ['pred_mean', 'pred_last', 'pred_drift', 'pred_shift'] ys = [mean_squared_error(test['value'], test[x]) for x in xs] plt.bar(xs, ys) plt.xlabel('Methods') plt.ylabel('MSE')

Out[17]:

Text(0, 0.5, 'MSE')

In [ ]: