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Python數據分析與機器學習46-時間序列案例

編輯：Python

文章目錄

一. 消費者信心指數數據分析
- 1.1 數據源介紹
- 1.2 時間序列圖及差分圖
- 1.3 AR圖
- 1.4 散點圖
- 1.5 更直觀的展示
二. 參數選擇
- 2.1 數據源介紹
- 2.2 直觀的圖形化展示
- 2.3 熱力圖
- 2.4 AIC/BIC以及殘差分析正態分布 QQ圖線性
參考：

一. 消費者信心指數數據分析

1.1 數據源介紹

sentiment.csv
美國消費者信心指數

1.2 時間序列圖及差分圖

代碼:

from __future__ import absolute_import, division, print_function
# http://www.lfd.uci.edu/~gohlke/pythonlibs/#xgboost
import sys
import os
import pandas as pd
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.tsa.api as smt
import matplotlib.pylab as plt
import seaborn as sns
# 一些配置項
pd.set_option('display.float_format', lambda x: '%.5f' % x) # pandas
np.set_printoptions(precision=5, suppress=True) # numpy
pd.set_option('display.max_columns', 100)
pd.set_option('display.max_rows', 100)
sns.set(style='ticks', context='poster')
# 美國消費者信心指數
Sentiment = 'E:/file/sentiment.csv'
Sentiment = pd.read_csv(Sentiment, index_col=0, parse_dates=[0])
sentiment_short = Sentiment.loc['2005':'2016']
sentiment_short.plot(figsize=(12,8))
plt.legend(bbox_to_anchor=(1.25, 0.5))
plt.title("Consumer Sentiment")
sns.despine()
sentiment_short['diff_1'] = sentiment_short['UMCSENT'].diff(1)
sentiment_short['diff_2'] = sentiment_short['diff_1'].diff(1)
sentiment_short.plot(subplots=True, figsize=(18, 12))
del sentiment_short['diff_2']
del sentiment_short['diff_1']
fig = plt.figure(figsize=(12,8))
ax1 = fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(sentiment_short, lags=20,ax=ax1)
ax1.xaxis.set_ticks_position('bottom')
fig.tight_layout();
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(sentiment_short, lags=20, ax=ax2)
ax2.xaxis.set_ticks_position('bottom')
fig.tight_layout();
# 散點圖也可以表示
lags=9
ncols=3
nrows=int(np.ceil(lags/ncols))
fig, axes = plt.subplots(ncols=ncols, nrows=nrows, figsize=(4*ncols, 4*nrows))
for ax, lag in zip(axes.flat, np.arange(1,lags+1, 1)):
lag_str = 't-{}'.format(lag)
X = (pd.concat([sentiment_short, sentiment_short.shift(-lag)], axis=1,
keys=['y'] + [lag_str]).dropna())
X.plot(ax=ax, kind='scatter', y='y', x=lag_str);
corr = X.corr().iloc[:,:].values[0][1]
ax.set_ylabel('Original')
ax.set_title('Lag: {} (corr={:.2f})'.format(lag_str, corr));
ax.set_aspect('equal');
sns.despine();
fig.tight_layout();
# 更直觀一些
def tsplot(y, lags=None, title='', figsize=(14, 8)):
fig = plt.figure(figsize=figsize)
layout = (2, 2)
ts_ax = plt.subplot2grid(layout, (0, 0))
hist_ax = plt.subplot2grid(layout, (0, 1))
acf_ax = plt.subplot2grid(layout, (1, 0))
pacf_ax = plt.subplot2grid(layout, (1, 1))
y.plot(ax=ts_ax)
ts_ax.set_title(title)
y.plot(ax=hist_ax, kind='hist', bins=25)
hist_ax.set_title('Histogram')
smt.graphics.plot_acf(y, lags=lags, ax=acf_ax)
smt.graphics.plot_pacf(y, lags=lags, ax=pacf_ax)
[ax.set_xlim(0) for ax in [acf_ax, pacf_ax]]
sns.despine()
plt.tight_layout()
return ts_ax, acf_ax, pacf_ax
tsplot(sentiment_short, title='Consumer Sentiment', lags=36);
plt.show()

測試記錄:

1.3 AR圖

代碼:

from __future__ import absolute_import, division, print_function
# http://www.lfd.uci.edu/~gohlke/pythonlibs/#xgboost
import sys
import os
import pandas as pd
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.tsa.api as smt
import matplotlib.pylab as plt
import seaborn as sns
# 一些配置項
pd.set_option('display.float_format', lambda x: '%.5f' % x) # pandas
np.set_printoptions(precision=5, suppress=True) # numpy
pd.set_option('display.max_columns', 100)
pd.set_option('display.max_rows', 100)
sns.set(style='ticks', context='poster')
# 讀取數據
Sentiment = 'E:/file/sentiment.csv'
Sentiment = pd.read_csv(Sentiment, index_col=0, parse_dates=[0])
sentiment_short = Sentiment.loc['2005':'2016']
# 自相關圖
fig = plt.figure(figsize=(12,8))
ax1 = fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(sentiment_short, lags=20,ax=ax1)
ax1.xaxis.set_ticks_position('bottom')
fig.tight_layout();
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(sentiment_short, lags=20, ax=ax2)
ax2.xaxis.set_ticks_position('bottom')
fig.tight_layout();
plt.show()

測試記錄:

1.4 散點圖

代碼:

from __future__ import absolute_import, division, print_function
# http://www.lfd.uci.edu/~gohlke/pythonlibs/#xgboost
import sys
import os
import pandas as pd
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.tsa.api as smt
import matplotlib.pylab as plt
import seaborn as sns
# 一些配置項
pd.set_option('display.float_format', lambda x: '%.5f' % x) # pandas
np.set_printoptions(precision=5, suppress=True) # numpy
pd.set_option('display.max_columns', 100)
pd.set_option('display.max_rows', 100)
sns.set(style='ticks', context='poster')
# 讀取數據
Sentiment = 'E:/file/sentiment.csv'
Sentiment = pd.read_csv(Sentiment, index_col=0, parse_dates=[0])
sentiment_short = Sentiment.loc['2005':'2016']
# 散點圖也可以表示
lags=9
ncols=3
nrows=int(np.ceil(lags/ncols))
fig, axes = plt.subplots(ncols=ncols, nrows=nrows, figsize=(4*ncols, 4*nrows))
for ax, lag in zip(axes.flat, np.arange(1,lags+1, 1)):
lag_str = 't-{}'.format(lag)
X = (pd.concat([sentiment_short, sentiment_short.shift(-lag)], axis=1,
keys=['y'] + [lag_str]).dropna())
X.plot(ax=ax, kind='scatter', y='y', x=lag_str);
corr = X.corr().iloc[:,:].values[0][1]
ax.set_ylabel('Original')
ax.set_title('Lag: {} (corr={:.2f})'.format(lag_str, corr));
ax.set_aspect('equal');
sns.despine();
fig.tight_layout();
plt.show()

測試記錄:

1.5 更直觀的展示

代碼:

from __future__ import absolute_import, division, print_function
# http://www.lfd.uci.edu/~gohlke/pythonlibs/#xgboost
import sys
import os
import pandas as pd
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.tsa.api as smt
import matplotlib.pylab as plt
import seaborn as sns
# 一些配置項
pd.set_option('display.float_format', lambda x: '%.5f' % x) # pandas
np.set_printoptions(precision=5, suppress=True) # numpy
pd.set_option('display.max_columns', 100)
pd.set_option('display.max_rows', 100)
sns.set(style='ticks', context='poster')
# 讀取數據
Sentiment = 'E:/file/sentiment.csv'
Sentiment = pd.read_csv(Sentiment, index_col=0, parse_dates=[0])
sentiment_short = Sentiment.loc['2005':'2016']
# 更直觀一些
def tsplot(y, lags=None, title='', figsize=(14, 8)):
fig = plt.figure(figsize=figsize)
layout = (2, 2)
ts_ax = plt.subplot2grid(layout, (0, 0))
hist_ax = plt.subplot2grid(layout, (0, 1))
acf_ax = plt.subplot2grid(layout, (1, 0))
pacf_ax = plt.subplot2grid(layout, (1, 1))
y.plot(ax=ts_ax)
ts_ax.set_title(title)
y.plot(ax=hist_ax, kind='hist', bins=25)
hist_ax.set_title('Histogram')
smt.graphics.plot_acf(y, lags=lags, ax=acf_ax)
smt.graphics.plot_pacf(y, lags=lags, ax=pacf_ax)
[ax.set_xlim(0) for ax in [acf_ax, pacf_ax]]
sns.despine()
plt.tight_layout()
return ts_ax, acf_ax, pacf_ax
tsplot(sentiment_short, title='Consumer Sentiment', lags=36);
plt.show()

測試記錄：

二. 參數選擇

2.1 數據源介紹

series1.csv
一個標准的時間序列數據

2.2 直觀的圖形化展示

代碼:

from __future__ import absolute_import, division, print_function
# http://www.lfd.uci.edu/~gohlke/pythonlibs/#xgboost
import sys
import os
import pandas as pd
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.tsa.api as smt
import matplotlib.pylab as plt
import seaborn as sns
# 一些配置項
pd.set_option('display.float_format', lambda x: '%.5f' % x) # pandas
np.set_printoptions(precision=5, suppress=True) # numpy
pd.set_option('display.max_columns', 100)
pd.set_option('display.max_rows', 100)
sns.set(style='ticks', context='poster')
# 美國消費者信心指數
filename_ts = 'E:/file/series1.csv'
ts_df = pd.read_csv(filename_ts, index_col=0, parse_dates=[0])
n_sample = ts_df.shape[0]
# 劃分測試集和訓練集
n_train=int(0.95*n_sample)+1
n_forecast=n_sample-n_train
#ts_df
ts_train = ts_df.iloc[:n_train]['value']
ts_test = ts_df.iloc[n_train:]['value']
#print(ts_train.shape)
#print(ts_test.shape)
#print("Training Series:", "\n", ts_train.tail(), "\n")
#print("Testing Series:", "\n", ts_test.head())
def tsplot(y, lags=None, title='', figsize=(14, 8)):
fig = plt.figure(figsize=figsize)
layout = (2, 2)
ts_ax = plt.subplot2grid(layout, (0, 0))
hist_ax = plt.subplot2grid(layout, (0, 1))
acf_ax = plt.subplot2grid(layout, (1, 0))
pacf_ax = plt.subplot2grid(layout, (1, 1))
y.plot(ax=ts_ax)
ts_ax.set_title(title)
y.plot(ax=hist_ax, kind='hist', bins=25)
hist_ax.set_title('Histogram')
smt.graphics.plot_acf(y, lags=lags, ax=acf_ax)
smt.graphics.plot_pacf(y, lags=lags, ax=pacf_ax)
[ax.set_xlim(0) for ax in [acf_ax, pacf_ax]]
sns.despine()
fig.tight_layout()
return ts_ax, acf_ax, pacf_ax
tsplot(ts_train, title='A Given Training Series', lags=20);
plt.show()

測試記錄:

2.3 熱力圖

代碼:

from __future__ import absolute_import, division, print_function
# http://www.lfd.uci.edu/~gohlke/pythonlibs/#xgboost
import sys
import os
import pandas as pd
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.tsa.api as smt
import matplotlib.pylab as plt
import seaborn as sns
import itertools
# 一些配置項
pd.set_option('display.float_format', lambda x: '%.5f' % x) # pandas
np.set_printoptions(precision=5, suppress=True) # numpy
pd.set_option('display.max_columns', 100)
pd.set_option('display.max_rows', 100)
sns.set(style='ticks', context='poster')
# 美國消費者信心指數
filename_ts = 'E:/file/series1.csv'
ts_df = pd.read_csv(filename_ts, index_col=0, parse_dates=[0])
n_sample = ts_df.shape[0]
# 劃分訓練集和測試集
n_train=int(0.95*n_sample)+1
n_forecast=n_sample-n_train
#ts_df
ts_train = ts_df.iloc[:n_train]['value']
ts_test = ts_df.iloc[n_train:]['value']
# 訓練模型
arima200 = sm.tsa.SARIMAX(ts_train, order=(2,0,0))
model_results = arima200.fit()
# 選擇參數
p_min = 0
d_min = 0
q_min = 0
p_max = 4
d_max = 0
q_max = 4
# Initialize a DataFrame to store the results
results_bic = pd.DataFrame(index=['AR{}'.format(i) for i in range(p_min, p_max + 1)],
columns=['MA{}'.format(i) for i in range(q_min, q_max + 1)])
for p, d, q in itertools.product(range(p_min, p_max + 1),
range(d_min, d_max + 1),
range(q_min, q_max + 1)):
if p == 0 and d == 0 and q == 0:
results_bic.loc['AR{}'.format(p), 'MA{}'.format(q)] = np.nan
continue
try:
model = sm.tsa.SARIMAX(ts_train, order=(p, d, q),
# enforce_stationarity=False,
# enforce_invertibility=False,
)
results = model.fit()
results_bic.loc['AR{}'.format(p), 'MA{}'.format(q)] = results.bic
except:
continue
results_bic = results_bic[results_bic.columns].astype(float)
fig, ax = plt.subplots(figsize=(10, 8))
ax = sns.heatmap(results_bic,
mask=results_bic.isnull(),
ax=ax,
annot=True,
fmt='.2f',
);
ax.set_title('BIC');
plt.show()

測試記錄:

2.4 AIC/BIC以及殘差分析正態分布 QQ圖線性

代碼:

from __future__ import absolute_import, division, print_function
# http://www.lfd.uci.edu/~gohlke/pythonlibs/#xgboost
import sys
import os
import pandas as pd
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.tsa.api as smt
import matplotlib.pylab as plt
import seaborn as sns
import itertools
# 一些配置項
pd.set_option('display.float_format', lambda x: '%.5f' % x) # pandas
np.set_printoptions(precision=5, suppress=True) # numpy
pd.set_option('display.max_columns', 100)
pd.set_option('display.max_rows', 100)
sns.set(style='ticks', context='poster')
# 美國消費者信心指數
filename_ts = 'E:/file/series1.csv'
ts_df = pd.read_csv(filename_ts, index_col=0, parse_dates=[0])
n_sample = ts_df.shape[0]
# 劃分訓練集和測試集
n_train=int(0.95*n_sample)+1
n_forecast=n_sample-n_train
#ts_df
ts_train = ts_df.iloc[:n_train]['value']
ts_test = ts_df.iloc[n_train:]['value']
# 訓練模型
arima200 = sm.tsa.SARIMAX(ts_train, order=(2,0,0))
model_results = arima200.fit()
# AIC 和 BIC
#print(help(sm.tsa.arma_order_select_ic))
train_results = sm.tsa.arma_order_select_ic(ts_train, ic=['aic', 'bic'], trend='n', max_ar=4, max_ma=4)
print('AIC', train_results.aic_min_order)
print('BIC', train_results.bic_min_order)
#殘差分析 正態分布 QQ圖線性
model_results.plot_diagnostics(figsize=(16, 12));
plt.show()

測試記錄: