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Python数据分析与机器学习46-时间序列案例

Python数据分析与机器学习46-时间序列案例

作者: 只是甲 | 来源:发表于2022-08-04 09:42 被阅读0次

一. 消费者信心指数数据分析

1.1 数据源介绍

sentiment.csv
美国消费者信心指数

image.png

1.2 时间序列图及差分图

代码:

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

# 一些配置项
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')

# 美国消费者信心指数
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();


# 散点图也可以表示

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();


# 更直观一些
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()

测试记录:

image.png
image.png

1.3 AR图

代码:

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

# 一些配置项
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')

# 读取数据
Sentiment = 'E:/file/sentiment.csv'
Sentiment = pd.read_csv(Sentiment, index_col=0, parse_dates=[0])

sentiment_short = Sentiment.loc['2005':'2016']

# 自相关图
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()

测试记录:

image.png

1.4 散点图

代码:

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

# 一些配置项
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')

# 读取数据
Sentiment = 'E:/file/sentiment.csv'
Sentiment = pd.read_csv(Sentiment, index_col=0, parse_dates=[0])

sentiment_short = Sentiment.loc['2005':'2016']

# 散点图也可以表示
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()

测试记录:

image.png

1.5 更直观的展示

代码:

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

# 一些配置项
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')

# 读取数据
Sentiment = 'E:/file/sentiment.csv'
Sentiment = pd.read_csv(Sentiment, index_col=0, parse_dates=[0])

sentiment_short = Sentiment.loc['2005':'2016']

# 更直观一些
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()

测试记录：

image.png

二. 参数选择

2.1 数据源介绍

series1.csv
一个标准的时间序列数据

image.png

2.2 直观的图形化展示

代码:

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

# 一些配置项
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')

# 美国消费者信心指数
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]

# 划分测试集和训练集
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()

测试记录:

image.png

2.3 热力图

代码:

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

# 一些配置项
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')

# 美国消费者信心指数
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]

# 划分训练集和测试集
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']

# 训练模型
arima200 = sm.tsa.SARIMAX(ts_train, order=(2,0,0))
model_results = arima200.fit()

# 选择参数
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()

测试记录:

image.png

2.4 AIC/BIC以及残差分析 正态分布 QQ图线性

代码:

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

# 一些配置项
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')

# 美国消费者信心指数
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]

# 划分训练集和测试集
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']

# 训练模型
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)

#残差分析 正态分布 QQ图线性
model_results.plot_diagnostics(figsize=(16, 12));

plt.show()

测试记录:

AIC (3, 3)
BIC (1, 1)
image.png

参考：

  1. https://study.163.com/course/introduction.htm?courseId=1003590004#/courseDetail?tab=1

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