Python数据分析_第12课：时间序列分析_笔记

绝地灬酷狼 2021-10-30 01:14 668阅读 0赞

### 文章目录 ###

*  时间基本处理
 *  字符串转日期
 *  pands中的时间序列
 *  日期范围、频率与移动
 *  时间序列可视化
 *  时间序列案例分析
 *   *  参数初始化
     *  时序图
     *  自相关图
     *  平稳性检测
     *  差分后的结果
     *  时序图
     *  自相关图
     *  偏自相关图
     *  平稳性检测
     *  白噪声检验
     *  建立ARIMA模型（差分整合移动平均自回归模型）
     *  给出模型报告
     *  预测

GitHub: [https://github.com/RealEmperor/Python-for-Data-Analysis][https_github.com_RealEmperor_Python-for-Data-Analysis]

# 时间基本处理 #

import numpy as np
    import pandas as pd
    from pandas import Series, DataFrame
    import matplotlib.pyplot as plt
    
    %matplotlib inline
    
    pd.options.display.max_rows = 12
    np.set_printoptions(precision=4, suppress=True)
    
    plt.rc('figure', figsize=(12, 4))

from datetime import datetime
    
    now = datetime.now()
    now

datetime.datetime(2019, 8, 19, 10, 30, 15, 980592)

now.year, now.month, now.day

(2019, 8, 19)

delta = datetime(2019, 1, 1) - datetime(2008, 1, 1, 23, 59)
    delta

datetime.timedelta(4017, 60)

delta.days

4017

delta.seconds

from datetime import timedelta
    
    start = datetime(2019, 1, 1)
    start + timedelta(12)

datetime.datetime(2019, 1, 13, 0, 0)

start - 2 * timedelta(12)

datetime.datetime(2018, 12, 8, 0, 0)

# 字符串转日期 #

# 字符串转日期
    stamp = datetime(2019, 1, 31)
    str(stamp)
    stamp.strftime('%Y-%m-%d')

'2019-01-31'

value = '2019-01-31'
    datetime.strptime(value, '%Y-%m-%d')

datetime.datetime(2019, 1, 31, 0, 0)

datestrs = ['8/1/2019', '9/1/2019']
    [datetime.strptime(x, '%m/%d/%Y') for x in datestrs]

[datetime.datetime(2019, 8, 1, 0, 0), datetime.datetime(2019, 9, 1, 0, 0)]

from dateutil.parser import parse
    
    parse('2019-01-31')

datetime.datetime(2019, 1, 31, 0, 0)

parse('Jan 31, 2019 11:15 PM')

datetime.datetime(2019, 1, 31, 23, 15)

parse('12/31/2019', dayfirst=True)

datetime.datetime(2019, 12, 31, 0, 0)

print(datestrs)
    pd.to_datetime(datestrs)

['8/1/2019', '9/1/2019']
    
    
    
    
    
    DatetimeIndex(['2019-08-01', '2019-09-01'], dtype='datetime64[ns]', freq=None)

idx = pd.to_datetime(datestrs + [None])
    idx

DatetimeIndex(['2019-08-01', '2019-09-01', 'NaT'], dtype='datetime64[ns]', freq=None)

idx[2]

NaT

pd.isnull(idx)

array([False, False,  True], dtype=bool)

# pands中的时间序列 #

from datetime import datetime
    
    dates = [datetime(2019, 1, 2), datetime(2019, 1, 5), datetime(2019, 1, 7),
             datetime(2019, 1, 8), datetime(2019, 1, 10), datetime(2019, 1, 12)]
    ts = Series(np.random.randn(6), index=dates)
    ts

2019-01-02    0.172000
    2019-01-05   -0.424536
    2019-01-07   -0.214663
    2019-01-08   -0.645964
    2019-01-10    0.231748
    2019-01-12   -0.053887
    dtype: float64

type(ts)

pandas.core.series.Series

ts.index

DatetimeIndex(['2019-01-02', '2019-01-05', '2019-01-07', '2019-01-08',
                   '2019-01-10', '2019-01-12'],
                  dtype='datetime64[ns]', freq=None)

ts + ts[::2]

2019-01-02    0.344000
    2019-01-05         NaN
    2019-01-07   -0.429325
    2019-01-08         NaN
    2019-01-10    0.463496
    2019-01-12         NaN
    dtype: float64

ts.index.dtype

dtype('<M8[ns]')

stamp = ts.index[0]
    stamp

Timestamp('2019-01-02 00:00:00')

# 索引、选取与子集构造
    stamp = ts.index[2]
    ts[stamp]

-0.21466270986855687

# 月/日/年
    ts['1/10/2019']

0.23174790203572407

# 年月日
    ts['20190110']

0.23174790203572407

longer_ts = Series(np.random.randn(1000),
                       index=pd.date_range('1/1/2000', periods=1000))
    longer_ts

2000-01-01   -0.467172
    2000-01-02    0.330990
    2000-01-03    0.086903
    2000-01-04    0.387555
    2000-01-05    0.023073
    2000-01-06    0.021846
                    ...   
    2002-09-21   -0.617661
    2002-09-22   -0.284098
    2002-09-23   -0.455775
    2002-09-24   -1.401280
    2002-09-25    0.372429
    2002-09-26    1.501288
    Freq: D, Length: 1000, dtype: float64

longer_ts['2001']

2001-01-01   -0.751282
    2001-01-02    0.099974
    2001-01-03   -1.698063
    2001-01-04    0.408136
    2001-01-05    0.827402
    2001-01-06    0.410633
                    ...   
    2001-12-26    0.285561
    2001-12-27   -0.554660
    2001-12-28    0.484308
    2001-12-29   -0.673601
    2001-12-30   -0.797842
    2001-12-31    0.988648
    Freq: D, Length: 365, dtype: float64

longer_ts['2001-05']

2001-05-01   -0.801544
    2001-05-02    0.642389
    2001-05-03    0.164474
    2001-05-04   -1.068225
    2001-05-05    0.651158
    2001-05-06    0.920398
                    ...   
    2001-05-26   -0.284613
    2001-05-27   -0.176875
    2001-05-28    0.318221
    2001-05-29   -1.167438
    2001-05-30    0.560262
    2001-05-31   -0.250117
    Freq: D, Length: 31, dtype: float64

2019-01-02    0.172000
    2019-01-05   -0.424536
    2019-01-07   -0.214663
    2019-01-08   -0.645964
    2019-01-10    0.231748
    2019-01-12   -0.053887
    dtype: float64

ts[datetime(2019, 1, 7):]

2019-01-07   -0.214663
    2019-01-08   -0.645964
    2019-01-10    0.231748
    2019-01-12   -0.053887
    dtype: float64

# 截断 1/9/2019之后的数据
    ts.truncate(after='1/9/2019')

2019-01-02    0.172000
    2019-01-05   -0.424536
    2019-01-07   -0.214663
    2019-01-08   -0.645964
    dtype: float64

# freq='W-WED' 是每周周三
    dates = pd.date_range('1/1/2000', periods=100, freq='W-WED')
    dates

DatetimeIndex(['2000-01-05', '2000-01-12', '2000-01-19', '2000-01-26',
                   '2000-02-02', '2000-02-09', '2000-02-16', '2000-02-23',
                   '2000-03-01', '2000-03-08', '2000-03-15', '2000-03-22',
                   '2000-03-29', '2000-04-05', '2000-04-12', '2000-04-19',
                   '2000-04-26', '2000-05-03', '2000-05-10', '2000-05-17',
                   '2000-05-24', '2000-05-31', '2000-06-07', '2000-06-14',
                   '2000-06-21', '2000-06-28', '2000-07-05', '2000-07-12',
                   '2000-07-19', '2000-07-26', '2000-08-02', '2000-08-09',
                   '2000-08-16', '2000-08-23', '2000-08-30', '2000-09-06',
                   '2000-09-13', '2000-09-20', '2000-09-27', '2000-10-04',
                   '2000-10-11', '2000-10-18', '2000-10-25', '2000-11-01',
                   '2000-11-08', '2000-11-15', '2000-11-22', '2000-11-29',
                   '2000-12-06', '2000-12-13', '2000-12-20', '2000-12-27',
                   '2001-01-03', '2001-01-10', '2001-01-17', '2001-01-24',
                   '2001-01-31', '2001-02-07', '2001-02-14', '2001-02-21',
                   '2001-02-28', '2001-03-07', '2001-03-14', '2001-03-21',
                   '2001-03-28', '2001-04-04', '2001-04-11', '2001-04-18',
                   '2001-04-25', '2001-05-02', '2001-05-09', '2001-05-16',
                   '2001-05-23', '2001-05-30', '2001-06-06', '2001-06-13',
                   '2001-06-20', '2001-06-27', '2001-07-04', '2001-07-11',
                   '2001-07-18', '2001-07-25', '2001-08-01', '2001-08-08',
                   '2001-08-15', '2001-08-22', '2001-08-29', '2001-09-05',
                   '2001-09-12', '2001-09-19', '2001-09-26', '2001-10-03',
                   '2001-10-10', '2001-10-17', '2001-10-24', '2001-10-31',
                   '2001-11-07', '2001-11-14', '2001-11-21', '2001-11-28'],
                  dtype='datetime64[ns]', freq='W-WED')

data\_range函数频率参数值

<table> 
 <thead> 
  <tr> 
   <th>别名</th> 
   <th>描述</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td>B</td> 
   <td>交易日</td> 
  </tr> 
  <tr> 
   <td>C</td> 
   <td>自定义交易日（试验性）</td> 
  </tr> 
  <tr> 
   <td>D</td> 
   <td>日历日</td> 
  </tr> 
  <tr> 
   <td>W</td> 
   <td>每周</td> 
  </tr> 
  <tr> 
   <td>M</td> 
   <td>每月底</td> 
  </tr> 
  <tr> 
   <td>BM</td> 
   <td>每月最后一个交易日</td> 
  </tr> 
  <tr> 
   <td>MS</td> 
   <td>月初</td> 
  </tr> 
  <tr> 
   <td>BMS</td> 
   <td>每月第一个交易日</td> 
  </tr> 
  <tr> 
   <td>Q</td> 
   <td>季度末</td> 
  </tr> 
  <tr> 
   <td>BQ</td> 
   <td>每季度最后一个交易日</td> 
  </tr> 
  <tr> 
   <td>QS</td> 
   <td>季度初</td> 
  </tr> 
  <tr> 
   <td>BQS</td> 
   <td>每季度第一个交易日</td> 
  </tr> 
  <tr> 
   <td>A</td> 
   <td>每年底</td> 
  </tr> 
  <tr> 
   <td>BA</td> 
   <td>每年最后一个交易日</td> 
  </tr> 
  <tr> 
   <td>AS</td> 
   <td>每年初</td> 
  </tr> 
  <tr> 
   <td>BAS</td> 
   <td>每年第一个交易日</td> 
  </tr> 
  <tr> 
   <td>H</td> 
   <td>每小时</td> 
  </tr> 
  <tr> 
   <td>T</td> 
   <td>每分钟</td> 
  </tr> 
  <tr> 
   <td>S</td> 
   <td>每秒</td> 
  </tr> 
  <tr> 
   <td>L</td> 
   <td>毫秒</td> 
  </tr> 
  <tr> 
   <td>U</td> 
   <td>微秒</td> 
  </tr> 
 </tbody> 
</table>

long_df = DataFrame(np.random.randn(100, 4),
                        index=dates,
                        columns=['Colorado', 'Texas', 'New York', 'Ohio'])
    long_df

<table> 
 <thead> 
  <tr> 
   <th></th> 
   <th>Colorado</th> 
   <th>Texas</th> 
   <th>New York</th> 
   <th>Ohio</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <th>2000-01-05</th> 
   <td>0.782948</td> 
   <td>-0.890164</td> 
   <td>-0.028164</td> 
   <td>-0.493703</td> 
  </tr> 
  <tr> 
   <th>2000-01-12</th> 
   <td>-0.944077</td> 
   <td>0.896286</td> 
   <td>0.052383</td> 
   <td>-1.649585</td> 
  </tr> 
  <tr> 
   <th>2000-01-19</th> 
   <td>-3.143461</td> 
   <td>0.583063</td> 
   <td>1.952593</td> 
   <td>-1.034577</td> 
  </tr> 
  <tr> 
   <th>2000-01-26</th> 
   <td>1.002276</td> 
   <td>-0.390626</td> 
   <td>-1.275372</td> 
   <td>-1.293879</td> 
  </tr> 
  <tr> 
   <th>2000-02-02</th> 
   <td>-1.765939</td> 
   <td>-0.326712</td> 
   <td>0.209869</td> 
   <td>-1.566046</td> 
  </tr> 
  <tr> 
   <th>2000-02-09</th> 
   <td>-0.556474</td> 
   <td>0.854375</td> 
   <td>-2.278699</td> 
   <td>1.159897</td> 
  </tr> 
  <tr> 
   <th>...</th> 
   <td>...</td> 
   <td>...</td> 
   <td>...</td> 
   <td>...</td> 
  </tr> 
  <tr> 
   <th>2001-10-24</th> 
   <td>0.133905</td> 
   <td>-0.556946</td> 
   <td>-0.415174</td> 
   <td>-0.075620</td> 
  </tr> 
  <tr> 
   <th>2001-10-31</th> 
   <td>1.481011</td> 
   <td>0.176015</td> 
   <td>1.103585</td> 
   <td>0.221638</td> 
  </tr> 
  <tr> 
   <th>2001-11-07</th> 
   <td>-2.754221</td> 
   <td>0.000293</td> 
   <td>0.428568</td> 
   <td>-0.880257</td> 
  </tr> 
  <tr> 
   <th>2001-11-14</th> 
   <td>1.220620</td> 
   <td>-1.480246</td> 
   <td>2.478029</td> 
   <td>0.578780</td> 
  </tr> 
  <tr> 
   <th>2001-11-21</th> 
   <td>-1.274210</td> 
   <td>0.495101</td> 
   <td>-0.061771</td> 
   <td>-2.701273</td> 
  </tr> 
  <tr> 
   <th>2001-11-28</th> 
   <td>-0.245816</td> 
   <td>-0.784797</td> 
   <td>0.562159</td> 
   <td>0.103696</td> 
  </tr> 
 </tbody> 
</table>

100 rows × 4 columns

long_df.loc['5-2001']

<table> 
 <thead> 
  <tr> 
   <th></th> 
   <th>Colorado</th> 
   <th>Texas</th> 
   <th>New York</th> 
   <th>Ohio</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <th>2001-05-02</th> 
   <td>-0.670840</td> 
   <td>1.181421</td> 
   <td>-2.120271</td> 
   <td>1.729987</td> 
  </tr> 
  <tr> 
   <th>2001-05-09</th> 
   <td>-0.366307</td> 
   <td>0.215251</td> 
   <td>-0.720757</td> 
   <td>-0.473165</td> 
  </tr> 
  <tr> 
   <th>2001-05-16</th> 
   <td>0.676114</td> 
   <td>-0.008594</td> 
   <td>2.091617</td> 
   <td>-0.759926</td> 
  </tr> 
  <tr> 
   <th>2001-05-23</th> 
   <td>0.275334</td> 
   <td>0.030045</td> 
   <td>-0.267771</td> 
   <td>0.056039</td> 
  </tr> 
  <tr> 
   <th>2001-05-30</th> 
   <td>-0.171642</td> 
   <td>-1.135467</td> 
   <td>-0.534345</td> 
   <td>2.050312</td> 
  </tr> 
 </tbody> 
</table>

dates = pd.DatetimeIndex(['1/1/2000', '1/2/2000', '1/2/2000', '1/2/2000',
                              '1/3/2000'])
    dup_ts = Series(np.arange(5), index=dates)
    dup_ts

2000-01-01    0
    2000-01-02    1
    2000-01-02    2
    2000-01-02    3
    2000-01-03    4
    dtype: int32

dup_ts.index.is_unique

False

dup_ts['1/3/2000']

dup_ts['1/2/2000']

2000-01-02    1
    2000-01-02    2
    2000-01-02    3
    dtype: int32

grouped = dup_ts.groupby(level=0)
    grouped.mean()

2000-01-01    0
    2000-01-02    2
    2000-01-03    4
    dtype: int32

grouped.count()

2000-01-01    1
    2000-01-02    3
    2000-01-03    1
    dtype: int64

# 日期范围、频率与移动 #

2019-01-02    0.172000
    2019-01-05   -0.424536
    2019-01-07   -0.214663
    2019-01-08   -0.645964
    2019-01-10    0.231748
    2019-01-12   -0.053887
    dtype: float64

ts.resample('D').mean()

2019-01-02    0.172000
    2019-01-03         NaN
    2019-01-04         NaN
    2019-01-05   -0.424536
    2019-01-06         NaN
    2019-01-07   -0.214663
    2019-01-08   -0.645964
    2019-01-09         NaN
    2019-01-10    0.231748
    2019-01-11         NaN
    2019-01-12   -0.053887
    Freq: D, dtype: float64

index = pd.date_range('4/1/2012', '6/1/2012')
    index

DatetimeIndex(['2012-04-01', '2012-04-02', '2012-04-03', '2012-04-04',
                   '2012-04-05', '2012-04-06', '2012-04-07', '2012-04-08',
                   '2012-04-09', '2012-04-10', '2012-04-11', '2012-04-12',
                   '2012-04-13', '2012-04-14', '2012-04-15', '2012-04-16',
                   '2012-04-17', '2012-04-18', '2012-04-19', '2012-04-20',
                   '2012-04-21', '2012-04-22', '2012-04-23', '2012-04-24',
                   '2012-04-25', '2012-04-26', '2012-04-27', '2012-04-28',
                   '2012-04-29', '2012-04-30', '2012-05-01', '2012-05-02',
                   '2012-05-03', '2012-05-04', '2012-05-05', '2012-05-06',
                   '2012-05-07', '2012-05-08', '2012-05-09', '2012-05-10',
                   '2012-05-11', '2012-05-12', '2012-05-13', '2012-05-14',
                   '2012-05-15', '2012-05-16', '2012-05-17', '2012-05-18',
                   '2012-05-19', '2012-05-20', '2012-05-21', '2012-05-22',
                   '2012-05-23', '2012-05-24', '2012-05-25', '2012-05-26',
                   '2012-05-27', '2012-05-28', '2012-05-29', '2012-05-30',
                   '2012-05-31', '2012-06-01'],
                  dtype='datetime64[ns]', freq='D')

pd.date_range(start='4/1/2012', periods=20)

pd.date_range(end='6/1/2012', periods=20)

DatetimeIndex(['2012-05-13', '2012-05-14', '2012-05-15', '2012-05-16',
                   '2012-05-17', '2012-05-18', '2012-05-19', '2012-05-20',
                   '2012-05-21', '2012-05-22', '2012-05-23', '2012-05-24',
                   '2012-05-25', '2012-05-26', '2012-05-27', '2012-05-28',
                   '2012-05-29', '2012-05-30', '2012-05-31', '2012-06-01'],
                  dtype='datetime64[ns]', freq='D')

# B(business daily) ,M 月的最后一天
    pd.date_range('1/1/2000', '12/1/2000', freq='BM')

DatetimeIndex(['2000-01-31', '2000-02-29', '2000-03-31', '2000-04-28',
                   '2000-05-31', '2000-06-30', '2000-07-31', '2000-08-31',
                   '2000-09-29', '2000-10-31', '2000-11-30'],
                  dtype='datetime64[ns]', freq='BM')

pd.date_range('5/2/2012 12:56:31', periods=5)

DatetimeIndex(['2012-05-02 12:56:31', '2012-05-03 12:56:31',
                   '2012-05-04 12:56:31', '2012-05-05 12:56:31',
                   '2012-05-06 12:56:31'],
                  dtype='datetime64[ns]', freq='D')

pd.date_range('5/2/2012 12:56:31', periods=5, normalize=True)

DatetimeIndex(['2012-05-02', '2012-05-03', '2012-05-04', '2012-05-05',
                   '2012-05-06'],
                  dtype='datetime64[ns]', freq='D')

from pandas.tseries.offsets import Hour, Minute
    
    hour = Hour()
    hour

<Hour>

four_hours = Hour(4)
    four_hours

<4 * Hours>

pd.date_range('1/1/2000', '1/3/2000 23:59', freq='4h')

DatetimeIndex(['2000-01-01 00:00:00', '2000-01-01 04:00:00',
                   '2000-01-01 08:00:00', '2000-01-01 12:00:00',
                   '2000-01-01 16:00:00', '2000-01-01 20:00:00',
                   '2000-01-02 00:00:00', '2000-01-02 04:00:00',
                   '2000-01-02 08:00:00', '2000-01-02 12:00:00',
                   '2000-01-02 16:00:00', '2000-01-02 20:00:00',
                   '2000-01-03 00:00:00', '2000-01-03 04:00:00',
                   '2000-01-03 08:00:00', '2000-01-03 12:00:00',
                   '2000-01-03 16:00:00', '2000-01-03 20:00:00'],
                  dtype='datetime64[ns]', freq='4H')

Hour(2) + Minute(30)

<150 * Minutes>

pd.date_range('1/1/2000', periods=10, freq='1h30min')

DatetimeIndex(['2000-01-01 00:00:00', '2000-01-01 01:30:00',
                   '2000-01-01 03:00:00', '2000-01-01 04:30:00',
                   '2000-01-01 06:00:00', '2000-01-01 07:30:00',
                   '2000-01-01 09:00:00', '2000-01-01 10:30:00',
                   '2000-01-01 12:00:00', '2000-01-01 13:30:00'],
                  dtype='datetime64[ns]', freq='90T')

# freq='WOM-3FRI' 每个月第三个周五
    rng = pd.date_range('1/1/2012', '9/1/2012', freq='WOM-3FRI')
    list(rng)

[Timestamp('2012-01-20 00:00:00', freq='WOM-3FRI'),
     Timestamp('2012-02-17 00:00:00', freq='WOM-3FRI'),
     Timestamp('2012-03-16 00:00:00', freq='WOM-3FRI'),
     Timestamp('2012-04-20 00:00:00', freq='WOM-3FRI'),
     Timestamp('2012-05-18 00:00:00', freq='WOM-3FRI'),
     Timestamp('2012-06-15 00:00:00', freq='WOM-3FRI'),
     Timestamp('2012-07-20 00:00:00', freq='WOM-3FRI'),
     Timestamp('2012-08-17 00:00:00', freq='WOM-3FRI')]

ts = Series(np.random.randn(4),
                index=pd.date_range('1/1/2000', periods=4, freq='M'))
    ts

2000-01-31    0.598434
    2000-02-29    0.105109
    2000-03-31   -0.271298
    2000-04-30    0.060423
    Freq: M, dtype: float64

# 时间不变 ，数据向下错位
    ts.shift(2)

2000-01-31         NaN
    2000-02-29         NaN
    2000-03-31    0.598434
    2000-04-30    0.105109
    Freq: M, dtype: float64

ts.shift(-2)

2000-01-31   -0.271298
    2000-02-29    0.060423
    2000-03-31         NaN
    2000-04-30         NaN
    Freq: M, dtype: float64

# 求增长率
    ts / ts.shift(1) - 1

2000-01-31         NaN
    2000-02-29   -0.824359
    2000-03-31   -3.581107
    2000-04-30   -1.222718
    Freq: M, dtype: float64

# 数据不变，时间大小变化
    ts.shift(2, freq='M')

2000-03-31    0.598434
    2000-04-30    0.105109
    2000-05-31   -0.271298
    2000-06-30    0.060423
    Freq: M, dtype: float64

# 下移3天
    ts.shift(3, freq='D')

2000-02-03    0.598434
    2000-03-03    0.105109
    2000-04-03   -0.271298
    2000-05-03    0.060423
    dtype: float64

# 下移3天
    ts.shift(1, freq='3D')

2000-02-03    0.598434
    2000-03-03    0.105109
    2000-04-03   -0.271298
    2000-05-03    0.060423
    dtype: float64

# 下移90分钟
    ts.shift(1, freq='90T')

2000-01-31 01:30:00    0.598434
    2000-02-29 01:30:00    0.105109
    2000-03-31 01:30:00   -0.271298
    2000-04-30 01:30:00    0.060423
    Freq: M, dtype: float64

from pandas.tseries.offsets import Day, MonthEnd
    
    now = datetime(2019, 8, 18)
    now + 3 * Day()

Timestamp('2019-08-21 00:00:00')

now + MonthEnd()

Timestamp('2019-08-31 00:00:00')

now + MonthEnd(2)

Timestamp('2019-09-30 00:00:00')

offset = MonthEnd()
    offset.rollforward(now)

Timestamp('2019-08-31 00:00:00')

offset.rollback(now)

Timestamp('2019-07-31 00:00:00')

ts = Series(np.random.randn(20),
                index=pd.date_range('1/15/2000', periods=20, freq='4d'))
    ts

2000-01-15   -0.832137
    2000-01-19   -1.423202
    2000-01-23   -1.543921
    2000-01-27   -0.045328
    2000-01-31   -0.073373
    2000-02-04    0.824774
                    ...   
    2000-03-11   -1.036641
    2000-03-15    1.660434
    2000-03-19    0.080479
    2000-03-23    0.269037
    2000-03-27    0.842363
    2000-03-31   -1.380433
    Freq: 4D, Length: 20, dtype: float64

ts.groupby(offset.rollforward).mean()

2000-01-31   -0.783592
    2000-02-29    0.365774
    2000-03-31   -0.038601
    dtype: float64

ts.resample('M').mean()

2000-01-31   -0.783592
    2000-02-29    0.365774
    2000-03-31   -0.038601
    Freq: M, dtype: float64

# 时间序列可视化 #

close_px_all = pd.read_csv('data/stock_px.csv', parse_dates=True, index_col=0)
    close_px_all.head()

close_px = close_px_all[['AAPL', 'MSFT', 'XOM']]
    close_px.head()

close_px = close_px.resample('B').ffill()
    close_px.info()

<class 'pandas.core.frame.DataFrame'>
    DatetimeIndex: 2292 entries, 2003-01-02 to 2011-10-14
    Freq: B
    Data columns (total 3 columns):
    AAPL    2292 non-null float64
    MSFT    2292 non-null float64
    XOM     2292 non-null float64
    dtypes: float64(3)
    memory usage: 71.6 KB

close_px['AAPL'].plot()

<matplotlib.axes._subplots.AxesSubplot at 0x21ccfb53358>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70]

close_px.loc['2009'].plot()

<matplotlib.axes._subplots.AxesSubplot at 0x21ccfb8b198>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 1]

close_px['AAPL'].loc['01-2011':'03-2011'].plot()

<matplotlib.axes._subplots.AxesSubplot at 0x21ccfd112e8>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 2]

appl_q = close_px['AAPL'].resample('Q-DEC').ffill()
    appl_q.loc['2009':].plot()

<matplotlib.axes._subplots.AxesSubplot at 0x21cd01a1d30>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 3]

close_px = close_px.asfreq('B').fillna(method='ffill').ffill()
    close_px.AAPL.plot()

<matplotlib.axes._subplots.AxesSubplot at 0x21cd120b208>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 4]

close_px.AAPL.rolling(250).mean().plot()

<matplotlib.axes._subplots.AxesSubplot at 0x21ccfabe278>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 5]

appl_std250 = close_px.AAPL.rolling(250, min_periods=10).std()
    appl_std250[5:12]

2003-01-09         NaN
    2003-01-10         NaN
    2003-01-13         NaN
    2003-01-14         NaN
    2003-01-15    0.077496
    2003-01-16    0.074760
    2003-01-17    0.112368
    Freq: B, Name: AAPL, dtype: float64

appl_std250.plot()

<matplotlib.axes._subplots.AxesSubplot at 0x21cd124f7f0>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 6]

close_px.rolling(60).mean().plot(logy=True)

<matplotlib.axes._subplots.AxesSubplot at 0x21cd155d0f0>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 7]

fig, axes = plt.subplots(nrows=2, ncols=1, sharex=True, sharey=True,
                             figsize=(12, 7))
    
    aapl_px = close_px.AAPL['2005':'2009']
    
    ma60 = aapl_px.rolling(60, min_periods=50).mean()
    ewma60 = aapl_px.ewm(span=60).mean()
    
    aapl_px.plot(style='k-', ax=axes[0])
    ma60.plot(style='k--', ax=axes[0])
    aapl_px.plot(style='k-', ax=axes[1])
    ewma60.plot(style='k--', ax=axes[1])
    axes[0].set_title('Simple MA')
    axes[1].set_title('Exponentially-weighted MA')

<matplotlib.text.Text at 0x21cd1abd278>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 8]

close_px.head()

# 标普500指数
    spx_px = close_px_all['SPX']
    spx_px.head()

2003-01-02    909.03
    2003-01-03    908.59
    2003-01-06    929.01
    2003-01-07    922.93
    2003-01-08    909.93
    Name: SPX, dtype: float64

spx_rets = spx_px / spx_px.shift(1) - 1
    returns = close_px.pct_change()
    # 苹果股票和标普500指数的相关系数
    corr = returns.AAPL.rolling(125, min_periods=100).corr(spx_rets)
    corr.plot()

<matplotlib.axes._subplots.AxesSubplot at 0x21cd1c03278>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 9]

corr = returns.rolling(125, min_periods=100).corr(spx_rets)
    corr.plot()

<matplotlib.axes._subplots.AxesSubplot at 0x21cd1d34438>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 10]

from scipy.stats import percentileofscore
    
    score_at_2percent = lambda x: percentileofscore(x, 0.02)
    result = returns.AAPL.rolling(250).apply(score_at_2percent)
    result.plot()

<matplotlib.axes._subplots.AxesSubplot at 0x21cd3ac06d8>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 11]

# 时间序列案例分析 #

## 参数初始化 ##

discfile = 'data/arima_data.xls'
    forecastnum = 5
    
    # 读取数据，指定日期列为指标，Pandas自动将“日期”列识别为Datetime格式
    data = pd.read_excel(discfile, index_col=u'日期')
    data = pd.DataFrame(data, dtype=np.float64)
    data

37 rows × 1 columns

## 时序图 ##

# 时序图
    plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
    plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号
    data.plot()

<matplotlib.axes._subplots.AxesSubplot at 0x21cd3d71128>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 12]

## 自相关图 ##

# 自相关图
    from statsmodels.graphics.tsaplots import plot_acf
    
    plot_acf(data).show()

C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\compat\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.
      from pandas.core import datetools
    C:\ProgramData\Anaconda3\lib\site-packages\matplotlib\figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
      "matplotlib is currently using a non-GUI backend, "

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 13]

## 平稳性检测 ##

# 平稳性检测
    from statsmodels.tsa.stattools import adfuller as ADF
    
    ADF(data[u'销量'])
    # 返回值依次为adf、pvalue、usedlag、nobs、critical values、icbest、regresults、resstore

(1.8137710150945274,
     0.99837594215142644,
     10,
     26,
     {'1%': -3.7112123008648155,
      '10%': -2.6300945562130176,
      '5%': -2.9812468047337282},
     299.46989866024177)

pvalue=0.99837594215142644，足够大，不能拒绝原假设（数据非平稳），所以数据是非平稳的。

下面尝试做一下差分：

## 差分后的结果 ##

# 差分后的结果
    D_data = data.diff().dropna()
    D_data.columns = [u'销量差分']
    D_data

36 rows × 1 columns

## 时序图 ##

D_data.plot()  # 时序图

<matplotlib.axes._subplots.AxesSubplot at 0x21cd2fce6d8>

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 14]

## 自相关图 ##

plot_acf(D_data).show()  # 自相关图

C:\ProgramData\Anaconda3\lib\site-packages\matplotlib\figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
      "matplotlib is currently using a non-GUI backend, "

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 15]

## 偏自相关图 ##

from statsmodels.graphics.tsaplots import plot_pacf
    
    plot_pacf(D_data).show()  # 偏自相关图

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 16]

## 平稳性检测 ##

ADF(D_data[u'销量差分'])  # 平稳性检测

(-3.1560562366723537,
     0.022673435440048798,
     0,
     35,
     {'1%': -3.6327426647230316,
      '10%': -2.6130173469387756,
      '5%': -2.9485102040816327},
     287.59090907803341)

pvalue=0.022673435440048798，足够小，能拒绝原假设（数据非平稳），可以认为数据是平稳的。继续向下检验：

## 白噪声检验 ##

# 白噪声检验
    from statsmodels.stats.diagnostic import acorr_ljungbox
    
    acorr_ljungbox(D_data, lags=1)  # 返回统计量和p值

(array([ 11.304]), array([ 0.0008]))

pvalue=0.0008，足够小，可以认为数据不是白噪声，继续：

## 建立ARIMA模型（差分整合移动平均自回归模型） ##

from statsmodels.tsa.arima_model import ARIMA
    
    # 定阶
    pmax = int(len(D_data) / 10)  # 一般阶数不超过length/10
    qmax = int(len(D_data) / 10)  # 一般阶数不超过length/10
    bic_matrix = []  # bic矩阵
    for p in range(pmax + 1):
        tmp = []
        for q in range(qmax + 1):
            try:  # 存在部分报错，所以用try来跳过报错。
                tmp.append(ARIMA(data, (p, 1, q)).fit().bic)
            except:
                tmp.append(None)
        bic_matrix.append(tmp)

bic_matrix = pd.DataFrame(bic_matrix)  # 从中可以找出最小值
    bic_matrix

p, q = bic_matrix.stack().idxmin()  # 先用stack展平，然后用idxmin找出最小值位置。
    print(u'BIC最小的p值和q值为：%s、%s' % (p, q))

BIC最小的p值和q值为：0、1

model = ARIMA(data, (0, 1, 1)).fit()  # 建立ARIMA(0, 1, 1)模型

## 给出模型报告 ##

model.summary()  # 给出一份模型报告

<table>  ARIMA Model Results  
 <tbody> 
  <tr> 
   <th>Dep. Variable:</th> 
   <td>D.销量</td> 
   <th>No. Observations:</th> 
   <td>36</td> 
  </tr> 
  <tr> 
   <th>Model:</th> 
   <td>ARIMA(0, 1, 1)</td> 
   <th>Log Likelihood</th> 
   <td>-205.880</td> 
  </tr> 
  <tr> 
   <th>Method:</th> 
   <td>css-mle</td> 
   <th>S.D. of innovations</th> 
   <td>73.086</td> 
  </tr> 
  <tr> 
   <th>Date:</th> 
   <td>Mon, 19 Aug 2019</td> 
   <th>AIC</th> 
   <td>417.760</td> 
  </tr> 
  <tr> 
   <th>Time:</th> 
   <td>10:31:54</td> 
   <th>BIC</th> 
   <td>422.510</td> 
  </tr> 
  <tr> 
   <th>Sample:</th> 
   <td>01-02-2015</td> 
   <th>HQIC</th> 
   <td>419.418</td> 
  </tr> 
  <tr> 
   <th></th> 
   <td>- 02-06-2015</td> 
   <th></th> 
   <td></td> 
  </tr> 
 </tbody> 
</table>

<table> 
 <tbody> 
  <tr> 
   <td></td> 
   <th>coef</th> 
   <th>std err</th> 
   <th>z</th> 
   <th>P&gt;|z|</th> 
   <th>[0.025</th> 
   <th>0.975]</th> 
  </tr> 
  <tr> 
   <th>const</th> 
   <td>49.9564</td> 
   <td>20.139</td> 
   <td>2.481</td> 
   <td>0.018</td> 
   <td>10.485</td> 
   <td>89.428</td> 
  </tr> 
  <tr> 
   <th>ma.L1.D.销量</th> 
   <td>0.6710</td> 
   <td>0.165</td> 
   <td>4.071</td> 
   <td>0.000</td> 
   <td>0.348</td> 
   <td>0.994</td> 
  </tr> 
 </tbody> 
</table>

<table>  Roots  
 <tbody> 
  <tr> 
   <td></td> 
   <th>Real</th> 
   <th>Imaginary</th> 
   <th>Modulus</th> 
   <th>Frequency</th> 
  </tr> 
  <tr> 
   <th>MA.1</th> 
   <td>-1.4902</td> 
   <td>+0.0000j</td> 
   <td>1.4902</td> 
   <td>0.5000</td> 
  </tr> 
 </tbody> 
</table>

## 预测 ##

model.forecast(5)  # 作为期5天的预测，返回预测结果、标准误差、置信区间。

(array([ 4873.9667,  4923.9232,  4973.8796,  5023.836 ,  5073.7925]),
     array([  73.0857,  142.3268,  187.5428,  223.8028,  254.957 ]),
     array([[ 4730.7213,  5017.2122],
            [ 4644.9678,  5202.8786],
            [ 4606.3024,  5341.4568],
            [ 4585.1906,  5462.4815],
            [ 4574.0858,  5573.4991]]))

参考资料：炼数成金Python数据分析课程

[https_github.com_RealEmperor_Python-for-Data-Analysis]: https://github.com/RealEmperor/Python-for-Data-Analysis
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