Python completes the basics of time series analysis

Basic operation methods of Python time series analysis

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Recommended reading

1. Use Python to complete the basics of time series analysis
2. A practical case of SPSS establishing a time series multiplication season model
3. Practical case of building a time series ARIMA model in Python

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Import the required libraries

import pandas as pd
import numpy as np
import datetime as dt

sequentially

• Timestamp
• Fixed period (period)
• Interval
  

Generate time series

• You can specify the start time and period
• H: hour
• D: day
• M: month

# TIMES #2016 Jul 1 7/1/2016 1/7/2016 2016-07-01 2016/07/01
rng = pd.date_range('2016-07-01', periods = 10, freq = '3D')
rng

DatetimeIndex(['2016-07-01', '2016-07-04', '2016-07-07', '2016-07-10',
               '2016-07-13', '2016-07-16', '2016-07-19', '2016-07-22',
               '2016-07-25', '2016-07-28'],
              dtype='datetime64[ns]', freq='3D')

time=pd.Series(np.random.randn(20),
           index=pd.date_range(dt.datetime(2016,1,1),periods=20))
print(time)

2016-01-01   -0.067209
2016-01-02    0.480689
2016-01-03   -0.152052
2016-01-04    0.077139
2016-01-05   -1.775043
2016-01-06   -1.184273
Freq: D, dtype: float64

truncate filter

time.truncate(before='2016-1-10')

2016-01-10   -0.349605
2016-01-11    2.159193
2016-01-12    0.077578
2016-01-13    0.084981
2016-01-14   -0.099995
2016-01-15   -1.327124
2016-01-16    1.352626
Freq: D, dtype: float64

time.truncate(after='2016-1-10')

2016-01-01   -0.067209
2016-01-02    0.480689
2016-01-03   -0.152052
2016-01-04    0.077139
2016-01-05   -1.775043
2016-01-06   -1.184273
2016-01-07   -1.247371
2016-01-08   -0.686737
2016-01-09   -1.787544
2016-01-10   -0.349605
Freq: D, dtype: float64

print(time['2016-01-15'])

-1.3271240245020821

print(time['2016-01-15':'2016-01-20'])

2016-01-15   -1.327124
2016-01-16    1.352626
2016-01-17   -0.075599
2016-01-18    1.026780
2016-01-19   -0.286614
2016-01-20   -0.017546
Freq: D, dtype: float64

data=pd.date_range('2010-01-01','2011-01-01',freq='M')
print(data)

DatetimeIndex(['2010-01-31', '2010-02-28', '2010-03-31', '2010-04-30',
               '2010-05-31', '2010-06-30', '2010-07-31', '2010-08-31',
               '2010-09-30', '2010-10-31', '2010-11-30', '2010-12-31'],
              dtype='datetime64[ns]', freq='M')

Common format

Timestamp

pd.Timestamp('2016-07-10')

Timestamp('2016-07-10 00:00:00')

# 可以指定更多细节
pd.Timestamp('2016-07-10 10')

Timestamp('2016-07-10 10:00:00')

pd.Timestamp('2016-07-10 10:15')

Timestamp('2016-07-10 10:15:00')

# How much detail can you add?

t = pd.Timestamp('2016-07-10 10:15')

Time interval

pd.Period('2016-01')

Period('2016-01', 'M')

pd.Period('2016-01-01')

Period('2016-01-01', 'D')

# TIME OFFSETS
pd.Timedelta('1 day')

Timedelta('1 days 00:00:00')

pd.Period('2016-01-01 10:10') + pd.Timedelta('1 day')

Period('2016-01-02 10:10', 'T')

pd.Timestamp('2016-01-01 10:10') + pd.Timedelta('1 day')

Timestamp('2016-01-02 10:10:00')

pd.Timestamp('2016-01-01 10:10') + pd.Timedelta('15 ns')

Timestamp('2016-01-01 10:10:00.000000015')

p1 = pd.period_range('2016-01-01 10:10', freq = '25H', periods = 10)

p2 = pd.period_range('2016-01-01 10:10', freq = '1D1H', periods = 10)

p1

PeriodIndex(['2016-01-01 10:00', '2016-01-02 11:00', '2016-01-03 12:00',
             '2016-01-04 13:00', '2016-01-05 14:00', '2016-01-06 15:00',
             '2016-01-07 16:00', '2016-01-08 17:00', '2016-01-09 18:00',
             '2016-01-10 19:00'],
            dtype='period[25H]', freq='25H')

p2

PeriodIndex(['2016-01-01 10:00', '2016-01-02 11:00', '2016-01-03 12:00',
             '2016-01-04 13:00', '2016-01-05 14:00', '2016-01-06 15:00',
             '2016-01-07 16:00', '2016-01-08 17:00', '2016-01-09 18:00',
             '2016-01-10 19:00'],
            dtype='period[25H]', freq='25H')

Specify index

rng = pd.date_range('2016 Jul 1', periods = 10, freq = 'D')
rng
pd.Series(range(len(rng)), index = rng)

2016-07-01    0
2016-07-02    1
2016-07-03    2
2016-07-04    3
2016-07-05    4
2016-07-06    5
2016-07-07    6
2016-07-08    7
2016-07-09    8
2016-07-10    9
Freq: D, dtype: int64

periods = [pd.Period('2016-01'), pd.Period('2016-02'), pd.Period('2016-03')]
ts = pd.Series(np.random.randn(len(periods)), index = periods)
ts

2016-01   -0.559086
2016-02   -1.021617
2016-03    0.944657
Freq: M, dtype: float64

type(ts.index)

pandas.core.indexes.period.PeriodIndex

Timestamp and time period can be converted

ts = pd.Series(range(10), pd.date_range('07-10-16 8:00', periods = 10, freq = 'H'))
ts

2016-07-10 08:00:00    0
2016-07-10 09:00:00    1
2016-07-10 10:00:00    2
2016-07-10 11:00:00    3
2016-07-10 12:00:00    4
Freq: H, dtype: int64

ts_period = ts.to_period()
ts_period

2016-07-10 08:00    0
2016-07-10 09:00    1
2016-07-10 10:00    2
2016-07-10 11:00    3
2016-07-10 12:00    4
2016-07-10 13:00    5
2016-07-10 14:00    6
2016-07-10 15:00    7
2016-07-10 16:00    8
2016-07-10 17:00    9
Freq: H, dtype: int64

ts_period['2016-07-10 08:30':'2016-07-10 11:45'] 

2016-07-10 08:00    0
2016-07-10 09:00    1
2016-07-10 10:00    2
2016-07-10 11:00    3
Freq: H, dtype: int64

ts['2016-07-10 08:30':'2016-07-10 11:45'] 

2016-07-10 09:00:00    1
2016-07-10 10:00:00    2
2016-07-10 11:00:00    3
Freq: H, dtype: int64

Data resampling

• Time data is converted from one frequency to another

• Downsampling
• Upsampling

import pandas as pd
import numpy as np
rng = pd.date_range('1/1/2011', periods=90, freq='D')
ts = pd.Series(np.random.randn(len(rng)), index=rng)
ts.head()

2011-01-01   -0.225796
2011-01-02    0.890969
2011-01-03   -0.343222
2011-01-04   -0.884985
2011-01-05    0.859801
Freq: D, dtype: float64

Resample

• In months

ts.resample('M').sum()
ts.resample("M").sum()

2011-01-31   -3.221512
2011-02-28    9.660282
2011-03-31   -0.934169
Freq: M, dtype: float64

• In days

ts.resample('3D').sum()
ts.resample("2D").sum()

2011-01-01    0.665173
2011-01-03   -1.228207
2011-01-05    1.165821
2011-01-07   -2.507237
Freq: 2D, dtype: float64

• Calculate the mean

day3Ts = ts.resample('3D').mean()
day3Ts

2011-01-01    0.107317
2011-01-04    0.093612
2011-01-07   -1.156626
2011-01-10   -0.172981

Freq: 3D, dtype: float64

• resample() resampling and asfreq() frequency conversion

print(day3Ts.resample('D').asfreq())

2011-01-01    0.107317
2011-01-02         NaN
2011-01-03         NaN
2011-01-04    0.093612
2011-01-05         NaN
                ...   
2011-03-25         NaN
2011-03-26    0.804057
2011-03-27         NaN
2011-03-28         NaN
2011-03-29   -0.200729
Freq: D, Length: 88, dtype: float64

print(day3Ts.resample('D'))

DatetimeIndexResampler [freq=<Day>, axis=0, closed=left, label=left, convention=start, base=0]

Interpolation method

Upsampling may have problems, use interpolation methods for control

• ffill Null value takes the previous value
  bfill Null value takes the latter value
  interpolate linear value

day3Ts.resample('D').ffill(2)

2011-01-01    0.107317
2011-01-02    0.107317
2011-01-03    0.107317
2011-01-04    0.093612
2011-01-05    0.093612
                ...   
2011-03-25   -0.045712
2011-03-26    0.804057
2011-03-27    0.804057
2011-03-28    0.804057
2011-03-29   -0.200729
Freq: D, Length: 88, dtype: float64

day3Ts.resample('D').bfill(1)

2011-01-01    0.107317
2011-01-02         NaN
2011-01-03    0.093612
2011-01-04    0.093612
2011-01-05         NaN
                ...   
2011-03-25    0.804057
2011-03-26    0.804057
2011-03-27         NaN
2011-03-28   -0.200729
2011-03-29   -0.200729
Freq: D, Length: 88, dtype: float64

day3Ts.resample('D').interpolate("linear")

2011-01-01    0.107317
2011-01-02    0.102749
2011-01-03    0.098180
2011-01-04    0.093612
2011-01-05   -0.323134
                ...   
2011-03-25    0.520801
2011-03-26    0.804057
2011-03-27    0.469128
2011-03-28    0.134200
2011-03-29   -0.200729
Freq: D, Length: 88, dtype: float64

Recommended reading

1. Use Python to complete the basics of time series analysis
2. A practical case of SPSS establishing a time series multiplication season model
3. Practical case of building a time series ARIMA model in Python

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