Python时间序列分析与实战

• 时间序列分析
• • ARIMA
  • 自回归模型（AR）
  • 自回归模型的限制
  • 移动平均模型（MA）
  • 自回归移动平均模型（ARMA）
  • ARIMA(p，d，q)模型
  • 自相关函数ACF(autocorrelation function)
  • 偏自相关函数(PACF)(partial autocorrelation function)
  • ARIMA(p，d，q)阶数确定：
  • ARIMA建模流程：
• Pandas生成时间序列
• • Dates & Times
  • 时间序列
  • date_range
  • truncate过滤
• Pandas数据重采样
• • 数据重采样
  • 插值方法：
• Pandas滑动窗口
• ARIMA模型实例
• • 下载statsmodels库
  • 建立ARIMA模型
  • 参数选择
  • 用ARIMA模型进行时间序列预测-股票预测
• 使用tsfresh库进行分类任务
• • 安装tsfresh遇到的问题
  • 测试
• 维基百科词条EDA
• 遇到问题解决方案

时间序列分析

ARIMA

平稳性：平稳性就是要求经由样本时间序列所得到的拟合曲线在未来的一段期间内仍能顺着现有的形态“惯性”地延续下去
平稳性要求序列的均值和方差不发生明显变化

严平稳与弱平稳：
严平稳：严平稳表示的分布不随时间的改变而改变。如：白噪声（正态），无论怎么取，都是期望为0，方差为1
弱平稳：期望与相关系数（依赖性）不变未来某时刻的t的值Xt就要依赖于它的过去信息，所以需要依赖性

差分法：时间序列在t与t-1时刻的差值

自回归模型（AR）

描述当前值与历史值之间的关系，用变量自身的历史时间数据对自身进行预测
自回归模型必须满足平稳性的要求
p阶自回归过程的公式定义： y t = μ + ∑ i = 1 p γ i y t − i + ϵ t y_{t}=\mu+\sum_{i=1}^{p} \gamma_{i} y_{t-i}+\epsilon_{t} yt​=μ+∑i=1p​γi​yt−i​+ϵt​
y t y_{t} yt​是当前值 μ \mu μ是常数项 P 是阶数 γ i \gamma_{i} γi​是自相关系数 ϵ t \epsilon_{t} ϵt​是误差

自回归模型的限制

自回归模型是用自身的数据来进行预测
必须具有平稳性
必须具有自相关性，如果自相关系数(φi)小于0.5，则不宜采用
自回归只适用于预测与自身前期相关的现象

移动平均模型（MA）

移动平均模型关注的是自回归模型中的误差项的累加
q阶自回归过程的公式定义： y t = μ + ϵ t + ∑ i = 1 q θ i ϵ t − i y_{t}=\mu+\epsilon_{t}+\sum_{i=1}^{q} \theta_{i} \epsilon_{t-i} yt​=μ+ϵt​+∑i=1q​θi​ϵt−i​
移动平均法能有效地消除预测中的随机波动

自回归移动平均模型（ARMA）

自回归与移动平均的结合
公式定义： y t = μ + ∑ i = 1 p γ i y t − i + ϵ t + ∑ i = 1 q θ i ϵ t − i y_{t}=\mu+\sum_{i=1}^{p} \gamma_{i} y_{t-i}+\epsilon_{t}+\sum_{i=1}^{q} \theta_{i} \epsilon_{t-i} yt​=μ+∑i=1p​γi​yt−i​+ϵt​+∑i=1q​θi​ϵt−i​

ARIMA(p，d，q)模型

全称为差分自回归移动平均模型(Autoregressive Integrated Moving Average Model,简记ARIMA)

AR是自回归， p为自回归项； MA为移动平均，q为移动平均项数，d为时间序列成为平稳时所做的差分次数

原理：将非平稳时间序列转化为平稳时间序列然后将因变量仅对它的滞后值以及随机误差项的现值和滞后值进行回归所建立的模型

自相关函数ACF(autocorrelation function)

有序的随机变量序列与其自身相比较
自相关函数反映了同一序列在不同时序的取值之间的相关性
公式： A C F ( k ) = ρ k = Cov ⁡ ( y t , y t − k ) Var ⁡ ( y t ) A C F(k)=\rho_{k}=\frac{\operatorname{Cov}\left(y_{t}, y_{t-k}\right)}{\operatorname{Var}\left(y_{t}\right)} ACF(k)=ρk​=Var(yt​)Cov(yt​,yt−k​)​
Pk的取值范围为[-1,1]

偏自相关函数(PACF)(partial autocorrelation function)

对于一个平稳AR§模型，求出滞后k自相关系数p(k)时，实际上得到并不是x(t)与x(t-k)之间单纯的相关关系
x(t)同时还会受到中间k-1个随机变量x(t-1)、x(t-2)、……、x(t-k+1)的影响，而这k-1个随机变量又都和x(t-k)具有相关关系，所以自相关系数p(k)里实际掺杂了其他变量对x(t)与x(t-k)的影响
剔除了中间k-1个随机变量x(t-1)、x(t-2)、……、x(t-k+1)的干扰之后x(t-k)对x(t)影响的相关程度。
ACF还包含了其他变量的影响，而偏自相关系数PACF是严格这两个变量之间的相关性

ARIMA(p，d，q)阶数确定：

截尾：落在置信区间内（95%的点都符合该规则）

AR§ 看PACF；MA(q) 看ACF

ARIMA建模流程：

将序列平稳（差分法确定d）；p和q阶数确定：ACF与PACF；ARIMA（p,d,q）

模型选择AIC与BIC: 选择更简单的模型
AIC:赤池信息准则（Akaike Information Criterion，AIC）
A I C = 2 k − 2 ln ⁡ ( L ) A I C=2 k-2 \ln (L) AIC=2k−2ln(L)
BIC:贝叶斯信息准则（Bayesian Information Criterion，BIC）
B I C = k ln ⁡ ( n ) − 2 ln ⁡ ( L ) B I C=k \ln (n)-2 \ln (L) BIC=kln(n)−2ln(L)
k为模型参数个数，n为样本数量，L为似然函数

模型残差检验：ARIMA模型的残差是否是平均值为0且方差为常数的正态分布
QQ图：线性即正态分布

Pandas生成时间序列

Dates & Times

import pandas as pd
import numpy as np

时间序列

• 时间戳（timestamp）
• 固定周期（period）
• 时间间隔（interval）

date_range

• 可以指定开始时间与周期
• H：小时
• D：天
• M：月

# TIMES 
#2016 Jul 1； 7/1/2016； 1/7/2016； 2016-07-01； 2016/07/01
# freq指的是频率，'3D'就是3天
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’)

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

2016-01-01 -0.188009
2016-01-02 -0.368154
2016-01-03 0.192915
2016-01-04 -1.000698
2016-01-05 -0.324694
2016-01-06 0.570503
2016-01-07 0.014892
2016-01-08 1.441954
2016-01-09 0.768429
2016-01-10 -0.421610
2016-01-11 -0.056000
2016-01-12 0.480678
2016-01-13 1.551418
2016-01-14 0.054797
2016-01-15 0.505593
2016-01-16 -1.217634
2016-01-17 -0.243987
2016-01-18 -1.120619
2016-01-19 -0.492803
2016-01-20 -0.506725
Freq: D, dtype: float64

truncate过滤

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

2016-01-10 -0.421610
2016-01-11 -0.056000
2016-01-12 0.480678
2016-01-13 1.551418
2016-01-14 0.054797
2016-01-15 0.505593
2016-01-16 -1.217634
2016-01-17 -0.243987
2016-01-18 -1.120619
2016-01-19 -0.492803
2016-01-20 -0.506725
Freq: D, dtype: float64

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

2016-01-01 -0.188009
2016-01-02 -0.368154
2016-01-03 0.192915
2016-01-04 -1.000698
2016-01-05 -0.324694
2016-01-06 0.570503
2016-01-07 0.014892
2016-01-08 1.441954
2016-01-09 0.768429
2016-01-10 -0.421610
Freq: D, dtype: float64

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

0.5055933447272851

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

2016-01-15 0.505593
2016-01-16 -1.217634
2016-01-17 -0.243987
2016-01-18 -1.120619
2016-01-19 -0.492803
2016-01-20 -0.506725
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’)

#时间戳
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’)

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

# 时间区间
pd.Period('2016-01')

Period(‘2016-01’, ‘M’)

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

Period(‘2016-01-01’, ‘D’)

# TIME OFFSETS
# 时间加减
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]’)

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]’)

# 指定索引
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 0.340616
2016-02 0.255040
2016-03 -1.991041
Freq: M, dtype: float64

type(ts.index)

# 时间戳和时间周期可以转换
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
2016-07-10 13:00:00 5
2016-07-10 14:00:00 6
2016-07-10 15:00:00 7
2016-07-10 16:00:00 8
2016-07-10 17:00:00 9
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

Pandas数据重采样

import pandas as pd
import numpy as np

数据重采样

• 时间数据由一个频率转换到另一个频率
• 降采样
• 升采样

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 1.325061
2011-01-02 -0.007781
2011-01-03 -0.574297
2011-01-04 1.179030
2011-01-05 -1.892891
Freq: D, dtype: float64

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

2011-01-31 7.061535
2011-02-28 -1.360312
2011-03-31 -4.334479
Freq: M, dtype: float64

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

2011-01-01 0.742984
2011-01-04 1.168289
2011-01-07 -2.558146
2011-01-10 -0.596113
2011-01-13 -0.822468
2011-01-16 1.264703
2011-01-19 3.908058
2011-01-22 2.020699
2011-01-25 1.829759
2011-01-28 -0.606650
2011-01-31 1.142033
2011-02-03 1.605801
2011-02-06 -2.059437
2011-02-09 -0.432942
2011-02-12 0.403229
2011-02-15 2.503971
2011-02-18 1.992525
2011-02-21 -1.553652
2011-02-24 -1.669596
2011-02-27 -1.248293
2011-03-02 -5.028106
2011-03-05 -0.501333
2011-03-08 0.694710
2011-03-11 -1.223193
2011-03-14 -1.395738
2011-03-17 -0.689522
2011-03-20 2.783964
2011-03-23 0.465247
2011-03-26 -0.812388
2011-03-29 0.038350
Freq: 3D, dtype: float64

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

2011-01-01 0.247661
2011-01-04 0.389430
2011-01-07 -0.852715
2011-01-10 -0.198704
2011-01-13 -0.274156
2011-01-16 0.421568
2011-01-19 1.302686
2011-01-22 0.673566
2011-01-25 0.609920
2011-01-28 -0.202217
2011-01-31 0.380678
2011-02-03 0.535267
2011-02-06 -0.686479
2011-02-09 -0.144314
2011-02-12 0.134410
2011-02-15 0.834657
2011-02-18 0.664175
2011-02-21 -0.517884
2011-02-24 -0.556532
2011-02-27 -0.416098
2011-03-02 -1.676035
2011-03-05 -0.167111
2011-03-08 0.231570
2011-03-11 -0.407731
2011-03-14 -0.465246
2011-03-17 -0.229841
2011-03-20 0.927988
2011-03-23 0.155082
2011-03-26 -0.270796
2011-03-29 0.012783
Freq: 3D, dtype: float64

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

2011-01-01 0.247661
2011-01-02 NaN
2011-01-03 NaN
2011-01-04 0.389430
2011-01-05 NaN
…
2011-03-25 NaN
2011-03-26 -0.270796
2011-03-27 NaN
2011-03-28 NaN
2011-03-29 0.012783
Freq: D, Length: 88, dtype: float64

插值方法：

• ffill 空值取前面的值
• bfill 空值取后面的值
• interpolate 线性取值

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

2011-01-01 0.247661
2011-01-02 0.247661
2011-01-03 NaN
2011-01-04 0.389430
2011-01-05 0.389430
…
2011-03-25 NaN
2011-03-26 -0.270796
2011-03-27 -0.270796
2011-03-28 NaN
2011-03-29 0.012783
Freq: D, Length: 88, dtype: float64

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

2011-01-01 0.247661
2011-01-02 NaN
2011-01-03 0.389430
2011-01-04 0.389430
2011-01-05 NaN
…
2011-03-25 -0.270796
2011-03-26 -0.270796
2011-03-27 NaN
2011-03-28 0.012783
2011-03-29 0.012783
Freq: D, Length: 88, dtype: float64

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

2011-01-01 0.247661
2011-01-02 0.294917
2011-01-03 0.342174
2011-01-04 0.389430
2011-01-05 -0.024619
…
2011-03-25 -0.128836
2011-03-26 -0.270796
2011-03-27 -0.176269
2011-03-28 -0.081743
2011-03-29 0.012783
Freq: D, Length: 88, dtype: float64

Pandas滑动窗口

%matplotlib inline 
import matplotlib.pylab
import numpy as np
import pandas as pd

df = pd.Series(np.random.randn(600), index = pd.date_range('7/1/2016', freq = 'D', periods = 600))

df.head()

2016-07-01 1.427084
2016-07-02 0.074392
2016-07-03 -0.806538
2016-07-04 0.973909
2016-07-05 -0.196484
Freq: D, dtype: float64

r = df.rolling(window = 10)
r

Rolling [window=10,center=False,axis=0,method=single]

#r.max, r.median, r.std, r.skew, r.sum, r.var
print(r.mean())

2016-07-01 NaN
2016-07-02 NaN
2016-07-03 NaN
2016-07-04 NaN
2016-07-05 NaN
…
2018-02-16 -0.044556
2018-02-17 -0.172443
2018-02-18 -0.247636
2018-02-19 -0.109076
2018-02-20 -0.159144
Freq: D, Length: 600, dtype: float64

import matplotlib.pyplot as plt
%matplotlib inline

plt.figure(figsize=(15, 5))

df.plot(style='r--')
df.rolling(window=10).mean().plot(style='b')

ARIMA模型实例

下载statsmodels库

如果直接pip就会很慢，网络也容易断，让人很烦，建议去这个网站：https://www.lfd.uci.edu/~gohlke/pythonlibs/，搜索statsmodels，下载对应的版本，然后再本地pip下载这个库，不过感觉还是有点慢。

建立ARIMA模型

# http://www.lfd.uci.edu/~gohlke/pythonlibs/  库下载网站
from __future__ import absolute_import, division, print_function
%load_ext autoreload
%autoreload 2
%matplotlib inline
%config InlineBackend.figure_format='retina'



import sys
import os

import pandas as pd
import numpy as np

# # Remote Data Access
# import pandas_datareader.data as web
# import datetime
# # reference: https://pandas-datareader.readthedocs.io/en/latest/remote_data.html

# TSA from Statsmodels
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.tsa.api as smt

# Display and Plotting
import matplotlib.pylab as plt
import seaborn as sns

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)

# seaborn plotting style
sns.set(style='ticks', context='poster')

#Read the data
#美国消费者信心指数
Sentiment = 'data/sentiment.csv'
Sentiment = pd.read_csv(Sentiment, index_col=0, parse_dates=[0])

Sentiment.head()

# Select the series from 2005 - 2016
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']
sentiment_short.head()
print (type(sentiment_short))

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);

参数选择

from __future__ import absolute_import, division, print_function
%load_ext autoreload
%autoreload 2
%matplotlib inline
%config InlineBackend.figure_format='retina'



import sys
import os

import pandas as pd
import numpy as np

# TSA from Statsmodels
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.tsa.api as smt

# Display and Plotting
import matplotlib.pylab as plt
import seaborn as sns

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)

# seaborn plotting style
sns.set(style='ticks', context='poster')

filename_ts = 'data/series1.csv'
ts_df = pd.read_csv(filename_ts, index_col=0, parse_dates=[0])

n_sample = ts_df.shape[0]

print(ts_df.shape)
print(ts_df.head())

(120, 1)
value
2006-06-01 0.21507
2006-07-01 1.14225
2006-08-01 0.08077
2006-09-01 -0.73952
2006-10-01 0.53552

# Create a training sample and testing sample before analyzing the series

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())

(115,)
(5,)
Training Series:
2015-08-01 0.60371
2015-09-01 -1.27372
2015-10-01 -0.93284
2015-11-01 0.08552
2015-12-01 1.20534
Name: value, dtype: float64

Testing Series:
2016-01-01 2.16411
2016-02-01 0.95226
2016-03-01 0.36485
2016-04-01 -2.26487
2016-05-01 -2.38168
Name: value, dtype: float64

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);

#Model Estimation

# Fit the model
arima200 = sm.tsa.SARIMAX(ts_train, order=(2,0,0))
model_results = arima200.fit()

import itertools

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');

# Alternative model selection method, limited to only searching AR and MA parameters

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)

AIC (4, 4)
BIC (4, 4)

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

用ARIMA模型进行时间序列预测-股票预测

%matplotlib inline
import pandas as pd
import pandas_datareader
import datetime
import matplotlib.pylab as plt
import seaborn as sns
from matplotlib.pylab import style
# from statsmodels.tsa.arima_model import ARIMA
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

style.use('ggplot')    
plt.rcParams['font.sans-serif'] = ['SimHei'] 
plt.rcParams['axes.unicode_minus'] = False  

stockFile = 'data/T10yr.csv'
stock = pd.read_csv(stockFile, index_col=0, parse_dates=[0])
stock.head(10)

stock_week = stock['Close'].resample('W-MON').mean()
stock_train = stock_week['2000':'2015']

stock_train.plot(figsize=(12,8))
plt.legend(bbox_to_anchor=(1.25, 0.5))
plt.title("Stock Close")
sns.despine()

stock_diff = stock_train.diff()
stock_diff = stock_diff.dropna()

plt.figure()
plt.plot(stock_diff)
plt.title('一阶差分')
plt.show()

acf = plot_acf(stock_diff, lags=20)
plt.title("ACF")
acf.show()

pacf = plot_pacf(stock_diff, lags=20)
plt.title("PACF")
pacf.show()

import statsmodels.api as sm
model = sm.tsa.arima.ARIMA(stock_train, order=(1, 1, 1),freq='W-MON')

result = model.fit()
#print(result.summary())

pred = result.predict('20140609', '20160701',dynamic=True, typ='levels')
print (pred)

plt.figure(figsize=(6, 6))
plt.xticks(rotation=45)
plt.plot(pred)
plt.plot(stock_train)

使用tsfresh库进行分类任务

安装tsfresh遇到的问题

我是真服了，那个网站没有tsfresh的库，因此只能pip install tsfresh，但是果然出错了，不知道啥原因没安装成功，然后我重新安装，又遇到了一些问题，

1是解决无法安装和卸载“llvmlite”的问题，需要进入 anaconda3→Lib→site-packages ，找到相应的旧版文件，直接删掉就完事。（下面是我删除的）

参考博客https://blog.csdn.net/wasjrong/article/details/108419050

2是报错 ERROR: Could not install packages due to an EnvironmentError: [WinError 5] 拒绝访问，需要在pip install 后面加上 --user + 需要安装的包名，例如

pip install --user tsfresh

有时候真的讨厌直接pip install，真希望库网站能够多收集一些库，这样下载的时候也不会出现这么多问题。

测试

%matplotlib inline
import matplotlib.pylab as plt
import seaborn as sns
from tsfresh.examples.robot_execution_failures import download_robot_execution_failures, load_robot_execution_failures
from tsfresh import extract_features, extract_relevant_features, select_features
from tsfresh.utilities.dataframe_functions import impute
from tsfresh.feature_extraction import ComprehensiveFCParameters
from sklearn.tree import DecisionTreeClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report


#http://tsfresh.readthedocs.io/en/latest/text/quick_start.html 文档介绍

# 这里会报错ConnectionError:
# 参考文章https://blog.csdn.net/The_Time_Runner/article/details/110248835
download_robot_execution_failures()
df, y = load_robot_execution_failures()
df.head()

df[df.id == 3][['time', 'F_x', 'F_y', 'F_z', 'T_x', 'T_y', 'T_z']].plot(x='time', title='Success example (id 3)', figsize=(12, 6));
df[df.id == 20][['time', 'F_x', 'F_y', 'F_z', 'T_x', 'T_y', 'T_z']].plot(x='time', title='Failure example (id 20)', figsize=(12, 6));

extraction_settings = ComprehensiveFCParameters()

#column_id (str) – The name of the id column to group by
#column_sort (str) – The name of the sort column.
X = extract_features(df, 
                     column_id='id', column_sort='time',
                     default_fc_parameters=extraction_settings,
                     impute_function= impute)

X.head()

X.info()

<class ‘pandas.core.frame.DataFrame’>
Int64Index: 88 entries, 1 to 88
Columns: 4734 entries, F_x__variance_larger_than_standard_deviation to T_z__mean_n_absolute_max__number_of_maxima_7
dtypes: float64(4734)
memory usage: 3.2 MB

X_filtered = extract_relevant_features(df, y, 
                                       column_id='id', column_sort='time', 
                                       default_fc_parameters=extraction_settings)

X_filtered.head()

X_filtered.info()

<class ‘pandas.core.frame.DataFrame’>
Int64Index: 88 entries, 1 to 88
Columns: 682 entries, F_x__value_count__value_-1 to T_z__quantile__q_0.9
dtypes: float64(682)
memory usage: 469.6 KB

X_train, X_test, X_filtered_train, X_filtered_test, y_train, y_test = train_test_split(X, X_filtered, y, test_size=.4)

cl = DecisionTreeClassifier()
cl.fit(X_train, y_train)
print(classification_report(y_test, cl.predict(X_test)))

cl.n_features_

4734

cl2 = DecisionTreeClassifier()
cl2.fit(X_filtered_train, y_train)
print(classification_report(y_test, cl2.predict(X_filtered_test)))

cl2.n_features_

682

维基百科词条EDA

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import re
%matplotlib inline

train = pd.read_csv('train_1.csv').fillna(0)
train.head()

train.info()

<class ‘pandas.core.frame.DataFrame’>
RangeIndex: 145063 entries, 0 to 145062
Columns: 551 entries, Page to 2016-12-31
dtypes: float64(550), object(1)
memory usage: 609.8+ MB

for col in train.columns[1:]:
    train[col] = pd.to_numeric(train[col],downcast='integer')
train.head()

train.info()

<class ‘pandas.core.frame.DataFrame’>
RangeIndex: 145063 entries, 0 to 145062
Columns: 551 entries, Page to 2016-12-31
dtypes: int32(550), object(1)
memory usage: 305.5+ MB

def get_language(page):
    res = re.search('[a-z][a-z].wikipedia.org',page)
    #print (res.group()[0:2])
    if res:
        return res.group()[0:2]
    return 'na'

train['lang'] = train.Page.map(get_language)

from collections import Counter

print(Counter(train.lang))

Counter({‘en’: 24108, ‘ja’: 20431, ‘de’: 18547, ‘na’: 17855, ‘fr’: 17802, ‘zh’: 17229, ‘ru’: 15022, ‘es’: 14069})

lang_sets = {}
lang_sets['en'] = train[train.lang=='en'].iloc[:,0:-1]
lang_sets['ja'] = train[train.lang=='ja'].iloc[:,0:-1]
lang_sets['de'] = train[train.lang=='de'].iloc[:,0:-1]
lang_sets['na'] = train[train.lang=='na'].iloc[:,0:-1]
lang_sets['fr'] = train[train.lang=='fr'].iloc[:,0:-1]
lang_sets['zh'] = train[train.lang=='zh'].iloc[:,0:-1]
lang_sets['ru'] = train[train.lang=='ru'].iloc[:,0:-1]
lang_sets['es'] = train[train.lang=='es'].iloc[:,0:-1]

sums = {}
for key in lang_sets:
    sums[key] = lang_sets[key].iloc[:,1:].sum(axis=0) / lang_sets[key].shape[0]

days = [r for r in range(sums['en'].shape[0])]

fig = plt.figure(1,figsize=[10,10])
plt.ylabel('Views per Page')
plt.xlabel('Day')
plt.title('Pages in Different Languages')
labels={'en':'English','ja':'Japanese','de':'German',
        'na':'Media','fr':'French','zh':'Chinese',
        'ru':'Russian','es':'Spanish'
       }

for key in sums:
    plt.plot(days,sums[key],label = labels[key] )
    
plt.legend()
plt.show()

def plot_entry(key,idx):
    data = lang_sets[key].iloc[idx,1:]
    fig = plt.figure(1,figsize=(10,5))
    plt.plot(days,data)
    plt.xlabel('day')
    plt.ylabel('views')
    plt.title(train.iloc[lang_sets[key].index[idx],0])
    
    plt.show()

idx = [1, 5, 10, 50, 100, 250,500, 750,1000,1500,2000,3000,4000,5000]
for i in idx:
    plot_entry('en',i)

npages = 5
top_pages = {}
for key in lang_sets:
    print(key)
    sum_set = pd.DataFrame(lang_sets[key][['Page']])
    sum_set['total'] = lang_sets[key].sum(axis=1)
    sum_set = sum_set.sort_values('total',ascending=False)
    print(sum_set.head(10))
    top_pages[key] = sum_set.index[0]
    print('\n\n')

for key in top_pages:
    fig = plt.figure(1,figsize=(10,5))
    cols = train.columns
    cols = cols[1:-1]
    data = train.loc[top_pages[key],cols]
    plt.plot(days,data)
    plt.xlabel('Days')
    plt.ylabel('Views')
    plt.title(train.loc[top_pages[key],'Page'])
    plt.show()

遇到问题解决方案

1. for train_k, test_k in KFold(len(train_kobe), n_folds=10, shuffle=True):会报很多错
   需要改为for train_k, test_k in KFold(10, shuffle=True).split(train_kobe):

2. NameError: name ‘dt’ is not defined
   没导入包：import datetime as dt

3. AttributeError: ‘DataFrame’ object has no attribute 'as_matrix’
   将corr = X.corr().as_matrix()[0][1]改成corr = X.corr().iloc[:,:].values[0][1]

4. ModuleNotFoundError: No module named 'pandas_datareader’

   一般是没有安装，pip install pandas_datareader

5. model = ARIMA(stock_train, order=(1, 1, 1),freq=‘W-MON’)报错NotImplementedError: statsmodels.tsa.arima_model.ARMA and statsmodels.tsa.arima_model.ARIMA have been removed in favor of statsmodels.tsa.arima.model.ARIMA (note the . between arima and model) and statsmodels.tsa.SARIMAX.
   翻译过来就是由于 ARIMA 包“statsmodels\tsa\arima_model”的弃用。
   所以将这个from statsmodels.tsa.arima_model import ARIMA注释，改为import statsmodels.api as sm，引用时改为model = sm.tsa.arima.ARIMA(stock_train, order=(1, 1, 1),freq=‘W-MON’)
   参考：https://stackoverflow.com/questions/67601211/futurewarning-statsmodels-tsa-arima-model-arma-and-statsmodels-tsa-arima-model

6. download_robot_execution_failures()报错ConnectionError:

   打开https://github.com/MaxBenChrist/robot-failure-dataset/blob/master/lp1.data.txt，在 https://github.com/MaxBenChrist/robot-failure-dataset 手动下载code，将其中lp1.data.txt手动复制到~/anaconda3/lib/python3.8/site-packages/tsfresh/examples/data/robotfailure-mld 并改名为lp1.data。
   参考文章https://blog.csdn.net/The_Time_Runner/article/details/110248835