In [1]:

    

import warnings
warnings.filterwarnings('ignore')
import os
import pandas as pd

from plotly import __version__
print(__version__) # need 1.9.0 or greater
from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot
from plotly import graph_objs as go
import requests
import pandas as pd

init_notebook_mode(connected = True)

def plotly_df(df, title = ''):
    data = []
    
    for column in df.columns:
        trace = go.Scatter(
            x = df.index,
            y = df[column],
            mode = 'lines',
            name = column
        )
        data.append(trace)
    
    layout = dict(title = title)
    fig = dict(data = data, layout = layout)
    iplot(fig, show_link=False)
    
%matplotlib inline
import matplotlib.pyplot as plt
from scipy import stats
import statsmodels.api as sm


    

    




1.12.9






    

In [2]:

    

habr_df = pd.read_csv('../../data/howpop_train.csv')


    

In [3]:

    

habr_df['published'] = pd.to_datetime(habr_df.published)
habr_df = habr_df[['published', 'url']]
habr_df = habr_df.drop_duplicates()


    

In [4]:

    

aggr_habr_df = habr_df.groupby('published')[['url']].count()
aggr_habr_df.columns = ['posts']


    

In [5]:

    

aggr_habr_df = aggr_habr_df.resample('D').apply(sum)
plotly_df(aggr_habr_df.resample('W').apply(sum), 
          title = 'Опубликованные посты на Хабрахабре')


    

In [6]:

    

# pip install pystan
# pip install fbprophet
from fbprophet import Prophet


    

In [7]:

    

predictions = 30

df = aggr_habr_df.reset_index()
df.columns = ['ds', 'y']
df.tail()


    

    
Out[7]:






  

    

      

      
ds
      
y
    
  
  

    

      
3222
      
2016-10-27
      
58.0
    
    

      
3223
      
2016-10-28
      
53.0
    
    

      
3224
      
2016-10-29
      
14.0
    
    

      
3225
      
2016-10-30
      
27.0
    
    

      
3226
      
2016-10-31
      
80.0
    
  

In [8]:

    

train_df = df[:-predictions]


    

In [9]:

    

m = Prophet()
m.fit(train_df)


    

    
Out[9]:





<fbprophet.forecaster.Prophet at 0x119875080>

In [10]:

    

future = m.make_future_dataframe(periods=30)
future.tail()


    

    
Out[10]:






  

    

      

      
ds
    
  
  

    

      
3221
      
2016-10-27
    
    

      
3222
      
2016-10-28
    
    

      
3223
      
2016-10-29
    
    

      
3224
      
2016-10-30
    
    

      
3225
      
2016-10-31
    
  

In [11]:

    

forecast = m.predict(future)
forecast.tail()


    

    
Out[11]:






  

    

      

      
ds
      
t
      
trend
      
seasonal_lower
      
seasonal_upper
      
trend_lower
      
trend_upper
      
yhat_lower
      
yhat_upper
      
weekly
      
weekly_lower
      
weekly_upper
      
yearly
      
yearly_lower
      
yearly_upper
      
seasonal
      
yhat
    
  
  

    

      
3221
      
2016-10-27
      
1.008135
      
56.608968
      
10.722472
      
10.722472
      
56.608968
      
56.608968
      
53.600279
      
81.818657
      
8.474826
      
8.474826
      
8.474826
      
2.247646
      
2.247646
      
2.247646
      
10.722472
      
67.331440
    
    

      
3222
      
2016-10-28
      
1.008448
      
56.604998
      
6.923172
      
6.923172
      
56.604998
      
56.604998
      
48.507302
      
77.609165
      
4.654179
      
4.654179
      
4.654179
      
2.268994
      
2.268994
      
2.268994
      
6.923172
      
63.528170
    
    

      
3223
      
2016-10-29
      
1.008761
      
56.601028
      
-21.054205
      
-21.054205
      
56.601028
      
56.601028
      
21.122370
      
49.878969
      
-23.328565
      
-23.328565
      
-23.328565
      
2.274360
      
2.274360
      
2.274360
      
-21.054205
      
35.546823
    
    

      
3224
      
2016-10-30
      
1.009074
      
56.597059
      
-18.631615
      
-18.631615
      
56.597003
      
56.597059
      
22.584430
      
50.660919
      
-20.895913
      
-20.895913
      
-20.895913
      
2.264298
      
2.264298
      
2.264298
      
-18.631615
      
37.965443
    
    

      
3225
      
2016-10-31
      
1.009387
      
56.593089
      
11.827474
      
11.827474
      
56.592302
      
56.593089
      
53.324032
      
82.618584
      
9.587762
      
9.587762
      
9.587762
      
2.239712
      
2.239712
      
2.239712
      
11.827474
      
68.420563
    
  

In [12]:

    

print(', '.join(forecast.columns))


    

    




ds, t, trend, seasonal_lower, seasonal_upper, trend_lower, trend_upper, yhat_lower, yhat_upper, weekly, weekly_lower, weekly_upper, yearly, yearly_lower, yearly_upper, seasonal, yhat

In [13]:

    

m.plot(forecast)


    

    
Out[13]:












    

In [14]:

    

m.plot_components(forecast)


    

    
Out[14]:












    

In [15]:

    

cmp_df = forecast.set_index('ds')[['yhat', 'yhat_lower', 'yhat_upper']].join(df.set_index('ds'))


    

In [16]:

    

import numpy as np
cmp_df['e'] = cmp_df['y'] - cmp_df['yhat']
cmp_df['p'] = 100*cmp_df['e']/cmp_df['y']
np.mean(abs(cmp_df[-predictions:]['p'])), np.mean(abs(cmp_df[-predictions:]['e']))


    

    
Out[16]:





(37.34607096816031, 10.623727053544432)

In [18]:

    

def invboxcox(y, lmbda):
    if lmbda == 0:
        return(np.exp(y))
    else:
        return(np.exp(np.log(lmbda * y + 1) / lmbda))


    

In [19]:

    

train_df2 = train_df.copy().fillna(14)
train_df2 = train_df2.set_index('ds')
train_df2['y'], lmbda_prophet = stats.boxcox(train_df2['y'])

train_df2.reset_index(inplace=True)

m2 = Prophet()
m2.fit(train_df2)
future2 = m2.make_future_dataframe(periods=30)

forecast2 = m2.predict(future2)
forecast2['yhat'] = invboxcox(forecast2.yhat, lmbda_prophet)
forecast2['yhat_lower'] = invboxcox(forecast2.yhat_lower, lmbda_prophet)
forecast2['yhat_upper'] = invboxcox(forecast2.yhat_upper, lmbda_prophet)

cmp_df2 = forecast2.set_index('ds')[['yhat', 'yhat_lower', 'yhat_upper']].join(df.set_index('ds'))

cmp_df2['e'] = cmp_df2['y'] - cmp_df2['yhat']
cmp_df2['p'] = 100*cmp_df2['e']/cmp_df2['y']
np.mean(abs(cmp_df2[-predictions:]['p'])), np.mean(abs(cmp_df2[-predictions:]['e']))


    

    
Out[19]:





(26.789153086481026, 8.485639747730659)

In [20]:

    

def show_forecast(cmp_df, num_predictions, num_values):
    upper_bound = go.Scatter(
        name='Upper Bound',
        x=cmp_df.tail(num_predictions).index,
        y=cmp_df.tail(num_predictions).yhat_upper,
        mode='lines',
        marker=dict(color="444"),
        line=dict(width=0),
        fillcolor='rgba(68, 68, 68, 0.3)',
        fill='tonexty')

    forecast = go.Scatter(
        name='Prediction',
        x=cmp_df.tail(predictions).index,
        y=cmp_df.tail(predictions).yhat,
        mode='lines',
        line=dict(color='rgb(31, 119, 180)'),
    )

    lower_bound = go.Scatter(
        name='Lower Bound',
        x=cmp_df.tail(num_predictions).index,
        y=cmp_df.tail(num_predictions).yhat_lower,
        marker=dict(color="444"),
        line=dict(width=0),
        mode='lines')

    fact = go.Scatter(
        name='Fact',
        x=cmp_df.tail(num_values).index,
        y=cmp_df.tail(num_values).y,
        marker=dict(color="red"),
        mode='lines',
    )

    # Trace order can be important
    # with continuous error bars
    data = [lower_bound, upper_bound, forecast, fact]

    layout = go.Layout(
        yaxis=dict(title='Посты'),
        title='Опубликованные посты на Хабрахабре',
        showlegend = False)

    fig = go.Figure(data=data, layout=layout)
    iplot(fig, show_link=False)


    

In [21]:

    

show_forecast(cmp_df, predictions, 200)


    

In [22]:

    

train_df = train_df.fillna(14).set_index('ds')


    

In [23]:

    

plt.figure(figsize=(15,10))
sm.tsa.seasonal_decompose(train_df['y'].values, freq=7).plot();
print("Критерий Дики-Фуллера: p=%f" % sm.tsa.stattools.adfuller(train_df['y'])[1])


    

    




Критерий Дики-Фуллера: p=0.040528






    






<matplotlib.figure.Figure at 0x1175ea550>






    

In [24]:

    

train_df.index = pd.to_datetime(train_df.index)


    

In [25]:

    

train_df['y_box'], lmbda = stats.boxcox([1 if x == 0 else x for x in train_df['y']])
plt.figure(figsize=(15,7))
train_df.y.plot()
plt.ylabel(u'Posts on Habr')
print("Оптимальный параметр преобразования Бокса-Кокса: %f" % lmbda)
print("Критерий Дики-Фуллера: p=%f" % sm.tsa.stattools.adfuller(train_df['y'])[1])


    

    




Оптимальный параметр преобразования Бокса-Кокса: 0.415948
Критерий Дики-Фуллера: p=0.040528






    

In [26]:

    

train_df['y_box_diff'] = train_df.y_box - train_df.y_box.shift(7)
plt.figure(figsize=(15,10))
sm.tsa.seasonal_decompose(train_df.y_box_diff[12:].values, freq=7).plot();
print("Критерий Дики-Фуллера: p=%f" % sm.tsa.stattools.adfuller(train_df.y_box_diff[8:])[1])


    

    




Критерий Дики-Фуллера: p=0.000000






    






<matplotlib.figure.Figure at 0x117735cc0>






    

In [27]:

    

plt.figure(figsize=(15,8))
ax = plt.subplot(211)
sm.graphics.tsa.plot_acf(train_df.y_box_diff[13:].values.squeeze(), lags=48, ax=ax)
ax = plt.subplot(212)
sm.graphics.tsa.plot_pacf(train_df.y_box_diff[13:].values.squeeze(), lags=48, ax=ax)


    

    
Out[27]:












    

In [28]:

    

ps = range(0, 4)
d=1
qs = range(0, 5)
Ps = range(0, 7)
D=1
Qs = range(0, 2)


    

In [29]:

    

from itertools import product

parameters = product(ps, qs, Ps, Qs)
parameters_list = list(parameters)
len(parameters_list)


    

    
Out[29]:





280

In [30]:

    

%%time
results = []
best_aic = float("inf")



for param in parameters_list:
    print(param)
    #try except нужен, потому что на некоторых наборах параметров модель не обучается
    try:
        %time model=sm.tsa.statespace.SARIMAX(train_df.y_box, order=(param[0], d, param[1]), seasonal_order=(param[2], D, param[3], 7)).fit(disp=-1)
    #выводим параметры, на которых модель не обучается и переходим к следующему набору
    except ValueError:
        print('wrong parameters:', param)
        continue
    aic = model.aic
    #сохраняем лучшую модель, aic, параметры
    if aic < best_aic:
        best_model = model
        best_aic = aic
        best_param = param
    results.append([param, model.aic])
    
warnings.filterwarnings('default')


    

    




(0, 0, 0, 0)
wrong parameters: (0, 0, 0, 0)
(0, 0, 0, 1)
CPU times: user 1.62 s, sys: 55.2 ms, total: 1.68 s
Wall time: 1.1 s
(0, 0, 1, 0)
CPU times: user 1.41 s, sys: 36.2 ms, total: 1.44 s
Wall time: 858 ms
(0, 0, 1, 1)
CPU times: user 1.72 s, sys: 53.2 ms, total: 1.77 s
Wall time: 1.16 s
(0, 0, 2, 0)
CPU times: user 1.82 s, sys: 97.2 ms, total: 1.92 s
Wall time: 1.13 s
(0, 0, 2, 1)
CPU times: user 2.81 s, sys: 93.6 ms, total: 2.91 s
Wall time: 1.81 s
(0, 0, 3, 0)
CPU times: user 2.81 s, sys: 254 ms, total: 3.07 s
Wall time: 1.86 s
(0, 0, 3, 1)
CPU times: user 4.66 s, sys: 167 ms, total: 4.83 s
Wall time: 3.22 s
(0, 0, 4, 0)
CPU times: user 10.3 s, sys: 423 ms, total: 10.7 s
Wall time: 2.72 s
(0, 0, 4, 1)
CPU times: user 24.1 s, sys: 449 ms, total: 24.5 s
Wall time: 6.16 s
(0, 0, 5, 0)
CPU times: user 13.8 s, sys: 475 ms, total: 14.2 s
Wall time: 3.59 s
(0, 0, 5, 1)
CPU times: user 36.1 s, sys: 952 ms, total: 37.1 s
Wall time: 9.45 s
(0, 0, 6, 0)
CPU times: user 17.5 s, sys: 732 ms, total: 18.3 s
Wall time: 4.6 s
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CPU times: user 52.8 s, sys: 1.25 s, total: 54.1 s
Wall time: 13.7 s
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CPU times: user 2.3 s, sys: 223 ms, total: 2.52 s
Wall time: 1.47 s
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CPU times: user 2.03 s, sys: 136 ms, total: 2.17 s
Wall time: 1.45 s
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CPU times: user 1.54 s, sys: 36.4 ms, total: 1.57 s
Wall time: 991 ms
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CPU times: user 2 s, sys: 63.9 ms, total: 2.06 s
Wall time: 1.44 s
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CPU times: user 2.12 s, sys: 89.1 ms, total: 2.21 s
Wall time: 1.42 s
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CPU times: user 3.46 s, sys: 173 ms, total: 3.63 s
Wall time: 2.43 s
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CPU times: user 2.94 s, sys: 177 ms, total: 3.12 s
Wall time: 2.1 s
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CPU times: user 6.64 s, sys: 171 ms, total: 6.81 s
Wall time: 5.15 s
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CPU times: user 12.7 s, sys: 320 ms, total: 13 s
Wall time: 3.26 s
(0, 1, 4, 1)
CPU times: user 39.2 s, sys: 1.76 s, total: 40.9 s
Wall time: 10.8 s
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CPU times: user 18.2 s, sys: 522 ms, total: 18.8 s
Wall time: 4.72 s
(0, 1, 5, 1)
CPU times: user 50.5 s, sys: 1.65 s, total: 52.2 s
Wall time: 13.5 s
(0, 1, 6, 0)
CPU times: user 27 s, sys: 3.14 s, total: 30.2 s
Wall time: 8.76 s
(0, 1, 6, 1)
CPU times: user 1min 13s, sys: 2.47 s, total: 1min 15s
Wall time: 19.8 s
(0, 2, 0, 0)
CPU times: user 3.33 s, sys: 301 ms, total: 3.63 s
Wall time: 2.84 s
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CPU times: user 2.24 s, sys: 179 ms, total: 2.42 s
Wall time: 1.78 s
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CPU times: user 3.85 s, sys: 43.7 ms, total: 3.89 s
Wall time: 3.31 s
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CPU times: user 2.78 s, sys: 87.8 ms, total: 2.87 s
Wall time: 2.25 s
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CPU times: user 7.6 s, sys: 85.9 ms, total: 7.69 s
Wall time: 6.25 s
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CPU times: user 4.23 s, sys: 97.9 ms, total: 4.33 s
Wall time: 3.02 s
(0, 2, 3, 0)
CPU times: user 3.76 s, sys: 130 ms, total: 3.89 s
Wall time: 2.72 s
(0, 2, 3, 1)
CPU times: user 8.08 s, sys: 193 ms, total: 8.28 s
Wall time: 6.3 s
(0, 2, 4, 0)
CPU times: user 18.5 s, sys: 485 ms, total: 18.9 s
Wall time: 4.79 s
(0, 2, 4, 1)
CPU times: user 56.5 s, sys: 1.32 s, total: 57.8 s
Wall time: 14.8 s
(0, 2, 5, 0)
CPU times: user 26.7 s, sys: 2.17 s, total: 28.9 s
Wall time: 7.85 s
(0, 2, 5, 1)
CPU times: user 1min 34s, sys: 3.2 s, total: 1min 37s
Wall time: 25.6 s
(0, 2, 6, 0)
CPU times: user 35 s, sys: 1.63 s, total: 36.7 s
Wall time: 9.51 s
(0, 2, 6, 1)
CPU times: user 2min 14s, sys: 4.76 s, total: 2min 19s
Wall time: 36.8 s
(0, 3, 0, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 5.54 s, sys: 196 ms, total: 5.74 s
Wall time: 4.82 s
(0, 3, 0, 1)
CPU times: user 2.9 s, sys: 131 ms, total: 3.03 s
Wall time: 2.3 s
(0, 3, 1, 0)
CPU times: user 5.49 s, sys: 63.4 ms, total: 5.55 s
Wall time: 4.96 s
(0, 3, 1, 1)
CPU times: user 4.92 s, sys: 113 ms, total: 5.04 s
Wall time: 4.44 s
(0, 3, 2, 0)
CPU times: user 11.2 s, sys: 124 ms, total: 11.3 s
Wall time: 9.53 s
(0, 3, 2, 1)
CPU times: user 6.46 s, sys: 131 ms, total: 6.59 s
Wall time: 5.17 s
(0, 3, 3, 0)
CPU times: user 22.9 s, sys: 265 ms, total: 23.1 s
Wall time: 20.4 s
(0, 3, 3, 1)
CPU times: user 13.5 s, sys: 255 ms, total: 13.7 s
Wall time: 11.6 s
(0, 3, 4, 0)
CPU times: user 25.1 s, sys: 490 ms, total: 25.6 s
Wall time: 6.44 s
(0, 3, 4, 1)
CPU times: user 1min 45s, sys: 1.35 s, total: 1min 47s
Wall time: 27.2 s
(0, 3, 5, 0)
CPU times: user 24.1 s, sys: 719 ms, total: 24.8 s
Wall time: 6.31 s
(0, 3, 5, 1)
CPU times: user 1min 39s, sys: 4.94 s, total: 1min 44s
Wall time: 28.1 s
(0, 3, 6, 0)
CPU times: user 35.6 s, sys: 3.35 s, total: 39 s
Wall time: 11 s
(0, 3, 6, 1)
CPU times: user 2min 20s, sys: 6.78 s, total: 2min 27s
Wall time: 39.8 s
(0, 4, 0, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 5.85 s, sys: 230 ms, total: 6.08 s
Wall time: 5.19 s
(0, 4, 0, 1)
CPU times: user 5.1 s, sys: 139 ms, total: 5.24 s
Wall time: 4.5 s
(0, 4, 1, 0)
CPU times: user 5.65 s, sys: 66.6 ms, total: 5.72 s
Wall time: 5.12 s
(0, 4, 1, 1)
CPU times: user 4.11 s, sys: 103 ms, total: 4.21 s
Wall time: 3.58 s
(0, 4, 2, 0)
CPU times: user 11.2 s, sys: 130 ms, total: 11.3 s
Wall time: 9.08 s
(0, 4, 2, 1)
CPU times: user 7.96 s, sys: 169 ms, total: 8.13 s
Wall time: 6.66 s
(0, 4, 3, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 21.8 s, sys: 251 ms, total: 22 s
Wall time: 19.3 s
(0, 4, 3, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 16.4 s, sys: 179 ms, total: 16.6 s
Wall time: 14.6 s
(0, 4, 4, 0)
CPU times: user 2min 40s, sys: 1.1 s, total: 2min 41s
Wall time: 40.9 s
(0, 4, 4, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 2min 9s, sys: 1.65 s, total: 2min 10s
Wall time: 33.4 s
(0, 4, 5, 0)
CPU times: user 4min 12s, sys: 2.41 s, total: 4min 14s
Wall time: 1min 4s
(0, 4, 5, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 3min 56s, sys: 3.25 s, total: 3min 59s
Wall time: 1min 1s
(0, 4, 6, 0)
CPU times: user 5min 42s, sys: 3.09 s, total: 5min 45s
Wall time: 1min 27s
(0, 4, 6, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 3min 20s, sys: 2 s, total: 3min 22s
Wall time: 51.2 s
(1, 0, 0, 0)
CPU times: user 1.59 s, sys: 143 ms, total: 1.74 s
Wall time: 790 ms
(1, 0, 0, 1)
CPU times: user 1.81 s, sys: 99.8 ms, total: 1.91 s
Wall time: 1.18 s
(1, 0, 1, 0)
CPU times: user 1.52 s, sys: 52.8 ms, total: 1.57 s
Wall time: 950 ms
(1, 0, 1, 1)
CPU times: user 1.82 s, sys: 33.2 ms, total: 1.85 s
Wall time: 1.23 s
(1, 0, 2, 0)
CPU times: user 2.07 s, sys: 95 ms, total: 2.17 s
Wall time: 1.3 s
(1, 0, 2, 1)
CPU times: user 3.19 s, sys: 108 ms, total: 3.3 s
Wall time: 2.09 s
(1, 0, 3, 0)
CPU times: user 2.83 s, sys: 136 ms, total: 2.97 s
Wall time: 1.87 s
(1, 0, 3, 1)
CPU times: user 5.29 s, sys: 154 ms, total: 5.45 s
Wall time: 3.77 s
(1, 0, 4, 0)
CPU times: user 11.5 s, sys: 293 ms, total: 11.8 s
Wall time: 2.95 s
(1, 0, 4, 1)
CPU times: user 30.4 s, sys: 1.17 s, total: 31.6 s
Wall time: 8.37 s
(1, 0, 5, 0)
CPU times: user 15.2 s, sys: 500 ms, total: 15.7 s
Wall time: 3.99 s
(1, 0, 5, 1)
CPU times: user 40.1 s, sys: 768 ms, total: 40.9 s
Wall time: 10.3 s
(1, 0, 6, 0)
CPU times: user 20.9 s, sys: 656 ms, total: 21.5 s
Wall time: 5.43 s
(1, 0, 6, 1)
CPU times: user 1min 5s, sys: 2.7 s, total: 1min 8s
Wall time: 18.1 s
(1, 1, 0, 0)
CPU times: user 2.27 s, sys: 225 ms, total: 2.49 s
Wall time: 1.61 s
(1, 1, 0, 1)
CPU times: user 2.37 s, sys: 110 ms, total: 2.48 s
Wall time: 1.75 s
(1, 1, 1, 0)
CPU times: user 4.07 s, sys: 56.6 ms, total: 4.13 s
Wall time: 3.5 s
(1, 1, 1, 1)
CPU times: user 2.44 s, sys: 36.5 ms, total: 2.47 s
Wall time: 1.85 s
(1, 1, 2, 0)
CPU times: user 7.54 s, sys: 105 ms, total: 7.65 s
Wall time: 6.02 s
(1, 1, 2, 1)
CPU times: user 4.28 s, sys: 99.1 ms, total: 4.38 s
Wall time: 3.02 s
(1, 1, 3, 0)
CPU times: user 12.3 s, sys: 140 ms, total: 12.5 s
Wall time: 10.2 s
(1, 1, 3, 1)
CPU times: user 7.95 s, sys: 321 ms, total: 8.27 s
Wall time: 5.97 s
(1, 1, 4, 0)
CPU times: user 20.4 s, sys: 725 ms, total: 21.1 s
Wall time: 5.4 s
(1, 1, 4, 1)
CPU times: user 53.4 s, sys: 935 ms, total: 54.3 s
Wall time: 13.8 s
(1, 1, 5, 0)
CPU times: user 22.8 s, sys: 504 ms, total: 23.3 s
Wall time: 5.85 s
(1, 1, 5, 1)
CPU times: user 1min 9s, sys: 2.27 s, total: 1min 11s
Wall time: 18.9 s
(1, 1, 6, 0)
CPU times: user 30.5 s, sys: 757 ms, total: 31.3 s
Wall time: 7.85 s
(1, 1, 6, 1)
CPU times: user 1min 31s, sys: 991 ms, total: 1min 32s
Wall time: 23.3 s
(1, 2, 0, 0)
wrong parameters: (1, 2, 0, 0)
(1, 2, 0, 1)
wrong parameters: (1, 2, 0, 1)
(1, 2, 1, 0)
wrong parameters: (1, 2, 1, 0)
(1, 2, 1, 1)
wrong parameters: (1, 2, 1, 1)
(1, 2, 2, 0)
wrong parameters: (1, 2, 2, 0)
(1, 2, 2, 1)
wrong parameters: (1, 2, 2, 1)
(1, 2, 3, 0)
wrong parameters: (1, 2, 3, 0)
(1, 2, 3, 1)
wrong parameters: (1, 2, 3, 1)
(1, 2, 4, 0)
wrong parameters: (1, 2, 4, 0)
(1, 2, 4, 1)
wrong parameters: (1, 2, 4, 1)
(1, 2, 5, 0)
wrong parameters: (1, 2, 5, 0)
(1, 2, 5, 1)
wrong parameters: (1, 2, 5, 1)
(1, 2, 6, 0)
wrong parameters: (1, 2, 6, 0)
(1, 2, 6, 1)
wrong parameters: (1, 2, 6, 1)
(1, 3, 0, 0)
wrong parameters: (1, 3, 0, 0)
(1, 3, 0, 1)
wrong parameters: (1, 3, 0, 1)
(1, 3, 1, 0)
wrong parameters: (1, 3, 1, 0)
(1, 3, 1, 1)
wrong parameters: (1, 3, 1, 1)
(1, 3, 2, 0)
wrong parameters: (1, 3, 2, 0)
(1, 3, 2, 1)
wrong parameters: (1, 3, 2, 1)
(1, 3, 3, 0)
wrong parameters: (1, 3, 3, 0)
(1, 3, 3, 1)
wrong parameters: (1, 3, 3, 1)
(1, 3, 4, 0)
wrong parameters: (1, 3, 4, 0)
(1, 3, 4, 1)
wrong parameters: (1, 3, 4, 1)
(1, 3, 5, 0)
wrong parameters: (1, 3, 5, 0)
(1, 3, 5, 1)
wrong parameters: (1, 3, 5, 1)
(1, 3, 6, 0)
wrong parameters: (1, 3, 6, 0)
(1, 3, 6, 1)
wrong parameters: (1, 3, 6, 1)
(1, 4, 0, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 6.61 s, sys: 206 ms, total: 6.81 s
Wall time: 5.87 s
(1, 4, 0, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 6.69 s, sys: 178 ms, total: 6.87 s
Wall time: 6.19 s
(1, 4, 1, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 7.28 s, sys: 109 ms, total: 7.39 s
Wall time: 6.81 s
(1, 4, 1, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 7.44 s, sys: 136 ms, total: 7.58 s
Wall time: 7.01 s
(1, 4, 2, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 16.2 s, sys: 176 ms, total: 16.4 s
Wall time: 14.2 s
(1, 4, 2, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 13.1 s, sys: 202 ms, total: 13.3 s
Wall time: 11.4 s
(1, 4, 3, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 26.4 s, sys: 388 ms, total: 26.8 s
Wall time: 23.7 s
(1, 4, 3, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 21 s, sys: 301 ms, total: 21.3 s
Wall time: 19.1 s
(1, 4, 4, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 3min 41s, sys: 1.97 s, total: 3min 43s
Wall time: 56.6 s
(1, 4, 4, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 2min 25s, sys: 1.74 s, total: 2min 27s
Wall time: 37.5 s
(1, 4, 5, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 4min 56s, sys: 2.75 s, total: 4min 59s
Wall time: 1min 16s
(1, 4, 5, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 3min 40s, sys: 4.1 s, total: 3min 44s
Wall time: 57.8 s
(1, 4, 6, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 4min 12s, sys: 3.43 s, total: 4min 15s
Wall time: 1min 4s
(1, 4, 6, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 3min 45s, sys: 4.79 s, total: 3min 50s
Wall time: 59.3 s
(2, 0, 0, 0)
CPU times: user 1.79 s, sys: 227 ms, total: 2.02 s
Wall time: 995 ms
(2, 0, 0, 1)
CPU times: user 2.09 s, sys: 190 ms, total: 2.28 s
Wall time: 1.6 s
(2, 0, 1, 0)
CPU times: user 1.65 s, sys: 101 ms, total: 1.75 s
Wall time: 1.18 s
(2, 0, 1, 1)
CPU times: user 2.18 s, sys: 110 ms, total: 2.29 s
Wall time: 1.71 s
(2, 0, 2, 0)
CPU times: user 2.23 s, sys: 142 ms, total: 2.37 s
Wall time: 1.5 s
(2, 0, 2, 1)
CPU times: user 3.75 s, sys: 196 ms, total: 3.95 s
Wall time: 2.58 s
(2, 0, 3, 0)
CPU times: user 3.33 s, sys: 210 ms, total: 3.54 s
Wall time: 2.36 s
(2, 0, 3, 1)
CPU times: user 6.15 s, sys: 256 ms, total: 6.41 s
Wall time: 4.64 s
(2, 0, 4, 0)
CPU times: user 12.5 s, sys: 385 ms, total: 12.9 s
Wall time: 3.26 s
(2, 0, 4, 1)
CPU times: user 30.8 s, sys: 933 ms, total: 31.7 s
Wall time: 8.15 s
(2, 0, 5, 0)
CPU times: user 18.4 s, sys: 1.22 s, total: 19.7 s
Wall time: 5.32 s
(2, 0, 5, 1)
CPU times: user 49.6 s, sys: 1.41 s, total: 51 s
Wall time: 13 s
(2, 0, 6, 0)
CPU times: user 22.7 s, sys: 850 ms, total: 23.6 s
Wall time: 5.97 s
(2, 0, 6, 1)
CPU times: user 1min 7s, sys: 2.5 s, total: 1min 10s
Wall time: 18.4 s
(2, 1, 0, 0)
CPU times: user 3.14 s, sys: 144 ms, total: 3.29 s
Wall time: 2.37 s
(2, 1, 0, 1)
CPU times: user 2.71 s, sys: 104 ms, total: 2.81 s
Wall time: 2.16 s
(2, 1, 1, 0)
CPU times: user 4.24 s, sys: 75.2 ms, total: 4.32 s
Wall time: 3.69 s
(2, 1, 1, 1)
CPU times: user 3.25 s, sys: 61.9 ms, total: 3.32 s
Wall time: 2.73 s
(2, 1, 2, 0)
CPU times: user 8.09 s, sys: 144 ms, total: 8.23 s
Wall time: 6.55 s
(2, 1, 2, 1)
CPU times: user 5.21 s, sys: 168 ms, total: 5.38 s
Wall time: 3.71 s
(2, 1, 3, 0)
CPU times: user 14.5 s, sys: 244 ms, total: 14.7 s
Wall time: 12.2 s
(2, 1, 3, 1)
CPU times: user 9.04 s, sys: 374 ms, total: 9.41 s
Wall time: 6.98 s
(2, 1, 4, 0)
CPU times: user 1min 59s, sys: 2.53 s, total: 2min 2s
Wall time: 31.8 s
(2, 1, 4, 1)
CPU times: user 53 s, sys: 2.13 s, total: 55.1 s
Wall time: 14.5 s
(2, 1, 5, 0)
CPU times: user 2min 3s, sys: 3.77 s, total: 2min 7s
Wall time: 33 s
(2, 1, 5, 1)
CPU times: user 1min 29s, sys: 3.52 s, total: 1min 33s
Wall time: 24.7 s
(2, 1, 6, 0)
CPU times: user 2min 23s, sys: 5.34 s, total: 2min 28s
Wall time: 39.1 s
(2, 1, 6, 1)
CPU times: user 1min 53s, sys: 2.98 s, total: 1min 56s
Wall time: 30 s
(2, 2, 0, 0)
wrong parameters: (2, 2, 0, 0)
(2, 2, 0, 1)
wrong parameters: (2, 2, 0, 1)
(2, 2, 1, 0)
wrong parameters: (2, 2, 1, 0)
(2, 2, 1, 1)
wrong parameters: (2, 2, 1, 1)
(2, 2, 2, 0)
wrong parameters: (2, 2, 2, 0)
(2, 2, 2, 1)
wrong parameters: (2, 2, 2, 1)
(2, 2, 3, 0)
wrong parameters: (2, 2, 3, 0)
(2, 2, 3, 1)
wrong parameters: (2, 2, 3, 1)
(2, 2, 4, 0)
wrong parameters: (2, 2, 4, 0)
(2, 2, 4, 1)
wrong parameters: (2, 2, 4, 1)
(2, 2, 5, 0)
wrong parameters: (2, 2, 5, 0)
(2, 2, 5, 1)
wrong parameters: (2, 2, 5, 1)
(2, 2, 6, 0)
wrong parameters: (2, 2, 6, 0)
(2, 2, 6, 1)
wrong parameters: (2, 2, 6, 1)
(2, 3, 0, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 4.49 s, sys: 268 ms, total: 4.75 s
Wall time: 3.93 s
(2, 3, 0, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 6.82 s, sys: 236 ms, total: 7.06 s
Wall time: 6.48 s
(2, 3, 1, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 7.38 s, sys: 125 ms, total: 7.51 s
Wall time: 6.93 s
(2, 3, 1, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 7.48 s, sys: 129 ms, total: 7.61 s
Wall time: 7.05 s
(2, 3, 2, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 11.8 s, sys: 240 ms, total: 12 s
Wall time: 9.43 s
(2, 3, 2, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 10.6 s, sys: 150 ms, total: 10.8 s
Wall time: 9.05 s
(2, 3, 3, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 17 s, sys: 314 ms, total: 17.3 s
Wall time: 13.6 s
(2, 3, 3, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 19.5 s, sys: 324 ms, total: 19.8 s
Wall time: 16.9 s
(2, 3, 4, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 1min 35s, sys: 3.85 s, total: 1min 39s
Wall time: 26.2 s
(2, 3, 4, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 1min 58s, sys: 3.15 s, total: 2min 1s
Wall time: 31.5 s
(2, 3, 5, 0)
CPU times: user 58.5 s, sys: 2.1 s, total: 1min
Wall time: 15.8 s
(2, 3, 5, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 2min 57s, sys: 4.5 s, total: 3min 1s
Wall time: 47.1 s
(2, 3, 6, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 1min 55s, sys: 2.49 s, total: 1min 57s
Wall time: 30.3 s
(2, 3, 6, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 3min 8s, sys: 6.21 s, total: 3min 14s
Wall time: 51.1 s
(2, 4, 0, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 6.69 s, sys: 157 ms, total: 6.84 s
Wall time: 5.98 s
(2, 4, 0, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 7.28 s, sys: 125 ms, total: 7.41 s
Wall time: 6.73 s
(2, 4, 1, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 9.71 s, sys: 52.6 ms, total: 9.76 s
Wall time: 9.17 s
(2, 4, 1, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 8.29 s, sys: 93 ms, total: 8.39 s
Wall time: 7.75 s
(2, 4, 2, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 16.2 s, sys: 196 ms, total: 16.4 s
Wall time: 13.8 s
(2, 4, 2, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 12.9 s, sys: 221 ms, total: 13.1 s
Wall time: 11 s
(2, 4, 3, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 31.8 s, sys: 426 ms, total: 32.2 s
Wall time: 28.7 s
(2, 4, 3, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 22.2 s, sys: 394 ms, total: 22.6 s
Wall time: 19.9 s
(2, 4, 4, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 1min 27s, sys: 2.62 s, total: 1min 30s
Wall time: 23.4 s
(2, 4, 4, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 2min 12s, sys: 3.18 s, total: 2min 16s
Wall time: 35.1 s
(2, 4, 5, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 1min 28s, sys: 1.35 s, total: 1min 30s
Wall time: 22.7 s
(2, 4, 5, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 2min 49s, sys: 2.96 s, total: 2min 52s
Wall time: 44.2 s
(2, 4, 6, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 2min 53s, sys: 4.7 s, total: 2min 58s
Wall time: 46.1 s
(2, 4, 6, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 3min 31s, sys: 2.93 s, total: 3min 34s
Wall time: 54.4 s
(3, 0, 0, 0)
CPU times: user 1.65 s, sys: 152 ms, total: 1.81 s
Wall time: 945 ms
(3, 0, 0, 1)
CPU times: user 1.97 s, sys: 99.2 ms, total: 2.07 s
Wall time: 1.41 s
(3, 0, 1, 0)
CPU times: user 1.78 s, sys: 70.7 ms, total: 1.85 s
Wall time: 1.23 s
(3, 0, 1, 1)
CPU times: user 2.2 s, sys: 65 ms, total: 2.26 s
Wall time: 1.62 s
(3, 0, 2, 0)
CPU times: user 2.65 s, sys: 126 ms, total: 2.78 s
Wall time: 1.76 s
(3, 0, 2, 1)
CPU times: user 4.3 s, sys: 130 ms, total: 4.43 s
Wall time: 2.92 s
(3, 0, 3, 0)
CPU times: user 9.23 s, sys: 235 ms, total: 9.46 s
Wall time: 2.38 s
(3, 0, 3, 1)
CPU times: user 19 s, sys: 372 ms, total: 19.4 s
Wall time: 4.89 s
(3, 0, 4, 0)
CPU times: user 14 s, sys: 374 ms, total: 14.4 s
Wall time: 3.62 s
(3, 0, 4, 1)
CPU times: user 34.6 s, sys: 1.23 s, total: 35.8 s
Wall time: 9.3 s
(3, 0, 5, 0)
CPU times: user 19.4 s, sys: 1.6 s, total: 21 s
Wall time: 5.8 s
(3, 0, 5, 1)
CPU times: user 53.6 s, sys: 911 ms, total: 54.5 s
Wall time: 13.8 s
(3, 0, 6, 0)
CPU times: user 25.6 s, sys: 920 ms, total: 26.5 s
Wall time: 6.73 s
(3, 0, 6, 1)
CPU times: user 1min 14s, sys: 2.58 s, total: 1min 17s
Wall time: 20.2 s
(3, 1, 0, 0)
CPU times: user 3.78 s, sys: 143 ms, total: 3.93 s
Wall time: 3.03 s
(3, 1, 0, 1)
CPU times: user 2.97 s, sys: 91.3 ms, total: 3.06 s
Wall time: 2.39 s
(3, 1, 1, 0)
CPU times: user 7.21 s, sys: 69.6 ms, total: 7.28 s
Wall time: 6.65 s
(3, 1, 1, 1)
CPU times: user 3.57 s, sys: 67.3 ms, total: 3.63 s
Wall time: 2.99 s
(3, 1, 2, 0)
CPU times: user 10.8 s, sys: 166 ms, total: 10.9 s
Wall time: 8.28 s
(3, 1, 2, 1)
CPU times: user 6.58 s, sys: 115 ms, total: 6.7 s
Wall time: 5.01 s
(3, 1, 3, 0)
CPU times: user 1min 35s, sys: 496 ms, total: 1min 36s
Wall time: 24.1 s
(3, 1, 3, 1)
CPU times: user 38.3 s, sys: 339 ms, total: 38.6 s
Wall time: 9.67 s
(3, 1, 4, 0)
CPU times: user 1min 49s, sys: 848 ms, total: 1min 49s
Wall time: 27.7 s
(3, 1, 4, 1)
CPU times: user 55.3 s, sys: 1.25 s, total: 56.5 s
Wall time: 14.4 s
(3, 1, 5, 0)
CPU times: user 2min 55s, sys: 3.34 s, total: 2min 58s
Wall time: 45.9 s
(3, 1, 5, 1)
CPU times: user 1min 26s, sys: 4.24 s, total: 1min 31s
Wall time: 24.3 s
(3, 1, 6, 0)
CPU times: user 3min 15s, sys: 5.46 s, total: 3min 20s
Wall time: 53 s
(3, 1, 6, 1)
CPU times: user 1min 52s, sys: 4.76 s, total: 1min 57s
Wall time: 31 s
(3, 2, 0, 0)
wrong parameters: (3, 2, 0, 0)
(3, 2, 0, 1)
wrong parameters: (3, 2, 0, 1)
(3, 2, 1, 0)
wrong parameters: (3, 2, 1, 0)
(3, 2, 1, 1)
wrong parameters: (3, 2, 1, 1)
(3, 2, 2, 0)
wrong parameters: (3, 2, 2, 0)
(3, 2, 2, 1)
wrong parameters: (3, 2, 2, 1)
(3, 2, 3, 0)
wrong parameters: (3, 2, 3, 0)
(3, 2, 3, 1)
wrong parameters: (3, 2, 3, 1)
(3, 2, 4, 0)
wrong parameters: (3, 2, 4, 0)
(3, 2, 4, 1)
wrong parameters: (3, 2, 4, 1)
(3, 2, 5, 0)
wrong parameters: (3, 2, 5, 0)
(3, 2, 5, 1)
wrong parameters: (3, 2, 5, 1)
(3, 2, 6, 0)
wrong parameters: (3, 2, 6, 0)
(3, 2, 6, 1)
wrong parameters: (3, 2, 6, 1)
(3, 3, 0, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 4.18 s, sys: 179 ms, total: 4.36 s
Wall time: 3.5 s
(3, 3, 0, 1)
CPU times: user 5.77 s, sys: 142 ms, total: 5.91 s
Wall time: 5.29 s
(3, 3, 1, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 5.51 s, sys: 79.7 ms, total: 5.59 s
Wall time: 4.96 s
(3, 3, 1, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 7.86 s, sys: 65.8 ms, total: 7.92 s
Wall time: 7.29 s
(3, 3, 2, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 18.6 s, sys: 182 ms, total: 18.8 s
Wall time: 15.7 s
(3, 3, 2, 1)
CPU times: user 11.1 s, sys: 186 ms, total: 11.3 s
Wall time: 9.2 s
(3, 3, 3, 0)
CPU times: user 1min 50s, sys: 512 ms, total: 1min 50s
Wall time: 27.7 s
(3, 3, 3, 1)
CPU times: user 1min 9s, sys: 982 ms, total: 1min 10s
Wall time: 17.7 s
(3, 3, 4, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 3min 14s, sys: 676 ms, total: 3min 14s
Wall time: 48.8 s
(3, 3, 4, 1)
CPU times: user 1min 25s, sys: 1.28 s, total: 1min 26s
Wall time: 22 s
(3, 3, 5, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 1min 17s, sys: 1.76 s, total: 1min 19s
Wall time: 20.2 s
(3, 3, 5, 1)
CPU times: user 2min 30s, sys: 1.27 s, total: 2min 31s
Wall time: 38.1 s
(3, 3, 6, 0)
CPU times: user 1min 19s, sys: 1.11 s, total: 1min 21s
Wall time: 20.5 s
(3, 3, 6, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 3min 33s, sys: 2.05 s, total: 3min 35s
Wall time: 54.3 s
(3, 4, 0, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 7 s, sys: 153 ms, total: 7.15 s
Wall time: 6.27 s
(3, 4, 0, 1)
CPU times: user 7.69 s, sys: 116 ms, total: 7.81 s
Wall time: 7.12 s
(3, 4, 1, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 9.92 s, sys: 54.8 ms, total: 9.97 s
Wall time: 9.38 s
(3, 4, 1, 1)
CPU times: user 7.66 s, sys: 80.9 ms, total: 7.74 s
Wall time: 7.1 s
(3, 4, 2, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 20.9 s, sys: 159 ms, total: 21 s
Wall time: 17.9 s
(3, 4, 2, 1)
CPU times: user 16.2 s, sys: 164 ms, total: 16.4 s
Wall time: 14.4 s
(3, 4, 3, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 2min 24s, sys: 1.46 s, total: 2min 26s
Wall time: 37.1 s
(3, 4, 3, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 2min 19s, sys: 3.39 s, total: 2min 22s
Wall time: 37.4 s
(3, 4, 4, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 4min 2s, sys: 7.42 s, total: 4min 9s
Wall time: 1min 7s
(3, 4, 4, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 2min 34s, sys: 4.29 s, total: 2min 38s
Wall time: 41.7 s
(3, 4, 5, 0)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 5min 2s, sys: 2.84 s, total: 5min 5s
Wall time: 1min 17s
(3, 4, 5, 1)






    




/Users/y.kashnitsky/anaconda3/lib/python3.6/site-packages/statsmodels/base/model.py:475: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals







    




CPU times: user 3min 6s, sys: 3.45 s, total: 3min 10s
Wall time: 48.6 s
(3, 4, 6, 0)
CPU times: user 7min 57s, sys: 6.81 s, total: 8min 4s
Wall time: 2min 3s
(3, 4, 6, 1)
CPU times: user 4min 50s, sys: 6.8 s, total: 4min 57s
Wall time: 1min 16s
CPU times: user 3h 15min 1s, sys: 4min 11s, total: 3h 19min 12s
Wall time: 59min 21s

In [31]:

    

result_table = pd.DataFrame(results)
result_table.columns = ['parameters', 'aic']
print(result_table.sort_values(by = 'aic', ascending=True).head())


    

    




       parameters          aic
212  (3, 4, 1, 1)  9597.534822
214  (3, 4, 2, 1)  9598.589146
216  (3, 4, 3, 1)  9599.138188
220  (3, 4, 5, 1)  9600.614474
218  (3, 4, 4, 1)  9601.080671

In [32]:

    

print(best_model.summary())


    

    




                                 Statespace Model Results                                
=========================================================================================
Dep. Variable:                             y_box   No. Observations:                 3197
Model:             SARIMAX(3, 1, 4)x(1, 1, 1, 7)   Log Likelihood               -4788.767
Date:                           Thu, 23 Mar 2017   AIC                           9597.535
Time:                                   12:59:12   BIC                           9658.235
Sample:                               01-01-2008   HQIC                          9619.298
                                    - 10-01-2016                                         
Covariance Type:                             opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
ar.L1         -0.2363      0.217     -1.088      0.276      -0.662       0.189
ar.L2          0.1763      0.145      1.219      0.223      -0.107       0.460
ar.L3          0.5548      0.118      4.706      0.000       0.324       0.786
ma.L1         -0.5148      0.218     -2.359      0.018      -0.943      -0.087
ma.L2         -0.4601      0.267     -1.724      0.085      -0.983       0.063
ma.L3         -0.4193      0.176     -2.376      0.017      -0.765      -0.073
ma.L4          0.4077      0.097      4.220      0.000       0.218       0.597
ar.S.L7        0.0698      0.021      3.361      0.001       0.029       0.110
ma.S.L7       -0.9497      0.007   -140.392      0.000      -0.963      -0.936
sigma2         1.1727      0.021     57.035      0.000       1.132       1.213
===================================================================================
Ljung-Box (Q):                       73.57   Jarque-Bera (JB):              1197.96
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               1.25   Skew:                            -0.69
Prob(H) (two-sided):                  0.00   Kurtosis:                         5.66
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).

In [34]:

    

plt.figure(figsize=(15,8))
plt.subplot(211)
best_model.resid[13:].plot()
plt.ylabel(u'Residuals')

ax = plt.subplot(212)
sm.graphics.tsa.plot_acf(best_model.resid[13:].values.squeeze(), lags=48, ax=ax)

print("Критерий Стьюдента: p=%f" % stats.ttest_1samp(best_model.resid[13:], 0)[1])
print("Критерий Дики-Фуллера: p=%f" % sm.tsa.stattools.adfuller(best_model.resid[13:])[1])


    

    




Критерий Стьюдента: p=0.050812
Критерий Дики-Фуллера: p=0.000000






    

In [37]:

    

train_df['arima_model'] = invboxcox(best_model.fittedvalues, lmbda)
plt.figure(figsize=(15,7))
train_df.y.tail(200).plot()
train_df.arima_model[13:].tail(200).plot(color='r')
plt.ylabel('Posts on Habr');


    

In [55]:

    

arima_df = train_df2.set_index('ds')[['y']]

date_list = [pd.datetime.strptime("2016-10-01", "%Y-%m-%d") + 
             pd.Timedelta(x) for x in range(0, predictions+1)]
future = pd.DataFrame(index=date_list, columns= arima_df.columns)
arima_df = pd.concat([arima_df, future])
arima_df['forecast'] = invboxcox(best_model.predict(start=train_df.shape[0], end=train_df.shape[0]+predictions-1), lmbda)
plt.figure(figsize=(15,7))
arima_df.y.tail(200).plot()
arima_df.forecast.tail(200).plot(color='r')
plt.ylabel('Habr posts');


    

In [59]:

    

cmp_df.head()


    

    
Out[59]:






  

    

      

      
yhat
      
yhat_lower
      
yhat_upper
      
y
      
e
      
p
      
forecast
      
e_arima
      
p_arima
    
  
  

    

      
2008-01-01
      
18.623500
      
3.257950
      
32.626385
      
3.0
      
-15.623500
      
-520.783317
      
NaN
      
NaN
      
NaN
    
    

      
2008-01-02
      
16.464544
      
1.836996
      
31.509440
      
3.0
      
-13.464544
      
-448.818118
      
NaN
      
NaN
      
NaN
    
    

      
2008-01-03
      
15.108129
      
-0.062345
      
30.097931
      
4.0
      
-11.108129
      
-277.703219
      
NaN
      
NaN
      
NaN
    
    

      
2008-01-04
      
11.324859
      
-3.324523
      
26.584102
      
14.0
      
2.675141
      
19.108148
      
NaN
      
NaN
      
NaN
    
    

      
2008-01-05
      
-16.512771
      
-30.686008
      
-1.566509
      
4.0
      
20.512771
      
512.819264
      
NaN
      
NaN
      
NaN
    
  

In [62]:

    

cmp_df = cmp_df.join(arima_df[['forecast']])


    

In [63]:

    

import numpy as np
cmp_df['e_arima'] = cmp_df['y'] - cmp_df['forecast']
cmp_df['p_arima'] = 100*cmp_df['e_arima']/cmp_df['y']


    

In [64]:

    

num_values = 200

forecast = go.Scatter(
    name='Prophet',
    x=cmp_df.tail(predictions).index,
    y=cmp_df.tail(predictions).yhat,
    mode='lines',
    line=dict(color='rgb(31, 119, 180)'),
)


fact = go.Scatter(
    name='Fact',
    x=cmp_df.tail(num_values).index,
    y=cmp_df.tail(num_values).y,
    marker=dict(color="red"),
    mode='lines',
)

arima = go.Scatter(
    name='ARIMA',
    x=cmp_df.tail(predictions).index,
    y=cmp_df.tail(predictions).forecast,
    mode='lines'
)

# Trace order can be important
# with continuous error bars
data = [forecast, fact, arima]

layout = go.Layout(
    yaxis=dict(title='Посты'),
    title='Опубликованные посты на Хабрахабре',
    showlegend = True)

fig = go.Figure(data=data, layout=layout)
iplot(fig, show_link=False)