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In [1]:

    
import numpy as np
import pandas as pd

%matplotlib inline

# generate a daily signal covering one year 2016 in a pandas dataframe
N = 360
df_train = pd.DataFrame({"Date" : pd.date_range(start="2016-01-25", periods=N, freq='D'),
                         "Signal" : (np.arange(N)//40 + np.arange(N) % 21 + np.random.randn(N))})



In [2]:

    
df_train.head(12)



In [3]:

    
df_train.tail(12)



In [4]:

    
df_train.plot('Date' , ['Signal'])









    Out[4]:





<matplotlib.axes._subplots.AxesSubplot at 0x7fcc215ae190>



In [5]:

    
import pyaf.ForecastEngine as autof
# create a forecast engine. This is the main object handling all the operations
lEngine = autof.cForecastEngine()

# get the best time series model for predicting one week
lEngine.train(iInputDS = df_train, iTime = 'Date', iSignal = 'Signal', iHorizon = 7);
lEngine.getModelInfo() # => relative error 7% (MAPE)









    



INFO:pyaf.std:START_TRAINING 'Signal'
INFO:pyaf.std:END_TRAINING_TIME_IN_SECONDS 'Signal' 3.631828546524048
INFO:pyaf.std:TIME_DETAIL TimeVariable='Date' TimeMin=2016-01-25T00:00:00.000000 TimeMax=2016-11-01T00:00:00.000000 TimeDelta=<DateOffset: days=1> Horizon=7
INFO:pyaf.std:SIGNAL_DETAIL_ORIG SignalVariable='Signal' Length=360  Min=0.027145525383264396 Max=28.491166521760682  Mean=13.9752651851156 StdDev=6.745464386032752
INFO:pyaf.std:SIGNAL_DETAIL_TRANSFORMED TransformedSignalVariable='_Signal' Min=0.027145525383264396 Max=28.491166521760682  Mean=13.9752651851156 StdDev=6.745464386032752
INFO:pyaf.std:BEST_TRANSOFORMATION_TYPE '_'
INFO:pyaf.std:BEST_DECOMPOSITION  '_Signal_LinearTrend_residue_zeroCycle_residue_AR(64)' [LinearTrend + NoCycle + AR]
INFO:pyaf.std:TREND_DETAIL '_Signal_LinearTrend' [LinearTrend]
INFO:pyaf.std:CYCLE_DETAIL '_Signal_LinearTrend_residue_zeroCycle' [NoCycle]
INFO:pyaf.std:AUTOREG_DETAIL '_Signal_LinearTrend_residue_zeroCycle_residue_AR(64)' [AR]
INFO:pyaf.std:MODEL_MAPE MAPE_Fit=2.2173 MAPE_Forecast=0.0713 MAPE_Test=0.0595
INFO:pyaf.std:MODEL_SMAPE SMAPE_Fit=0.1361 SMAPE_Forecast=0.0698 SMAPE_Test=0.0585
INFO:pyaf.std:MODEL_MASE MASE_Fit=0.5431 MASE_Forecast=0.5007 MASE_Test=0.2778
INFO:pyaf.std:MODEL_L1 L1_Fit=1.195260193894542 L1_Forecast=1.060141286633323 L1_Test=1.1582861158218616
INFO:pyaf.std:MODEL_L2 L2_Fit=1.7177100349084475 L2_Forecast=1.3251401826407463 L2_Test=1.678482619786524
INFO:pyaf.std:MODEL_COMPLEXITY 80
INFO:pyaf.std:SIGNAL_TRANSFORMATION_DETAIL_START
INFO:pyaf.std:SIGNAL_TRANSFORMATION_MODEL_VALUES NoTransf None
INFO:pyaf.std:SIGNAL_TRANSFORMATION_DETAIL_END
INFO:pyaf.std:TREND_DETAIL_START
INFO:pyaf.std:LINEAR_RIDGE_TREND LinearTrend (9.403691122979271, array([6.98140088]))
INFO:pyaf.std:TREND_DETAIL_END
INFO:pyaf.std:CYCLE_MODEL_DETAIL_START
INFO:pyaf.std:ZERO_CYCLE_MODEL_VALUES _Signal_LinearTrend_residue_zeroCycle 0.0 {}
INFO:pyaf.std:CYCLE_MODEL_DETAIL_END
INFO:pyaf.std:AR_MODEL_DETAIL_START
INFO:pyaf.std:AR_MODEL_COEFF 1 _Signal_LinearTrend_residue_zeroCycle_residue_Lag21 0.6746522770771191
INFO:pyaf.std:AR_MODEL_COEFF 2 _Signal_LinearTrend_residue_zeroCycle_residue_Lag1 0.48637389973090045
INFO:pyaf.std:AR_MODEL_COEFF 3 _Signal_LinearTrend_residue_zeroCycle_residue_Lag22 -0.27524541489142673
INFO:pyaf.std:AR_MODEL_COEFF 4 _Signal_LinearTrend_residue_zeroCycle_residue_Lag60 -0.1993996620828393
INFO:pyaf.std:AR_MODEL_COEFF 5 _Signal_LinearTrend_residue_zeroCycle_residue_Lag39 0.15595896509711638
INFO:pyaf.std:AR_MODEL_COEFF 6 _Signal_LinearTrend_residue_zeroCycle_residue_Lag59 0.14597331930913565
INFO:pyaf.std:AR_MODEL_COEFF 7 _Signal_LinearTrend_residue_zeroCycle_residue_Lag42 0.14501063530572877
INFO:pyaf.std:AR_MODEL_COEFF 8 _Signal_LinearTrend_residue_zeroCycle_residue_Lag2 0.13893633403511302
INFO:pyaf.std:AR_MODEL_COEFF 9 _Signal_LinearTrend_residue_zeroCycle_residue_Lag63 0.12241844674616714
INFO:pyaf.std:AR_MODEL_COEFF 10 _Signal_LinearTrend_residue_zeroCycle_residue_Lag24 -0.11605535169842607
INFO:pyaf.std:AR_MODEL_DETAIL_END



In [ ]:



In [6]:

    
lEngine.standardPlots()









    



INFO:pyaf.std:START_PLOTTING
INFO:pyaf.std:END_PLOTTING_TIME_IN_SECONDS 1.3208849430084229



In [7]:

    
# predict one week
df_forecast = lEngine.forecast(iInputDS = df_train, iHorizon = 7)
# list the columns of the forecast dataset
print(df_forecast.columns) #

# print the real forecasts
# Future dates : ['2017-01-19T00:00:00.000000000' '2017-01-20T00:00:00.000000000' '2017-01-21T00:00:00.000000000' '2017-01-22T00:00:00.000000000' '2017-01-23T00:00:00.000000000' '2017-01-24T00:00:00.000000000' '2017-01-25T00:00:00.000000000']
print(df_forecast['Date'].tail(7).values)

# signal forecast : [ 9.74934646  10.04419761  12.15136455  12.20369717  14.09607727 15.68086323  16.22296559]
print(df_forecast['Signal_Forecast'].tail(7).values)









    



INFO:pyaf.std:START_FORECASTING 'Signal'
INFO:pyaf.std:END_FORECAST_TIME_IN_SECONDS  'Signal' 0.44658970832824707






    



Index(['Date', 'Signal', 'row_number', 'Date_Normalized', '_Signal',
       '_Signal_LinearTrend', '_Signal_LinearTrend_residue',
       '_Signal_LinearTrend_residue_zeroCycle',
       '_Signal_LinearTrend_residue_zeroCycle_residue',
       '_Signal_LinearTrend_residue_zeroCycle_residue_AR(64)',
       '_Signal_LinearTrend_residue_zeroCycle_residue_AR(64)_residue',
       '_Signal_Trend', '_Signal_Trend_residue', '_Signal_Cycle',
       '_Signal_Cycle_residue', '_Signal_AR', '_Signal_AR_residue',
       '_Signal_TransformedForecast', 'Signal_Forecast',
       '_Signal_TransformedResidue', 'Signal_Residue',
       'Signal_Forecast_Lower_Bound', 'Signal_Forecast_Upper_Bound'],
      dtype='object')
['2017-01-19T00:00:00.000000000' '2017-01-20T00:00:00.000000000'
 '2017-01-21T00:00:00.000000000' '2017-01-22T00:00:00.000000000'
 '2017-01-23T00:00:00.000000000' '2017-01-24T00:00:00.000000000'
 '2017-01-25T00:00:00.000000000']
[10.78370814 11.48682772 14.48123274 14.86866055 16.85808307 17.54883072
 17.84831708]



In [8]:

    
import pickle



In [9]:

    
lEngine_str = pickle.dumps(lEngine)



In [10]:

    
lEngine_reloaded = pickle.loads(lEngine_str)



In [11]:

    
df_forecast_aftrer_reload = lEngine_reloaded.forecast(iInputDS = df_train, iHorizon = 7)









    



INFO:pyaf.std:START_FORECASTING 'Signal'
INFO:pyaf.std:END_FORECAST_TIME_IN_SECONDS  'Signal' 0.44721293449401855



In [12]:

    
df_forecast_aftrer_reload









    Out[12]:







  
    
      
      Date
      Signal
      row_number
      Date_Normalized
      _Signal
      _Signal_LinearTrend
      _Signal_LinearTrend_residue
      _Signal_LinearTrend_residue_zeroCycle
      _Signal_LinearTrend_residue_zeroCycle_residue
      _Signal_LinearTrend_residue_zeroCycle_residue_AR(64)
      ...
      _Signal_Cycle
      _Signal_Cycle_residue
      _Signal_AR
      _Signal_AR_residue
      _Signal_TransformedForecast
      Signal_Forecast
      _Signal_TransformedResidue
      Signal_Residue
      Signal_Forecast_Lower_Bound
      Signal_Forecast_Upper_Bound
    
  
  
    
      0
      2016-01-25
      0.880853
      0
      0.000000
      0.880853
      9.403691
      -8.522838
      0.0
      -8.522838
      -5.349540
      ...
      0.0
      -8.522838
      -5.349540
      -3.173299
      4.054151
      4.054151
      -3.173299
      -3.173299
      NaN
      NaN
    
    
      1
      2016-01-26
      2.199877
      1
      0.003559
      2.199877
      9.428536
      -7.228659
      0.0
      -7.228659
      -5.349540
      ...
      0.0
      -7.228659
      -5.349540
      -1.879119
      4.078996
      4.078996
      -1.879119
      -1.879119
      NaN
      NaN
    
    
      2
      2016-01-27
      0.970246
      2
      0.007117
      0.970246
      9.453381
      -8.483135
      0.0
      -8.483135
      -4.720084
      ...
      0.0
      -8.483135
      -4.720084
      -3.763051
      4.733296
      4.733296
      -3.763051
      -3.763051
      NaN
      NaN
    
    
      3
      2016-01-28
      2.388152
      3
      0.010676
      2.388152
      9.478226
      -7.090074
      0.0
      -7.090074
      -5.150420
      ...
      0.0
      -7.090074
      -5.150420
      -1.939654
      4.327805
      4.327805
      -1.939654
      -1.939654
      NaN
      NaN
    
    
      4
      2016-01-29
      4.635198
      4
      0.014235
      4.635198
      9.503070
      -4.867872
      0.0
      -4.867872
      -4.506157
      ...
      0.0
      -4.867872
      -4.506157
      -0.361715
      4.996913
      4.996913
      -0.361715
      -0.361715
      NaN
      NaN
    
    
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
    
    
      362
      2017-01-21
      NaN
      362
      1.288256
      NaN
      18.397524
      NaN
      0.0
      NaN
      -3.916292
      ...
      0.0
      NaN
      -3.916292
      NaN
      14.481233
      14.481233
      NaN
      NaN
      10.306208
      18.656258
    
    
      363
      2017-01-22
      NaN
      363
      1.291815
      NaN
      18.422369
      NaN
      0.0
      NaN
      -3.553709
      ...
      0.0
      NaN
      -3.553709
      NaN
      14.868661
      14.868661
      NaN
      NaN
      7.486350
      22.250971
    
    
      364
      2017-01-23
      NaN
      364
      1.295374
      NaN
      18.447214
      NaN
      0.0
      NaN
      -1.589131
      ...
      0.0
      NaN
      -1.589131
      NaN
      16.858083
      16.858083
      NaN
      NaN
      1.011813
      32.704353
    
    
      365
      2017-01-24
      NaN
      365
      1.298932
      NaN
      18.472059
      NaN
      0.0
      NaN
      -0.923228
      ...
      0.0
      NaN
      -0.923228
      NaN
      17.548831
      17.548831
      NaN
      NaN
      -22.589787
      57.687449
    
    
      366
      2017-01-25
      NaN
      366
      1.302491
      NaN
      18.496904
      NaN
      0.0
      NaN
      -0.648587
      ...
      0.0
      NaN
      -0.648587
      NaN
      17.848317
      17.848317
      NaN
      NaN
      -79.809275
      115.505909
    
  

367 rows × 23 columns



In [13]:

    
lEngine_reloaded.standardPlots()









    



INFO:pyaf.std:START_PLOTTING
INFO:pyaf.std:END_PLOTTING_TIME_IN_SECONDS 1.3359224796295166



In [14]:

    
df_forecast.describe()









    Out[14]:







  
    
      
      Signal
      row_number
      Date_Normalized
      _Signal
      _Signal_LinearTrend
      _Signal_LinearTrend_residue
      _Signal_LinearTrend_residue_zeroCycle
      _Signal_LinearTrend_residue_zeroCycle_residue
      _Signal_LinearTrend_residue_zeroCycle_residue_AR(64)
      _Signal_LinearTrend_residue_zeroCycle_residue_AR(64)_residue
      ...
      _Signal_Cycle
      _Signal_Cycle_residue
      _Signal_AR
      _Signal_AR_residue
      _Signal_TransformedForecast
      Signal_Forecast
      _Signal_TransformedResidue
      Signal_Residue
      Signal_Forecast_Lower_Bound
      Signal_Forecast_Upper_Bound
    
  
  
    
      count
      360.000000
      367.000000
      367.000000
      360.000000
      367.000000
      360.000000
      367.0
      360.000000
      367.000000
      360.000000
      ...
      367.0
      360.000000
      367.000000
      360.000000
      367.000000
      367.000000
      360.000000
      360.000000
      7.000000
      7.000000
    
    
      mean
      13.975265
      183.000000
      0.651246
      13.975265
      13.950297
      0.111925
      0.0
      0.111925
      0.039526
      0.001961
      ...
      0.0
      0.111925
      0.039526
      0.001961
      13.989823
      13.989823
      0.001961
      0.001961
      -9.625397
      39.304157
    
    
      std
      6.754853
      106.088014
      0.377537
      6.754853
      2.635740
      6.159258
      0.0
      6.159258
      5.905480
      1.649212
      ...
      0.0
      6.159258
      5.905480
      1.649212
      6.492373
      6.492373
      1.649212
      1.649212
      32.979980
      36.902631
    
    
      min
      0.027146
      0.000000
      0.000000
      0.027146
      9.403691
      -11.036882
      0.0
      -11.036882
      -10.758659
      -14.825938
      ...
      0.0
      -11.036882
      -10.758659
      -14.825938
      1.204604
      1.204604
      -14.825938
      -14.825938
      -79.809275
      13.380983
    
    
      25%
      8.697157
      91.500000
      0.325623
      8.697157
      11.676994
      -5.180797
      0.0
      -5.180797
      -4.913539
      -0.937420
      ...
      0.0
      -5.180797
      -4.913539
      -0.937420
      8.641517
      8.641517
      -0.937420
      -0.937420
      -10.788987
      16.799716
    
    
      50%
      14.135705
      183.000000
      0.651246
      14.135705
      13.950297
      -0.031308
      0.0
      -0.031308
      -0.202544
      0.059820
      ...
      0.0
      -0.031308
      -0.202544
      0.059820
      13.738942
      13.738942
      0.059820
      0.059820
      7.486350
      22.250971
    
    
      75%
      19.039487
      274.500000
      0.976868
      19.039487
      16.223601
      5.604705
      0.0
      5.604705
      4.733548
      0.967600
      ...
      0.0
      5.604705
      4.733548
      0.967600
      18.975615
      18.975615
      0.967600
      0.967600
      8.108457
      45.195901
    
    
      max
      28.491167
      366.000000
      1.302491
      28.491167
      18.496904
      11.586469
      0.0
      11.586469
      11.653094
      6.079158
      ...
      0.0
      11.586469
      11.653094
      6.079158
      29.345681
      29.345681
      6.079158
      6.079158
      10.306208
      115.505909
    
  

8 rows × 22 columns



In [15]:

    
df_forecast_aftrer_reload.describe()









    Out[15]:







  
    
      
      Signal
      row_number
      Date_Normalized
      _Signal
      _Signal_LinearTrend
      _Signal_LinearTrend_residue
      _Signal_LinearTrend_residue_zeroCycle
      _Signal_LinearTrend_residue_zeroCycle_residue
      _Signal_LinearTrend_residue_zeroCycle_residue_AR(64)
      _Signal_LinearTrend_residue_zeroCycle_residue_AR(64)_residue
      ...
      _Signal_Cycle
      _Signal_Cycle_residue
      _Signal_AR
      _Signal_AR_residue
      _Signal_TransformedForecast
      Signal_Forecast
      _Signal_TransformedResidue
      Signal_Residue
      Signal_Forecast_Lower_Bound
      Signal_Forecast_Upper_Bound
    
  
  
    
      count
      360.000000
      367.000000
      367.000000
      360.000000
      367.000000
      360.000000
      367.0
      360.000000
      367.000000
      360.000000
      ...
      367.0
      360.000000
      367.000000
      360.000000
      367.000000
      367.000000
      360.000000
      360.000000
      7.000000
      7.000000
    
    
      mean
      13.975265
      183.000000
      0.651246
      13.975265
      13.950297
      0.111925
      0.0
      0.111925
      0.039526
      0.001961
      ...
      0.0
      0.111925
      0.039526
      0.001961
      13.989823
      13.989823
      0.001961
      0.001961
      -9.625397
      39.304157
    
    
      std
      6.754853
      106.088014
      0.377537
      6.754853
      2.635740
      6.159258
      0.0
      6.159258
      5.905480
      1.649212
      ...
      0.0
      6.159258
      5.905480
      1.649212
      6.492373
      6.492373
      1.649212
      1.649212
      32.979980
      36.902631
    
    
      min
      0.027146
      0.000000
      0.000000
      0.027146
      9.403691
      -11.036882
      0.0
      -11.036882
      -10.758659
      -14.825938
      ...
      0.0
      -11.036882
      -10.758659
      -14.825938
      1.204604
      1.204604
      -14.825938
      -14.825938
      -79.809275
      13.380983
    
    
      25%
      8.697157
      91.500000
      0.325623
      8.697157
      11.676994
      -5.180797
      0.0
      -5.180797
      -4.913539
      -0.937420
      ...
      0.0
      -5.180797
      -4.913539
      -0.937420
      8.641517
      8.641517
      -0.937420
      -0.937420
      -10.788987
      16.799716
    
    
      50%
      14.135705
      183.000000
      0.651246
      14.135705
      13.950297
      -0.031308
      0.0
      -0.031308
      -0.202544
      0.059820
      ...
      0.0
      -0.031308
      -0.202544
      0.059820
      13.738942
      13.738942
      0.059820
      0.059820
      7.486350
      22.250971
    
    
      75%
      19.039487
      274.500000
      0.976868
      19.039487
      16.223601
      5.604705
      0.0
      5.604705
      4.733548
      0.967600
      ...
      0.0
      5.604705
      4.733548
      0.967600
      18.975615
      18.975615
      0.967600
      0.967600
      8.108457
      45.195901
    
    
      max
      28.491167
      366.000000
      1.302491
      28.491167
      18.496904
      11.586469
      0.0
      11.586469
      11.653094
      6.079158
      ...
      0.0
      11.586469
      11.653094
      6.079158
      29.345681
      29.345681
      6.079158
      6.079158
      10.306208
      115.505909
    
  

8 rows × 22 columns



In [ ]:

	Date	Signal
348	2017-01-07	18.144331
349	2017-01-08	19.602178
350	2017-01-09	23.108227
351	2017-01-10	23.150759
352	2017-01-11	26.321980
353	2017-01-12	27.944177
354	2017-01-13	25.644317
355	2017-01-14	27.213906
356	2017-01-15	27.459849
357	2017-01-16	8.232758
358	2017-01-17	8.911270
359	2017-01-18	9.905317

	Date	Signal
0	2016-01-25	0.880853
1	2016-01-26	2.199877
2	2016-01-27	0.970246
3	2016-01-28	2.388152
4	2016-01-29	4.635198
5	2016-01-30	3.948748
6	2016-01-31	6.447459
7	2016-02-01	6.695498
8	2016-02-02	8.606010
9	2016-02-03	8.940483
10	2016-02-04	10.707869
11	2016-02-05	10.426022

	Date	Signal	row_number	Date_Normalized	_Signal	_Signal_LinearTrend	_Signal_LinearTrend_residue	_Signal_LinearTrend_residue_zeroCycle	_Signal_LinearTrend_residue_zeroCycle_residue	_Signal_LinearTrend_residue_zeroCycle_residue_AR(64)	...	_Signal_Cycle	_Signal_Cycle_residue	_Signal_AR	_Signal_AR_residue	_Signal_TransformedForecast	Signal_Forecast	_Signal_TransformedResidue	Signal_Residue	Signal_Forecast_Lower_Bound	Signal_Forecast_Upper_Bound
0	2016-01-25	0.880853	0	0.000000	0.880853	9.403691	-8.522838	0.0	-8.522838	-5.349540	...	0.0	-8.522838	-5.349540	-3.173299	4.054151	4.054151	-3.173299	-3.173299	NaN	NaN
1	2016-01-26	2.199877	1	0.003559	2.199877	9.428536	-7.228659	0.0	-7.228659	-5.349540	...	0.0	-7.228659	-5.349540	-1.879119	4.078996	4.078996	-1.879119	-1.879119	NaN	NaN
2	2016-01-27	0.970246	2	0.007117	0.970246	9.453381	-8.483135	0.0	-8.483135	-4.720084	...	0.0	-8.483135	-4.720084	-3.763051	4.733296	4.733296	-3.763051	-3.763051	NaN	NaN
3	2016-01-28	2.388152	3	0.010676	2.388152	9.478226	-7.090074	0.0	-7.090074	-5.150420	...	0.0	-7.090074	-5.150420	-1.939654	4.327805	4.327805	-1.939654	-1.939654	NaN	NaN
4	2016-01-29	4.635198	4	0.014235	4.635198	9.503070	-4.867872	0.0	-4.867872	-4.506157	...	0.0	-4.867872	-4.506157	-0.361715	4.996913	4.996913	-0.361715	-0.361715	NaN	NaN
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
362	2017-01-21	NaN	362	1.288256	NaN	18.397524	NaN	0.0	NaN	-3.916292	...	0.0	NaN	-3.916292	NaN	14.481233	14.481233	NaN	NaN	10.306208	18.656258
363	2017-01-22	NaN	363	1.291815	NaN	18.422369	NaN	0.0	NaN	-3.553709	...	0.0	NaN	-3.553709	NaN	14.868661	14.868661	NaN	NaN	7.486350	22.250971
364	2017-01-23	NaN	364	1.295374	NaN	18.447214	NaN	0.0	NaN	-1.589131	...	0.0	NaN	-1.589131	NaN	16.858083	16.858083	NaN	NaN	1.011813	32.704353
365	2017-01-24	NaN	365	1.298932	NaN	18.472059	NaN	0.0	NaN	-0.923228	...	0.0	NaN	-0.923228	NaN	17.548831	17.548831	NaN	NaN	-22.589787	57.687449
366	2017-01-25	NaN	366	1.302491	NaN	18.496904	NaN	0.0	NaN	-0.648587	...	0.0	NaN	-0.648587	NaN	17.848317	17.848317	NaN	NaN	-79.809275	115.505909

	Signal	row_number	Date_Normalized	_Signal	_Signal_LinearTrend	_Signal_LinearTrend_residue	_Signal_LinearTrend_residue_zeroCycle	_Signal_LinearTrend_residue_zeroCycle_residue	_Signal_LinearTrend_residue_zeroCycle_residue_AR(64)	_Signal_LinearTrend_residue_zeroCycle_residue_AR(64)_residue	...	_Signal_Cycle	_Signal_Cycle_residue	_Signal_AR	_Signal_AR_residue	_Signal_TransformedForecast	Signal_Forecast	_Signal_TransformedResidue	Signal_Residue	Signal_Forecast_Lower_Bound	Signal_Forecast_Upper_Bound
count	360.000000	367.000000	367.000000	360.000000	367.000000	360.000000	367.0	360.000000	367.000000	360.000000	...	367.0	360.000000	367.000000	360.000000	367.000000	367.000000	360.000000	360.000000	7.000000	7.000000
mean	13.975265	183.000000	0.651246	13.975265	13.950297	0.111925	0.0	0.111925	0.039526	0.001961	...	0.0	0.111925	0.039526	0.001961	13.989823	13.989823	0.001961	0.001961	-9.625397	39.304157
std	6.754853	106.088014	0.377537	6.754853	2.635740	6.159258	0.0	6.159258	5.905480	1.649212	...	0.0	6.159258	5.905480	1.649212	6.492373	6.492373	1.649212	1.649212	32.979980	36.902631
min	0.027146	0.000000	0.000000	0.027146	9.403691	-11.036882	0.0	-11.036882	-10.758659	-14.825938	...	0.0	-11.036882	-10.758659	-14.825938	1.204604	1.204604	-14.825938	-14.825938	-79.809275	13.380983
25%	8.697157	91.500000	0.325623	8.697157	11.676994	-5.180797	0.0	-5.180797	-4.913539	-0.937420	...	0.0	-5.180797	-4.913539	-0.937420	8.641517	8.641517	-0.937420	-0.937420	-10.788987	16.799716
50%	14.135705	183.000000	0.651246	14.135705	13.950297	-0.031308	0.0	-0.031308	-0.202544	0.059820	...	0.0	-0.031308	-0.202544	0.059820	13.738942	13.738942	0.059820	0.059820	7.486350	22.250971
75%	19.039487	274.500000	0.976868	19.039487	16.223601	5.604705	0.0	5.604705	4.733548	0.967600	...	0.0	5.604705	4.733548	0.967600	18.975615	18.975615	0.967600	0.967600	8.108457	45.195901
max	28.491167	366.000000	1.302491	28.491167	18.496904	11.586469	0.0	11.586469	11.653094	6.079158	...	0.0	11.586469	11.653094	6.079158	29.345681	29.345681	6.079158	6.079158	10.306208	115.505909