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In [1]:



    


import pandas as pd
import numpy as np

import pyaf.ForecastEngine as autof
import pyaf.Bench.TS_datasets as tsds


%matplotlib inline



    











In [2]:



    


# insert some logging
import logging
import logging.config

# remove the notebook root logger.
logger = logging.getLogger()
logger.handlers = []

# set default level
logging.basicConfig(level=logging.INFO)



    











In [3]:



    


b1 = tsds.load_ozone()
df = b1.mPastData



    


















    






     Month  Ozone       Time
0  1955-01    2.7 1955-01-01
1  1955-02    2.0 1955-02-01
2  1955-03    3.6 1955-03-01
3  1955-04    5.0 1955-04-01
4  1955-05    6.5 1955-05-01

















In [4]:



    


df.head()



    


















    
Out[4]:










  
    

      
      Month
      Ozone
      Time
    

  
  
    

      0
      1955-01
      2.7
      1955-01-01
    

    

      1
      1955-02
      2.0
      1955-02-01
    

    

      2
      1955-03
      3.6
      1955-03-01
    

    

      3
      1955-04
      5.0
      1955-04-01
    

    

      4
      1955-05
      6.5
      1955-05-01
    

  




















In [5]:



    


df.describe()



    


















    
Out[5]:










  
    

      
      Ozone
    

  
  
    

      count
      204.000000
    

    

      mean
      3.835784
    

    

      std
      1.495228
    

    

      min
      1.200000
    

    

      25%
      2.600000
    

    

      50%
      3.750000
    

    

      75%
      4.825000
    

    

      max
      8.700000
    

  




















In [6]:



    


lEngine = autof.cForecastEngine()
lEngine.mOptions.mParallelMode = False;
lEngine.mOptions.mEnableRNNModels = True;
lEngine

#lEngine.mOptions.enable_slow_mode()
#lEngine.mOptions.mCycle_Criterion = "L2";
#lEngine.mOptions.mCycle_Criterion_Threshold = 10000.2;



    


















    
Out[6]:








<pyaf.ForecastEngine.cForecastEngine at 0x7fea59590eb8>

















In [7]:



    


lEngine.train(df , 'Time' , 'Ozone', 12)



    


















    






INFO:pyaf.std:START_TRAINING 'Ozone'










    






ESTIMATE_RNN_MODEL_START _Ozone_PolyTrend_residue_bestCycle_byL2_residue










    






Using Theano backend.










    






ESTIMATE_RNN_MODEL_END _Ozone_PolyTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_PolyTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END _Ozone_PolyTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START _Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END _Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END _Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START _Ozone_ConstantTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END _Ozone_ConstantTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_ConstantTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END _Ozone_ConstantTrend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START _Ozone_Lag1Trend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END _Ozone_Lag1Trend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_Lag1Trend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END _Ozone_Lag1Trend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START _Ozone_LinearTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END _Ozone_LinearTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_LinearTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END _Ozone_LinearTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START _Ozone_PolyTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END _Ozone_PolyTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_PolyTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END _Ozone_PolyTrend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START _Ozone_LinearTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END _Ozone_LinearTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_LinearTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END _Ozone_LinearTrend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START _Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END _Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END _Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START _Ozone_ConstantTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END _Ozone_ConstantTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_ConstantTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END _Ozone_ConstantTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START _Ozone_Lag1Trend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END _Ozone_Lag1Trend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_Lag1Trend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END _Ozone_Lag1Trend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START _Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END _Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START _Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END _Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_Lag1Trend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_Lag1Trend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_Lag1Trend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_Lag1Trend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_LinearTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_LinearTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_LinearTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_LinearTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_ConstantTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_ConstantTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_ConstantTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_ConstantTrend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_Lag1Trend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_Lag1Trend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_Lag1Trend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_Lag1Trend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_PolyTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_PolyTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_PolyTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_PolyTrend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_ConstantTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_ConstantTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_ConstantTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_ConstantTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_LinearTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_LinearTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_LinearTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_LinearTrend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_PolyTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_PolyTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START Diff_Ozone_PolyTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END Diff_Ozone_PolyTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_PolyTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_PolyTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_PolyTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_PolyTrend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_LinearTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_LinearTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_LinearTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_LinearTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_LinearTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_LinearTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_LinearTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_LinearTrend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_Lag1Trend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_Lag1Trend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_Lag1Trend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_Lag1Trend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_ConstantTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_ConstantTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_ConstantTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_ConstantTrend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_ConstantTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_ConstantTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_ConstantTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_ConstantTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_Lag1Trend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_Lag1Trend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_Lag1Trend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_Lag1Trend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_PolyTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_PolyTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START RelDiff_Ozone_PolyTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END RelDiff_Ozone_PolyTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_PolyTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_Lag1Trend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_Lag1Trend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_Lag1Trend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_Lag1Trend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_ConstantTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_ConstantTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_ConstantTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_ConstantTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_LinearTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_ConstantTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_ConstantTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_ConstantTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_ConstantTrend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_PolyTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_PolyTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_PolyTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_PolyTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_PolyTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_PolyTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_PolyTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_PolyTrend_residue_zeroCycle_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_LinearTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_LinearTrend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_LinearTrend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_LinearTrend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_Lag1Trend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_Lag1Trend_residue_bestCycle_byL2_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_Lag1Trend_residue_bestCycle_byL2_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_Lag1Trend_residue_bestCycle_byL2_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_residue_MLP(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_LinearTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_LinearTrend_residue_zeroCycle_residue_LSTM(51)
ESTIMATE_RNN_MODEL_START CumSum_Ozone_LinearTrend_residue_zeroCycle_residue
ESTIMATE_RNN_MODEL_END CumSum_Ozone_LinearTrend_residue_zeroCycle_residue_MLP(51)










    






INFO:pyaf.std:END_TRAINING_TIME_IN_SECONDS 'Ozone' 272.17447447776794

















In [8]:



    


lEngine.getModelInfo()



    


















    






INFO:pyaf.std:TIME_DETAIL TimeVariable='Time' TimeMin=1955-01-01 00:00:00 TimeMax=1967-09-01 00:00:00 TimeDelta=30 days 10:25:15.789473 Estimation = (0 , 153) Validation = (153 , 192) Test = (192 , 204) Horizon=12
INFO:pyaf.std:SIGNAL_DETAIL SignalVariable='_Ozone' Min=1.2 Max=8.7  Mean=3.83578431373 StdDev=1.49155921594
INFO:pyaf.std:BEST_TRANSOFORMATION_TYPE '_'
INFO:pyaf.std:BEST_DECOMPOSITION  '_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)' [ConstantTrend + Seasonal_MonthOfYear + MLP(51)]
INFO:pyaf.std:TREND_DETAIL '_Ozone_ConstantTrend' [ConstantTrend]
INFO:pyaf.std:CYCLE_DETAIL '_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear' [Seasonal_MonthOfYear]
INFO:pyaf.std:AUTOREG_DETAIL '_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)' [MLP(51)]
INFO:pyaf.std:MODEL_MAPE MAPE_Fit=0.1745 MAPE_Forecast=0.1708 MAPE_Test=0.1679
INFO:pyaf.std:MODEL_L2 L2_Fit=0.856468397209 L2_Forecast=0.674872470161 L2_Test=0.460811489513
INFO:pyaf.std:MODEL_COMPLEXITY 55
INFO:pyaf.std:AR_MODEL_DETAIL_START
INFO:pyaf.std:AR_MODEL_DETAIL_END

















In [ ]:



    






    











In [9]:



    


type1 = np.dtype(df.Time)



    











In [10]:



    


type1.kind



    


















    
Out[10]:








'M'

















In [11]:



    


lEngine.mSignalDecomposition.mTrPerfDetails.head(14)



    


















    
Out[11]:










  
    

      
      Transformation
      Model
      Complexity
      FitCount
      FitL2
      FitMAPE
      ForecastCount
      ForecastL2
      ForecastMAPE
      TestCount
      TestL2
      TestMAPE
    

  
  
    

      41
      _Ozone
      _Ozone_LinearTrend_residue_Seasonal_MonthOfYea...
      20
      153
      0.896389
      0.1865
      39
      0.641888
      0.1796
      12
      0.678665
      0.2567
    

    

      3
      _Ozone
      _Ozone_LinearTrend_residue_bestCycle_byL2_resi...
      24
      153
      0.896389
      0.1865
      39
      0.641888
      0.1796
      12
      0.678665
      0.2567
    

    

      22
      _Ozone
      _Ozone_PolyTrend_residue_zeroCycle_residue_MLP...
      67
      153
      0.924430
      0.1907
      39
      0.660720
      0.1761
      12
      0.363398
      0.1100
    

    

      12
      _Ozone
      _Ozone_ConstantTrend_residue_zeroCycle_residue...
      51
      153
      0.929299
      0.1920
      39
      0.662870
      0.1831
      12
      0.372741
      0.1150
    

    

      28
      _Ozone
      _Ozone_LinearTrend_residue_zeroCycle_residue_M...
      67
      153
      0.924907
      0.1905
      39
      0.664863
      0.1685
      12
      0.352461
      0.1206
    

    

      21
      _Ozone
      _Ozone_PolyTrend_residue_Seasonal_MonthOfYear_...
      71
      153
      0.850663
      0.1740
      39
      0.674463
      0.1699
      12
      0.459306
      0.1637
    

    

      8
      _Ozone
      _Ozone_PolyTrend_residue_bestCycle_byL2_residu...
      75
      153
      0.850663
      0.1740
      39
      0.674463
      0.1699
      12
      0.459306
      0.1637
    

    

      2
      _Ozone
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfY...
      55
      153
      0.856468
      0.1745
      39
      0.674872
      0.1708
      12
      0.460811
      0.1679
    

    

      32
      _Ozone
      _Ozone_ConstantTrend_residue_bestCycle_byL2_re...
      59
      153
      0.856468
      0.1745
      39
      0.674872
      0.1708
      12
      0.460811
      0.1679
    

    

      33
      _Ozone
      _Ozone_LinearTrend_residue_Seasonal_MonthOfYea...
      71
      153
      0.851036
      0.1734
      39
      0.677740
      0.1708
      12
      0.449907
      0.1675
    

    

      11
      _Ozone
      _Ozone_LinearTrend_residue_bestCycle_byL2_resi...
      75
      153
      0.851036
      0.1734
      39
      0.677740
      0.1708
      12
      0.449907
      0.1675
    

    

      176
      CumSum_Ozone
      CumSum_Ozone_LinearTrend_residue_zeroCycle_res...
      99
      153
      1.192555
      0.2174
      39
      0.683213
      0.1915
      12
      0.369690
      0.1197
    

    

      165
      CumSum_Ozone
      CumSum_Ozone_PolyTrend_residue_zeroCycle_resid...
      99
      153
      1.358089
      0.2266
      39
      0.735697
      0.2189
      12
      0.507191
      0.1697
    

    

      13
      _Ozone
      _Ozone_PolyTrend_residue_zeroCycle_residue_AR(51)
      67
      153
      0.775068
      0.1520
      39
      0.769429
      0.1929
      12
      0.883996
      0.3055
    

  




















In [12]:



    


lEngine.getModelInfo()



    


















    






INFO:pyaf.std:TIME_DETAIL TimeVariable='Time' TimeMin=1955-01-01 00:00:00 TimeMax=1967-09-01 00:00:00 TimeDelta=30 days 10:25:15.789473 Estimation = (0 , 153) Validation = (153 , 192) Test = (192 , 204) Horizon=12
INFO:pyaf.std:SIGNAL_DETAIL SignalVariable='_Ozone' Min=1.2 Max=8.7  Mean=3.83578431373 StdDev=1.49155921594
INFO:pyaf.std:BEST_TRANSOFORMATION_TYPE '_'
INFO:pyaf.std:BEST_DECOMPOSITION  '_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)' [ConstantTrend + Seasonal_MonthOfYear + MLP(51)]
INFO:pyaf.std:TREND_DETAIL '_Ozone_ConstantTrend' [ConstantTrend]
INFO:pyaf.std:CYCLE_DETAIL '_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear' [Seasonal_MonthOfYear]
INFO:pyaf.std:AUTOREG_DETAIL '_Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)' [MLP(51)]
INFO:pyaf.std:MODEL_MAPE MAPE_Fit=0.1745 MAPE_Forecast=0.1708 MAPE_Test=0.1679
INFO:pyaf.std:MODEL_L2 L2_Fit=0.856468397209 L2_Forecast=0.674872470161 L2_Test=0.460811489513
INFO:pyaf.std:MODEL_COMPLEXITY 55
INFO:pyaf.std:AR_MODEL_DETAIL_START
INFO:pyaf.std:AR_MODEL_DETAIL_END

















In [13]:



    


lEngine.standrdPlots()



    


















    






/usr/lib/python3/dist-packages/matplotlib/__init__.py:1359: UserWarning:  This call to matplotlib.use() has no effect
because the backend has already been chosen;
matplotlib.use() must be called *before* pylab, matplotlib.pyplot,
or matplotlib.backends is imported for the first time.

  warnings.warn(_use_error_msg)










    

















    

















    

















    

















    
























In [14]:



    


lEngine.mSignalDecomposition.mBestModel.mTimeInfo.mTimeDelta



    


















    
Out[14]:








Timedelta('30 days 10:25:15.789473')

















In [15]:



    


dfapp = df.copy();



    











In [16]:



    


dfapp.head()



    


















    
Out[16]:










  
    

      
      Month
      Ozone
      Time
    

  
  
    

      0
      1955-01
      2.7
      1955-01-01
    

    

      1
      1955-02
      2.0
      1955-02-01
    

    

      2
      1955-03
      3.6
      1955-03-01
    

    

      3
      1955-04
      5.0
      1955-04-01
    

    

      4
      1955-05
      6.5
      1955-05-01
    

  




















In [ ]:



    






    











In [17]:



    


dfapp1 = lEngine.forecast(dfapp, 36);



    











In [18]:



    


dfapp1.head()



    


















    
Out[18]:










  
    

      
      Ozone
      Time
      _Ozone
      row_number
      Time_Normalized
      _Ozone_ConstantTrend
      _Ozone_ConstantTrend_residue
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
      ...
      _Ozone_Cycle
      _Ozone_Cycle_residue
      _Ozone_AR
      _Ozone_AR_residue
      _Ozone_TransformedForecast
      _Ozone_TransformedResidue
      Ozone_Forecast
      Ozone_Residue
      Ozone_Forecast_Lower_Bound
      Ozone_Forecast_Upper_Bound
    

  
  
    

      0
      2.7
      1955-01-01
      2.7
      0
      0.000000
      4.10915
      -1.40915
      -1.670689
      0.261538
      0.141487
      ...
      -1.670689
      0.261538
      0.141487
      0.120051
      2.579949
      0.120051
      2.579949
      0.120051
      NaN
      NaN
    

    

      1
      2.0
      1955-02-01
      2.0
      1
      0.006701
      4.10915
      -2.10915
      -1.447612
      -0.661538
      0.141487
      ...
      -1.447612
      -0.661538
      0.141487
      -0.803026
      2.803026
      -0.803026
      2.803026
      -0.803026
      NaN
      NaN
    

    

      2
      3.6
      1955-03-01
      3.6
      2
      0.012754
      4.10915
      -0.50915
      -0.762996
      0.253846
      -0.234731
      ...
      -0.762996
      0.253846
      -0.234731
      0.488577
      3.111423
      0.488577
      3.111423
      0.488577
      NaN
      NaN
    

    

      3
      5.0
      1955-04-01
      5.0
      3
      0.019455
      4.10915
      0.89085
      -0.209150
      1.100000
      -0.132631
      ...
      -0.209150
      1.100000
      -0.132631
      1.232631
      3.767369
      1.232631
      3.767369
      1.232631
      NaN
      NaN
    

    

      4
      6.5
      1955-05-01
      6.5
      4
      0.025940
      4.10915
      2.39085
      -0.093766
      2.484615
      0.311920
      ...
      -0.093766
      2.484615
      0.311920
      2.172695
      4.327305
      2.172695
      4.327305
      2.172695
      NaN
      NaN
    

  



5 rows × 23 columns



















In [19]:



    


dfapp1.tail(20)



    


















    
Out[19]:










  
    

      
      Ozone
      Time
      _Ozone
      row_number
      Time_Normalized
      _Ozone_ConstantTrend
      _Ozone_ConstantTrend_residue
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
      ...
      _Ozone_Cycle
      _Ozone_Cycle_residue
      _Ozone_AR
      _Ozone_AR_residue
      _Ozone_TransformedForecast
      _Ozone_TransformedResidue
      Ozone_Forecast
      Ozone_Residue
      Ozone_Forecast_Lower_Bound
      Ozone_Forecast_Upper_Bound
    

  
  
    

      220
      NaN
      1973-05-01
      3.601028
      220
      1.447255
      4.10915
      -0.508123
      -0.093766
      -0.414357
      -0.414357
      ...
      -0.093766
      -0.414357
      -0.414357
      0.000000e+00
      3.601028
      0.000000
      3.601028
      0.000000
      NaN
      NaN
    

    

      221
      NaN
      1973-06-01
      4.182711
      221
      1.453956
      4.10915
      0.073561
      0.806234
      -0.732674
      -0.732674
      ...
      0.806234
      -0.732674
      -0.732674
      3.330669e-16
      4.182711
      0.000000
      4.182711
      0.000000
      NaN
      NaN
    

    

      222
      NaN
      1973-07-01
      4.475823
      222
      1.460441
      4.10915
      0.366672
      1.298542
      -0.931870
      -0.931870
      ...
      1.298542
      -0.931870
      -0.931870
      -2.220446e-16
      4.475823
      0.000000
      4.475823
      0.000000
      NaN
      NaN
    

    

      223
      NaN
      1973-08-01
      4.373968
      223
      1.467142
      4.10915
      0.264818
      1.213927
      -0.949109
      -0.949109
      ...
      1.213927
      -0.949109
      -0.949109
      4.440892e-16
      4.373968
      0.000000
      4.373968
      0.000000
      NaN
      NaN
    

    

      224
      NaN
      1973-09-01
      4.560535
      224
      1.473843
      4.10915
      0.451385
      1.337004
      -0.885618
      -0.885618
      ...
      1.337004
      -0.885618
      -0.885618
      0.000000e+00
      4.560535
      0.000000
      4.560535
      0.000000
      NaN
      NaN
    

    

      225
      NaN
      1973-10-01
      3.970060
      225
      1.480329
      4.10915
      -0.139090
      0.899183
      -1.038273
      -1.038273
      ...
      0.899183
      -1.038273
      -1.038273
      -4.440892e-16
      3.970060
      0.000000
      3.970060
      0.000000
      NaN
      NaN
    

    

      226
      NaN
      1973-11-01
      2.961759
      226
      1.487030
      4.10915
      -1.147391
      -0.242484
      -0.904907
      -0.904907
      ...
      -0.242484
      -0.904907
      -0.904907
      0.000000e+00
      2.961759
      0.000000
      2.961759
      0.000000
      NaN
      NaN
    

    

      227
      NaN
      1973-12-01
      2.343474
      227
      1.493515
      4.10915
      -1.765676
      -1.167484
      -0.598193
      -0.598193
      ...
      -1.167484
      -0.598193
      -0.598193
      -2.220446e-16
      2.343474
      0.000000
      2.343474
      0.000000
      NaN
      NaN
    

    

      228
      NaN
      1974-01-01
      2.234247
      228
      1.500216
      4.10915
      -1.874903
      -1.670689
      -0.204214
      -0.204214
      ...
      -1.670689
      -0.204214
      -0.204214
      0.000000e+00
      2.234247
      0.000000
      2.234247
      0.000000
      NaN
      NaN
    

    

      229
      NaN
      1974-02-01
      2.658737
      229
      1.506917
      4.10915
      -1.450413
      -1.447612
      -0.002801
      -0.002801
      ...
      -1.447612
      -0.002801
      -0.002801
      0.000000e+00
      2.658737
      0.000000
      2.658737
      0.000000
      NaN
      NaN
    

    

      230
      NaN
      1974-03-01
      3.326651
      230
      1.512970
      4.10915
      -0.782499
      -0.762996
      -0.019502
      -0.019502
      ...
      -0.762996
      -0.019502
      -0.019502
      0.000000e+00
      3.326651
      0.000000
      3.326651
      0.000000
      NaN
      NaN
    

    

      231
      NaN
      1974-04-01
      3.836049
      231
      1.519671
      4.10915
      -0.273101
      -0.209150
      -0.063951
      -0.063951
      ...
      -0.209150
      -0.063951
      -0.063951
      -5.551115e-17
      3.836049
      0.000000
      3.836049
      0.000000
      NaN
      NaN
    

    

      232
      NaN
      1974-05-01
      3.830630
      232
      1.526157
      4.10915
      -0.278520
      -0.093766
      -0.184755
      -0.184755
      ...
      -0.093766
      -0.184755
      -0.184755
      2.775558e-17
      3.830630
      0.000000
      3.830630
      0.000000
      NaN
      NaN
    

    

      233
      NaN
      1974-06-01
      4.454764
      233
      1.532858
      4.10915
      0.345614
      0.806234
      -0.460620
      -0.460620
      ...
      0.806234
      -0.460620
      -0.460620
      3.330669e-16
      4.454764
      0.000000
      4.454764
      0.000000
      NaN
      NaN
    

    

      234
      NaN
      1974-07-01
      4.731885
      234
      1.539343
      4.10915
      0.622735
      1.298542
      -0.675807
      -0.675807
      ...
      1.298542
      -0.675807
      -0.675807
      -2.220446e-16
      4.731885
      0.000000
      4.731885
      0.000000
      NaN
      NaN
    

    

      235
      NaN
      1974-08-01
      4.630499
      235
      1.546044
      4.10915
      0.521348
      1.213927
      -0.692578
      -0.692578
      ...
      1.213927
      -0.692578
      -0.692578
      4.440892e-16
      4.630499
      0.000000
      4.630499
      0.000000
      NaN
      NaN
    

    

      236
      NaN
      1974-09-01
      4.725635
      236
      1.552745
      4.10915
      0.616485
      1.337004
      -0.720519
      -0.720519
      ...
      1.337004
      -0.720519
      -0.720519
      0.000000e+00
      4.725635
      0.000000
      4.725635
      0.000000
      NaN
      NaN
    

    

      237
      NaN
      1974-10-01
      4.245539
      237
      1.559230
      4.10915
      0.136389
      0.899183
      -0.762794
      -0.762794
      ...
      0.899183
      -0.762794
      -0.762794
      -3.330669e-16
      4.245539
      0.000000
      4.245539
      0.000000
      NaN
      NaN
    

    

      238
      NaN
      1974-11-01
      3.184436
      238
      1.565932
      4.10915
      -0.924714
      -0.242484
      -0.682230
      -0.682230
      ...
      -0.242484
      -0.682230
      -0.682230
      0.000000e+00
      3.184436
      0.000000
      3.184436
      0.000000
      NaN
      NaN
    

    

      239
      NaN
      1974-12-01
      3.184436
      239
      1.572417
      4.10915
      -0.924714
      -1.167484
      0.242770
      -0.380521
      ...
      -1.167484
      0.242770
      -0.380521
      6.232906e-01
      2.561146
      0.623291
      2.561146
      0.623291
      NaN
      NaN
    

  



20 rows × 23 columns



















In [20]:



    


#trdec.mTimeInfo.mTimeDelta



    











In [21]:



    


#trdec.mBestModelCycle.mDefaultValue



    











In [22]:



    


delta1 = np.mean(df['Time'] - df['Time'].shift(1))
delta1



    


















    
Out[22]:








Timedelta('30 days 10:24:14.187192')

















In [23]:



    


delta1.days



    


















    
Out[23]:








30

















In [24]:



    


import datetime as dt

#delta1/dt.timedelta(month = 1)



    











In [25]:



    


from dateutil import relativedelta
from datetime import datetime

date1 = datetime.strptime(str('2011-08-15 12:00:00'), '%Y-%m-%d %H:%M:%S')
date2 = datetime.strptime(str('2012-02-15'), '%Y-%m-%d')
r = relativedelta.relativedelta(date1, date2)
r 




In [26]:



    


r.months



    


















    
Out[26]:








-5

















In [27]:



    


r.weekday



    











In [28]:



    


dfapp.tail()



    


















    
Out[28]:










  
    

      
      Month
      Ozone
      Time
    

  
  
    

      199
      1971-08
      3.3
      1971-08-01
    

    

      200
      1971-09
      2.7
      1971-09-01
    

    

      201
      1971-10
      2.5
      1971-10-01
    

    

      202
      1971-11
      1.6
      1971-11-01
    

    

      203
      1971-12
      1.2
      1971-12-01
    

  




















In [29]:



    


lDecomp = lEngine.mSignalDecomposition



    











In [30]:



    


dfapp1 = lDecomp.forecast(dfapp, 36);
dfapp2 = dfapp1;
dfapp2['Ozone'] = df['Ozone']



    











In [31]:



    


dfapp1.tail(15)



    


















    
Out[31]:










  
    

      
      Ozone
      Time
      _Ozone
      row_number
      Time_Normalized
      _Ozone_ConstantTrend
      _Ozone_ConstantTrend_residue
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
      ...
      _Ozone_Cycle
      _Ozone_Cycle_residue
      _Ozone_AR
      _Ozone_AR_residue
      _Ozone_TransformedForecast
      _Ozone_TransformedResidue
      Ozone_Forecast
      Ozone_Residue
      Ozone_Forecast_Lower_Bound
      Ozone_Forecast_Upper_Bound
    

  
  
    

      225
      NaN
      1973-10-01
      3.970060
      225
      1.480329
      4.10915
      -0.139090
      0.899183
      -1.038273
      -1.038273
      ...
      0.899183
      -1.038273
      -1.038273
      -4.440892e-16
      3.970060
      0.000000
      3.970060
      0.000000
      NaN
      NaN
    

    

      226
      NaN
      1973-11-01
      2.961759
      226
      1.487030
      4.10915
      -1.147391
      -0.242484
      -0.904907
      -0.904907
      ...
      -0.242484
      -0.904907
      -0.904907
      0.000000e+00
      2.961759
      0.000000
      2.961759
      0.000000
      NaN
      NaN
    

    

      227
      NaN
      1973-12-01
      2.343474
      227
      1.493515
      4.10915
      -1.765676
      -1.167484
      -0.598193
      -0.598193
      ...
      -1.167484
      -0.598193
      -0.598193
      -2.220446e-16
      2.343474
      0.000000
      2.343474
      0.000000
      NaN
      NaN
    

    

      228
      NaN
      1974-01-01
      2.234247
      228
      1.500216
      4.10915
      -1.874903
      -1.670689
      -0.204214
      -0.204214
      ...
      -1.670689
      -0.204214
      -0.204214
      0.000000e+00
      2.234247
      0.000000
      2.234247
      0.000000
      NaN
      NaN
    

    

      229
      NaN
      1974-02-01
      2.658737
      229
      1.506917
      4.10915
      -1.450413
      -1.447612
      -0.002801
      -0.002801
      ...
      -1.447612
      -0.002801
      -0.002801
      0.000000e+00
      2.658737
      0.000000
      2.658737
      0.000000
      NaN
      NaN
    

    

      230
      NaN
      1974-03-01
      3.326651
      230
      1.512970
      4.10915
      -0.782499
      -0.762996
      -0.019502
      -0.019502
      ...
      -0.762996
      -0.019502
      -0.019502
      0.000000e+00
      3.326651
      0.000000
      3.326651
      0.000000
      NaN
      NaN
    

    

      231
      NaN
      1974-04-01
      3.836049
      231
      1.519671
      4.10915
      -0.273101
      -0.209150
      -0.063951
      -0.063951
      ...
      -0.209150
      -0.063951
      -0.063951
      -5.551115e-17
      3.836049
      0.000000
      3.836049
      0.000000
      NaN
      NaN
    

    

      232
      NaN
      1974-05-01
      3.830630
      232
      1.526157
      4.10915
      -0.278520
      -0.093766
      -0.184755
      -0.184755
      ...
      -0.093766
      -0.184755
      -0.184755
      2.775558e-17
      3.830630
      0.000000
      3.830630
      0.000000
      NaN
      NaN
    

    

      233
      NaN
      1974-06-01
      4.454764
      233
      1.532858
      4.10915
      0.345614
      0.806234
      -0.460620
      -0.460620
      ...
      0.806234
      -0.460620
      -0.460620
      3.330669e-16
      4.454764
      0.000000
      4.454764
      0.000000
      NaN
      NaN
    

    

      234
      NaN
      1974-07-01
      4.731885
      234
      1.539343
      4.10915
      0.622735
      1.298542
      -0.675807
      -0.675807
      ...
      1.298542
      -0.675807
      -0.675807
      -2.220446e-16
      4.731885
      0.000000
      4.731885
      0.000000
      NaN
      NaN
    

    

      235
      NaN
      1974-08-01
      4.630499
      235
      1.546044
      4.10915
      0.521348
      1.213927
      -0.692578
      -0.692578
      ...
      1.213927
      -0.692578
      -0.692578
      4.440892e-16
      4.630499
      0.000000
      4.630499
      0.000000
      NaN
      NaN
    

    

      236
      NaN
      1974-09-01
      4.725635
      236
      1.552745
      4.10915
      0.616485
      1.337004
      -0.720519
      -0.720519
      ...
      1.337004
      -0.720519
      -0.720519
      0.000000e+00
      4.725635
      0.000000
      4.725635
      0.000000
      NaN
      NaN
    

    

      237
      NaN
      1974-10-01
      4.245539
      237
      1.559230
      4.10915
      0.136389
      0.899183
      -0.762794
      -0.762794
      ...
      0.899183
      -0.762794
      -0.762794
      -3.330669e-16
      4.245539
      0.000000
      4.245539
      0.000000
      NaN
      NaN
    

    

      238
      NaN
      1974-11-01
      3.184436
      238
      1.565932
      4.10915
      -0.924714
      -0.242484
      -0.682230
      -0.682230
      ...
      -0.242484
      -0.682230
      -0.682230
      0.000000e+00
      3.184436
      0.000000
      3.184436
      0.000000
      NaN
      NaN
    

    

      239
      NaN
      1974-12-01
      3.184436
      239
      1.572417
      4.10915
      -0.924714
      -1.167484
      0.242770
      -0.380521
      ...
      -1.167484
      0.242770
      -0.380521
      6.232906e-01
      2.561146
      0.623291
      2.561146
      0.623291
      NaN
      NaN
    

  



15 rows × 23 columns



















In [32]:



    


dfapp1.describe()



    


















    
Out[32]:










  
    

      
      Ozone
      _Ozone
      row_number
      Time_Normalized
      _Ozone_ConstantTrend
      _Ozone_ConstantTrend_residue
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)
      _Ozone_ConstantTrend_residue_Seasonal_MonthOfYear_residue_MLP(51)_residue
      ...
      _Ozone_Cycle
      _Ozone_Cycle_residue
      _Ozone_AR
      _Ozone_AR_residue
      _Ozone_TransformedForecast
      _Ozone_TransformedResidue
      Ozone_Forecast
      Ozone_Residue
      Ozone_Forecast_Lower_Bound
      Ozone_Forecast_Upper_Bound
    

  
  
    

      count
      204.000000
      240.000000
      240.00000
      240.000000
      2.400000e+02
      240.000000
      240.000000
      240.000000
      240.000000
      240.000000
      ...
      240.000000
      240.000000
      240.000000
      240.000000
      240.000000
      240.000000
      240.000000
      240.000000
      12.000000
      12.000000
    

    

      mean
      3.835784
      3.758242
      119.50000
      0.786145
      4.109150e+00
      -0.350908
      -0.003274
      -0.347634
      -0.381532
      0.033898
      ...
      -0.003274
      -0.347634
      -0.381532
      0.033898
      3.724344
      0.033898
      3.724344
      0.033898
      -0.054176
      5.620173
    

    

      std
      1.495228
      1.441084
      69.42622
      0.456804
      8.900346e-16
      1.441084
      1.056921
      1.057402
      0.827585
      0.745011
      ...
      1.056921
      1.057402
      0.827585
      0.745011
      1.315879
      0.745011
      1.315879
      0.745011
      2.537772
      2.444325
    

    

      min
      1.200000
      0.853364
      0.00000
      0.000000
      4.109150e+00
      -3.255786
      -1.670689
      -2.746154
      -2.274348
      -2.026227
      ...
      -1.670689
      -2.746154
      -2.274348
      -2.026227
      0.796675
      -2.026227
      0.796675
      -2.026227
      -6.472498
      2.203109
    

    

      25%
      2.600000
      2.600000
      59.75000
      0.393050
      4.109150e+00
      -1.509150
      -0.864118
      -1.042788
      -0.906137
      -0.416839
      ...
      -0.864118
      -1.042788
      -0.906137
      -0.416839
      2.732796
      -0.416839
      2.732796
      -0.416839
      -0.511775
      4.032679
    

    

      50%
      3.750000
      3.700000
      119.50000
      0.786316
      4.109150e+00
      -0.409150
      -0.151458
      -0.543910
      -0.518504
      0.000000
      ...
      -0.151458
      -0.543910
      -0.518504
      0.000000
      3.693467
      0.000000
      3.693467
      0.000000
      1.015992
      5.528884
    

    

      75%
      4.825000
      4.700000
      179.25000
      1.179367
      4.109150e+00
      0.590850
      0.977869
      0.180609
      -0.057490
      0.414728
      ...
      0.977869
      0.180609
      -0.057490
      0.414728
      4.587987
      0.414728
      4.587987
      0.414728
      1.466851
      6.875519
    

    

      max
      8.700000
      8.700000
      239.00000
      1.572417
      4.109150e+00
      4.590850
      1.337004
      4.333333
      2.239536
      3.436709
      ...
      1.337004
      4.333333
      2.239536
      3.436709
      7.326227
      3.436709
      7.326227
      3.436709
      1.952849
      10.489833
    

  



8 rows × 22 columns



















In [ ]:



    






    











In [ ]:

Content source: antoinecarme/pyaf

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