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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 [ ]:



In [2]:

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



In [3]:

    
lEngine = autof.cForecastEngine()
lEngine.mOptions.set_active_autoregressions(['XGB']);
lEngine









    Out[3]:





<pyaf.ForecastEngine.cForecastEngine at 0x7f83ac05e748>



In [4]:

    
lEngine.train(df , 'time' , 'AirPassengers' , 12)









    



INFO:pyaf.std:START_TRAINING 'AirPassengers'
INFO:pyaf.std:END_TRAINING_TIME_IN_SECONDS 'AirPassengers' 2.235266923904419



In [5]:

    
lEngine.getModelInfo()









    



INFO:pyaf.std:TIME_DETAIL TimeVariable='time' TimeMin=1949.0 TimeMax=1956.91666666667 TimeDelta=0.08333333333336763 Estimation = (0 , 96) Validation = (96 , 120) Test = (120 , 132) Horizon=12
INFO:pyaf.std:SIGNAL_DETAIL_ORIG SignalVariable='AirPassengers' Min=104 Max=559  Mean=262.49242424242425 StdDev=106.22114554451818
INFO:pyaf.std:SIGNAL_DETAIL_TRANSFORMED TransformedSignalVariable='_AirPassengers' Min=104 Max=559  Mean=262.49242424242425 StdDev=106.22114554451818
INFO:pyaf.std:BEST_TRANSOFORMATION_TYPE '_'
INFO:pyaf.std:BEST_DECOMPOSITION  '_AirPassengers_Lag1Trend_residue_zeroCycle_residue_XGB(33)' [Lag1Trend + NoCycle + XGB(33)]
INFO:pyaf.std:TREND_DETAIL '_AirPassengers_Lag1Trend' [Lag1Trend]
INFO:pyaf.std:CYCLE_DETAIL '_AirPassengers_Lag1Trend_residue_zeroCycle' [NoCycle]
INFO:pyaf.std:AUTOREG_DETAIL '_AirPassengers_Lag1Trend_residue_zeroCycle_residue_XGB(33)' [XGB(33)]
INFO:pyaf.std:MODEL_MAPE MAPE_Fit=0.0462 MAPE_Forecast=0.0573 MAPE_Test=0.0605
INFO:pyaf.std:MODEL_SMAPE SMAPE_Fit=0.0463 SMAPE_Forecast=0.0567 SMAPE_Test=0.0604
INFO:pyaf.std:MODEL_MASE MASE_Fit=0.509 MASE_Forecast=0.5932 MASE_Test=0.5862
INFO:pyaf.std:MODEL_L1 L1_Fit=9.515539964661002 L1_Forecast=21.974543072283268 L1_Test=26.379404107729595
INFO:pyaf.std:MODEL_L2 L2_Fit=11.98602826027876 L2_Forecast=28.4310550998623 L2_Test=33.615401234524924
INFO:pyaf.std:MODEL_COMPLEXITY 98
INFO:pyaf.std:AR_MODEL_DETAIL_START
INFO:pyaf.std:AR_MODEL_DETAIL_END



In [6]:

    
lEngine.standardPlots()









    



INFO:pyaf.std:START_PLOTTING
INFO:pyaf.std:END_PLOTTING_TIME_IN_SECONDS 2.2884480953216553



In [ ]:



In [7]:

    
lEngine.mSignalDecomposition.mTrPerfDetails









    Out[7]:







  
    
      
      Transformation
      Model
      Complexity
      FitMAPE
      ForecastMAPE
      TestMAPE
    
  
  
    
      0
      _AirPassengers
      _AirPassengers_Lag1Trend_residue_zeroCycle_res...
      98
      4.620000e-02
      5.730000e-02
      6.050000e-02
    
    
      1
      _AirPassengers
      _AirPassengers_Lag1Trend_residue_bestCycle_byL...
      106
      4.570000e-02
      5.890000e-02
      6.230000e-02
    
    
      2
      Diff_AirPassengers
      Diff_AirPassengers_PolyTrend_residue_bestCycle...
      122
      8.130000e-02
      6.790000e-02
      2.069000e-01
    
    
      3
      Diff_AirPassengers
      Diff_AirPassengers_PolyTrend_residue_zeroCycle...
      114
      9.200000e-02
      6.800000e-02
      1.862000e-01
    
    
      4
      Diff_AirPassengers
      Diff_AirPassengers_Lag1Trend_residue_zeroCycle...
      130
      6.530000e-02
      7.330000e-02
      8.010000e-02
    
    
      5
      _AirPassengers
      _AirPassengers_LinearTrend_residue_bestCycle_b...
      90
      5.860000e-02
      8.310000e-02
      9.560000e-02
    
    
      6
      Diff_AirPassengers
      Diff_AirPassengers_Lag1Trend_residue_bestCycle...
      138
      8.160000e-02
      8.310000e-02
      6.930000e-02
    
    
      7
      _AirPassengers
      _AirPassengers_LinearTrend_residue_zeroCycle_r...
      82
      5.930000e-02
      8.460000e-02
      9.330000e-02
    
    
      8
      Diff_AirPassengers
      Diff_AirPassengers_ConstantTrend_residue_zeroC...
      98
      1.012000e-01
      8.570000e-02
      7.740000e-02
    
    
      9
      Diff_AirPassengers
      Diff_AirPassengers_LinearTrend_residue_zeroCyc...
      114
      7.360000e-02
      8.650000e-02
      7.990000e-02
    
    
      10
      Diff_AirPassengers
      Diff_AirPassengers_LinearTrend_residue_bestCyc...
      122
      6.290000e-02
      8.980000e-02
      7.710000e-02
    
    
      11
      Diff_AirPassengers
      Diff_AirPassengers_ConstantTrend_residue_bestC...
      106
      6.540000e-02
      9.310000e-02
      8.030000e-02
    
    
      12
      CumSum_AirPassengers
      CumSum_AirPassengers_Lag1Trend_residue_zeroCyc...
      130
      6.950000e-02
      9.760000e-02
      9.900000e-02
    
    
      13
      CumSum_AirPassengers
      CumSum_AirPassengers_Lag1Trend_residue_bestCyc...
      138
      7.650000e-02
      9.940000e-02
      9.960000e-02
    
    
      14
      _AirPassengers
      _AirPassengers_PolyTrend_residue_bestCycle_byL...
      90
      5.430000e-02
      1.205000e-01
      1.713000e-01
    
    
      15
      _AirPassengers
      _AirPassengers_PolyTrend_residue_zeroCycle_res...
      82
      5.520000e-02
      1.207000e-01
      1.721000e-01
    
    
      16
      CumSum_AirPassengers
      CumSum_AirPassengers_PolyTrend_residue_zeroCyc...
      114
      1.581000e-01
      1.750000e-01
      2.691000e-01
    
    
      17
      _AirPassengers
      _AirPassengers_ConstantTrend_residue_zeroCycle...
      66
      1.218000e-01
      2.009000e-01
      2.950000e-01
    
    
      18
      _AirPassengers
      _AirPassengers_ConstantTrend_residue_bestCycle...
      74
      1.222000e-01
      2.010000e-01
      2.940000e-01
    
    
      19
      CumSum_AirPassengers
      CumSum_AirPassengers_PolyTrend_residue_bestCyc...
      122
      1.766000e-01
      2.038000e-01
      2.943000e-01
    
    
      20
      CumSum_AirPassengers
      CumSum_AirPassengers_LinearTrend_residue_zeroC...
      114
      1.810000e-01
      4.856000e-01
      5.501000e-01
    
    
      21
      CumSum_AirPassengers
      CumSum_AirPassengers_LinearTrend_residue_bestC...
      122
      3.361000e-01
      4.956000e-01
      5.648000e-01
    
    
      22
      CumSum_AirPassengers
      CumSum_AirPassengers_ConstantTrend_residue_bes...
      106
      1.068600e+00
      9.788000e-01
      1.148800e+00
    
    
      23
      CumSum_AirPassengers
      CumSum_AirPassengers_ConstantTrend_residue_zer...
      98
      9.103000e-01
      1.000000e+00
      1.000000e+00
    
    
      24
      RelDiff_AirPassengers
      RelDiff_AirPassengers_ConstantTrend_residue_ze...
      98
      4.106115e+06
      2.183870e+06
      1.910118e+06
    
    
      25
      RelDiff_AirPassengers
      RelDiff_AirPassengers_LinearTrend_residue_best...
      122
      4.106168e+06
      2.183870e+06
      1.910118e+06
    
    
      26
      RelDiff_AirPassengers
      RelDiff_AirPassengers_PolyTrend_residue_bestCy...
      122
      4.106172e+06
      2.183870e+06
      1.910119e+06
    
    
      27
      RelDiff_AirPassengers
      RelDiff_AirPassengers_PolyTrend_residue_zeroCy...
      114
      4.106204e+06
      2.183870e+06
      1.910118e+06
    
    
      28
      RelDiff_AirPassengers
      RelDiff_AirPassengers_ConstantTrend_residue_be...
      106
      4.106115e+06
      2.183870e+06
      1.910119e+06
    
    
      29
      RelDiff_AirPassengers
      RelDiff_AirPassengers_LinearTrend_residue_zero...
      114
      4.106200e+06
      2.183870e+06
      1.910119e+06
    
    
      30
      RelDiff_AirPassengers
      RelDiff_AirPassengers_Lag1Trend_residue_zeroCy...
      130
      4.035498e+06
      2.183870e+06
      1.910119e+06
    
    
      31
      RelDiff_AirPassengers
      RelDiff_AirPassengers_Lag1Trend_residue_bestCy...
      138
      4.106113e+06
      2.183870e+06
      1.910119e+06



In [8]:

    
dfapp = df.copy();
dfapp.tail()









    Out[8]:







  
    
      
      time
      AirPassengers
    
    
      ID
      
      
    
  
  
    
      128
      1959.583333
      559
    
    
      129
      1959.666667
      463
    
    
      130
      1959.750000
      407
    
    
      131
      1959.833333
      362
    
    
      132
      1959.916667
      405



In [9]:

    
dfapp1 = lEngine.forecast(dfapp, 15);









    



INFO:pyaf.std:START_FORECASTING
INFO:pyaf.std:END_FORECAST_TIME_IN_SECONDS 1.1618320941925049



In [10]:

    
dfapp1.info()









    



<class 'pandas.core.frame.DataFrame'>
RangeIndex: 147 entries, 0 to 146
Data columns (total 23 columns):
time                                                                  147 non-null float64
AirPassengers                                                         132 non-null float64
_AirPassengers                                                        132 non-null float64
row_number                                                            147 non-null int64
time_Normalized                                                       147 non-null float64
_AirPassengers_Lag1Trend                                              147 non-null float64
_AirPassengers_Lag1Trend_residue                                      132 non-null float64
_AirPassengers_Lag1Trend_residue_zeroCycle                            147 non-null float64
_AirPassengers_Lag1Trend_residue_zeroCycle_residue                    132 non-null float64
_AirPassengers_Lag1Trend_residue_zeroCycle_residue_XGB(33)            147 non-null float32
_AirPassengers_Lag1Trend_residue_zeroCycle_residue_XGB(33)_residue    132 non-null float64
_AirPassengers_Trend                                                  147 non-null float64
_AirPassengers_Trend_residue                                          132 non-null float64
_AirPassengers_Cycle                                                  147 non-null float64
_AirPassengers_Cycle_residue                                          132 non-null float64
_AirPassengers_AR                                                     147 non-null float32
_AirPassengers_AR_residue                                             132 non-null float64
_AirPassengers_TransformedForecast                                    147 non-null float64
AirPassengers_Forecast                                                147 non-null float64
_AirPassengers_TransformedResidue                                     132 non-null float64
AirPassengers_Residue                                                 132 non-null float64
AirPassengers_Forecast_Lower_Bound                                    12 non-null float64
AirPassengers_Forecast_Upper_Bound                                    12 non-null float64
dtypes: float32(2), float64(20), int64(1)
memory usage: 25.3 KB



In [11]:

    
dfapp1.tail(15)









    Out[11]:







  
    
      
      time
      AirPassengers
      _AirPassengers
      row_number
      time_Normalized
      _AirPassengers_Lag1Trend
      _AirPassengers_Lag1Trend_residue
      _AirPassengers_Lag1Trend_residue_zeroCycle
      _AirPassengers_Lag1Trend_residue_zeroCycle_residue
      _AirPassengers_Lag1Trend_residue_zeroCycle_residue_XGB(33)
      ...
      _AirPassengers_Cycle
      _AirPassengers_Cycle_residue
      _AirPassengers_AR
      _AirPassengers_AR_residue
      _AirPassengers_TransformedForecast
      AirPassengers_Forecast
      _AirPassengers_TransformedResidue
      AirPassengers_Residue
      AirPassengers_Forecast_Lower_Bound
      AirPassengers_Forecast_Upper_Bound
    
  
  
    
      132
      1960.000000
      NaN
      NaN
      132
      1.389474
      405.000000
      NaN
      0.0
      NaN
      11.257255
      ...
      0.0
      NaN
      11.257255
      NaN
      416.257255
      416.257255
      NaN
      NaN
      360.532387
      471.982123
    
    
      133
      1960.083333
      NaN
      NaN
      133
      1.400000
      416.257255
      NaN
      0.0
      NaN
      -12.380074
      ...
      0.0
      NaN
      -12.380074
      NaN
      403.877181
      403.877181
      NaN
      NaN
      315.148449
      492.605913
    
    
      134
      1960.166667
      NaN
      NaN
      134
      1.410526
      403.877181
      NaN
      0.0
      NaN
      22.446426
      ...
      0.0
      NaN
      22.446426
      NaN
      426.323607
      426.323607
      NaN
      NaN
      312.866133
      539.781081
    
    
      135
      1960.250000
      NaN
      NaN
      135
      1.421053
      426.323607
      NaN
      0.0
      NaN
      -2.562091
      ...
      0.0
      NaN
      -2.562091
      NaN
      423.761517
      423.761517
      NaN
      NaN
      302.807124
      544.715909
    
    
      136
      1960.333333
      NaN
      NaN
      136
      1.431579
      423.761517
      NaN
      0.0
      NaN
      15.197581
      ...
      0.0
      NaN
      15.197581
      NaN
      438.959098
      438.959098
      NaN
      NaN
      307.866554
      570.051642
    
    
      137
      1960.416667
      NaN
      NaN
      137
      1.442105
      438.959098
      NaN
      0.0
      NaN
      21.488630
      ...
      0.0
      NaN
      21.488630
      NaN
      460.447728
      460.447728
      NaN
      NaN
      314.138663
      606.756793
    
    
      138
      1960.500000
      NaN
      NaN
      138
      1.452632
      460.447728
      NaN
      0.0
      NaN
      22.423498
      ...
      0.0
      NaN
      22.423498
      NaN
      482.871226
      482.871226
      NaN
      NaN
      318.740413
      647.002039
    
    
      139
      1960.583333
      NaN
      NaN
      139
      1.463158
      482.871226
      NaN
      0.0
      NaN
      5.331924
      ...
      0.0
      NaN
      5.331924
      NaN
      488.203151
      488.203151
      NaN
      NaN
      302.369406
      674.036895
    
    
      140
      1960.666667
      NaN
      NaN
      140
      1.473684
      488.203151
      NaN
      0.0
      NaN
      -22.371239
      ...
      0.0
      NaN
      -22.371239
      NaN
      465.831912
      465.831912
      NaN
      NaN
      260.836887
      670.826937
    
    
      141
      1960.750000
      NaN
      NaN
      141
      1.484211
      465.831912
      NaN
      0.0
      NaN
      -22.371239
      ...
      0.0
      NaN
      -22.371239
      NaN
      443.460673
      443.460673
      NaN
      NaN
      221.547867
      665.373479
    
    
      142
      1960.833333
      NaN
      NaN
      142
      1.494737
      443.460673
      NaN
      0.0
      NaN
      -20.387133
      ...
      0.0
      NaN
      -20.387133
      NaN
      423.073541
      423.073541
      NaN
      NaN
      187.552105
      658.594976
    
    
      143
      1960.916667
      NaN
      NaN
      143
      1.505263
      423.073541
      NaN
      0.0
      NaN
      23.381294
      ...
      0.0
      NaN
      23.381294
      NaN
      446.454835
      446.454835
      NaN
      NaN
      201.624799
      691.284871
    
    
      144
      1961.000000
      NaN
      NaN
      144
      1.515789
      446.454835
      NaN
      0.0
      NaN
      11.764988
      ...
      0.0
      NaN
      11.764988
      NaN
      458.219823
      458.219823
      NaN
      NaN
      NaN
      NaN
    
    
      145
      1961.083333
      NaN
      NaN
      145
      1.526316
      458.219823
      NaN
      0.0
      NaN
      -4.271869
      ...
      0.0
      NaN
      -4.271869
      NaN
      453.947954
      453.947954
      NaN
      NaN
      NaN
      NaN
    
    
      146
      1961.166667
      NaN
      NaN
      146
      1.536842
      453.947954
      NaN
      0.0
      NaN
      17.950855
      ...
      0.0
      NaN
      17.950855
      NaN
      471.898809
      471.898809
      NaN
      NaN
      NaN
      NaN
    
  

15 rows × 23 columns



In [12]:

    
dfapp1.describe()









    Out[12]:







  
    
      
      time
      AirPassengers
      _AirPassengers
      row_number
      time_Normalized
      _AirPassengers_Lag1Trend
      _AirPassengers_Lag1Trend_residue
      _AirPassengers_Lag1Trend_residue_zeroCycle
      _AirPassengers_Lag1Trend_residue_zeroCycle_residue
      _AirPassengers_Lag1Trend_residue_zeroCycle_residue_XGB(33)
      ...
      _AirPassengers_Cycle
      _AirPassengers_Cycle_residue
      _AirPassengers_AR
      _AirPassengers_AR_residue
      _AirPassengers_TransformedForecast
      AirPassengers_Forecast
      _AirPassengers_TransformedResidue
      AirPassengers_Residue
      AirPassengers_Forecast_Lower_Bound
      AirPassengers_Forecast_Upper_Bound
    
  
  
    
      count
      147.000000
      132.000000
      132.000000
      147.000000
      147.000000
      147.000000
      132.000000
      147.0
      132.000000
      147.000000
      ...
      147.0
      132.000000
      147.000000
      132.000000
      147.000000
      147.000000
      132.000000
      132.000000
      12.000000
      12.000000
    
    
      mean
      1955.083333
      262.492424
      262.492424
      73.000000
      0.768421
      278.861833
      2.219697
      0.0
      2.219697
      1.925769
      ...
      0.0
      2.219697
      1.925769
      0.581900
      280.787602
      280.787602
      0.581900
      0.581900
      283.835899
      602.751055
    
    
      std
      3.548278
      106.625799
      106.625799
      42.579338
      0.448204
      115.498181
      31.252802
      0.0
      31.252802
      14.649807
      ...
      0.0
      31.252802
      14.649807
      18.882293
      115.069530
      115.069530
      18.882293
      18.882293
      53.564763
      76.398211
    
    
      min
      1949.000000
      104.000000
      104.000000
      0.000000
      0.000000
      104.000000
      -101.000000
      0.0
      -101.000000
      -22.371239
      ...
      0.0
      -101.000000
      -22.371239
      -78.628761
      105.451597
      105.451597
      -78.628761
      -78.628761
      187.552105
      471.982123
    
    
      25%
      1952.041667
      176.500000
      176.500000
      36.500000
      0.384211
      180.000000
      -15.250000
      0.0
      -15.250000
      -9.029420
      ...
      0.0
      -15.250000
      -9.029420
      -9.078444
      185.123296
      185.123296
      -9.078444
      -9.078444
      251.014632
      543.482202
    
    
      50%
      1955.083333
      239.500000
      239.500000
      73.000000
      0.768421
      267.000000
      2.500000
      0.0
      2.500000
      0.738561
      ...
      0.0
      2.500000
      0.738561
      0.449085
      266.509766
      266.509766
      0.449085
      0.449085
      305.336839
      626.879416
    
    
      75%
      1958.125000
      343.250000
      343.250000
      109.500000
      1.152632
      362.000000
      21.000000
      0.0
      21.000000
      15.197581
      ...
      0.0
      21.000000
      15.197581
      11.660267
      371.413860
      371.413860
      11.660267
      11.660267
      314.391110
      666.736844
    
    
      max
      1961.166667
      559.000000
      559.000000
      146.000000
      1.536842
      559.000000
      76.000000
      0.0
      76.000000
      23.381294
      ...
      0.0
      76.000000
      23.381294
      53.576502
      560.192122
      560.192122
      53.576502
      53.576502
      360.532387
      691.284871
    
  

8 rows × 23 columns



In [ ]:

	Transformation	Model	Complexity	FitMAPE	ForecastMAPE	TestMAPE
0	_AirPassengers	_AirPassengers_Lag1Trend_residue_zeroCycle_res...	98	4.620000e-02	5.730000e-02	6.050000e-02
1	_AirPassengers	_AirPassengers_Lag1Trend_residue_bestCycle_byL...	106	4.570000e-02	5.890000e-02	6.230000e-02
2	Diff_AirPassengers	Diff_AirPassengers_PolyTrend_residue_bestCycle...	122	8.130000e-02	6.790000e-02	2.069000e-01
3	Diff_AirPassengers	Diff_AirPassengers_PolyTrend_residue_zeroCycle...	114	9.200000e-02	6.800000e-02	1.862000e-01
4	Diff_AirPassengers	Diff_AirPassengers_Lag1Trend_residue_zeroCycle...	130	6.530000e-02	7.330000e-02	8.010000e-02
5	_AirPassengers	_AirPassengers_LinearTrend_residue_bestCycle_b...	90	5.860000e-02	8.310000e-02	9.560000e-02
6	Diff_AirPassengers	Diff_AirPassengers_Lag1Trend_residue_bestCycle...	138	8.160000e-02	8.310000e-02	6.930000e-02
7	_AirPassengers	_AirPassengers_LinearTrend_residue_zeroCycle_r...	82	5.930000e-02	8.460000e-02	9.330000e-02
8	Diff_AirPassengers	Diff_AirPassengers_ConstantTrend_residue_zeroC...	98	1.012000e-01	8.570000e-02	7.740000e-02
9	Diff_AirPassengers	Diff_AirPassengers_LinearTrend_residue_zeroCyc...	114	7.360000e-02	8.650000e-02	7.990000e-02
10	Diff_AirPassengers	Diff_AirPassengers_LinearTrend_residue_bestCyc...	122	6.290000e-02	8.980000e-02	7.710000e-02
11	Diff_AirPassengers	Diff_AirPassengers_ConstantTrend_residue_bestC...	106	6.540000e-02	9.310000e-02	8.030000e-02
12	CumSum_AirPassengers	CumSum_AirPassengers_Lag1Trend_residue_zeroCyc...	130	6.950000e-02	9.760000e-02	9.900000e-02
13	CumSum_AirPassengers	CumSum_AirPassengers_Lag1Trend_residue_bestCyc...	138	7.650000e-02	9.940000e-02	9.960000e-02
14	_AirPassengers	_AirPassengers_PolyTrend_residue_bestCycle_byL...	90	5.430000e-02	1.205000e-01	1.713000e-01
15	_AirPassengers	_AirPassengers_PolyTrend_residue_zeroCycle_res...	82	5.520000e-02	1.207000e-01	1.721000e-01
16	CumSum_AirPassengers	CumSum_AirPassengers_PolyTrend_residue_zeroCyc...	114	1.581000e-01	1.750000e-01	2.691000e-01
17	_AirPassengers	_AirPassengers_ConstantTrend_residue_zeroCycle...	66	1.218000e-01	2.009000e-01	2.950000e-01
18	_AirPassengers	_AirPassengers_ConstantTrend_residue_bestCycle...	74	1.222000e-01	2.010000e-01	2.940000e-01
19	CumSum_AirPassengers	CumSum_AirPassengers_PolyTrend_residue_bestCyc...	122	1.766000e-01	2.038000e-01	2.943000e-01
20	CumSum_AirPassengers	CumSum_AirPassengers_LinearTrend_residue_zeroC...	114	1.810000e-01	4.856000e-01	5.501000e-01
21	CumSum_AirPassengers	CumSum_AirPassengers_LinearTrend_residue_bestC...	122	3.361000e-01	4.956000e-01	5.648000e-01
22	CumSum_AirPassengers	CumSum_AirPassengers_ConstantTrend_residue_bes...	106	1.068600e+00	9.788000e-01	1.148800e+00
23	CumSum_AirPassengers	CumSum_AirPassengers_ConstantTrend_residue_zer...	98	9.103000e-01	1.000000e+00	1.000000e+00
24	RelDiff_AirPassengers	RelDiff_AirPassengers_ConstantTrend_residue_ze...	98	4.106115e+06	2.183870e+06	1.910118e+06
25	RelDiff_AirPassengers	RelDiff_AirPassengers_LinearTrend_residue_best...	122	4.106168e+06	2.183870e+06	1.910118e+06
26	RelDiff_AirPassengers	RelDiff_AirPassengers_PolyTrend_residue_bestCy...	122	4.106172e+06	2.183870e+06	1.910119e+06
27	RelDiff_AirPassengers	RelDiff_AirPassengers_PolyTrend_residue_zeroCy...	114	4.106204e+06	2.183870e+06	1.910118e+06
28	RelDiff_AirPassengers	RelDiff_AirPassengers_ConstantTrend_residue_be...	106	4.106115e+06	2.183870e+06	1.910119e+06
29	RelDiff_AirPassengers	RelDiff_AirPassengers_LinearTrend_residue_zero...	114	4.106200e+06	2.183870e+06	1.910119e+06
30	RelDiff_AirPassengers	RelDiff_AirPassengers_Lag1Trend_residue_zeroCy...	130	4.035498e+06	2.183870e+06	1.910119e+06
31	RelDiff_AirPassengers	RelDiff_AirPassengers_Lag1Trend_residue_bestCy...	138	4.106113e+06	2.183870e+06	1.910119e+06

	time	AirPassengers
ID
128	1959.583333	559
129	1959.666667	463
130	1959.750000	407
131	1959.833333	362
132	1959.916667	405

	time	AirPassengers	_AirPassengers	row_number	time_Normalized	_AirPassengers_Lag1Trend	_AirPassengers_Lag1Trend_residue	_AirPassengers_Lag1Trend_residue_zeroCycle_residue	_AirPassengers_Lag1Trend_residue_zeroCycle_residue_XGB(33)	...	_AirPassengers_Cycle_residue	_AirPassengers_AR	_AirPassengers_AR_residue	_AirPassengers_TransformedForecast	AirPassengers_Forecast	_AirPassengers_TransformedResidue	AirPassengers_Residue	AirPassengers_Forecast_Lower_Bound	AirPassengers_Forecast_Upper_Bound
132	1960.000000	NaN	NaN	132	1.389474	405.000000	NaN	NaN	11.257255	...	NaN	11.257255	NaN	416.257255	416.257255	NaN	NaN	360.532387	471.982123
133	1960.083333	NaN	NaN	133	1.400000	416.257255	NaN	NaN	-12.380074	...	NaN	-12.380074	NaN	403.877181	403.877181	NaN	NaN	315.148449	492.605913
134	1960.166667	NaN	NaN	134	1.410526	403.877181	NaN	NaN	22.446426	...	NaN	22.446426	NaN	426.323607	426.323607	NaN	NaN	312.866133	539.781081
135	1960.250000	NaN	NaN	135	1.421053	426.323607	NaN	NaN	-2.562091	...	NaN	-2.562091	NaN	423.761517	423.761517	NaN	NaN	302.807124	544.715909
136	1960.333333	NaN	NaN	136	1.431579	423.761517	NaN	NaN	15.197581	...	NaN	15.197581	NaN	438.959098	438.959098	NaN	NaN	307.866554	570.051642
137	1960.416667	NaN	NaN	137	1.442105	438.959098	NaN	NaN	21.488630	...	NaN	21.488630	NaN	460.447728	460.447728	NaN	NaN	314.138663	606.756793
138	1960.500000	NaN	NaN	138	1.452632	460.447728	NaN	NaN	22.423498	...	NaN	22.423498	NaN	482.871226	482.871226	NaN	NaN	318.740413	647.002039
139	1960.583333	NaN	NaN	139	1.463158	482.871226	NaN	NaN	5.331924	...	NaN	5.331924	NaN	488.203151	488.203151	NaN	NaN	302.369406	674.036895
140	1960.666667	NaN	NaN	140	1.473684	488.203151	NaN	NaN	-22.371239	...	NaN	-22.371239	NaN	465.831912	465.831912	NaN	NaN	260.836887	670.826937
141	1960.750000	NaN	NaN	141	1.484211	465.831912	NaN	NaN	-22.371239	...	NaN	-22.371239	NaN	443.460673	443.460673	NaN	NaN	221.547867	665.373479
142	1960.833333	NaN	NaN	142	1.494737	443.460673	NaN	NaN	-20.387133	...	NaN	-20.387133	NaN	423.073541	423.073541	NaN	NaN	187.552105	658.594976
143	1960.916667	NaN	NaN	143	1.505263	423.073541	NaN	NaN	23.381294	...	NaN	23.381294	NaN	446.454835	446.454835	NaN	NaN	201.624799	691.284871
144	1961.000000	NaN	NaN	144	1.515789	446.454835	NaN	NaN	11.764988	...	NaN	11.764988	NaN	458.219823	458.219823	NaN	NaN	NaN	NaN
145	1961.083333	NaN	NaN	145	1.526316	458.219823	NaN	NaN	-4.271869	...	NaN	-4.271869	NaN	453.947954	453.947954	NaN	NaN	NaN	NaN
146	1961.166667	NaN	NaN	146	1.536842	453.947954	NaN	NaN	17.950855	...	NaN	17.950855	NaN	471.898809	471.898809	NaN	NaN	NaN	NaN

	time	AirPassengers	_AirPassengers	row_number	time_Normalized	_AirPassengers_Lag1Trend	_AirPassengers_Lag1Trend_residue	_AirPassengers_Lag1Trend_residue_zeroCycle	_AirPassengers_Lag1Trend_residue_zeroCycle_residue	_AirPassengers_Lag1Trend_residue_zeroCycle_residue_XGB(33)	...	_AirPassengers_Cycle	_AirPassengers_Cycle_residue	_AirPassengers_AR	_AirPassengers_AR_residue	_AirPassengers_TransformedForecast	AirPassengers_Forecast	_AirPassengers_TransformedResidue	AirPassengers_Residue	AirPassengers_Forecast_Lower_Bound	AirPassengers_Forecast_Upper_Bound
count	147.000000	132.000000	132.000000	147.000000	147.000000	147.000000	132.000000	147.0	132.000000	147.000000	...	147.0	132.000000	147.000000	132.000000	147.000000	147.000000	132.000000	132.000000	12.000000	12.000000
mean	1955.083333	262.492424	262.492424	73.000000	0.768421	278.861833	2.219697	0.0	2.219697	1.925769	...	0.0	2.219697	1.925769	0.581900	280.787602	280.787602	0.581900	0.581900	283.835899	602.751055
std	3.548278	106.625799	106.625799	42.579338	0.448204	115.498181	31.252802	0.0	31.252802	14.649807	...	0.0	31.252802	14.649807	18.882293	115.069530	115.069530	18.882293	18.882293	53.564763	76.398211
min	1949.000000	104.000000	104.000000	0.000000	0.000000	104.000000	-101.000000	0.0	-101.000000	-22.371239	...	0.0	-101.000000	-22.371239	-78.628761	105.451597	105.451597	-78.628761	-78.628761	187.552105	471.982123
25%	1952.041667	176.500000	176.500000	36.500000	0.384211	180.000000	-15.250000	0.0	-15.250000	-9.029420	...	0.0	-15.250000	-9.029420	-9.078444	185.123296	185.123296	-9.078444	-9.078444	251.014632	543.482202
50%	1955.083333	239.500000	239.500000	73.000000	0.768421	267.000000	2.500000	0.0	2.500000	0.738561	...	0.0	2.500000	0.738561	0.449085	266.509766	266.509766	0.449085	0.449085	305.336839	626.879416
75%	1958.125000	343.250000	343.250000	109.500000	1.152632	362.000000	21.000000	0.0	21.000000	15.197581	...	0.0	21.000000	15.197581	11.660267	371.413860	371.413860	11.660267	11.660267	314.391110	666.736844
max	1961.166667	559.000000	559.000000	146.000000	1.536842	559.000000	76.000000	0.0	76.000000	23.381294	...	0.0	76.000000	23.381294	53.576502	560.192122	560.192122	53.576502	53.576502	360.532387	691.284871