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_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 [3]:
df.head()


Out[3]:
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.describe()


Out[4]:
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 [5]:
lEngine = autof.cForecastEngine()
lEngine.mOptions.mEnableSeasonals = True;
lEngine

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


Out[5]:
<pyaf.ForecastEngine.cForecastEngine at 0x7f68851a5fd0>

In [6]:
lEngine.train(df , 'Time' , 'Ozone', 12)

In [7]:
lEngine.getModelInfo()

In [ ]:


In [8]:
type1 = np.dtype(df.Time)

In [9]:
type1.kind


Out[9]:
'M'

In [10]:
lEngine.mSignalDecomposition.mTrPerfDetails


Out[10]:
Transformation Model Complexity FitCount FitL2 FitMAPE ForecastCount ForecastL2 ForecastMAPE TestCount TestL2 TestMAPE
0 _Ozone _Ozone_LinearTrend_residue_zeroCycle_residue_A... 67 153 0.809570 0.1641 39 0.731569 0.1595 12 0.551943 0.1740
1 _Ozone _Ozone_PolyTrend_residue_zeroCycle_residue_AR(51) 67 153 0.807517 0.1640 39 0.696189 0.1657 12 0.904002 0.3430
2 _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
4 Diff_Ozone Diff_Ozone_Lag1Trend_residue_zeroCycle_residue... 115 153 1.035123 0.2233 39 0.826093 0.1799 12 0.550160 0.2262
5 _Ozone _Ozone_ConstantTrend_residue_zeroCycle_residue... 51 153 0.836761 0.1735 39 0.761725 0.1949 12 0.809034 0.2837
6 _Ozone _Ozone_Lag1Trend_residue_zeroCycle_residue_AR(51) 83 153 0.887150 0.1770 39 0.843003 0.1959 12 0.617458 0.2499
7 _Ozone _Ozone_ConstantTrend_residue_Seasonal_MonthOfY... 55 153 0.765350 0.1607 39 0.738275 0.1988 12 0.673162 0.2767
8 _Ozone _Ozone_ConstantTrend_residue_bestCycle_byL2_re... 59 153 0.765350 0.1607 39 0.738275 0.1988 12 0.673162 0.2767
9 _Ozone _Ozone_PolyTrend_residue_Seasonal_MonthOfYear_... 71 153 0.733858 0.1478 39 0.758797 0.1992 12 1.034883 0.3860
10 _Ozone _Ozone_PolyTrend_residue_bestCycle_byL2_residu... 75 153 0.733858 0.1478 39 0.758797 0.1992 12 1.034883 0.3860
11 _Ozone _Ozone_LinearTrend_residue_Seasonal_MonthOfYea... 71 153 0.735503 0.1473 39 0.781543 0.2137 12 0.727837 0.2607
12 _Ozone _Ozone_LinearTrend_residue_bestCycle_byL2_resi... 75 153 0.735503 0.1473 39 0.781543 0.2137 12 0.727837 0.2607
13 _Ozone _Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_... 87 153 0.784502 0.1663 39 0.829156 0.2164 12 0.738018 0.3010
14 _Ozone _Ozone_Lag1Trend_residue_bestCycle_byL2_residu... 91 153 0.784502 0.1663 39 0.829156 0.2164 12 0.738018 0.3010
15 _Ozone _Ozone_Lag1Trend_residue_Seasonal_MonthOfYear_... 36 153 0.990160 0.2078 39 0.871032 0.2172 12 0.506352 0.2001
16 _Ozone _Ozone_Lag1Trend_residue_bestCycle_byL2_residu... 40 153 0.990160 0.2078 39 0.871032 0.2172 12 0.506352 0.2001
17 CumSum_Ozone CumSum_Ozone_Lag1Trend_residue_Seasonal_MonthO... 68 153 1.013436 0.2142 39 0.877057 0.2199 12 0.542821 0.2144
18 CumSum_Ozone CumSum_Ozone_Lag1Trend_residue_bestCycle_byL2_... 72 153 1.013436 0.2142 39 0.877057 0.2199 12 0.542821 0.2144
19 Diff_Ozone Diff_Ozone_Lag1Trend_residue_bestCycle_byL2_re... 123 153 1.171231 0.2296 39 0.888236 0.2223 12 0.718709 0.2695
20 Diff_Ozone Diff_Ozone_ConstantTrend_residue_Seasonal_Mont... 87 153 1.760679 0.3593 39 0.755665 0.2269 12 1.660573 0.6312
21 Diff_Ozone Diff_Ozone_ConstantTrend_residue_bestCycle_byL... 91 153 1.760679 0.3593 39 0.755665 0.2269 12 1.660573 0.6312
22 _Ozone _Ozone_PolyTrend_residue_Seasonal_MonthOfYear_... 20 153 0.871898 0.1783 39 0.795697 0.2313 12 1.582731 0.6180
23 _Ozone _Ozone_PolyTrend_residue_bestCycle_byL2_residu... 24 153 0.871898 0.1783 39 0.795697 0.2313 12 1.582731 0.6180
24 Diff_Ozone Diff_Ozone_ConstantTrend_residue_Seasonal_Mont... 36 153 1.043832 0.1833 39 0.859494 0.2319 12 0.667235 0.2500
25 Diff_Ozone Diff_Ozone_ConstantTrend_residue_bestCycle_byL... 40 153 1.043832 0.1833 39 0.859494 0.2319 12 0.667235 0.2500
26 _Ozone _Ozone_Lag1Trend_residue_zeroCycle_residue_NoAR 32 153 1.165742 0.2381 39 0.965826 0.2778 12 0.573730 0.2132
27 CumSum_Ozone CumSum_Ozone_Lag1Trend_residue_zeroCycle_resid... 64 153 1.175540 0.2423 39 0.965826 0.2778 12 0.573730 0.2132
28 Diff_Ozone Diff_Ozone_Lag1Trend_residue_zeroCycle_residue... 64 153 1.165742 0.2381 39 0.965826 0.2778 12 0.573730 0.2132
29 RelDiff_Ozone RelDiff_Ozone_Lag1Trend_residue_zeroCycle_resi... 64 153 1.165742 0.2381 39 0.965826 0.2778 12 0.573730 0.2132
... ... ... ... ... ... ... ... ... ... ... ... ...
66 Diff_Ozone Diff_Ozone_Lag1Trend_residue_Seasonal_MonthOfY... 119 153 1.505787 0.3210 39 2.034252 0.6881 12 2.875626 1.3183
67 Diff_Ozone Diff_Ozone_PolyTrend_residue_zeroCycle_residue... 48 153 1.606444 0.3605 39 1.943295 0.7082 12 4.400230 2.0528
68 CumSum_Ozone CumSum_Ozone_PolyTrend_residue_zeroCycle_resid... 48 153 6.437529 0.5949 39 2.008141 0.7655 12 2.744419 1.2889
69 Diff_Ozone Diff_Ozone_Lag1Trend_residue_Seasonal_MonthOfY... 68 153 1.407886 0.3124 39 2.474665 0.8255 12 2.770257 1.2574
70 CumSum_Ozone CumSum_Ozone_PolyTrend_residue_bestCycle_byL2_... 56 153 6.467215 0.6900 39 2.495028 0.9177 12 2.989847 1.2066
71 CumSum_Ozone CumSum_Ozone_PolyTrend_residue_Seasonal_MonthO... 52 153 6.415188 0.6938 39 2.689038 0.9277 12 3.505022 1.5031
72 CumSum_Ozone CumSum_Ozone_ConstantTrend_residue_zeroCycle_r... 32 153 27.750282 1.8140 39 3.361738 1.0000 12 2.578275 1.0000
73 RelDiff_Ozone RelDiff_Ozone_Lag1Trend_residue_Seasonal_Month... 119 153 1.493649 0.3472 39 3.005381 1.0020 12 2.619120 1.0353
74 RelDiff_Ozone RelDiff_Ozone_Lag1Trend_residue_bestCycle_byL2... 123 153 3.189273 0.8971 39 4.688305 1.7025 12 4.376293 1.8781
75 RelDiff_Ozone RelDiff_Ozone_Lag1Trend_residue_zeroCycle_resi... 115 153 2.941637 0.8148 39 5.051294 1.8623 12 5.242798 2.3143
76 RelDiff_Ozone RelDiff_Ozone_LinearTrend_residue_Seasonal_Mon... 103 153 4.198736 1.2193 39 5.263902 1.9539 12 5.695453 2.5591
77 RelDiff_Ozone RelDiff_Ozone_LinearTrend_residue_bestCycle_by... 107 153 4.198736 1.2193 39 5.263902 1.9539 12 5.695453 2.5591
78 CumSum_Ozone CumSum_Ozone_ConstantTrend_residue_Seasonal_Mo... 36 153 27.839286 2.2845 39 10.002328 2.0574 12 9.636285 2.4834
79 CumSum_Ozone CumSum_Ozone_ConstantTrend_residue_bestCycle_b... 40 153 27.839286 2.2845 39 10.002328 2.0574 12 9.636285 2.4834
80 RelDiff_Ozone RelDiff_Ozone_LinearTrend_residue_Seasonal_Mon... 52 153 4.163113 1.2076 39 5.519645 2.0775 12 6.000930 2.7321
81 RelDiff_Ozone RelDiff_Ozone_LinearTrend_residue_bestCycle_by... 56 153 4.163113 1.2076 39 5.519645 2.0775 12 6.000930 2.7321
82 RelDiff_Ozone RelDiff_Ozone_ConstantTrend_residue_Seasonal_M... 87 153 3.761847 1.0638 39 5.546233 2.0948 12 6.266777 2.8884
83 RelDiff_Ozone RelDiff_Ozone_ConstantTrend_residue_bestCycle_... 91 153 3.761847 1.0638 39 5.546233 2.0948 12 6.266777 2.8884
84 RelDiff_Ozone RelDiff_Ozone_PolyTrend_residue_Seasonal_Month... 103 153 3.891278 1.1195 39 5.582340 2.1109 12 6.266777 2.8884
85 RelDiff_Ozone RelDiff_Ozone_PolyTrend_residue_bestCycle_byL2... 107 153 3.891278 1.1195 39 5.582340 2.1109 12 6.266777 2.8884
86 RelDiff_Ozone RelDiff_Ozone_ConstantTrend_residue_Seasonal_M... 36 153 3.612171 1.0038 39 5.618841 2.1275 12 6.266777 2.8884
87 RelDiff_Ozone RelDiff_Ozone_ConstantTrend_residue_bestCycle_... 40 153 3.612171 1.0038 39 5.618841 2.1275 12 6.266777 2.8884
88 RelDiff_Ozone RelDiff_Ozone_PolyTrend_residue_Seasonal_Month... 52 153 4.022741 1.1638 39 5.621574 2.1286 12 6.266777 2.8884
89 RelDiff_Ozone RelDiff_Ozone_PolyTrend_residue_bestCycle_byL2... 56 153 4.022741 1.1638 39 5.621574 2.1286 12 6.266777 2.8884
90 RelDiff_Ozone RelDiff_Ozone_ConstantTrend_residue_zeroCycle_... 32 153 4.214493 1.2164 39 5.623486 2.1294 12 6.266777 2.8884
91 RelDiff_Ozone RelDiff_Ozone_LinearTrend_residue_zeroCycle_re... 48 153 4.421386 1.2987 39 5.623486 2.1294 12 6.266777 2.8884
92 RelDiff_Ozone RelDiff_Ozone_PolyTrend_residue_zeroCycle_resi... 48 153 4.459119 1.3137 39 5.623486 2.1294 12 6.266777 2.8884
93 RelDiff_Ozone RelDiff_Ozone_ConstantTrend_residue_zeroCycle_... 83 153 3.748131 1.0304 39 5.623486 2.1294 12 6.266777 2.8884
94 RelDiff_Ozone RelDiff_Ozone_LinearTrend_residue_zeroCycle_re... 99 153 4.137395 1.1831 39 5.623486 2.1294 12 6.266777 2.8884
95 RelDiff_Ozone RelDiff_Ozone_PolyTrend_residue_zeroCycle_resi... 99 153 3.730886 1.0485 39 5.623486 2.1294 12 6.266777 2.8884

96 rows × 12 columns


In [11]:
lEngine.standrdPlots()


/usr/lib/python3/dist-packages/matplotlib/__init__.py:1403: 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 [12]:
lEngine.mSignalDecomposition.mBestModel.mTimeInfo.mTimeDelta


Out[12]:
Timedelta('30 days 10:25:16')

In [13]:
dfapp = df.copy();

In [14]:
dfapp.head()


Out[14]:
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 [15]:
dfapp1 = lEngine.forecast(dfapp, 36);

In [16]:
dfapp1.head()


Out[16]:
Ozone Time _Ozone row_number Time_Normalized _Ozone_LinearTrend _Ozone_LinearTrend_residue _Ozone_LinearTrend_residue_zeroCycle _Ozone_LinearTrend_residue_zeroCycle_residue _Ozone_LinearTrend_residue_zeroCycle_residue_AR(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 5.022578 -2.322578 0.0 -2.322578 -0.939548 ... 0.0 -2.322578 -0.939548 -1.383030 4.083030 -1.383030 4.083030 -1.383030 NaN NaN
1 2.0 1955-02-01 2.0 1 0.006701 5.010334 -3.010334 0.0 -3.010334 -0.939548 ... 0.0 -3.010334 -0.939548 -2.070786 4.070786 -2.070786 4.070786 -2.070786 NaN NaN
2 3.6 1955-03-01 3.6 2 0.012754 4.999275 -1.399275 0.0 -1.399275 -1.238697 ... 0.0 -1.399275 -1.238697 -0.160578 3.760578 -0.160578 3.760578 -0.160578 NaN NaN
3 5.0 1955-04-01 5.0 3 0.019455 4.987031 0.012969 0.0 0.012969 -0.589263 ... 0.0 0.012969 -0.589263 0.602232 4.397768 0.602232 4.397768 0.602232 NaN NaN
4 6.5 1955-05-01 6.5 4 0.025940 4.975182 1.524818 0.0 1.524818 0.145223 ... 0.0 1.524818 0.145223 1.379596 5.120404 1.379596 5.120404 1.379596 NaN NaN

5 rows × 23 columns


In [17]:
dfapp1.tail(20)


Out[17]:
Ozone Time _Ozone row_number Time_Normalized _Ozone_LinearTrend _Ozone_LinearTrend_residue _Ozone_LinearTrend_residue_zeroCycle _Ozone_LinearTrend_residue_zeroCycle_residue _Ozone_LinearTrend_residue_zeroCycle_residue_AR(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 2.944415 220 1.447255 2.378257 0.566158 0.0 0.566158 0.566158 ... 0.0 0.566158 0.566158 2.220446e-16 2.944415 0.000000 2.944415 0.000000 NaN NaN
221 NaN 1973-06-01 2.819216 221 1.453956 2.366013 0.453203 0.0 0.453203 0.453203 ... 0.0 0.453203 0.453203 -5.551115e-17 2.819216 0.000000 2.819216 0.000000 NaN NaN
222 NaN 1973-07-01 3.135386 222 1.460441 2.354164 0.781223 0.0 0.781223 0.781223 ... 0.0 0.781223 0.781223 -2.220446e-16 3.135386 0.000000 3.135386 0.000000 NaN NaN
223 NaN 1973-08-01 3.178274 223 1.467142 2.341920 0.836354 0.0 0.836354 0.836354 ... 0.0 0.836354 0.836354 2.220446e-16 3.178274 0.000000 3.178274 0.000000 NaN NaN
224 NaN 1973-09-01 2.919884 224 1.473843 2.329676 0.590209 0.0 0.590209 0.590209 ... 0.0 0.590209 0.590209 0.000000e+00 2.919884 0.000000 2.919884 0.000000 NaN NaN
225 NaN 1973-10-01 2.203963 225 1.480329 2.317826 -0.113864 0.0 -0.113864 -0.113864 ... 0.0 -0.113864 -0.113864 -1.110223e-16 2.203963 0.000000 2.203963 0.000000 NaN NaN
226 NaN 1973-11-01 0.882882 226 1.487030 2.305582 -1.422701 0.0 -1.422701 -1.422701 ... 0.0 -1.422701 -1.422701 0.000000e+00 0.882882 0.000000 0.882882 0.000000 NaN NaN
227 NaN 1973-12-01 0.511542 227 1.493515 2.293733 -1.782191 0.0 -1.782191 -1.782191 ... 0.0 -1.782191 -1.782191 0.000000e+00 0.511542 0.000000 0.511542 0.000000 NaN NaN
228 NaN 1974-01-01 0.829787 228 1.500216 2.281489 -1.451702 0.0 -1.451702 -1.451702 ... 0.0 -1.451702 -1.451702 0.000000e+00 0.829787 0.000000 0.829787 0.000000 NaN NaN
229 NaN 1974-02-01 1.428053 229 1.506917 2.269245 -0.841193 0.0 -0.841193 -0.841193 ... 0.0 -0.841193 -0.841193 0.000000e+00 1.428053 0.000000 1.428053 0.000000 NaN NaN
230 NaN 1974-03-01 1.849976 230 1.512970 2.258186 -0.408210 0.0 -0.408210 -0.408210 ... 0.0 -0.408210 -0.408210 0.000000e+00 1.849976 0.000000 1.849976 0.000000 NaN NaN
231 NaN 1974-04-01 2.518120 231 1.519671 2.245942 0.272178 0.0 0.272178 0.272178 ... 0.0 0.272178 0.272178 -2.220446e-16 2.518120 0.000000 2.518120 0.000000 NaN NaN
232 NaN 1974-05-01 2.720288 232 1.526157 2.234093 0.486195 0.0 0.486195 0.486195 ... 0.0 0.486195 0.486195 -1.665335e-16 2.720288 0.000000 2.720288 0.000000 NaN NaN
233 NaN 1974-06-01 3.017658 233 1.532858 2.221849 0.795809 0.0 0.795809 0.795809 ... 0.0 0.795809 0.795809 2.220446e-16 3.017658 0.000000 3.017658 0.000000 NaN NaN
234 NaN 1974-07-01 3.150487 234 1.539343 2.210000 0.940487 0.0 0.940487 0.940487 ... 0.0 0.940487 0.940487 -2.220446e-16 3.150487 0.000000 3.150487 0.000000 NaN NaN
235 NaN 1974-08-01 3.288616 235 1.546044 2.197756 1.090860 0.0 1.090860 1.090860 ... 0.0 1.090860 1.090860 2.220446e-16 3.288616 0.000000 3.288616 0.000000 NaN NaN
236 NaN 1974-09-01 2.691775 236 1.552745 2.185512 0.506264 0.0 0.506264 0.506264 ... 0.0 0.506264 0.506264 -2.220446e-16 2.691775 0.000000 2.691775 0.000000 NaN NaN
237 NaN 1974-10-01 1.774404 237 1.559230 2.173663 -0.399259 0.0 -0.399259 -0.399259 ... 0.0 -0.399259 -0.399259 -5.551115e-17 1.774404 0.000000 1.774404 0.000000 NaN NaN
238 NaN 1974-11-01 0.854985 238 1.565932 2.161419 -1.306433 0.0 -1.306433 -1.306433 ... 0.0 -1.306433 -1.306433 0.000000e+00 0.854985 0.000000 0.854985 0.000000 NaN NaN
239 NaN 1974-12-01 0.854985 239 1.572417 2.149569 -1.294584 0.0 -1.294584 -1.555925 ... 0.0 -1.294584 -1.555925 2.613410e-01 0.593644 0.261341 0.593644 0.261341 NaN NaN

20 rows × 23 columns


In [18]:
#trdec.mTimeInfo.mTimeDelta

In [19]:
#trdec.mBestModelCycle.mDefaultValue

In [20]:
delta1 = np.mean(df['Time'] - df['Time'].shift(1))
delta1


Out[20]:
Timedelta('30 days 10:24:14.187192')

In [21]:
delta1.days


Out[21]:
30

In [22]:
import datetime as dt

#delta1/dt.timedelta(month = 1)

In [23]:
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 [24]:
r.months


Out[24]:
-5

In [25]:
r.weekday

In [26]:
dfapp.tail()


Out[26]:
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 [27]:
lDecomp = lEngine.mSignalDecomposition

In [28]:
dfapp1 = lDecomp.forecast(dfapp, 36);
dfapp2 = dfapp1;
dfapp2['Ozone'] = df['Ozone']

In [29]:
dfapp1.tail(15)


Out[29]:
Ozone Time _Ozone row_number Time_Normalized _Ozone_LinearTrend _Ozone_LinearTrend_residue _Ozone_LinearTrend_residue_zeroCycle _Ozone_LinearTrend_residue_zeroCycle_residue _Ozone_LinearTrend_residue_zeroCycle_residue_AR(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 2.203963 225 1.480329 2.317826 -0.113864 0.0 -0.113864 -0.113864 ... 0.0 -0.113864 -0.113864 -1.110223e-16 2.203963 0.000000 2.203963 0.000000 NaN NaN
226 NaN 1973-11-01 0.882882 226 1.487030 2.305582 -1.422701 0.0 -1.422701 -1.422701 ... 0.0 -1.422701 -1.422701 0.000000e+00 0.882882 0.000000 0.882882 0.000000 NaN NaN
227 NaN 1973-12-01 0.511542 227 1.493515 2.293733 -1.782191 0.0 -1.782191 -1.782191 ... 0.0 -1.782191 -1.782191 0.000000e+00 0.511542 0.000000 0.511542 0.000000 NaN NaN
228 NaN 1974-01-01 0.829787 228 1.500216 2.281489 -1.451702 0.0 -1.451702 -1.451702 ... 0.0 -1.451702 -1.451702 0.000000e+00 0.829787 0.000000 0.829787 0.000000 NaN NaN
229 NaN 1974-02-01 1.428053 229 1.506917 2.269245 -0.841193 0.0 -0.841193 -0.841193 ... 0.0 -0.841193 -0.841193 0.000000e+00 1.428053 0.000000 1.428053 0.000000 NaN NaN
230 NaN 1974-03-01 1.849976 230 1.512970 2.258186 -0.408210 0.0 -0.408210 -0.408210 ... 0.0 -0.408210 -0.408210 0.000000e+00 1.849976 0.000000 1.849976 0.000000 NaN NaN
231 NaN 1974-04-01 2.518120 231 1.519671 2.245942 0.272178 0.0 0.272178 0.272178 ... 0.0 0.272178 0.272178 -2.220446e-16 2.518120 0.000000 2.518120 0.000000 NaN NaN
232 NaN 1974-05-01 2.720288 232 1.526157 2.234093 0.486195 0.0 0.486195 0.486195 ... 0.0 0.486195 0.486195 -1.665335e-16 2.720288 0.000000 2.720288 0.000000 NaN NaN
233 NaN 1974-06-01 3.017658 233 1.532858 2.221849 0.795809 0.0 0.795809 0.795809 ... 0.0 0.795809 0.795809 2.220446e-16 3.017658 0.000000 3.017658 0.000000 NaN NaN
234 NaN 1974-07-01 3.150487 234 1.539343 2.210000 0.940487 0.0 0.940487 0.940487 ... 0.0 0.940487 0.940487 -2.220446e-16 3.150487 0.000000 3.150487 0.000000 NaN NaN
235 NaN 1974-08-01 3.288616 235 1.546044 2.197756 1.090860 0.0 1.090860 1.090860 ... 0.0 1.090860 1.090860 2.220446e-16 3.288616 0.000000 3.288616 0.000000 NaN NaN
236 NaN 1974-09-01 2.691775 236 1.552745 2.185512 0.506264 0.0 0.506264 0.506264 ... 0.0 0.506264 0.506264 -2.220446e-16 2.691775 0.000000 2.691775 0.000000 NaN NaN
237 NaN 1974-10-01 1.774404 237 1.559230 2.173663 -0.399259 0.0 -0.399259 -0.399259 ... 0.0 -0.399259 -0.399259 -5.551115e-17 1.774404 0.000000 1.774404 0.000000 NaN NaN
238 NaN 1974-11-01 0.854985 238 1.565932 2.161419 -1.306433 0.0 -1.306433 -1.306433 ... 0.0 -1.306433 -1.306433 0.000000e+00 0.854985 0.000000 0.854985 0.000000 NaN NaN
239 NaN 1974-12-01 0.854985 239 1.572417 2.149569 -1.294584 0.0 -1.294584 -1.555925 ... 0.0 -1.294584 -1.555925 2.613410e-01 0.593644 0.261341 0.593644 0.261341 NaN NaN

15 rows × 23 columns


In [30]:
dfapp1.describe()


Out[30]:
Ozone _Ozone row_number Time_Normalized _Ozone_LinearTrend _Ozone_LinearTrend_residue _Ozone_LinearTrend_residue_zeroCycle _Ozone_LinearTrend_residue_zeroCycle_residue _Ozone_LinearTrend_residue_zeroCycle_residue_AR(51) _Ozone_LinearTrend_residue_zeroCycle_residue_AR(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 240.000000 240.000000 240.0 240.000000 240.000000 2.400000e+02 ... 240.0 240.000000 240.000000 2.400000e+02 240.000000 240.000000 240.000000 240.000000 12.000000 12.000000
mean 3.835784 3.578026 119.50000 0.786145 3.586189 -0.008163 0.0 -0.008163 -0.058529 5.036576e-02 ... 0.0 -0.008163 -0.058529 5.036576e-02 3.527660 0.050366 3.527660 0.050366 0.176283 4.207166
std 1.495228 1.550364 69.42622 0.456804 0.834640 1.274152 0.0 1.274152 1.096723 7.210652e-01 ... 0.0 1.274152 1.096723 7.210652e-01 1.433810 0.721065 1.433810 0.721065 1.223818 0.982817
min 1.200000 0.511542 0.00000 0.000000 2.149569 -3.010334 0.0 -3.010334 -2.620354 -2.138210e+00 ... 0.0 -3.010334 -2.620354 -2.138210e+00 0.511542 -2.138210 0.511542 -2.138210 -2.496705 2.074284
25% 2.600000 2.400000 59.75000 0.393050 2.867723 -0.996405 0.0 -0.996405 -0.939548 -2.731912e-01 ... 0.0 -0.996405 -0.939548 -2.731912e-01 2.372688 -0.273191 2.372688 -0.273191 -0.397188 3.768683
50% 3.750000 3.400000 119.50000 0.786316 3.585876 0.026643 0.0 0.026643 0.127051 2.775558e-17 ... 0.0 0.026643 0.127051 2.775558e-17 3.483277 0.000000 3.483277 0.000000 0.654258 4.246188
75% 4.825000 4.700000 179.25000 1.179367 4.304425 0.843794 0.0 0.843794 0.706800 4.218601e-01 ... 0.0 0.843794 0.706800 4.218601e-01 4.573273 0.421860 4.573273 0.421860 1.057629 5.073057
max 8.700000 8.700000 239.00000 1.572417 5.022578 3.917958 0.0 3.917958 2.708861 2.638317e+00 ... 0.0 3.917958 2.708861 2.638317e+00 7.346739 2.638317 7.346739 2.638317 1.437735 5.468830

8 rows × 22 columns


In [ ]:


In [ ]: