PFA(prévision)
January 17, 2022
[25]: import pandas as pd
import numpy as np
import os
import matplotlib.pyplot as plt
from sklearn.model_selection import ParameterGrid
from statsmodels.tsa.api import SimpleExpSmoothing
from statsmodels.tsa.api import Holt
from statsmodels.tsa.api import ExponentialSmoothing
from sklearn import metrics
[26]: dataset=pd.read_excel('pfa.xlsx') #import excel file(Mois,Na)
[27]: dataset.info()
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 60 entries, 0 to 59
Data columns (total 2 columns):
#
---
0
1
Column Non-Null Count Dtype
------ -------------- -----
Mois
Na
60 non-null
60 non-null
datetime64[ns]
int64
dtypes: datetime64[ns](1), int64(1)
memory usage: 1.1 KB
[28]: dataset.head() #the first five values of our dataset
[28]:
Mois
Na
0 2017-01-01 1999
1 2017-02-01 2999
2 2017-03-01 6715
3 2017-04-01 7010
4 2017-05-01 8500
[29]: dataset.isnull().sum() #no value is emty
1
[29]: Mois
0
0
Na
dtype: int64
[30]: dataset=dataset.groupby('Mois').sum() #set the index as Mois
[31]: dataset.head(10) #the first ten values of our dataset
[31]:
Na
Mois
1999
2017-01-01
2999
2017-02-01
6715
2017-03-01
7010
2017-04-01
2017-05-01
8500
2017-06-01 23905
2017-07-01 44300
2017-08-01 43788
2017-09-01 22563
2017-10-01 19300
[32]: dataset.plot()
[32]: <AxesSubplot:xlabel='Mois'>
2
[33]: import warnings
warnings.filterwarnings('ignore')
1 Moving Average
[50]: Moving_Average=dataset['Na'].rolling(window =3).mean()
Moving_Average.plot()
#moving average with the inisialisation of the first values with the mean of␣
,→the first thre values
[50]: <AxesSubplot:xlabel='Mois'>
[51]: dataset['Na'].plot(figsize=(10,6))
Moving_Average.plot()
[51]: <AxesSubplot:xlabel='Mois'>
3
[52]: Moving_Average #moving average values
[52]: Mois
2017-01-01
2017-02-01
2017-03-01
2017-04-01
2017-05-01
2017-06-01
2017-07-01
2017-08-01
2017-09-01
2017-10-01
2017-11-01
2017-12-01
2018-01-01
2018-02-01
2018-03-01
2018-04-01
2018-05-01
2018-06-01
2018-07-01
2018-08-01
2018-09-01
2018-10-01
NaN
NaN
3904.333333
5574.666667
7408.333333
Publicité
13138.333333
25568.333333
37331.000000
36883.666667
28550.333333
17247.000000
14263.000000
8513.000000
6220.333333
3942.333333
5659.000000
7492.333333
13101.666667
25631.000000
37359.333333
37108.666667
28548.000000
4
2018-11-01
2018-12-01
2019-01-01
2019-02-01
2019-03-01
2019-04-01
2019-05-01
2019-06-01
2019-07-01
2019-08-01
2019-09-01
2019-10-01
2019-11-01
2019-12-01
2020-01-01
2020-02-01
2020-03-01
2020-04-01
2020-05-01
2020-06-01
2020-07-01
2020-08-01
2020-09-01
2020-10-01
2020-11-01
2020-12-01
2021-01-01
2021-02-01
2021-03-01
2021-04-01
2021-05-01
2021-06-01
2021-07-01
2021-08-01
2021-09-01
2021-10-01
2021-11-01
2021-12-01
Name: Na, dtype: float64
17316.666667
14034.000000
8365.333333
6101.666667
4066.666667
5748.333333
7603.333333
13270.000000
25674.333333
37969.333333
37650.000000
29350.666667
17380.666667
14353.333333
8711.666667
6551.666667
4105.000000
5685.000000
7561.333333
13202.000000
25380.333333
36816.333333
36648.333333
28520.666667
17389.666667
14238.000000
8457.333333
6242.333333
4020.000000
5659.333333
7554.666667
13184.333333
25661.666667
37376.000000
36994.333333
28672.000000
17271.666667
14322.000000
[38]: from sklearn.metrics import mean_squared_error
[54]: RMSE=np.sqrt(mean_squared_error(dataset[2:],Moving_Average[2:]))
#Root Mean Square Eroor between the actual dataset and the moving average values
[55]: RMSE
5
[55]: 8844.115882511662
2 Simple Exponential Smoothing
[83]: fit1=SimpleExpSmoothing(dataset).fit(smoothing_level=1,optimized=False) #alpha␣
,→is optimised with excel solver
[84]: dataset.plot(legend=True, label='demande', figsize=(18,8))
fit1.fittedvalues.plot(legend=True, label='Forecast')
[84]: <AxesSubplot:xlabel='Mois'>
[85]: fit1.summary()
[85]: <class 'statsmodels.iolib.summary.Summary'>
"""
Publicité
SimpleExpSmoothing Model Results
==============================================================================
Dep. Variable:
60
6703434090.000
Model:
1115.892
Optimized:
1120.081
Trend:
1116.620
Seasonal:
Sun, 16 Jan 2022
Seasonal Periods:
Box-Cox:
16:05:21
Box-Cox Coeff.:
==============================================================================
Na
SimpleExpSmoothing
False
None
None
None
False
None
No. Observations:
SSE
AIC
BIC
AICC
Date:
Time:
------------------------------------------------------------------------------
coeff
code
optimized
6
False
smoothing_level
initial_level
False
------------------------------------------------------------------------------
"""
1.0000000
1999.0000
alpha
l.0
[86]: from sklearn.metrics import mean_squared_error
[87]: RMSE=np.sqrt(mean_squared_error(dataset,fit1.fittedvalues))
[88]: RMSE
[88]: 10569.952767160315
3 Double Exponential Smoothing
[89]: fit1= Holt(dataset).fit(smoothing_level=1,smoothing_trend=0,optimized=False)
#alpha and beta are optimised with excel solver
[90]: dataset.plot(legend=True, label='demande', figsize=(18,8))
fit1.fittedvalues.plot(legend=True, label='linear trend')
[90]: <AxesSubplot:xlabel='Mois'>
[91]: fit1.summary()
[91]: <class 'statsmodels.iolib.summary.Summary'>
"""
Holt Model Results
==============================================================================
7
Dep. Variable:
Model:
Optimized:
Trend:
Seasonal:
Seasonal Periods:
Box-Cox:
Box-Cox Coeff.:
==============================================================================
No. Observations:
SSE
AIC
BIC
AICC
Date:
Time:
60
6740010090.000
1120.219
1128.596
1121.804
Sun, 16 Jan 2022
16:05:23
Na
Holt
False
Additive
None
None
False
None
coeff
code
optimized
------------------------------------------------------------------------------
False
smoothing_level
False
smoothing_trend
False
initial_level
False
initial_trend
------------------------------------------------------------------------------
"""
1.0000000
Publicité
0.000000
1999.0000
1000.0000
alpha
beta
l.0
b.0
[92]: RMSE=np.sqrt(mean_squared_error(dataset,fit1.fittedvalues))
[93]: RMSE
[93]: 10598.749997051538
4 Triple Exponential Smoothing
[68]: import statsmodels.api as sm
from statsmodels.tsa.seasonal import seasonal_decompose
[69]: seasonal_decompose(dataset,model='additive',period=12).plot(); #seasonal␣
,→decompose of our dataset
8
[70]: train= dataset.iloc[:-12] # values from 2017 to 2020
test=dataset.iloc[-12:] #values of the last year (2021)
[71]: modelhw= ExponentialSmoothing(train['Na'],trend='add', seasonal='add',␣
,→seasonal_periods=12).fit()
#alpha, beta and gamma are optimiser with python
[72]: test_pred=modelhw.forecast(12) # the prediction of 2021
[73]: train['Na'].plot(legend=True,label='train',figsize=(18,9))
#actuals values␣
,→from 2017 to 2020
test_pred.plot(legend=True,label='predicted') #forecasted values of 2021
test['Na'].plot(legend=True,label='test') #actuals values of 2021
[73]: <AxesSubplot:xlabel='Mois'>
9
[74]: test_pred # the prediction values of 2021
[74]: 2021-01-01
2021-02-01
2021-03-01
2021-04-01
2021-05-01
2021-06-01
2021-07-01
2021-08-01
2021-09-01
2021-10-01
2021-11-01
2021-12-01
Freq: MS, dtype: float64
2249.928896
3192.954948
6777.983412
7248.332151
8761.936719
23698.820626
44529.363258
44413.569455
22827.526849
19332.229703
9907.131471
13533.511987
[75]: from sklearn.metrics import mean_squared_error
[76]: RMSE=np.sqrt(mean_squared_error(test,test_pred))
[77]: RMSE
[77]: 187.72249831939774
[78]: dataset.Na.mean(),np.sqrt(dataset.Na.var())
#mean and standar deviation are very high compared to RMSE, so, it is a good␣
,→prediction
10
[78]: (17121.5, 13998.367830402738)
[79]: final_model=modelhw= ExponentialSmoothing(dataset['Na'],trend='add',␣
,→seasonal='add', seasonal_periods=12).fit()
[80]: prediction=final_model.forecast(12) # the prediction of 2022
[81]: prediction # the forecasted values of 2022
[81]: 2022-01-01
2022-02-01
2022-03-01
2022-04-01
2022-05-01
2022-06-01
2022-07-01
2022-08-01
2022-09-01
2022-10-01
2022-11-01
2022-12-01
Freq: MS, dtype: float64
2214.430815
3174.982592
6773.250377
7175.758614
8770.684634
23685.807776
44357.254975
44122.378515
22865.366012
19365.574312
9893.741114
13530.571756
[82]: dataset['Na'].plot(legend=True,label='actuals',figsize=(18,9))
#actuals␣
,→values from 2017 to 2021
prediction.plot(legend=True,label='forcasted') #forecasted values of 2022
[82]: <AxesSubplot:xlabel='Mois'>
11
[83]: final_model.summary()
[83]: <class 'statsmodels.iolib.summary.Summary'>
"""
ExponentialSmoothing Model Results
================================================================================
Dep. Variable:
60
5635098.318
Model:
719.011
Optimized:
Publicité
752.520
Trend:
Seasonal:
735.694
Mon, 17 Jan 2022
Seasonal Periods:
Box-Cox:
17:44:02
Box-Cox Coeff.:
================================================================================
=
Na
ExponentialSmoothing
True
Additive
Additive
12
False
None
No. Observations:
SSE
AIC
BIC
AICC
Date:
Time:
coeff
code
optimized
b.0
l.0
beta
gamma
alpha
0.0001090
0.0757245
0.0002102
1.7716978
17041.058
-14936.623
--------------------------------------------------------------------------------
-
smoothing_level
True
smoothing_trend
True
smoothing_seasonal
True
initial_level
True
initial_trend
True
initial_seasons.0
True
initial_seasons.1
True
initial_seasons.2
True
initial_seasons.3
True
initial_seasons.4
True
initial_seasons.5
True
initial_seasons.6
True
initial_seasons.7
True
initial_seasons.8
True
-13977.855
-9980.6248
-10381.385
-8387.4487
27195.526
6525.7988
26958.923
5700.1722
s.5
s.0
s.2
s.4
s.3
s.6
s.1
s.7
s.8
12
2198.5191
initial_seasons.9
True
initial_seasons.10
True
initial_seasons.11
True
--------------------------------------------------------------------------------
-
"""
-3639.9977
-7275.0411
s.10
s.11
s.9
[ ]:
13