#+begin_src python :results output :exports both :session s1
import numpy as np
import pandas as pd
values = np.array([14.0, 7.6, 11.2, 12.8, 12.5, 9.9, 14.9, 9.4, 16.9, 10.2, 14.9, 18.1, 7.3, 9.8, 10.9,12.2, 9.9, 2.9, 2.8, 15.4, 15.7, 9.7, 13.1, 13.2, 12.3, 11.7, 16.0, 12.4, 17.9, 12.2, 16.2, 18.7, 8.9, 11.9, 12.1, 14.6, 12.1, 4.7, 3.9, 16.9, 16.8, 11.3, 14.4, 15.7, 14.0, 13.6, 18.0, 13.6, 19.9, 13.7, 17.0, 20.5, 9.9, 12.5, 13.2, 16.1, 13.5, 6.3, 6.4, 17.6, 19.1, 12.8, 15.5, 16.3, 15.2, 14.6, 19.1, 14.4, 21.4, 15.1, 19.6, 21.7, 11.3, 15.0, 14.3, 16.8, 14.0, 6.8, 8.2, 19.9, 20.4, 14.6, 16.4, 18.7, 16.8, 15.8, 20.4, 15.8, 22.4, 16.2, 20.3, 23.4, 12.1, 15.5, 15.4, 18.4, 15.7, 10.2, 8.9, 21.0])
print(values.shape)
#+end_src

#+RESULTS:
: (100,)

#+begin_src python :results file :session s1 :var matplot_lib_filename=(org-babel-temp-file "figure" ".png") :exports both
import matplotlib.pyplot as plt
plt.figure(figsize=(10,5))
plt.plot(values)
plt.tight_layout()

plt.savefig(matplot_lib_filename)
matplot_lib_filename
#+end_src

#+RESULTS:
[[file:/tmp/babel-ckBwwa/figureT2xwWJ.png]]
Nous allons étudier la saisonnalité des données fournies par le MOOC.
L'idée est de décomposer le signal en une tendance(trend), une
composante saisonnière et des résidus.

#+begin_src python :results output :exports both :session s1
import statsmodels.api as sm

# set arbitrary time index to study seasonality
time_index = pd.date_range('1/1/2000', periods=len(values), freq='D')
series = pd.Series(values, index=time_index)
df = pd.DataFrame({'series': series})
print(df.head())
#+end_src

#+RESULTS:
: series
: 2000-01-01    14.0
: 2000-01-02     7.6
: 2000-01-03    11.2
: 2000-01-04    12.8
: 2000-01-05    12.5

#+begin_src python :results file :var matplot_lib_filename=(org-babel-temp-file "figure" ".png") :exports both :session s1
res = sm.tsa.seasonal_decompose(df)
resplot = res.plot()
plt.tight_layout()
resplot.savefig(matplot_lib_filename)
matplot_lib_filename
#+end_src

#+RESULTS:
[[file:/tmp/babel-ckBwwa/figure6n6cj7.png]]

Apparemment, la tendance comporte elle aussi une saisonnalité,
essayons de l'exhiber:

#+begin_src python :results file :session s1 :var matplot_lib_filename=(org-babel-temp-file "figure" ".png") :exports both
df_trend = pd.DataFrame({'trend': res.trend.dropna()})
res_trend = sm.tsa.seasonal_decompose(df_trend)
resplot_trend = res_trend.plot()
plt.tight_layout()
resplot_trend.savefig(matplot_lib_filename)
matplot_lib_filename
#+end_src

#+RESULTS:
[[file:/tmp/babel-ckBwwa/figuresLDoXm.png]]

On observe une belle saisonnalité au sein même de la tendance !
Il semblerait qu'il existe une tendance linéaire au sein même de la
tendance. Vérifions cela:

#+begin_src python :results file :session s1 :var matplot_lib_filename=(org-babel-temp-file "figure" ".png") :exports both
df_trend_bis = pd.DataFrame({'trend_bis': res_trend.trend.dropna()})
res_trend_bis = sm.tsa.seasonal_decompose(df_trend_bis)
resplot_trend_bis = res_trend_bis.plot()
plt.tight_layout()
resplot_trend_bis.savefig(matplot_lib_filename)
matplot_lib_filename
#+end_src

#+RESULTS:
[[file:/tmp/babel-ckBwwa/figure6dAIC9.png]]