diff --git a/module3/exo3/exercice.ipynb b/module3/exo3/exercice.ipynb
index 8bea51e7548b74bfe1c797de03f2e362e3cbc131..4e1b05446aa66bbd5eed67a5fc4b201ec3886a88 100644
--- a/module3/exo3/exercice.ipynb
+++ b/module3/exo3/exercice.ipynb
@@ -12,7 +12,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 475,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -44,7 +44,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 476,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -329,7 +329,7 @@
        "[756 rows x 10 columns]"
       ]
      },
-     "execution_count": 2,
+     "execution_count": 476,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -364,7 +364,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 477,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -651,7 +651,7 @@
        "[756 rows x 10 columns]"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 477,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -675,7 +675,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 478,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -725,7 +725,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 479,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -747,7 +747,7 @@
        "dtype: bool"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 479,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -769,7 +769,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 480,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true,
@@ -917,7 +917,7 @@
        "1958-07-01  315.22  315.86  315.19  "
       ]
      },
-     "execution_count": 6,
+     "execution_count": 480,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -944,7 +944,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 481,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -981,7 +981,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 482,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -1039,7 +1039,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 483,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true,
@@ -1114,7 +1114,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 484,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -1171,7 +1171,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 485,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -1197,7 +1197,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 486,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true,
@@ -1242,7 +1242,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 363,
+   "execution_count": 487,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true,
@@ -1278,7 +1278,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 371,
+   "execution_count": 488,
    "metadata": {},
    "outputs": [
     {
@@ -1287,7 +1287,7 @@
        "0.7829981215405544"
       ]
      },
-     "execution_count": 371,
+     "execution_count": 488,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -1322,7 +1322,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 347,
+   "execution_count": 489,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -1335,314 +1335,6 @@
       " Période lente 30.958333333333332\n",
       " Période rapide 0.9986559139784947\n"
      ]
-    },
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe tbody tr th {\n",
-       "        vertical-align: top;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
-       "    }\n",
-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>index</th>\n",
-       "      <th>Yr</th>\n",
-       "      <th>Mn</th>\n",
-       "      <th>Date 1</th>\n",
-       "      <th>Date 2</th>\n",
-       "      <th>s1</th>\n",
-       "      <th>s2</th>\n",
-       "      <th>s3</th>\n",
-       "      <th>s4</th>\n",
-       "      <th>s5</th>\n",
-       "      <th>s6</th>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>period</th>\n",
-       "      <th></th>\n",
-       "      <th></th>\n",
-       "      <th></th>\n",
-       "      <th></th>\n",
-       "      <th></th>\n",
-       "      <th></th>\n",
-       "      <th></th>\n",
-       "      <th></th>\n",
-       "      <th></th>\n",
-       "      <th></th>\n",
-       "      <th></th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>1958-03-01</th>\n",
-       "      <td>2</td>\n",
-       "      <td>1958</td>\n",
-       "      <td>3</td>\n",
-       "      <td>21259</td>\n",
-       "      <td>1958.2027</td>\n",
-       "      <td>315.70</td>\n",
-       "      <td>314.44</td>\n",
-       "      <td>316.19</td>\n",
-       "      <td>314.91</td>\n",
-       "      <td>315.70</td>\n",
-       "      <td>314.44</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1958-04-01</th>\n",
-       "      <td>3</td>\n",
-       "      <td>1958</td>\n",
-       "      <td>4</td>\n",
-       "      <td>21290</td>\n",
-       "      <td>1958.2877</td>\n",
-       "      <td>317.45</td>\n",
-       "      <td>315.16</td>\n",
-       "      <td>317.30</td>\n",
-       "      <td>314.99</td>\n",
-       "      <td>317.45</td>\n",
-       "      <td>315.16</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1958-05-01</th>\n",
-       "      <td>4</td>\n",
-       "      <td>1958</td>\n",
-       "      <td>5</td>\n",
-       "      <td>21320</td>\n",
-       "      <td>1958.3699</td>\n",
-       "      <td>317.51</td>\n",
-       "      <td>314.71</td>\n",
-       "      <td>317.86</td>\n",
-       "      <td>315.06</td>\n",
-       "      <td>317.51</td>\n",
-       "      <td>314.71</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1958-06-01</th>\n",
-       "      <td>5</td>\n",
-       "      <td>1958</td>\n",
-       "      <td>6</td>\n",
-       "      <td>21351</td>\n",
-       "      <td>1958.4548</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>317.24</td>\n",
-       "      <td>315.14</td>\n",
-       "      <td>317.24</td>\n",
-       "      <td>315.14</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1958-07-01</th>\n",
-       "      <td>6</td>\n",
-       "      <td>1958</td>\n",
-       "      <td>7</td>\n",
-       "      <td>21381</td>\n",
-       "      <td>1958.5370</td>\n",
-       "      <td>315.86</td>\n",
-       "      <td>315.19</td>\n",
-       "      <td>315.86</td>\n",
-       "      <td>315.22</td>\n",
-       "      <td>315.86</td>\n",
-       "      <td>315.19</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1958-08-01</th>\n",
-       "      <td>7</td>\n",
-       "      <td>1958</td>\n",
-       "      <td>8</td>\n",
-       "      <td>21412</td>\n",
-       "      <td>1958.6219</td>\n",
-       "      <td>314.93</td>\n",
-       "      <td>316.19</td>\n",
-       "      <td>314.00</td>\n",
-       "      <td>315.29</td>\n",
-       "      <td>314.93</td>\n",
-       "      <td>316.19</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1958-09-01</th>\n",
-       "      <td>8</td>\n",
-       "      <td>1958</td>\n",
-       "      <td>9</td>\n",
-       "      <td>21443</td>\n",
-       "      <td>1958.7068</td>\n",
-       "      <td>313.21</td>\n",
-       "      <td>316.08</td>\n",
-       "      <td>312.46</td>\n",
-       "      <td>315.35</td>\n",
-       "      <td>313.21</td>\n",
-       "      <td>316.08</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>...</th>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2019-07-01</th>\n",
-       "      <td>738</td>\n",
-       "      <td>2019</td>\n",
-       "      <td>7</td>\n",
-       "      <td>43661</td>\n",
-       "      <td>2019.5370</td>\n",
-       "      <td>411.85</td>\n",
-       "      <td>411.03</td>\n",
-       "      <td>412.36</td>\n",
-       "      <td>411.57</td>\n",
-       "      <td>411.85</td>\n",
-       "      <td>411.03</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2019-08-01</th>\n",
-       "      <td>739</td>\n",
-       "      <td>2019</td>\n",
-       "      <td>8</td>\n",
-       "      <td>43692</td>\n",
-       "      <td>2019.6219</td>\n",
-       "      <td>410.08</td>\n",
-       "      <td>411.62</td>\n",
-       "      <td>410.23</td>\n",
-       "      <td>411.81</td>\n",
-       "      <td>410.08</td>\n",
-       "      <td>411.62</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2019-09-01</th>\n",
-       "      <td>740</td>\n",
-       "      <td>2019</td>\n",
-       "      <td>9</td>\n",
-       "      <td>43723</td>\n",
-       "      <td>2019.7068</td>\n",
-       "      <td>408.55</td>\n",
-       "      <td>412.06</td>\n",
-       "      <td>408.52</td>\n",
-       "      <td>412.05</td>\n",
-       "      <td>408.55</td>\n",
-       "      <td>412.06</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2019-10-01</th>\n",
-       "      <td>741</td>\n",
-       "      <td>2019</td>\n",
-       "      <td>10</td>\n",
-       "      <td>43753</td>\n",
-       "      <td>2019.7890</td>\n",
-       "      <td>408.43</td>\n",
-       "      <td>412.07</td>\n",
-       "      <td>408.67</td>\n",
-       "      <td>412.29</td>\n",
-       "      <td>408.43</td>\n",
-       "      <td>412.07</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2019-11-01</th>\n",
-       "      <td>742</td>\n",
-       "      <td>2019</td>\n",
-       "      <td>11</td>\n",
-       "      <td>43784</td>\n",
-       "      <td>2019.8740</td>\n",
-       "      <td>410.28</td>\n",
-       "      <td>412.56</td>\n",
-       "      <td>410.29</td>\n",
-       "      <td>412.54</td>\n",
-       "      <td>410.28</td>\n",
-       "      <td>412.56</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2019-12-01</th>\n",
-       "      <td>743</td>\n",
-       "      <td>2019</td>\n",
-       "      <td>12</td>\n",
-       "      <td>43814</td>\n",
-       "      <td>2019.9562</td>\n",
-       "      <td>411.85</td>\n",
-       "      <td>412.78</td>\n",
-       "      <td>411.88</td>\n",
-       "      <td>412.79</td>\n",
-       "      <td>411.85</td>\n",
-       "      <td>412.78</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2020-01-01</th>\n",
-       "      <td>744</td>\n",
-       "      <td>2020</td>\n",
-       "      <td>1</td>\n",
-       "      <td>43845</td>\n",
-       "      <td>2020.0410</td>\n",
-       "      <td>413.37</td>\n",
-       "      <td>413.33</td>\n",
-       "      <td>413.11</td>\n",
-       "      <td>413.05</td>\n",
-       "      <td>413.37</td>\n",
-       "      <td>413.33</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "<p>743 rows × 11 columns</p>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "            index    Yr  Mn  Date 1     Date 2      s1      s2      s3  \\\n",
-       "period                                                                   \n",
-       "1958-03-01      2  1958   3   21259  1958.2027  315.70  314.44  316.19   \n",
-       "1958-04-01      3  1958   4   21290  1958.2877  317.45  315.16  317.30   \n",
-       "1958-05-01      4  1958   5   21320  1958.3699  317.51  314.71  317.86   \n",
-       "1958-06-01      5  1958   6   21351  1958.4548     NaN     NaN  317.24   \n",
-       "1958-07-01      6  1958   7   21381  1958.5370  315.86  315.19  315.86   \n",
-       "1958-08-01      7  1958   8   21412  1958.6219  314.93  316.19  314.00   \n",
-       "1958-09-01      8  1958   9   21443  1958.7068  313.21  316.08  312.46   \n",
-       "...           ...   ...  ..     ...        ...     ...     ...     ...   \n",
-       "2019-07-01    738  2019   7   43661  2019.5370  411.85  411.03  412.36   \n",
-       "2019-08-01    739  2019   8   43692  2019.6219  410.08  411.62  410.23   \n",
-       "2019-09-01    740  2019   9   43723  2019.7068  408.55  412.06  408.52   \n",
-       "2019-10-01    741  2019  10   43753  2019.7890  408.43  412.07  408.67   \n",
-       "2019-11-01    742  2019  11   43784  2019.8740  410.28  412.56  410.29   \n",
-       "2019-12-01    743  2019  12   43814  2019.9562  411.85  412.78  411.88   \n",
-       "2020-01-01    744  2020   1   43845  2020.0410  413.37  413.33  413.11   \n",
-       "\n",
-       "                s4      s5      s6  \n",
-       "period                              \n",
-       "1958-03-01  314.91  315.70  314.44  \n",
-       "1958-04-01  314.99  317.45  315.16  \n",
-       "1958-05-01  315.06  317.51  314.71  \n",
-       "1958-06-01  315.14  317.24  315.14  \n",
-       "1958-07-01  315.22  315.86  315.19  \n",
-       "1958-08-01  315.29  314.93  316.19  \n",
-       "1958-09-01  315.35  313.21  316.08  \n",
-       "...            ...     ...     ...  \n",
-       "2019-07-01  411.57  411.85  411.03  \n",
-       "2019-08-01  411.81  410.08  411.62  \n",
-       "2019-09-01  412.05  408.55  412.06  \n",
-       "2019-10-01  412.29  408.43  412.07  \n",
-       "2019-11-01  412.54  410.28  412.56  \n",
-       "2019-12-01  412.79  411.85  412.78  \n",
-       "2020-01-01  413.05  413.37  413.33  \n",
-       "\n",
-       "[743 rows x 11 columns]"
-      ]
-     },
-     "execution_count": 347,
-     "metadata": {},
-     "output_type": "execute_result"
     }
    ],
    "source": [
@@ -1662,7 +1354,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 350,
+   "execution_count": 490,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -1989,7 +1681,7 @@
        "[63 rows x 12 columns]"
       ]
      },
-     "execution_count": 350,
+     "execution_count": 490,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2001,7 +1693,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 491,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
@@ -2189,7 +1881,7 @@
        "max    411.850000  410.080000  408.550000  408.430000  410.280000  411.850000  "
       ]
      },
-     "execution_count": 17,
+     "execution_count": 491,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2200,7 +1892,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 492,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true,
@@ -2355,7 +2047,7 @@
        "1962  0.7890  0.8740  0.9562  "
       ]
      },
-     "execution_count": 32,
+     "execution_count": 492,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2389,40 +2081,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 329,
+   "execution_count": 501,
    "metadata": {
     "hideCode": true,
     "hidePrompt": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([2020])"
-      ]
-     },
-     "execution_count": 329,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "#df_inter = df[['Yr','Mn','Date 2','s5']]\n",
-    "an_b = df2.loc[1960, : ]\n",
-    "an_n = df2.loc[1961, : ]\n",
-    "year, mois = df[-1:]['Yr'].values, df[-1:]['Mn'].values\n",
-    "#for val in per1: \n",
-    "#    print(val.date()) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 334,
-   "metadata": {
-    "hideCode": true,
-    "hidePrompt": true,
-    "scrolled": false
-   },
    "outputs": [
     {
      "data": {
@@ -2445,133 +2108,96 @@
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
-       "      <th>Data 2</th>\n",
-       "      <th>Mn</th>\n",
+       "      <th>index</th>\n",
        "      <th>Yr</th>\n",
+       "      <th>Mn</th>\n",
+       "      <th>Date 1</th>\n",
+       "      <th>Date 2</th>\n",
+       "      <th>s1</th>\n",
+       "      <th>s2</th>\n",
+       "      <th>s3</th>\n",
+       "      <th>s4</th>\n",
+       "      <th>s5</th>\n",
+       "      <th>s6</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>period</th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>2020-01-01</th>\n",
-       "      <td>2020.0410</td>\n",
-       "      <td>1</td>\n",
-       "      <td>2020</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2020-02-01</th>\n",
-       "      <td>2020.1257</td>\n",
-       "      <td>2</td>\n",
-       "      <td>2020</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2020-03-01</th>\n",
-       "      <td>2020.2049</td>\n",
-       "      <td>3</td>\n",
-       "      <td>2020</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2020-04-01</th>\n",
-       "      <td>2020.2896</td>\n",
-       "      <td>4</td>\n",
-       "      <td>2020</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2020-05-01</th>\n",
-       "      <td>2020.3716</td>\n",
-       "      <td>5</td>\n",
-       "      <td>2020</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2020-06-01</th>\n",
-       "      <td>2020.4563</td>\n",
-       "      <td>6</td>\n",
-       "      <td>2020</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2020-07-01</th>\n",
-       "      <td>2020.5383</td>\n",
-       "      <td>7</td>\n",
+       "      <td>744</td>\n",
        "      <td>2020</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>...</th>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2025-06-01</th>\n",
-       "      <td>2025.4548</td>\n",
-       "      <td>6</td>\n",
-       "      <td>2025</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2025-07-01</th>\n",
-       "      <td>2025.5370</td>\n",
-       "      <td>7</td>\n",
-       "      <td>2025</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2025-08-01</th>\n",
-       "      <td>2025.6219</td>\n",
-       "      <td>8</td>\n",
-       "      <td>2025</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2025-09-01</th>\n",
-       "      <td>2025.7068</td>\n",
-       "      <td>9</td>\n",
-       "      <td>2025</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2025-10-01</th>\n",
-       "      <td>2025.7890</td>\n",
-       "      <td>10</td>\n",
-       "      <td>2025</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2025-11-01</th>\n",
-       "      <td>2025.8740</td>\n",
-       "      <td>11</td>\n",
-       "      <td>2025</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2025-12-01</th>\n",
-       "      <td>2025.9562</td>\n",
-       "      <td>12</td>\n",
-       "      <td>2025</td>\n",
+       "      <td>1</td>\n",
+       "      <td>43845</td>\n",
+       "      <td>2020.041</td>\n",
+       "      <td>413.37</td>\n",
+       "      <td>413.33</td>\n",
+       "      <td>413.11</td>\n",
+       "      <td>413.05</td>\n",
+       "      <td>413.37</td>\n",
+       "      <td>413.33</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
-       "<p>72 rows × 3 columns</p>\n",
        "</div>"
       ],
       "text/plain": [
-       "               Data 2  Mn    Yr\n",
-       "2020-01-01  2020.0410   1  2020\n",
-       "2020-02-01  2020.1257   2  2020\n",
-       "2020-03-01  2020.2049   3  2020\n",
-       "2020-04-01  2020.2896   4  2020\n",
-       "2020-05-01  2020.3716   5  2020\n",
-       "2020-06-01  2020.4563   6  2020\n",
-       "2020-07-01  2020.5383   7  2020\n",
-       "...               ...  ..   ...\n",
-       "2025-06-01  2025.4548   6  2025\n",
-       "2025-07-01  2025.5370   7  2025\n",
-       "2025-08-01  2025.6219   8  2025\n",
-       "2025-09-01  2025.7068   9  2025\n",
-       "2025-10-01  2025.7890  10  2025\n",
-       "2025-11-01  2025.8740  11  2025\n",
-       "2025-12-01  2025.9562  12  2025\n",
+       "            index    Yr  Mn  Date 1    Date 2      s1      s2      s3      s4  \\\n",
+       "period                                                                          \n",
+       "2020-01-01    744  2020   1   43845  2020.041  413.37  413.33  413.11  413.05   \n",
        "\n",
-       "[72 rows x 3 columns]"
+       "                s5      s6  \n",
+       "period                      \n",
+       "2020-01-01  413.37  413.33  "
       ]
      },
-     "execution_count": 334,
+     "execution_count": 501,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
+   "source": [
+    "#df_inter = df[['Yr','Mn','Date 2','s5']]\n",
+    "an_b = df2.loc[1960, : ]\n",
+    "an_n = df2.loc[1961, : ]\n",
+    "year, mois = df[-1:]['Yr'].values, df[-1:]['Mn'].values\n",
+    "#for val in per1: \n",
+    "#    print(val.date()) \n",
+    "df[-1:].index\n",
+    "df[-1:]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 508,
+   "metadata": {
+    "hideCode": true,
+    "hidePrompt": true,
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "ename": "SyntaxError",
+     "evalue": "invalid syntax (<ipython-input-508-73a8dd18a141>, line 11)",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-508-73a8dd18a141>\"\u001b[0;36m, line \u001b[0;32m11\u001b[0m\n\u001b[0;31m    iser ....\u001b[0m\n\u001b[0m           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
+     ]
+    }
+   ],
    "source": [
     "# Année de fin d'extrapolation \n",
     "year_f = 2025\n",
@@ -2582,29 +2208,39 @@
     "Yr = pd.Series([q.year for q in per1],index = per1 )\n",
     "Mn = pd.Series([q.month for q in per1],index = per1)\n",
     "    \n",
-    "s = []         # oblication d'initialiser ....\n",
+    "s = []         # oblication d'initial\n",
+    "iser ....\n",
     "[s.extend(list(an_n)) if i%4!=0 else s.extend(list(an_b))  for i in np.arange(ymj_fin.year- year[0]+1)]\n",
     "Data2 = pd.Series(s,index = per1)\n",
     "df_inter = pd.DataFrame({'Yr' : Yr,'Mn' : Mn,'Data 2' : Data2 + Yr})\n",
     "#dfa = pd.DataFrame({'Data2' : Data2})\n",
+    "\n",
+    "\n",
+    "df_inter.drop(index = df_inter[-1:].index[0], :)\n",
+    "\n",
     "df_inter"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {
-    "scrolled": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "ylent_inter = my_sin(df_inter['Data 2'],popt_l[0],popt_l[1],popt_l[2],popt_l[3])\n",
     "yrapide_inter = my_sin(df_inter['Data 2'],popt_r[0],popt_r[1],popt_r[2],popt_r[3]) \n",
     "\n",
+    "mu, sigma = 0, bruit['std'] \n",
+    "# creating a noise\n",
+    "noise = np.random.normal(mu, sigma, len(df_inter['Data 2']))\n",
+    "evolution = fcube(df_inter['Data 2'])\n",
+    "\n",
+    "df_inter['evolution'] = evolution\n",
     "df_inter['s5_lent'] = ylent_inter\n",
-    "df_inter['s5_rapide'] = ylent_rapide\n",
-    "df_inter\n",
-    "\n"
+    "df_inter['s5_rapide'] = yrapide_inter\n",
+    "df_inter['noise'] = noise\n",
+    "df_inter['s5_inter'] =  df_inter.s5_lent + df_inter.s5_rapide + df_inter.noise+df_inter.evolution\n",
+    "df_inter"
    ]
   },
   {
@@ -2619,15 +2255,10 @@
     "ax1.grid(linestyle='--', linewidth=1)\n",
     "ax2.grid(linestyle='--', linewidth=1)\n",
     "\n",
-    "mu, sigma = 0, bruit['std'] \n",
-    "# creating a noise\n",
-    "noise = np.random.normal(mu, sigma, len(df_inter['Data 2'])) \n",
-    "\n",
     "ax1.set(title = 'Interpolation concentration CO2 lente',xlabel='Période',ylabel='Concentration (ppm)')\n",
-    "ax1.plot(df_inter['Data 2'],ylent_inter);\n",
+    "ax1.plot(df_inter['Data 2'],df_inter.s5_lent);\n",
     "ax2.set(title = 'Interpolation concentration CO2 rapide',xlabel='Période',ylabel='Concentration (ppm)')\n",
-    "ax2.plot(df_inter['Data 2'],yrapide_inter + noise);\n",
-    "\n"
+    "ax2.plot(df_inter['Data 2'],df_inter.s5_rapide);"
    ]
   },
   {
@@ -2635,14 +2266,47 @@
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "fig = plt.figure(figsize=(18,5))\n",
+    "ax1 = fig.add_subplot(111)\n",
+    "ax1.grid(linestyle='--', linewidth=1)\n",
+    "\n",
+    "ax1.set(title = 'Interpolation concentration CO2 + bruit',xlabel='Période',ylabel='Concentration (ppm)')\n",
+    "ax1.plot(df_inter['Data 2'],df_inter.s5_lent + df_inter.s5_rapide + df_inter.noise);\n",
+    "#ax2.set(title = 'Interpolation concentration CO2 rapide',xlabel='Période',ylabel='Concentration (ppm)')\n",
+    "#ax2.plot(df_inter['Data 2'],df_inter.s5_rapide);"
+   ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "fig = plt.figure(figsize=(18,5))\n",
+    "ax1 = fig.add_subplot(111)\n",
+    "ax1.grid(linestyle='--', linewidth=1)\n",
+    "\n",
+    "ax1.set(title = 'Interpolation concentration CO2 + bruit',xlabel='Période',ylabel='Concentration (ppm)')\n",
+    "ax1.plot(df_inter['Data 2'],df_inter.s5_inter);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\n",
+    "\n",
+    "\n",
+    "fig = plt.figure(figsize=(18,5))\n",
+    "ax1 = fig.add_subplot(111)\n",
+    "ax1.grid(linestyle='--', linewidth=1)\n",
+    "\n",
+    "ax1.set(title = 'Interpolation concentration CO2 + bruit',xlabel='Période',ylabel='Concentration (ppm)')\n",
+    "ax1.plot(df_inter['Data 2'],df_inter.s5_lent + df_inter.s5_rapide + df_inter.noise+df_inter.evolution);"
+   ]
   }
  ],
  "metadata": {