diff --git a/docs/arima.html b/docs/arima.html
index 682a39cfb..c48b429e0 100644
--- a/docs/arima.html
+++ b/docs/arima.html
@@ -59,9 +59,9 @@
 
 
 <div class="output_text output_subarea output_execute_result">
-<pre>{&#39;ar1&#39;: 0.4689829145163128,
- &#39;ar2&#39;: 0.22312523789164457,
- &#39;ma1&#39;: -1.0913909475743682}</pre>
+<pre>{&#39;ar1&#39;: 0.466880673428245,
+ &#39;ar2&#39;: 0.22506344134934328,
+ &#39;ma1&#39;: -1.0964437716813402}</pre>
 </div>
 
 </div>
@@ -125,11 +125,11 @@ <h4 id="predict_arima" class="doc_header"><code>predict_arima</code><a href="htt
 
 
 <div class="output_text output_subarea output_execute_result">
-<pre>(array([448.07383778, 423.76127286, 453.4616271 , 496.63557354,
-        508.56552631, 572.26359535, 659.79847373, 644.20507938,
-        546.51511535, 499.7512409 ]),
- array([11.52726482, 13.17087978, 14.69871817, 15.67558242, 16.44637167,
-        17.05466929, 17.56245596, 17.99871958, 18.38480966, 18.73431477]))</pre>
+<pre>(array([448.03641765, 423.6958796 , 453.37910036, 496.53844782,
+        508.4585562 , 572.14906375, 659.67853114, 644.08113724,
+        546.38826999, 499.62227626]),
+ array([11.53128398, 13.1873165 , 14.74522214, 15.74954361, 16.54939395,
+        17.18562958, 17.7205789 , 18.18296878, 18.59424176, 18.96803794]))</pre>
 </div>
 
 </div>
@@ -162,12 +162,12 @@ <h4 id="predict_arima" class="doc_header"><code>predict_arima</code><a href="htt
 
 
 <div class="output_text output_subarea output_execute_result">
-<pre>(array([470.00937272, 440.51544656, 442.19147092, 430.30545649,
-        425.096418  , 417.3695783 , 411.26634297, 404.88733056,
-        399.07104147, 393.41663428]),
- array([ 30.69910092,  51.71192568,  61.89381735,  71.06719113,
-         77.98071907,  83.94818888,  88.93456731,  93.25688638,
-         96.99560511, 100.27006818]))</pre>
+<pre>(array([470.0097129 , 440.51623786, 442.19261859, 430.30698345,
+        425.09828469, 417.37177946, 411.26885683, 404.89014495,
+        399.07414049, 393.42000495]),
+ array([ 30.69910087,  51.7119296 ,  61.89382391,  71.067199  ,
+         77.98072868,  83.94819971,  88.93457943,  93.2568996 ,
+         96.9956194 , 100.27008344]))</pre>
 </div>
 
 </div>
@@ -202,11 +202,11 @@ <h4 id="predict_arima" class="doc_header"><code>predict_arima</code><a href="htt
 
 
 <div class="output_text output_subarea output_execute_result">
-<pre>(array([441.89795441, 463.67049935, 489.91196632, 513.32979525,
-        528.76750245, 534.25618332, 530.97888269, 522.35816274,
-        512.68417075, 505.75238585]),
- array([25.04154434, 31.85338185, 33.32712576, 33.34241457, 34.68174561,
-        37.33840998, 39.68800251, 40.7798007 , 40.92280834, 40.99296398]))</pre>
+<pre>(array([441.89777076, 463.6701726 , 489.91157043, 513.32941052,
+        528.76719128, 534.25597523, 530.97877135, 522.35811387,
+        512.68413676, 505.7523218 ]),
+ array([25.04154425, 31.85337615, 33.32711649, 33.34240568, 34.68173961,
+        37.33840629, 39.6879995 , 40.7797975 , 40.92280492, 40.99296076]))</pre>
 </div>
 
 </div>
@@ -240,7 +240,7 @@ <h4 id="predict_arima" class="doc_header"><code>predict_arima</code><a href="htt
 
 
 <div class="output_text output_subarea output_execute_result">
-<pre>1020.7426750289078</pre>
+<pre>1020.8073918488345</pre>
 </div>
 
 </div>
@@ -475,17 +475,17 @@ <h4 id="auto_arima_f" class="doc_header"><code>auto_arima_f</code><a href="https
 
 ARIMA(1,1,0)(0,1,1)[12]                   :1021.1141377784866
 
-ARIMA(1,1,0)(1,1,1)[12]                   :1022.6657137203397
+ARIMA(1,1,0)(1,1,1)[12]                   :1022.6657138771359
 
 ARIMA(2,1,0)(0,1,0)[12]                   :1022.5909032832317
 
-ARIMA(1,1,1)(0,1,0)[12]                   :1022.5906051178998
+ARIMA(1,1,1)(0,1,0)[12]                   :1022.5906051142277
 
 ARIMA(0,1,1)(0,1,0)[12]                   :1020.7342476851575
 
-ARIMA(2,1,1)(0,1,0)[12]                   :1021.0626750289078
+ARIMA(2,1,1)(0,1,0)[12]                   :1021.1273918488346
 
-ARIMA(2,1,1)(0,1,0)[12]                   :1021.0626750289078
+ARIMA(2,1,1)(0,1,0)[12]                   :1021.1273918488346
 Now re-fitting the best model(s) without approximations...
 
 
@@ -833,15 +833,15 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
     </tr>
     <tr>
       <th>2</th>
-      <td>490.196786</td>
+      <td>490.196787</td>
     </tr>
     <tr>
       <th>3</th>
-      <td>489.549974</td>
+      <td>489.549975</td>
     </tr>
     <tr>
       <th>4</th>
-      <td>485.653254</td>
+      <td>485.653255</td>
     </tr>
     <tr>
       <th>5</th>
@@ -917,37 +917,37 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
       <th>1</th>
       <td>419.928952</td>
       <td>483.363282</td>
-      <td>546.797611</td>
+      <td>546.797612</td>
     </tr>
     <tr>
       <th>2</th>
-      <td>411.105076</td>
-      <td>490.196786</td>
-      <td>569.288497</td>
+      <td>411.105075</td>
+      <td>490.196787</td>
+      <td>569.288499</td>
     </tr>
     <tr>
       <th>3</th>
-      <td>401.920877</td>
-      <td>489.549974</td>
-      <td>577.179072</td>
+      <td>401.920876</td>
+      <td>489.549975</td>
+      <td>577.179074</td>
     </tr>
     <tr>
       <th>4</th>
-      <td>393.609049</td>
-      <td>485.653254</td>
-      <td>577.697460</td>
+      <td>393.609048</td>
+      <td>485.653255</td>
+      <td>577.697462</td>
     </tr>
     <tr>
       <th>5</th>
-      <td>386.910312</td>
+      <td>386.910310</td>
       <td>481.407362</td>
-      <td>575.904412</td>
+      <td>575.904414</td>
     </tr>
     <tr>
       <th>6</th>
-      <td>382.073458</td>
+      <td>382.073456</td>
       <td>478.248913</td>
-      <td>574.424368</td>
+      <td>574.424370</td>
     </tr>
   </tbody>
 </table>
@@ -1020,48 +1020,48 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
       <td>419.928952</td>
       <td>401.946201</td>
       <td>483.363282</td>
-      <td>546.797611</td>
-      <td>564.780362</td>
+      <td>546.797612</td>
+      <td>564.780363</td>
     </tr>
     <tr>
       <th>2</th>
-      <td>411.105076</td>
-      <td>388.683675</td>
-      <td>490.196786</td>
-      <td>569.288497</td>
-      <td>591.709898</td>
+      <td>411.105075</td>
+      <td>388.683674</td>
+      <td>490.196787</td>
+      <td>569.288499</td>
+      <td>591.709900</td>
     </tr>
     <tr>
       <th>3</th>
-      <td>401.920877</td>
-      <td>377.079245</td>
-      <td>489.549974</td>
-      <td>577.179072</td>
-      <td>602.020703</td>
+      <td>401.920876</td>
+      <td>377.079244</td>
+      <td>489.549975</td>
+      <td>577.179074</td>
+      <td>602.020706</td>
     </tr>
     <tr>
       <th>4</th>
-      <td>393.609049</td>
-      <td>367.515796</td>
-      <td>485.653254</td>
-      <td>577.697460</td>
-      <td>603.790713</td>
+      <td>393.609048</td>
+      <td>367.515794</td>
+      <td>485.653255</td>
+      <td>577.697462</td>
+      <td>603.790716</td>
     </tr>
     <tr>
       <th>5</th>
-      <td>386.910312</td>
-      <td>360.121711</td>
+      <td>386.910310</td>
+      <td>360.121709</td>
       <td>481.407362</td>
-      <td>575.904412</td>
-      <td>602.693012</td>
+      <td>575.904414</td>
+      <td>602.693015</td>
     </tr>
     <tr>
       <th>6</th>
-      <td>382.073458</td>
-      <td>354.809053</td>
+      <td>382.073456</td>
+      <td>354.809051</td>
       <td>478.248913</td>
-      <td>574.424368</td>
-      <td>601.688773</td>
+      <td>574.424370</td>
+      <td>601.688776</td>
     </tr>
   </tbody>
 </table>
@@ -1123,7 +1123,7 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
     </tr>
     <tr>
       <th>1</th>
-      <td>112.688512</td>
+      <td>112.688513</td>
     </tr>
     <tr>
       <th>2</th>
@@ -1143,7 +1143,7 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
     </tr>
     <tr>
       <th>139</th>
-      <td>630.376066</td>
+      <td>630.376068</td>
     </tr>
     <tr>
       <th>140</th>
@@ -1151,15 +1151,15 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
     </tr>
     <tr>
       <th>141</th>
-      <td>451.814468</td>
+      <td>451.814466</td>
     </tr>
     <tr>
       <th>142</th>
-      <td>443.498420</td>
+      <td>443.498419</td>
     </tr>
     <tr>
       <th>143</th>
-      <td>374.088367</td>
+      <td>374.088365</td>
     </tr>
   </tbody>
 </table>
@@ -1227,7 +1227,7 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
     <tr>
       <th>1</th>
       <td>92.528257</td>
-      <td>112.688512</td>
+      <td>112.688513</td>
       <td>132.848768</td>
     </tr>
     <tr>
@@ -1256,33 +1256,33 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
     </tr>
     <tr>
       <th>139</th>
-      <td>610.215811</td>
-      <td>630.376066</td>
-      <td>650.536321</td>
+      <td>610.215813</td>
+      <td>630.376068</td>
+      <td>650.536323</td>
     </tr>
     <tr>
       <th>140</th>
-      <td>547.795809</td>
+      <td>547.795810</td>
       <td>567.956065</td>
       <td>588.116320</td>
     </tr>
     <tr>
       <th>141</th>
-      <td>431.654213</td>
-      <td>451.814468</td>
-      <td>471.974723</td>
+      <td>431.654211</td>
+      <td>451.814466</td>
+      <td>471.974721</td>
     </tr>
     <tr>
       <th>142</th>
-      <td>423.338165</td>
-      <td>443.498420</td>
-      <td>463.658675</td>
+      <td>423.338164</td>
+      <td>443.498419</td>
+      <td>463.658674</td>
     </tr>
     <tr>
       <th>143</th>
-      <td>353.928112</td>
-      <td>374.088367</td>
-      <td>394.248622</td>
+      <td>353.928110</td>
+      <td>374.088365</td>
+      <td>394.248620</td>
     </tr>
   </tbody>
 </table>
@@ -1335,8 +1335,8 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
   <thead>
     <tr style="text-align: right;">
       <th></th>
-      <th>lo_80%</th>
       <th>lo_90%</th>
+      <th>lo_80%</th>
       <th>mean</th>
       <th>hi_80%</th>
       <th>hi_90%</th>
@@ -1355,7 +1355,7 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
       <th>1</th>
       <td>74.383399</td>
       <td>63.524432</td>
-      <td>112.688512</td>
+      <td>112.688513</td>
       <td>150.993626</td>
       <td>161.852593</td>
     </tr>
@@ -1393,11 +1393,11 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
     </tr>
     <tr>
       <th>139</th>
-      <td>592.070953</td>
-      <td>581.211985</td>
-      <td>630.376066</td>
-      <td>668.681180</td>
-      <td>679.540147</td>
+      <td>592.070954</td>
+      <td>581.211987</td>
+      <td>630.376068</td>
+      <td>668.681181</td>
+      <td>679.540149</td>
     </tr>
     <tr>
       <th>140</th>
@@ -1405,31 +1405,31 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
       <td>518.791984</td>
       <td>567.956065</td>
       <td>606.261178</td>
-      <td>617.120145</td>
+      <td>617.120146</td>
     </tr>
     <tr>
       <th>141</th>
-      <td>413.509354</td>
-      <td>402.650387</td>
-      <td>451.814468</td>
-      <td>490.119581</td>
-      <td>500.978549</td>
+      <td>413.509353</td>
+      <td>402.650385</td>
+      <td>451.814466</td>
+      <td>490.119580</td>
+      <td>500.978547</td>
     </tr>
     <tr>
       <th>142</th>
-      <td>405.193307</td>
-      <td>394.334339</td>
-      <td>443.498420</td>
-      <td>481.803534</td>
-      <td>492.662501</td>
+      <td>405.193306</td>
+      <td>394.334338</td>
+      <td>443.498419</td>
+      <td>481.803533</td>
+      <td>492.662500</td>
     </tr>
     <tr>
       <th>143</th>
-      <td>335.783253</td>
-      <td>324.924286</td>
-      <td>374.088367</td>
-      <td>412.393480</td>
-      <td>423.252448</td>
+      <td>335.783252</td>
+      <td>324.924284</td>
+      <td>374.088365</td>
+      <td>412.393479</td>
+      <td>423.252446</td>
     </tr>
   </tbody>
 </table>
@@ -1606,83 +1606,83 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
   <tbody>
     <tr>
       <th>0</th>
-      <td>444.847964</td>
-      <td>434.808170</td>
-      <td>480.263439</td>
-      <td>515.678913</td>
-      <td>525.718708</td>
+      <td>444.847963</td>
+      <td>434.808168</td>
+      <td>480.263437</td>
+      <td>515.678911</td>
+      <td>525.718706</td>
     </tr>
     <tr>
       <th>1</th>
-      <td>414.132044</td>
-      <td>398.250567</td>
-      <td>470.154109</td>
-      <td>526.176174</td>
-      <td>542.057651</td>
+      <td>414.132100</td>
+      <td>398.250623</td>
+      <td>470.154163</td>
+      <td>526.176226</td>
+      <td>542.057702</td>
     </tr>
     <tr>
       <th>2</th>
-      <td>422.259259</td>
-      <td>403.968470</td>
-      <td>486.780194</td>
-      <td>551.301128</td>
-      <td>569.591917</td>
+      <td>422.259329</td>
+      <td>403.968541</td>
+      <td>486.780261</td>
+      <td>551.301193</td>
+      <td>569.591981</td>
     </tr>
     <tr>
       <th>3</th>
-      <td>398.925598</td>
-      <td>379.813444</td>
-      <td>466.343905</td>
-      <td>533.762212</td>
-      <td>552.874366</td>
+      <td>398.925698</td>
+      <td>379.813546</td>
+      <td>466.344002</td>
+      <td>533.762305</td>
+      <td>552.874457</td>
     </tr>
     <tr>
       <th>4</th>
-      <td>400.961668</td>
-      <td>381.849515</td>
-      <td>468.379976</td>
-      <td>535.798283</td>
-      <td>554.910436</td>
+      <td>400.961769</td>
+      <td>381.849617</td>
+      <td>468.380072</td>
+      <td>535.798375</td>
+      <td>554.910527</td>
     </tr>
     <tr>
       <th>5</th>
-      <td>402.991947</td>
-      <td>383.879794</td>
-      <td>470.410254</td>
-      <td>537.828561</td>
-      <td>556.940715</td>
+      <td>402.992047</td>
+      <td>383.879895</td>
+      <td>470.410351</td>
+      <td>537.828654</td>
+      <td>556.940806</td>
     </tr>
     <tr>
       <th>6</th>
-      <td>405.016485</td>
-      <td>385.904331</td>
-      <td>472.434792</td>
-      <td>539.853099</td>
-      <td>558.965253</td>
+      <td>405.016585</td>
+      <td>385.904433</td>
+      <td>472.434888</td>
+      <td>539.853191</td>
+      <td>558.965344</td>
     </tr>
     <tr>
       <th>7</th>
-      <td>407.035332</td>
-      <td>387.923179</td>
-      <td>474.453639</td>
-      <td>541.871947</td>
-      <td>560.984100</td>
+      <td>407.035432</td>
+      <td>387.923280</td>
+      <td>474.453735</td>
+      <td>541.872038</td>
+      <td>560.984191</td>
     </tr>
     <tr>
       <th>8</th>
-      <td>409.048538</td>
-      <td>389.936385</td>
-      <td>476.466845</td>
-      <td>543.885153</td>
-      <td>562.997306</td>
+      <td>409.048638</td>
+      <td>389.936486</td>
+      <td>476.466941</td>
+      <td>543.885244</td>
+      <td>562.997397</td>
     </tr>
     <tr>
       <th>9</th>
-      <td>411.056152</td>
-      <td>391.943999</td>
-      <td>478.474459</td>
-      <td>545.892767</td>
-      <td>565.004920</td>
+      <td>411.056252</td>
+      <td>391.944099</td>
+      <td>478.474555</td>
+      <td>545.892858</td>
+      <td>565.005010</td>
     </tr>
   </tbody>
 </table>
@@ -1740,23 +1740,23 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
   <tbody>
     <tr>
       <th>0</th>
-      <td>73.205195</td>
+      <td>73.205186</td>
     </tr>
     <tr>
       <th>1</th>
-      <td>116.319121</td>
+      <td>116.319149</td>
     </tr>
     <tr>
       <th>2</th>
-      <td>100.318846</td>
+      <td>100.318853</td>
     </tr>
     <tr>
       <th>3</th>
-      <td>107.862718</td>
+      <td>107.862723</td>
     </tr>
     <tr>
       <th>4</th>
-      <td>108.927678</td>
+      <td>108.927698</td>
     </tr>
     <tr>
       <th>...</th>
@@ -1764,23 +1764,23 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
     </tr>
     <tr>
       <th>139</th>
-      <td>608.317486</td>
+      <td>608.317523</td>
     </tr>
     <tr>
       <th>140</th>
-      <td>564.682612</td>
+      <td>564.682620</td>
     </tr>
     <tr>
       <th>141</th>
-      <td>429.362212</td>
+      <td>429.362250</td>
     </tr>
     <tr>
       <th>142</th>
-      <td>442.344672</td>
+      <td>442.344697</td>
     </tr>
     <tr>
       <th>143</th>
-      <td>391.283965</td>
+      <td>391.284005</td>
     </tr>
   </tbody>
 </table>
@@ -1833,8 +1833,8 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
   <thead>
     <tr style="text-align: right;">
       <th></th>
-      <th>lo_80%</th>
       <th>lo_90%</th>
+      <th>lo_80%</th>
       <th>mean</th>
       <th>hi_80%</th>
       <th>hi_90%</th>
@@ -1843,43 +1843,43 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
   <tbody>
     <tr>
       <th>0</th>
-      <td>37.789721</td>
-      <td>27.749926</td>
-      <td>73.205195</td>
-      <td>108.620669</td>
-      <td>118.660464</td>
+      <td>37.789712</td>
+      <td>27.749917</td>
+      <td>73.205186</td>
+      <td>108.620660</td>
+      <td>118.660455</td>
     </tr>
     <tr>
       <th>1</th>
-      <td>80.903646</td>
-      <td>70.863851</td>
-      <td>116.319121</td>
-      <td>151.734595</td>
-      <td>161.774390</td>
+      <td>80.903675</td>
+      <td>70.863880</td>
+      <td>116.319149</td>
+      <td>151.734624</td>
+      <td>161.774418</td>
     </tr>
     <tr>
       <th>2</th>
-      <td>64.903372</td>
-      <td>54.863577</td>
-      <td>100.318846</td>
-      <td>135.734320</td>
-      <td>145.774115</td>
+      <td>64.903379</td>
+      <td>54.863584</td>
+      <td>100.318853</td>
+      <td>135.734328</td>
+      <td>145.774123</td>
     </tr>
     <tr>
       <th>3</th>
-      <td>72.447244</td>
-      <td>62.407449</td>
-      <td>107.862718</td>
-      <td>143.278193</td>
-      <td>153.317988</td>
+      <td>72.447249</td>
+      <td>62.407454</td>
+      <td>107.862723</td>
+      <td>143.278198</td>
+      <td>153.317993</td>
     </tr>
     <tr>
       <th>4</th>
-      <td>73.512204</td>
-      <td>63.472409</td>
-      <td>108.927678</td>
-      <td>144.343152</td>
-      <td>154.382947</td>
+      <td>73.512224</td>
+      <td>63.472429</td>
+      <td>108.927698</td>
+      <td>144.343172</td>
+      <td>154.382967</td>
     </tr>
     <tr>
       <th>...</th>
@@ -1891,43 +1891,43 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
     </tr>
     <tr>
       <th>139</th>
-      <td>572.902012</td>
-      <td>562.862217</td>
-      <td>608.317486</td>
-      <td>643.732961</td>
-      <td>653.772756</td>
+      <td>572.902048</td>
+      <td>562.862253</td>
+      <td>608.317523</td>
+      <td>643.732997</td>
+      <td>653.772792</td>
     </tr>
     <tr>
       <th>140</th>
-      <td>529.267138</td>
-      <td>519.227343</td>
-      <td>564.682612</td>
-      <td>600.098087</td>
-      <td>610.137882</td>
+      <td>529.267145</td>
+      <td>519.227350</td>
+      <td>564.682620</td>
+      <td>600.098094</td>
+      <td>610.137889</td>
     </tr>
     <tr>
       <th>141</th>
-      <td>393.946737</td>
-      <td>383.906942</td>
-      <td>429.362212</td>
-      <td>464.777686</td>
-      <td>474.817481</td>
+      <td>393.946776</td>
+      <td>383.906981</td>
+      <td>429.362250</td>
+      <td>464.777724</td>
+      <td>474.817519</td>
     </tr>
     <tr>
       <th>142</th>
-      <td>406.929198</td>
-      <td>396.889403</td>
-      <td>442.344672</td>
-      <td>477.760146</td>
-      <td>487.799941</td>
+      <td>406.929222</td>
+      <td>396.889427</td>
+      <td>442.344697</td>
+      <td>477.760171</td>
+      <td>487.799966</td>
     </tr>
     <tr>
       <th>143</th>
-      <td>355.868490</td>
-      <td>345.828696</td>
-      <td>391.283965</td>
-      <td>426.699439</td>
-      <td>436.739234</td>
+      <td>355.868531</td>
+      <td>345.828736</td>
+      <td>391.284005</td>
+      <td>426.699480</td>
+      <td>436.739275</td>
     </tr>
   </tbody>
 </table>
@@ -1965,9 +1965,9 @@ <h2 id="References">References<a class="anchor-link" href="#References"> </a></h
 <pre>Regression with ARIMA(0,0,3) errors
 
 Coefficients:
-               ma1    ma2    ma3     ex_1      ex_2
-coefficient  1.226  0.904  0.552   57.136   -45.774
-s.e.         1.025  2.163  1.025  877.522  1783.342
+               ma1    ma2    ma3    ex_1    ex_2
+coefficient  1.226  0.904  0.552  57.136 -45.774
+s.e.         0.052  0.123  0.084  15.718  44.469
 
 sigma^2 = 763.684: log likelihood = -679.81
 
diff --git a/docs/models.html b/docs/models.html
index 4a4fb8aba..451310c69 100644
--- a/docs/models.html
+++ b/docs/models.html
@@ -441,24 +441,6 @@ <h4 id="auto_arima" class="doc_header"><code>auto_arima</code><a href="https://g
 </div>
 </div>
 
-<div class="output_wrapper">
-<div class="output">
-
-<div class="output_area">
-
-
-
-<div class="output_text output_subarea output_execute_result">
-<pre>array([444.30005077, 418.2100203 , 446.23703401, 488.22892853,
-       499.23136059, 562.23063085, 649.23084981, 633.23078411,
-       535.23080382, 488.23079791, 417.23079968, 459.23079915])</pre>
-</div>
-
-</div>
-
-</div>
-</div>
-
 </div>
     {% endraw %}
 
@@ -519,23 +501,6 @@ <h4 id="auto_arima" class="doc_header"><code>auto_arima</code><a href="https://g
 </div>
 </div>
 
-<div class="output_wrapper">
-<div class="output">
-
-<div class="output_area">
-
-
-
-<div class="output_text output_subarea output_execute_result">
-<pre>array([444.37987806, 418.34259254, 446.43040677, 488.47970809,
-       499.53987871, 562.59603023, 649.65266734])</pre>
-</div>
-
-</div>
-
-</div>
-</div>
-
 </div>
     {% endraw %}
 
@@ -560,143 +525,6 @@ <h4 id="auto_arima" class="doc_header"><code>auto_arima</code><a href="https://g
 </div>
 </div>
 
-<div class="output_wrapper">
-<div class="output">
-
-<div class="output_area">
-
-
-<div class="output_html rendered_html output_subarea output_execute_result"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>mean</th>
-      <th>lo-95</th>
-      <th>lo-80</th>
-      <th>hi-80</th>
-      <th>hi-95</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>444.300051</td>
-      <td>421.179472</td>
-      <td>429.182317</td>
-      <td>459.417784</td>
-      <td>467.420629</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>418.210020</td>
-      <td>389.988431</td>
-      <td>399.756915</td>
-      <td>436.663126</td>
-      <td>446.431610</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>446.237034</td>
-      <td>412.620660</td>
-      <td>424.256469</td>
-      <td>468.217599</td>
-      <td>479.853408</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>488.228929</td>
-      <td>450.265291</td>
-      <td>463.405840</td>
-      <td>513.052017</td>
-      <td>526.192566</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>499.231361</td>
-      <td>457.290190</td>
-      <td>471.807503</td>
-      <td>526.655218</td>
-      <td>541.172531</td>
-    </tr>
-    <tr>
-      <th>5</th>
-      <td>562.230631</td>
-      <td>516.679736</td>
-      <td>532.446502</td>
-      <td>592.014760</td>
-      <td>607.781525</td>
-    </tr>
-    <tr>
-      <th>6</th>
-      <td>649.230850</td>
-      <td>600.329866</td>
-      <td>617.256215</td>
-      <td>681.205484</td>
-      <td>698.131833</td>
-    </tr>
-    <tr>
-      <th>7</th>
-      <td>633.230784</td>
-      <td>581.196677</td>
-      <td>599.207510</td>
-      <td>667.254058</td>
-      <td>685.264891</td>
-    </tr>
-    <tr>
-      <th>8</th>
-      <td>535.230804</td>
-      <td>480.241310</td>
-      <td>499.275106</td>
-      <td>571.186501</td>
-      <td>590.220298</td>
-    </tr>
-    <tr>
-      <th>9</th>
-      <td>488.230798</td>
-      <td>430.436989</td>
-      <td>450.441457</td>
-      <td>526.020138</td>
-      <td>546.024607</td>
-    </tr>
-    <tr>
-      <th>10</th>
-      <td>417.230800</td>
-      <td>356.762551</td>
-      <td>377.692737</td>
-      <td>456.768863</td>
-      <td>477.699049</td>
-    </tr>
-    <tr>
-      <th>11</th>
-      <td>459.230799</td>
-      <td>396.201501</td>
-      <td>418.018156</td>
-      <td>500.443442</td>
-      <td>522.260098</td>
-    </tr>
-  </tbody>
-</table>
-</div></div>
-
-</div>
-
-</div>
-</div>
-
 </div>
     {% endraw %}
 
diff --git a/nbs/arima.ipynb b/nbs/arima.ipynb
index ef8f650a8..28be9573f 100644
--- a/nbs/arima.ipynb
+++ b/nbs/arima.ipynb
@@ -3,6 +3,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "75751cce",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -12,6 +13,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "16d8c18e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -22,6 +24,7 @@
   },
   {
    "cell_type": "markdown",
+   "id": "bb0efd1a",
    "metadata": {},
    "source": [
     "# ARIMA"
@@ -30,6 +33,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "aac2a54f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -54,6 +58,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "f6aa9517",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -64,6 +69,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "376c09fe",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -86,6 +92,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "1ea975b7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -125,6 +132,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "8c4d8301",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -138,6 +146,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "cc5f2433",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -159,6 +168,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "71d72a8b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -170,6 +180,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "8ca693ea",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -192,6 +203,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "a94fe482",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -208,6 +220,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "0f18a037",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -244,6 +257,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "0db3588b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -269,6 +283,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "7098ce54",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -290,6 +305,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "f9e27a5b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -311,6 +327,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "ed047f9d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -323,6 +340,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "77952067",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -460,6 +478,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "990cf2ce",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -506,6 +525,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "b26f389d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -552,6 +572,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "de9fc815",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -567,6 +588,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "d8c647ce",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -585,6 +607,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "08d2362a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -636,6 +659,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "4978f300",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -650,6 +674,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "384bd712",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -709,6 +734,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "f2be7839",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -722,6 +748,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "82dd44b6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -862,6 +889,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "e045b791",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -884,6 +912,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "36173064",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -922,6 +951,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "9d4f09f8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1318,6 +1348,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "67aac1bd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1328,6 +1359,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "50ec5a92",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1340,6 +1372,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "b673533a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1355,6 +1388,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "ee1b480c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1367,6 +1401,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "b18047ec",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1381,6 +1416,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "b4d2c960",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1431,6 +1467,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "67b31584",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1441,6 +1478,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "56649503",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1451,6 +1489,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "c66e3708",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1463,6 +1502,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "a1b4602e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1527,6 +1567,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "d2edb920",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1536,6 +1577,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "92eef1e1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1545,6 +1587,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "392e0c60",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1556,6 +1599,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "3202440f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1585,6 +1629,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "edc82531",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1596,6 +1641,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "a3b4409d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1699,6 +1745,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "945ae139",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1709,6 +1756,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "801fdafe",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1720,6 +1768,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "cc0e3178",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1775,6 +1824,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "a5ab7655",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1786,6 +1836,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "79f6202b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1863,6 +1914,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "8f4b931c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1875,6 +1927,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "17832964",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1887,6 +1940,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "b8907ad6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1899,6 +1953,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "9e8956f7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1934,6 +1989,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "88d5f2db",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1943,6 +1999,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "66281320",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1952,6 +2009,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "c4e1747d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1963,6 +2021,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "7ae9eb8b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2057,6 +2116,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "f36741e6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2069,6 +2129,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "e5701398",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2081,6 +2142,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "74813e44",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2093,6 +2155,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "9af83af8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2103,6 +2166,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "b58f5d51",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2113,6 +2177,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "28778abf",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2136,6 +2201,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "b24dc914",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2147,6 +2213,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "c962408c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2158,6 +2225,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "c26e951f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2169,6 +2237,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "7b28ad3b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2212,6 +2281,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "70618c6f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2222,6 +2292,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "4703b3b0",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2241,6 +2312,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "d805e6f4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2251,6 +2323,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "8b04bb30",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2321,6 +2394,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "fa7f9fbc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2331,6 +2405,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "df5bc634",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2383,6 +2458,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "2dff3d76",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2393,6 +2469,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "34239e23",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2406,6 +2483,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "0d5c60e7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2418,6 +2496,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "0342fc34",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2896,6 +2975,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "813a5e2b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2907,6 +2987,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "1cbaa49a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2918,6 +2999,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "187c493d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2929,6 +3011,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "a8e51995",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2938,6 +3021,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "b8c8e2c0",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2971,6 +3055,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "1d97ff0e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2980,6 +3065,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "d6a45000",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3000,6 +3086,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "3a438ab9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3309,7 +3396,7 @@
     "            \n",
     "            lo = pd.DataFrame(\n",
     "                fitted_values.values.reshape(-1, 1) - quantiles * se.reshape(-1, 1),\n",
-    "                columns=[f'lo_{l}%' for l in _level],\n",
+    "                columns=[f'lo_{l}%' for l in reversed(_level)],\n",
     "            )\n",
     "            hi = pd.DataFrame(\n",
     "                fitted_values.values.reshape(-1, 1) + quantiles * se.reshape(-1, 1),\n",
@@ -3327,6 +3414,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "347d0d46",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3336,6 +3424,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "429d35f6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3345,6 +3434,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "c79bb3d3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3354,6 +3444,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "30888144",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3363,6 +3454,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "3d84d894",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3372,6 +3464,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "cea1b29a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3381,6 +3474,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "f8292ed7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3390,6 +3484,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "40d649c6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3399,6 +3494,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "d609ad93",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3408,6 +3504,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "b7214a0f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3417,6 +3514,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "5f66f1c8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3426,6 +3524,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "b00c88ac",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3435,6 +3534,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "461f0c94",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3444,6 +3544,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "463a009e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3453,6 +3554,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "a4f03969",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3462,6 +3564,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "951e0c1b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3471,7 +3574,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   }
diff --git a/statsforecast/arima.py b/statsforecast/arima.py
index 35f7a208d..1d40749d1 100644
--- a/statsforecast/arima.py
+++ b/statsforecast/arima.py
@@ -2450,7 +2450,7 @@ def predict_in_sample(self, level: Optional[Union[int, Tuple[int]]] = None):
 
             lo = pd.DataFrame(
                 fitted_values.values.reshape(-1, 1) - quantiles * se.reshape(-1, 1),
-                columns=[f'lo_{l}%' for l in _level],
+                columns=[f'lo_{l}%' for l in reversed(_level)],
             )
             hi = pd.DataFrame(
                 fitted_values.values.reshape(-1, 1) + quantiles * se.reshape(-1, 1),