Houston Weather Predictions

class: center, middle, inverse, title-slide

.title[
# Houston Weather Predictions
]
.subtitle[
## 🌞Time Series Model
]
.author[
### Tyler Battaglini
]
.date[
### 2025-02-09
]

---

## Agenda

<ul style="font-size: 1.5em;">
  <li>Exploratory Data Analysis
    <ul>
      <li>Data Cleaning</li>
      <li>Accuracy Measure</li>
    </ul>
  </li>
  <li>Visualization
    <ul>
      <li>Model of Original Time Series</li>
      <li>Model of Forecasted Results</li>
    </ul>
  </li>
  <li>Final Model</li>
</ul>

---

## Exploratory Data Analysis

- Focus on the last 150 observations, split into 138 training and 12 test data points, with the training set converted to a monthly time series.
- Fit 8 different models to identify the best fit for the data.

<table class="table table-striped table-hover table-condensed table-responsive" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;">
<caption>Accuracy Measures for Exponential Smoothing Models</caption>
 <thead>
  <tr>
   <th style="text-align:left;font-weight: bold;font-size: 14px;">  </th>
   <th style="text-align:right;font-weight: bold;font-size: 14px;"> ME </th>
   <th style="text-align:right;font-weight: bold;font-size: 14px;"> RMSE </th>
   <th style="text-align:right;font-weight: bold;font-size: 14px;"> MAE </th>
   <th style="text-align:right;font-weight: bold;font-size: 14px;"> MPE </th>
   <th style="text-align:right;font-weight: bold;font-size: 14px;"> MAPE </th>
   <th style="text-align:right;font-weight: bold;font-size: 14px;"> MASE </th>
   <th style="text-align:right;font-weight: bold;font-size: 14px;"> ACF1 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> SES </td>
   <td style="text-align:right;"> -0.2210 </td>
   <td style="text-align:right;"> 6.3659 </td>
   <td style="text-align:right;"> 5.3461 </td>
   <td style="text-align:right;"> -0.7799 </td>
   <td style="text-align:right;"> 7.8880 </td>
   <td style="text-align:right;"> 2.0777 </td>
   <td style="text-align:right;"> 0.6116 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> Holt Linear </td>
   <td style="text-align:right;"> -0.0587 </td>
   <td style="text-align:right;"> 5.3786 </td>
   <td style="text-align:right;"> 4.2739 </td>
   <td style="text-align:right;"> 0.5114 </td>
   <td style="text-align:right;"> 6.3078 </td>
   <td style="text-align:right;"> 1.6610 </td>
   <td style="text-align:right;"> 0.0460 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> Holt Add. Damped </td>
   <td style="text-align:right;"> -0.0907 </td>
   <td style="text-align:right;"> 5.0365 </td>
   <td style="text-align:right;"> 4.0451 </td>
   <td style="text-align:right;"> 0.2195 </td>
   <td style="text-align:right;"> 5.9348 </td>
   <td style="text-align:right;"> 1.5721 </td>
   <td style="text-align:right;"> 0.0545 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> Holt Exp. Damped </td>
   <td style="text-align:right;"> -0.5602 </td>
   <td style="text-align:right;"> 5.1376 </td>
   <td style="text-align:right;"> 4.1367 </td>
   <td style="text-align:right;"> -0.4293 </td>
   <td style="text-align:right;"> 6.0188 </td>
   <td style="text-align:right;"> 1.6077 </td>
   <td style="text-align:right;"> 0.0352 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> HW Add. </td>
   <td style="text-align:right;"> -0.0498 </td>
   <td style="text-align:right;"> 2.2572 </td>
   <td style="text-align:right;"> 1.8184 </td>
   <td style="text-align:right;"> -0.2023 </td>
   <td style="text-align:right;"> 2.7012 </td>
   <td style="text-align:right;"> 0.7067 </td>
   <td style="text-align:right;"> 0.1684 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> HW Exp. </td>
   <td style="text-align:right;"> -0.1411 </td>
   <td style="text-align:right;"> 2.3253 </td>
   <td style="text-align:right;"> 1.7499 </td>
   <td style="text-align:right;"> -0.3550 </td>
   <td style="text-align:right;"> 2.6720 </td>
   <td style="text-align:right;"> 0.6801 </td>
   <td style="text-align:right;"> 0.3866 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> HW Add. Damp </td>
   <td style="text-align:right;"> -0.0747 </td>
   <td style="text-align:right;"> 2.2400 </td>
   <td style="text-align:right;"> 1.8105 </td>
   <td style="text-align:right;"> -0.2256 </td>
   <td style="text-align:right;"> 2.6920 </td>
   <td style="text-align:right;"> 0.7037 </td>
   <td style="text-align:right;"> 0.1563 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> HW Exp. Damp </td>
   <td style="text-align:right;"> -0.0829 </td>
   <td style="text-align:right;"> 2.3408 </td>
   <td style="text-align:right;"> 1.8635 </td>
   <td style="text-align:right;"> -0.2395 </td>
   <td style="text-align:right;"> 2.7574 </td>
   <td style="text-align:right;"> 0.7242 </td>
   <td style="text-align:right;"> 0.1470 </td>
  </tr>
</tbody>
</table>

---
## Visualization

<div class="figure" style="text-align: center">
<img src="FirstNinjaPrez_files/figure-html/unnamed-chunk-4-1.png" alt="Comparing exponential smoothing models." width="100%" />
<p class="caption">Comparing exponential smoothing models.</p>
</div>

---

## Final Model

- HW.Add is the best model with lowest values
- Estimated values of the smoothing parameters in HW. Add
  - alpha - 0.1305680, beta 0.0001000, gamma    0.0001006

<table class="table table-striped table-hover table-condensed" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;">
<caption>Final Accuracy Measures</caption>
 <thead>
<tr>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Model Accuracy</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">MSE</div></th>
</tr>
  <tr>
   <th style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(44, 62, 80, 255) !important;font-size: 14px;">  </th>
   <th style="text-align:right;font-weight: bold;color: white !important;background-color: rgba(44, 62, 80, 255) !important;font-size: 14px;"> MSE </th>
   <th style="text-align:right;font-weight: bold;color: white !important;background-color: rgba(44, 62, 80, 255) !important;font-size: 14px;"> MAPE </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> SES </td>
   <td style="text-align:right;color: black !important;background-color: rgba(226, 234, 240, 255) !important;"> 420.027941 </td>
   <td style="text-align:right;"> 32.430511 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> Holt.Add </td>
   <td style="text-align:right;color: black !important;background-color: rgba(226, 234, 240, 255) !important;"> 5921.842465 </td>
   <td style="text-align:right;"> 607.491932 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> Holt.Add.Damp </td>
   <td style="text-align:right;color: black !important;background-color: rgba(226, 234, 240, 255) !important;"> 1759.165800 </td>
   <td style="text-align:right;"> 137.916182 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> Holt.Exp </td>
   <td style="text-align:right;color: black !important;background-color: rgba(226, 234, 240, 255) !important;"> 1768.349891 </td>
   <td style="text-align:right;"> 139.113295 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> HW.Add </td>
   <td style="text-align:right;color: black !important;background-color: rgba(226, 234, 240, 255) !important;"> 5.111103 </td>
   <td style="text-align:right;"> 2.972308 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> HW.Exp </td>
   <td style="text-align:right;color: black !important;background-color: rgba(226, 234, 240, 255) !important;"> 8.833668 </td>
   <td style="text-align:right;"> 3.593340 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> HW.Add.Damp </td>
   <td style="text-align:right;color: black !important;background-color: rgba(226, 234, 240, 255) !important;"> 4.973422 </td>
   <td style="text-align:right;"> 2.981870 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: white !important;background-color: rgba(19, 129, 176, 255) !important;"> HW.Exp.Damp </td>
   <td style="text-align:right;color: black !important;background-color: rgba(226, 234, 240, 255) !important;"> 7.161286 </td>
   <td style="text-align:right;"> 3.597887 </td>
  </tr>
</tbody>
</table>