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presentation_slides.html
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<!DOCTYPE html>
<html lang="en"><head>
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<meta name="generator" content="quarto-1.3.294">
<meta name="author" content="Nicklas Prochazka">
<title>An introduction to Time Series Forecasting using a case study of predicting sales of an Ecuadorian store chain</title>
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<body class="quarto-light">
<div class="reveal">
<div class="slides">
<section id="title-slide" class="quarto-title-block center">
<h1 class="title">An introduction to Time Series Forecasting using a case study of predicting sales of an Ecuadorian store chain</h1>
<div class="quarto-title-authors">
<div class="quarto-title-author">
<div class="quarto-title-author-name">
Nicklas Prochazka
</div>
</div>
</div>
</section>
<section id="project-goal-and-outline" class="title-slide slide level1 center">
<h1>Project Goal and Outline</h1>
<ul>
<li><p>Explain the basics of Time Series analysis and forecasting</p></li>
<li><p>Showcase them using data from Kaggle of sales of an Ecuadorian store chain</p></li>
<li><p>Give insights into the process of developing and publishing a (small) Python package</p></li>
<li><p>Compare and discuss results and next possible steps</p></li>
</ul>
</section>
<section id="intoduction-to-data-and-features" class="title-slide slide level1 center">
<h1>Intoduction to data and features</h1>
<ul>
<li><p>Sales data for 54 stores and 33 product families between 2013-01-01 to 2017-08-31 (~3mil data points)</p></li>
<li><p>Some auxiliary data (transactions, holidays, oil price)</p></li>
</ul>
</section>
<section id="preprocessing" class="title-slide slide level1 center">
<h1>Preprocessing</h1>
<ul>
<li><p>Aggregation of the sales data for a given date over all stores and product families</p></li>
<li><p>Splitting the data into training, validation and test set</p></li>
<li><p>Only use data of national holidays</p></li>
</ul>
</section>
<section>
<section id="eda" class="title-slide slide level1 center">
<h1>EDA</h1>
</section>
<section id="sales-data-overview" class="slide level2">
<h2>Sales data (overview)</h2>
<p>Sales data per store and product family</p>
<table>
<colgroup>
<col style="width: 13%">
<col style="width: 17%">
<col style="width: 16%">
<col style="width: 17%">
<col style="width: 14%">
<col style="width: 19%">
</colgroup>
<thead>
<tr class="header">
<th>id</th>
<th>date</th>
<th>store_nbr</th>
<th>family</th>
<th>sales</th>
<th>onpromotion</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>2215752</td>
<td>2016-05-31</td>
<td>3</td>
<td>AUTOMOTIVE</td>
<td>15.000</td>
<td>0</td>
</tr>
<tr class="even">
<td>2215753</td>
<td>2016-05-31</td>
<td>3</td>
<td>BABY CARE</td>
<td>0.000</td>
<td>0</td>
</tr>
<tr class="odd">
<td>2215754</td>
<td>2016-05-31</td>
<td>3</td>
<td>BEAUTY</td>
<td>23.000</td>
<td>1</td>
</tr>
<tr class="even">
<td>2215755</td>
<td>2016-05-31</td>
<td>3</td>
<td>BEVERAGES</td>
<td>9098.000</td>
<td>51</td>
</tr>
<tr class="odd">
<td>2215756</td>
<td>2016-05-31</td>
<td>3</td>
<td>BOOKS</td>
<td>0.000</td>
<td>0</td>
</tr>
</tbody>
</table>
<p>Sales data aggregated</p>
<table>
<thead>
<tr class="header">
<th>date</th>
<th>sales</th>
<th>onpromotion</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>2016-05-31</td>
<td>9.743280e+05</td>
<td>14668</td>
</tr>
<tr class="even">
<td>2016-06-01</td>
<td>8.115253e+05</td>
<td>15912</td>
</tr>
<tr class="odd">
<td>2016-06-02</td>
<td>6.945359e+05</td>
<td>8059</td>
</tr>
<tr class="even">
<td>2016-06-03</td>
<td>7.423631e+05</td>
<td>11747</td>
</tr>
<tr class="odd">
<td>2016-06-04</td>
<td>1.011997e+06</td>
<td>6666</td>
</tr>
</tbody>
</table>
</section>
<section id="sales-data-temporal-breakdown" class="slide level2">
<h2>Sales data (temporal breakdown)</h2>
<img data-src="./figures/images/store_sales_analysis.png" class="quarto-discovered-preview-image r-stretch quarto-figure-center"><p class="caption">Figure 1: store_sales_analysis</p></section>
<section id="sales-data-per-family-breakdown" class="slide level2">
<h2>Sales data (per family breakdown)</h2>
<img data-src="./figures/images/average_sales_families.png" class="r-stretch quarto-figure-center"><p class="caption">Figure 2: average_sales_families</p></section>
<section id="correlation-sales-vs.-transactions" class="slide level2">
<h2>Correlation sales vs. transactions</h2>
<img data-src="./figures/images/sales_vs_transactions.png" class="r-stretch quarto-figure-center"><p class="caption">Figure 3: sales_vs_transactions</p><p>Pearson correlation coefficient between sales and transactions: 0.8373 (high).</p>
</section>
<section id="correlation-among-stores" class="slide level2">
<h2>Correlation among stores</h2>
<img data-src="./figures/images/corr_stores.png" style="width:100.0%" class="r-stretch quarto-figure-center"><p class="caption">Figure 4: correlation_stores</p><p>Average Pearson correlation coefficient between stores: 0.8047 (high).</p>
</section>
<section id="correlation-among-product-families" class="slide level2">
<h2>Correlation among product families</h2>
<img data-src="./figures/images/corr_families.png" style="width:100.0%" class="r-stretch quarto-figure-center"><p class="caption">Figure 5: correlation_families</p><p>Average Pearson correlation coefficient between product families: 0.4241 (moderate/low).</p>
</section>
<section id="other-correlations" class="slide level2">
<h2>Other correlations</h2>
<p>Pearson correlation coefficient between sales and number of items on promotion: 0.5749 (moderate)</p>
<p>Pearson correlation coefficient between sales and oil price: -0.5008 (moderate, negative)</p>
</section>
<section id="stl-decomposition-weekly" class="slide level2">
<h2>STL Decomposition (weekly)</h2>
<img data-src="./figures/images/decomposition.png" class="r-stretch quarto-figure-center"><p class="caption">Figure 6: decomposition_weekly</p></section>
<section id="stl-decomposition-yearly" class="slide level2">
<h2>STL Decomposition (yearly)</h2>
<img data-src="./figures/images/decomposition_yearly.png" class="r-stretch quarto-figure-center"><p class="caption">Figure 7: decomposition_yearly</p></section>
<section id="autocorrelation-1" class="slide level2">
<h2>Autocorrelation 1</h2>
<img data-src="./figures/images/acf_pacf.png" style="width:100.0%" class="r-stretch quarto-figure-center"><p class="caption">Figure 8: autocorrelation1</p></section>
<section id="autocorrelation-2" class="slide level2">
<h2>Autocorrelation 2</h2>
<img data-src="./figures/images/acf_pacf_365.png" style="width:100.0%" class="r-stretch quarto-figure-center"><p class="caption">Figure 9: autocorrelation2</p></section>
<section id="test-for-stationarity-augmented-dickey-fuller" class="slide level2">
<h2>Test for stationarity (Augmented Dickey-Fuller)</h2>
<img data-src="./figures/images/adf.png" style="width:100.0%" class="r-stretch quarto-figure-center"><p class="caption">Figure 10: augmented_dickey_fuller</p></section></section>
<section>
<section id="model-selection" class="title-slide slide level1 center">
<h1>Model Selection</h1>
</section>
<section id="exponential-smoothing" class="slide level2">
<h2>Exponential Smoothing</h2>
<img data-src="./figures/images/expsm_fc.png" class="r-stretch quarto-figure-center"><p class="caption">Figure 11: exponential_smoothing_baseline</p></section>
<section id="hyperparameter-optimization-expsm" class="slide level2">
<h2>Hyperparameter Optimization ExpSm</h2>
<div class="sourceCode" id="cb1"><pre class="sourceCode numberSource {{python}} number-lines code-with-copy"><code class="sourceCode"><span id="cb1-1"><a href="#cb1-1"></a>trend = ['add', 'mul', None]</span>
<span id="cb1-2"><a href="#cb1-2"></a>damped_trend = [True, False]</span>
<span id="cb1-3"><a href="#cb1-3"></a>seasonal = ['add', 'mul', None]</span>
<span id="cb1-4"><a href="#cb1-4"></a>periods = [7]</span>
<span id="cb1-5"><a href="#cb1-5"></a>use_boxcox = [True, False]</span>
<span id="cb1-6"><a href="#cb1-6"></a>remove_bias = [True, False]</span>
<span id="cb1-7"><a href="#cb1-7"></a></span>
<span id="cb1-8"><a href="#cb1-8"></a># best:</span>
<span id="cb1-9"><a href="#cb1-9"></a>{'trend': 'add', 'damped_trend': True, 'seasonal': 'mul', 'periods': 7, 'use_boxcox': True, 'remove_bias': True}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p>RMSE: 108003.45</p>
</section>
<section id="sarima" class="slide level2">
<h2>SARIMA</h2>
<img data-src="./figures/images/sarima.png" class="r-stretch quarto-figure-center"><p class="caption">Figure 12: sarima</p></section>
<section id="hyperparameter-optimization-sarima" class="slide level2">
<h2>Hyperparameter Optimization SARIMA</h2>
<div class="sourceCode" id="cb2"><pre class="sourceCode numberSource {{python}} number-lines code-with-copy"><code class="sourceCode"><span id="cb2-1"><a href="#cb2-1"></a>params_sarima = [</span>
<span id="cb2-2"><a href="#cb2-2"></a> [(1, 1, 1), (1, 1, 1, 7)],</span>
<span id="cb2-3"><a href="#cb2-3"></a> [(1, 1, 0), (1, 1, 1, 7)],</span>
<span id="cb2-4"><a href="#cb2-4"></a> [(1, 1, 0), (1, 1, 0, 7)],</span>
<span id="cb2-5"><a href="#cb2-5"></a> [(1, 1, 0), (0, 1, 0, 7)],</span>
<span id="cb2-6"><a href="#cb2-6"></a> [(1, 1, 1), (1, 1, 0, 7)],</span>
<span id="cb2-7"><a href="#cb2-7"></a> [(1, 1, 1), (2, 1, 0, 7)],</span>
<span id="cb2-8"><a href="#cb2-8"></a> [(1, 1, 2), (1, 1, 2, 7)],</span>
<span id="cb2-9"><a href="#cb2-9"></a> [(1, 1, 1), (1, 1, 2, 7)],</span>
<span id="cb2-10"><a href="#cb2-10"></a> [(1, 1, 1), (2, 1, 2, 7)],</span>
<span id="cb2-11"><a href="#cb2-11"></a> [(1, 1, 0), (1, 1, 2, 7)],</span>
<span id="cb2-12"><a href="#cb2-12"></a> [(2, 1, 1), (2, 1, 1, 7)],</span>
<span id="cb2-13"><a href="#cb2-13"></a> [(2, 1, 1), (1, 1, 1, 7)],</span>
<span id="cb2-14"><a href="#cb2-14"></a> [(2, 1, 1), (1, 1, 0, 7)],</span>
<span id="cb2-15"><a href="#cb2-15"></a> [(1, 1, 2), (2, 1, 2, 7)],</span>
<span id="cb2-16"><a href="#cb2-16"></a> [(1, 1, 2), (1, 1, 0, 7)],</span>
<span id="cb2-17"><a href="#cb2-17"></a> [(0, 1, 1), (1, 1, 1, 7)]</span>
<span id="cb2-18"><a href="#cb2-18"></a>]</span>
<span id="cb2-19"><a href="#cb2-19"></a></span>
<span id="cb2-20"><a href="#cb2-20"></a># best:</span>
<span id="cb2-21"><a href="#cb2-21"></a>[(1, 1, 1), (1, 1, 1, 7)]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p>RMSE: 97702.51</p>
</section>
<section id="sarimax" class="slide level2">
<h2>SARIMAX</h2>
<h3 id="feature-generation">Feature generation</h3>
<table style="width:100%;">
<colgroup>
<col style="width: 6%">
<col style="width: 9%">
<col style="width: 10%">
<col style="width: 12%">
<col style="width: 12%">
<col style="width: 12%">
<col style="width: 12%">
<col style="width: 12%">
<col style="width: 12%">
</colgroup>
<thead>
<tr class="header">
<th>date</th>
<th>sales</th>
<th>onpromotion</th>
<th>day_of_week_1</th>
<th>day_of_week_2</th>
<th>day_of_week_3</th>
<th>day_of_week_4</th>
<th>day_of_week_5</th>
<th>day_of_week_6</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>2017-07-27</td>
<td>6.598498e+05</td>
<td>8001</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="even">
<td>2017-07-28</td>
<td>8.350997e+05</td>
<td>13850</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>0</td>
</tr>
<tr class="odd">
<td>2017-07-29</td>
<td>1.032311e+06</td>
<td>9099</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>1</td>
</tr>
<tr class="even">
<td>2017-07-30</td>
<td>1.123752e+06</td>
<td>10227</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>2017-07-31</td>
<td>8.858568e+05</td>
<td>8649</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
</tbody>
</table>
<p>RMSE: 88867.16</p>
</section></section>
<section>
<section id="model-comparisonforecasting" class="title-slide slide level1 center">
<h1>Model Comparison/Forecasting</h1>
</section>
<section id="forecasting" class="slide level2">
<h2>Forecasting</h2>
<img data-src="./figures/images/all_preds.png" class="r-stretch quarto-figure-center"><p class="caption">Figure 13: all_predicitons</p></section>
<section id="metrics" class="slide level2">
<h2>Metrics</h2>
<table>
<thead>
<tr class="header">
<th>Model</th>
<th>MAE</th>
<th>RMSE</th>
<th>RMSLE</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>Exponential Smoothing</td>
<td>92287.5</td>
<td>125555.8</td>
<td>0.1386</td>
</tr>
<tr class="even">
<td>SARIMA</td>
<td>84461.0</td>
<td>116867.5</td>
<td>0.1302</td>
</tr>
<tr class="odd">
<td>SARIMAX</td>
<td>89452.3</td>
<td>110509.4</td>
<td>0.1205</td>
</tr>
<tr class="even">
<td>SARIMAX (no time features)</td>
<td>87837.6</td>
<td>117312.6</td>
<td>0.132</td>
</tr>
</tbody>
</table>
</section></section>
<section>
<section id="python-package-for-parallel-hyperparameter-optimization-using-grid-search-and-cv" class="title-slide slide level1 center">
<h1>Python package for parallel Hyperparameter Optimization using Grid Search and CV</h1>
<img data-src="./figures/images/ts-hyperparam-opt_PyPI.png" class="r-stretch quarto-figure-center"></section>
<section id="main-function" class="slide level2">
<h2>Main function</h2>
<div class="sourceCode" id="cb3"><pre class="sourceCode numberSource {{python}} number-lines code-with-copy"><code class="sourceCode"><span id="cb3-1"><a href="#cb3-1"></a>def optimize_hyperparams(hyperparams: list, data, func: str, n_steps=1, n_splits=10, runs_per_split=1):</span>
<span id="cb3-2"><a href="#cb3-2"></a></span>
<span id="cb3-3"><a href="#cb3-3"></a> # bring data into right format</span>
<span id="cb3-4"><a href="#cb3-4"></a> data = pd.DataFrame(data)</span>
<span id="cb3-5"><a href="#cb3-5"></a> data = data.reset_index(drop=True)</span>
<span id="cb3-6"><a href="#cb3-6"></a> tscv = TimeSeriesSplit(n_splits = n_splits, test_size=n_steps)</span>
<span id="cb3-7"><a href="#cb3-7"></a> rmse_split = list()</span>
<span id="cb3-8"><a href="#cb3-8"></a> </span>
<span id="cb3-9"><a href="#cb3-9"></a> # evaluate params on every split</span>
<span id="cb3-10"><a href="#cb3-10"></a> for train_index, test_index in tscv.split(data):</span>
<span id="cb3-11"><a href="#cb3-11"></a> cv_train, cv_test = data.iloc[train_index], data.iloc[test_index]</span>
<span id="cb3-12"><a href="#cb3-12"></a> rmse = list()</span>
<span id="cb3-13"><a href="#cb3-13"></a> for i in range(0, runs_per_split):</span>
<span id="cb3-14"><a href="#cb3-14"></a> try:</span>
<span id="cb3-15"><a href="#cb3-15"></a> preds = globals()[func](hyperparams, cv_train, n_steps, cv_test)</span>
<span id="cb3-16"><a href="#cb3-16"></a> except:</span>
<span id="cb3-17"><a href="#cb3-17"></a> print(hyperparams)</span>
<span id="cb3-18"><a href="#cb3-18"></a> traceback.print_exc()</span>
<span id="cb3-19"><a href="#cb3-19"></a> return</span>
<span id="cb3-20"><a href="#cb3-20"></a></span>
<span id="cb3-21"><a href="#cb3-21"></a> true_values = cv_test.iloc[:,0].values</span>
<span id="cb3-22"><a href="#cb3-22"></a> rmse.append(sqrt(mean_squared_error(true_values, preds)))</span>
<span id="cb3-23"><a href="#cb3-23"></a></span>
<span id="cb3-24"><a href="#cb3-24"></a> rmse_split.append(np.mean(rmse))</span>
<span id="cb3-25"><a href="#cb3-25"></a></span>
<span id="cb3-26"><a href="#cb3-26"></a> rmse_all = dict()</span>
<span id="cb3-27"><a href="#cb3-27"></a> rmse_all[str(hyperparams)] = round(np.mean(rmse_split), 2)</span>
<span id="cb3-28"><a href="#cb3-28"></a> return rmse_all</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</section>
<section id="supported-models" class="slide level2">
<h2>Supported models</h2>
<h3 id="exponential-smoothing-1">Exponential Smoothing</h3>
<div class="sourceCode" id="cb4"><pre class="sourceCode numberSource {{python}} number-lines code-with-copy"><code class="sourceCode"><span id="cb4-1"><a href="#cb4-1"></a>def exp_smoothing(hyperparams, cv_train, n_steps, cv_test):</span>
<span id="cb4-2"><a href="#cb4-2"></a> return ExponentialSmoothing(</span>
<span id="cb4-3"><a href="#cb4-3"></a> cv_train.astype(float),</span>
<span id="cb4-4"><a href="#cb4-4"></a> seasonal_periods=hyperparams["periods"],</span>
<span id="cb4-5"><a href="#cb4-5"></a> trend=hyperparams["trend"],</span>
<span id="cb4-6"><a href="#cb4-6"></a> seasonal=hyperparams["seasonal"],</span>
<span id="cb4-7"><a href="#cb4-7"></a> damped_trend=hyperparams["damped_trend"],</span>
<span id="cb4-8"><a href="#cb4-8"></a> use_boxcox=hyperparams["use_boxcox"],</span>
<span id="cb4-9"><a href="#cb4-9"></a> initialization_method="estimated",</span>
<span id="cb4-10"><a href="#cb4-10"></a> ).fit(remove_bias=hyperparams["remove_bias"]).simulate(n_steps, repetitions=100, error="mul").mean(axis=1)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p><br>
</p>
<h3 id="sarima-1">SARIMA</h3>
<div class="sourceCode" id="cb5"><pre class="sourceCode numberSource {{python}} number-lines code-with-copy"><code class="sourceCode"><span id="cb5-1"><a href="#cb5-1"></a>def sarima(hyperparams, cv_train, n_steps, cv_test):</span>
<span id="cb5-2"><a href="#cb5-2"></a> return SARIMAX(</span>
<span id="cb5-3"><a href="#cb5-3"></a> cv_train.astype(float),</span>
<span id="cb5-4"><a href="#cb5-4"></a> order=hyperparams[0],</span>
<span id="cb5-5"><a href="#cb5-5"></a> seasonal_order=hyperparams[1]</span>
<span id="cb5-6"><a href="#cb5-6"></a> ).fit().forecast(steps=n_steps)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p><br>
</p>
<h3 id="sarimax-1">SARIMAX</h3>
<div class="sourceCode" id="cb6"><pre class="sourceCode numberSource {{python}} number-lines code-with-copy"><code class="sourceCode"><span id="cb6-1"><a href="#cb6-1"></a>def sarimax(hyperparams, cv_train, n_steps, cv_test):</span>
<span id="cb6-2"><a href="#cb6-2"></a> return SARIMAX(</span>
<span id="cb6-3"><a href="#cb6-3"></a> endog=cv_train.iloc[:,0],</span>
<span id="cb6-4"><a href="#cb6-4"></a> exog=cv_train.iloc[:,1:],</span>
<span id="cb6-5"><a href="#cb6-5"></a> order=hyperparams[0],</span>
<span id="cb6-6"><a href="#cb6-6"></a> seasonal_order=hyperparams[1]</span>
<span id="cb6-7"><a href="#cb6-7"></a> ).fit().forecast(steps=n_steps, exog=cv_test.iloc[:,1:])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</section>
<section id="usage" class="slide level2">
<h2>Usage</h2>
<h3 id="parallel-hyperparameter-optimization">Parallel hyperparameter optimization</h3>
<div class="sourceCode" id="cb7"><pre class="sourceCode numberSource {{python}} number-lines code-with-copy"><code class="sourceCode"><span id="cb7-1"><a href="#cb7-1"></a>from ts_hyperparam_opt import parallel_hyperparameter_optimization as pho</span>
<span id="cb7-2"><a href="#cb7-2"></a></span>
<span id="cb7-3"><a href="#cb7-3"></a>if __name__ == '__main__':</span>
<span id="cb7-4"><a href="#cb7-4"></a> freeze_support()</span>
<span id="cb7-5"><a href="#cb7-5"></a> results_exp_smoothing = process_map(partial(pho.optimize_hyperparams, data=df_sales_train, func="exp_smoothing",</span>
<span id="cb7-6"><a href="#cb7-6"></a> n_steps=15, runs_per_split=10), params_exp_smoothing)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p>Output:</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode numberSource {{python}} number-lines code-with-copy"><code class="sourceCode"><span id="cb8-1"><a href="#cb8-1"></a>[{"{'trend': 'add', 'damped_trend': True, 'seasonal': 'mul', 'periods': 7, 'use_boxcox': True, 'remove_bias': True}": 108003.45},</span>
<span id="cb8-2"><a href="#cb8-2"></a> {"{'trend': None, 'damped_trend': False, 'seasonal': 'mul', 'periods': 7, 'use_boxcox': True, 'remove_bias': True}": 108611.14},</span>
<span id="cb8-3"><a href="#cb8-3"></a> {"{'trend': 'mul', 'damped_trend': True, 'seasonal': 'mul', 'periods': 7, 'use_boxcox': True, 'remove_bias': False}": 108993.4}, </span>
<span id="cb8-4"><a href="#cb8-4"></a> [...]</span>
<span id="cb8-5"><a href="#cb8-5"></a> ]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p><br>
</p>
<h3 id="model-evaluation-using-cv">Model evaluation using CV</h3>
<div class="sourceCode" id="cb9"><pre class="sourceCode numberSource {{python}} number-lines code-with-copy"><code class="sourceCode"><span id="cb9-1"><a href="#cb9-1"></a>pho.optimize_hyperparams([(1, 1, 1), (1, 1, 1, 7)], df_sales_ext_train, "sarimax", n_steps=15)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p>Output:</p>
<div class="sourceCode" id="cb10"><pre class="sourceCode numberSource {{python}} number-lines code-with-copy"><code class="sourceCode"><span id="cb10-1"><a href="#cb10-1"></a>{'[(1, 1, 1), (1, 1, 1, 7)]': 88867.16}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</section>
<section id="future-work-and-discussion" class="slide level2">
<h2>Future Work and Discussion</h2>
<p>There are several areas where the model could be improved in future iterations.</p>
<ul>
<li><p>using a bottom-up approach</p></li>
<li><p>collecting more (potentially) meaningful exogenous features</p></li>
<li><p>using more sophisticated methods like Prophet or (LSTM) Neural Networks</p></li>
</ul>
<div class="footer footer-default">
</div>
</section></section>
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