fixing ARIMA article, part 1

Author: steven-ja

content/posts/finance/stock_prediction/ARIMA/arima_example.ipynb

@@ -34,16 +34,17 @@ def test_stationarity(timeseries):
 
 # Forecast
 forecast = results.forecast(steps=30)
-help(forecast)
+# help(forecast)
+print(forecast)
 
 # Plot the results
 plt.figure(figsize=(12,6))
 plt.plot(ts.index[-100:], ts.values[-100:], label='Observed')
 plt.plot(forecast.index, forecast.values, color='r', label='Forecast')
-plt.fill_between(forecast.index, 
-                 forecast.conf_int().iloc[:, 0], 
-                 forecast.conf_int().iloc[:, 1], 
-                 color='pink', alpha=0.3)
+# plt.fill_between(forecast.index, 
+#                  forecast.iloc[:, 0], 
+#                  forecast.iloc[:, 1], 
+#                  color='pink', alpha=0.3)
 plt.title(f'{ticker} Stock Price Prediction')
 plt.legend()
 plt.show()

content/posts/finance/stock_prediction/ARIMA/arima_example.py

@@ -8,7 +8,7 @@ menu:
     identifier: ARIMA
     parent: stock_prediction 
     weight: 10
-hero: 
+hero: images/find_d.png
 tags: ["Finance", "Statistics", "Forecasting"]
 categories: ["Finance"]
 ---
@@ -93,6 +93,7 @@ def test_stationarity(timeseries):
     print('ADF Statistic:', result[0])
     print('p-value:', result[1])
 
+# if p-value is > 0.05, it means the series is not stationary.
 test_stationarity(ts)
 
 # If non-stationary, difference the series
@@ -134,6 +135,23 @@ Choosing the right ARIMA model involves selecting appropriate values for p, d, a
 2. **Grid search**: Trying different combinations of p, d, and q and selecting the best based on information criteria like AIC or BIC.
 3. **Diagnostic checking**: Analyzing residuals to ensure they resemble white noise.
 
+### Finding ARIMA Parameters (p, d, q)
+Determining the optimal ARIMA parameters involves a combination of statistical tests, visual inspection, and iterative processes. Here's a systematic approach to finding p, d, and q:
+
+* Determine d (Differencing Order): 
+  - Use the Augmented Dickey-Fuller test to check for stationarity.
+  - If the series is not stationary, difference it and test again until stationarity is achieved.
+* Determine p (AR Order) and q (MA Order): 
+  - After differencing, use ACF (Autocorrelation Function) and PACF (Partial Autocorrelation Function) plots.
+  - The lag where the ACF cuts off indicates the q value.
+  - The lag where the PACF cuts off indicates the p value.
+* Fine-tune with Information Criteria:
+  - Use AIC (Akaike Information Criterion) or BIC (Bayesian Information Criterion) to compare different models.
+
+### Finding d values from plots
+
+
+### Grid Search
 Here's a Python function to perform a grid search:
 
 ```python

content/posts/finance/stock_prediction/ARIMA/images/find_d.png

@@ -34,16 +34,17 @@ def test_stationarity(timeseries):
 
 # Forecast
 forecast = results.forecast(steps=30)
-help(forecast)
+# help(forecast)
+print(forecast)
 
 # Plot the results
 plt.figure(figsize=(12,6))
 plt.plot(ts.index[-100:], ts.values[-100:], label='Observed')
 plt.plot(forecast.index, forecast.values, color='r', label='Forecast')
-plt.fill_between(forecast.index, 
-                 forecast.conf_int().iloc[:, 0], 
-                 forecast.conf_int().iloc[:, 1], 
-                 color='pink', alpha=0.3)
+# plt.fill_between(forecast.index, 
+#                  forecast.iloc[:, 0], 
+#                  forecast.iloc[:, 1], 
+#                  color='pink', alpha=0.3)
 plt.title(f'{ticker} Stock Price Prediction')
 plt.legend()
 plt.show()

content/posts/finance/stock_prediction/ARIMA/index.md

@@ -438,7 +438,7 @@
   <div class="content">
     <div class="container p-0 read-area">
 
-      <div class="hero-area col-sm-12" id="hero-area" style='background-image: url(/images/default-hero.jpg);'>
+      <div class="hero-area col-sm-12" id="hero-area" style='background-image: url(/posts/finance/stock_prediction/arima/images/find_d.png);'>
       </div>
 
 
@@ -447,7 +447,7 @@
         <div class="author-profile ms-auto align-self-lg-center">
           <img class="rounded-circle" src='/images/author/profile_hu8a567cefac8c1a165d433ac0796ac418_3088978_120x120_fit_q75_box.jpg' alt="Author Image">
           <h5 class="author-name">Stefano Giannini</h5>
-          <p class="text-muted">Friday, June 28, 2024 | 5 minutes</p>
+          <p class="text-muted">Friday, June 28, 2024 | 6 minutes</p>
         </div>
 
 
@@ -541,6 +541,7 @@ <h2 id="4-implementing-arima-models-in-python">4. Implementing ARIMA Models in P
 </span></span><span style="display:flex;"><span>    print(<span style="color:#e6db74">&#39;ADF Statistic:&#39;</span>, result[<span style="color:#ae81ff">0</span>])
 </span></span><span style="display:flex;"><span>    print(<span style="color:#e6db74">&#39;p-value:&#39;</span>, result[<span style="color:#ae81ff">1</span>])
 </span></span><span style="display:flex;"><span>
+</span></span><span style="display:flex;"><span><span style="color:#75715e"># if p-value is &gt; 0.05, it means the series is not stationary.</span>
 </span></span><span style="display:flex;"><span>test_stationarity(ts)
 </span></span><span style="display:flex;"><span>
 </span></span><span style="display:flex;"><span><span style="color:#75715e"># If non-stationary, difference the series</span>
@@ -578,6 +579,30 @@ <h2 id="5-model-selection-and-diagnostic-checking">5. Model Selection and Diagno
 <li><strong>Grid search</strong>: Trying different combinations of p, d, and q and selecting the best based on information criteria like AIC or BIC.</li>
 <li><strong>Diagnostic checking</strong>: Analyzing residuals to ensure they resemble white noise.</li>
 </ol>
+<h3 id="finding-arima-parameters-p-d-q">Finding ARIMA Parameters (p, d, q)</h3>
+<p>Determining the optimal ARIMA parameters involves a combination of statistical tests, visual inspection, and iterative processes. Here&rsquo;s a systematic approach to finding p, d, and q:</p>
+<ul>
+<li>Determine d (Differencing Order):
+<ul>
+<li>Use the Augmented Dickey-Fuller test to check for stationarity.</li>
+<li>If the series is not stationary, difference it and test again until stationarity is achieved.</li>
+</ul>
+</li>
+<li>Determine p (AR Order) and q (MA Order):
+<ul>
+<li>After differencing, use ACF (Autocorrelation Function) and PACF (Partial Autocorrelation Function) plots.</li>
+<li>The lag where the ACF cuts off indicates the q value.</li>
+<li>The lag where the PACF cuts off indicates the p value.</li>
+</ul>
+</li>
+<li>Fine-tune with Information Criteria:
+<ul>
+<li>Use AIC (Akaike Information Criterion) or BIC (Bayesian Information Criterion) to compare different models.</li>
+</ul>
+</li>
+</ul>
+<h3 id="finding-d-values-from-plots">Finding d values from plots</h3>
+<h3 id="grid-search">Grid Search</h3>
 <p>Here&rsquo;s a Python function to perform a grid search:</p>
 <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-python" data-lang="python"><span style="display:flex;"><span><span style="color:#66d9ef">def</span> <span style="color:#a6e22e">grid_search_arima</span>(ts, p_range, d_range, q_range):
 </span></span><span style="display:flex;"><span>    best_aic <span style="color:#f92672">=</span> float(<span style="color:#e6db74">&#39;inf&#39;</span>)
@@ -788,7 +813,13 @@ <h5 class="text-center ps-3">Table of Contents</h5>
       </ul>
     </li>
     <li><a href="#4-implementing-arima-models-in-python">4. Implementing ARIMA Models in Python</a></li>
-    <li><a href="#5-model-selection-and-diagnostic-checking">5. Model Selection and Diagnostic Checking</a></li>
+    <li><a href="#5-model-selection-and-diagnostic-checking">5. Model Selection and Diagnostic Checking</a>
+      <ul>
+        <li><a href="#finding-arima-parameters-p-d-q">Finding ARIMA Parameters (p, d, q)</a></li>
+        <li><a href="#finding-d-values-from-plots">Finding d values from plots</a></li>
+        <li><a href="#grid-search">Grid Search</a></li>
+      </ul>
+    </li>
     <li><a href="#6-limitations-and-considerations">6. Limitations and Considerations</a></li>
     <li><a href="#7-advanced-topics-and-extensions">7. Advanced Topics and Extensions</a></li>
     <li><a href="#8-conclusion">8. Conclusion</a></li>

public/index.json

@@ -430,7 +430,7 @@
   <div class="card">
     <div class="card-head">
       <a href="/posts/finance/stock_prediction/arima/" class="post-card-link">
-        <img class="card-img-top" src='/images/default-hero.jpg' alt="Hero Image">
+        <img class="card-img-top" src='/posts/finance/stock_prediction/arima/images/find_d.png' alt="Hero Image">
       </a>
     </div>
     <div class="card-body">
@@ -460,7 +460,7 @@ <h5 class="card-title">Time Series Analysis and ARIMA Models for Stock Price Pre
     <div class="card-footer">
       <span class="float-start">
           Friday, June 28, 2024
-           | 5 minutes </span>
+           | 6 minutes </span>
       <a
       href="/posts/finance/stock_prediction/arima/"
       class="float-end btn btn-outline-info btn-sm">Read</a>