finding p

Author: steven-ja

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

@@ -179,7 +179,24 @@ plt.show()
 Indeed, from the plot, *d=2* is probably a better solution since we have few coefficient that goes above the confidence threshold. 
 
 ### Finding p parameter from plots
+As suggest previously, Partical Correlation Plot is adopted to find the **p** parameter.
 
+```python
+plt.rcParams.update({'figure.figsize':(15,5), 'figure.dpi':80})
+fig, axes = plt.subplots(1, 2, sharex=False)
+axes[0].plot(df.index, df.Close.diff()); axes[0].set_title('1st Differencing')
+axes[1].set(ylim=(0,5))
+plot_pacf(df.Close.diff().dropna(), ax=axes[1], lags=20, color='k', auto_ylims=True, zero=False)
+
+plt.tight_layout()
+plt.show()
+```
+
+![png](images/find_p.png)
+
+A possible choice of **p** can 8 or 18, where the coefficient crosses the confidence intervals.
+
+### Finding q parameter from plots
 
 ### Grid Search
 Here's a Python function to perform a grid search:

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

@@ -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 | 6 minutes</p>
+          <p class="text-muted">Friday, June 28, 2024 | 7 minutes</p>
         </div>
 
 
@@ -600,7 +600,7 @@ <h3 id="finding-arima-parameters-p-d-q">Finding ARIMA Parameters (p, d, q)</h3>
 </ul>
 </li>
 </ul>
-<h3 id="finding-d-values-from-plots">Finding d values from plots</h3>
+<h3 id="finding-d-parameter-from-plots">Finding d parameter from plots</h3>
 <p>Since, the stationary was already checkd in the previous, this paragraph is useful for graphical and comphrension purpose. Moreover, with autocorrelation parameters, it is possible to find better values of d that the ADF test cannot recognize.</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:#f92672">from</span> statsmodels.graphics.tsaplots <span style="color:#f92672">import</span> plot_acf, plot_pacf
 </span></span><span style="display:flex;"><span>
@@ -625,6 +625,20 @@ <h3 id="finding-d-values-from-plots">Finding d values from plots</h3>
 </span></span><span style="display:flex;"><span>plt<span style="color:#f92672">.</span>tight_layout()
 </span></span><span style="display:flex;"><span>plt<span style="color:#f92672">.</span>show()
 </span></span></code></pre></div><p><img alt="png" src="/posts/finance/stock_prediction/arima/images/find_d.png"></p>
+<p>Indeed, from the plot, <em>d=2</em> is probably a better solution since we have few coefficient that goes above the confidence threshold.</p>
+<h3 id="finding-p-parameter-from-plots">Finding p parameter from plots</h3>
+<p>As suggest previously, Partical Correlation Plot is adopted to find the <strong>p</strong> parameter.</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>plt<span style="color:#f92672">.</span>rcParams<span style="color:#f92672">.</span>update({<span style="color:#e6db74">&#39;figure.figsize&#39;</span>:(<span style="color:#ae81ff">15</span>,<span style="color:#ae81ff">5</span>), <span style="color:#e6db74">&#39;figure.dpi&#39;</span>:<span style="color:#ae81ff">80</span>})
+</span></span><span style="display:flex;"><span>fig, axes <span style="color:#f92672">=</span> plt<span style="color:#f92672">.</span>subplots(<span style="color:#ae81ff">1</span>, <span style="color:#ae81ff">2</span>, sharex<span style="color:#f92672">=</span><span style="color:#66d9ef">False</span>)
+</span></span><span style="display:flex;"><span>axes[<span style="color:#ae81ff">0</span>]<span style="color:#f92672">.</span>plot(df<span style="color:#f92672">.</span>index, df<span style="color:#f92672">.</span>Close<span style="color:#f92672">.</span>diff()); axes[<span style="color:#ae81ff">0</span>]<span style="color:#f92672">.</span>set_title(<span style="color:#e6db74">&#39;1st Differencing&#39;</span>)
+</span></span><span style="display:flex;"><span>axes[<span style="color:#ae81ff">1</span>]<span style="color:#f92672">.</span>set(ylim<span style="color:#f92672">=</span>(<span style="color:#ae81ff">0</span>,<span style="color:#ae81ff">5</span>))
+</span></span><span style="display:flex;"><span>plot_pacf(df<span style="color:#f92672">.</span>Close<span style="color:#f92672">.</span>diff()<span style="color:#f92672">.</span>dropna(), ax<span style="color:#f92672">=</span>axes[<span style="color:#ae81ff">1</span>], lags<span style="color:#f92672">=</span><span style="color:#ae81ff">20</span>, color<span style="color:#f92672">=</span><span style="color:#e6db74">&#39;k&#39;</span>, auto_ylims<span style="color:#f92672">=</span><span style="color:#66d9ef">True</span>, zero<span style="color:#f92672">=</span><span style="color:#66d9ef">False</span>)
+</span></span><span style="display:flex;"><span>
+</span></span><span style="display:flex;"><span>plt<span style="color:#f92672">.</span>tight_layout()
+</span></span><span style="display:flex;"><span>plt<span style="color:#f92672">.</span>show()
+</span></span></code></pre></div><p><img alt="png" src="/posts/finance/stock_prediction/arima/images/find_p.png"></p>
+<p>A possible choice of <strong>p</strong> can 8 or 18, where the coefficient crosses the confidence intervals.</p>
+<h3 id="finding-q-parameter-from-plots">Finding q parameter 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):
@@ -645,8 +659,7 @@ <h3 id="grid-search">Grid Search</h3>
 </span></span><span style="display:flex;"><span>    <span style="color:#66d9ef">return</span> best_order
 </span></span><span style="display:flex;"><span>
 </span></span><span style="display:flex;"><span>best_order <span style="color:#f92672">=</span> grid_search_arima(ts_diff, range(<span style="color:#ae81ff">3</span>), range(<span style="color:#ae81ff">2</span>), range(<span style="color:#ae81ff">3</span>))
-</span></span></code></pre></div><p>Indeed, from the plot, <em>d=2</em> is probably a better solution since we have few coefficient that goes above the confidence threshold.</p>
-<h2 id="6-limitations-and-considerations">6. Limitations and Considerations</h2>
+</span></span></code></pre></div><h2 id="6-limitations-and-considerations">6. Limitations and Considerations</h2>
 <p>While ARIMA models can be powerful for time series prediction, they have limitations:</p>
 <ol>
 <li><strong>Assumption of linearity</strong>: ARIMA models assume linear relationships, which may not hold for complex financial data.</li>
@@ -840,7 +853,9 @@ <h5 class="text-center ps-3">Table of Contents</h5>
     <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="#finding-d-parameter-from-plots">Finding d parameter from plots</a></li>
+        <li><a href="#finding-p-parameter-from-plots">Finding p parameter from plots</a></li>
+        <li><a href="#finding-q-parameter-from-plots">Finding q parameter from plots</a></li>
         <li><a href="#grid-search">Grid Search</a></li>
       </ul>
     </li>

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

@@ -466,7 +466,7 @@ <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
-           | 6 minutes </span>
+           | 7 minutes </span>
       <a
       href="/posts/finance/stock_prediction/arima/"
       class="float-end btn btn-outline-info btn-sm">Read</a>

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

@@ -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
-           | 6 minutes </span>
+           | 7 minutes </span>
       <a
       href="/posts/finance/stock_prediction/arima/"
       class="float-end btn btn-outline-info btn-sm">Read</a>