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diff --git a/_modules/arch/bootstrap/base.html b/_modules/arch/bootstrap/base.html
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diff --git a/_modules/arch/typing.html b/_modules/arch/typing.html
diff --git a/_modules/arch/unitroot/_engle_granger.html b/_modules/arch/unitroot/_engle_granger.html
@@ -15,7 +15,7 @@
 
 
 
-        <title>arch.unitroot._engle_granger - arch 7.0.0</title>
+        <title>arch.unitroot._engle_granger - arch 7.2.0</title>
 
 
 
@@ -47,7 +47,7 @@
         <style>:root{--md-text-font:"Roboto";--md-code-font:"Roboto Mono"}</style>
 
 
-        <link rel="stylesheet" type="text/css" href="../../../_static/sphinx_immaterial_theme.359ec555e2989f00f.min.css?v=b000af5c" />
+        <link rel="stylesheet" type="text/css" href="../../../_static/sphinx_immaterial_theme.4b4a8c74e2ff2ab5b.min.css?v=afa97f93" />
         <link rel="stylesheet" type="text/css" href="../../../_static/css/small_fixes.css?v=64f7a1ef" />
     <script>__md_scope=new URL("../../..",location),__md_hash=e=>[...e].reduce((e,_)=>(e<<5)-e+_.charCodeAt(0),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script>
 
@@ -87,7 +87,7 @@
 
 <header class="md-header" data-md-component="header">
   <nav class="md-header__inner md-grid" aria-label="Header">
-    <a href="../../../index.html" title="arch 7.0.0" class="md-header__button md-logo" aria-label="arch 7.0.0" data-md-component="logo">
+    <a href="../../../index.html" title="arch 7.2.0" class="md-header__button md-logo" aria-label="arch 7.2.0" data-md-component="logo">
       <img src="../../../_static/bw-logo.svg" alt="logo">
     </a>
     <label class="md-header__button md-icon" for="__drawer">
@@ -97,7 +97,7 @@
       <div class="md-header__ellipsis">
         <div class="md-header__topic">
           <span class="md-ellipsis">
-            arch 7.0.0
+            arch 7.2.0
           </span>
         </div>
         <div class="md-header__topic" data-md-component="header-topic">
@@ -184,10 +184,10 @@
 
 <nav class="md-nav md-nav--primary" aria-label="Navigation" data-md-level="0">
   <label class="md-nav__title" for="__drawer">
-    <a href="../../../index.html" title="arch 7.0.0" class="md-nav__button md-logo" aria-label="arch 7.0.0" data-md-component="logo">
+    <a href="../../../index.html" title="arch 7.2.0" class="md-nav__button md-logo" aria-label="arch 7.2.0" data-md-component="logo">
       <img src="../../../_static/bw-logo.svg" alt="logo">
     </a>
-    arch 7.0.0
+    arch 7.2.0
   </label>
 
     <div class="md-nav__source">
@@ -324,6 +324,22 @@
 
 
 
+    <li class="md-nav__item">
+      <a href="../../../types.html" class="md-nav__link">
+        <span title="/types.rst (reference label)" class="md-ellipsis">Common Type Definitions</span>
+      </a>
+    </li>
+
+
+
+
+
+
+
+
+
+
+
     <li class="md-nav__item">
       <a href="../../../changes.html" class="md-nav__link">
         <span title="/changes.rst (reference label)" class="md-ellipsis">Change Log</span>
@@ -364,7 +380,7 @@
 
 
 <h1>Source code for arch.unitroot._engle_granger</h1><div class="highlight"><pre>
-<span></span><code><span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">annotations</span>
+<span></span><code><span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Optional</span><span class="p">,</span> <span class="n">Union</span>
 
 <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
@@ -397,10 +413,10 @@ <h1>Source code for arch.unitroot._engle_granger</h1><div class="highlight"><pre
     <span class="n">x</span><span class="p">:</span> <span class="n">ArrayLike2D</span><span class="p">,</span>
     <span class="n">trend</span><span class="p">:</span> <span class="n">UnitRootTrend</span> <span class="o">=</span> <span class="s2">&quot;c&quot;</span><span class="p">,</span>
     <span class="o">*</span><span class="p">,</span>
-    <span class="n">lags</span><span class="p">:</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-    <span class="n">max_lags</span><span class="p">:</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+    <span class="n">lags</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+    <span class="n">max_lags</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
     <span class="n">method</span><span class="p">:</span> <span class="n">Literal</span><span class="p">[</span><span class="s2">&quot;aic&quot;</span><span class="p">,</span> <span class="s2">&quot;bic&quot;</span><span class="p">,</span> <span class="s2">&quot;t-stat&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;bic&quot;</span><span class="p">,</span>
-<span class="p">)</span> <span class="o">-&gt;</span> <span class="n">EngleGrangerTestResults</span><span class="p">:</span>
+<span class="p">)</span> <span class="o">-&gt;</span> <span class="s2">&quot;EngleGrangerTestResults&quot;</span><span class="p">:</span>
 <span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Test for cointegration within a set of time series.</span>
 
@@ -514,8 +530,8 @@ <h1>Source code for arch.unitroot._engle_granger</h1><div class="highlight"><pre
         <span class="n">alternative</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;Cointegration&quot;</span><span class="p">,</span>
         <span class="n">trend</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;c&quot;</span><span class="p">,</span>
         <span class="n">order</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">2</span><span class="p">,</span>
-        <span class="n">adf</span><span class="p">:</span> <span class="n">ADF</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-        <span class="n">xsection</span><span class="p">:</span> <span class="n">RegressionResults</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">adf</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">ADF</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">xsection</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">RegressionResults</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
     <span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
         <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span>
             <span class="n">stat</span><span class="p">,</span> <span class="n">pvalue</span><span class="p">,</span> <span class="n">crit_vals</span><span class="p">,</span> <span class="n">null</span><span class="p">,</span> <span class="n">alternative</span><span class="p">,</span> <span class="n">trend</span><span class="p">,</span> <span class="n">order</span><span class="p">,</span> <span class="n">xsection</span>
@@ -538,7 +554,7 @@ <h1>Source code for arch.unitroot._engle_granger</h1><div class="highlight"><pre
         <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_adf</span><span class="o">.</span><span class="n">lags</span>
 
     <span class="nd">@property</span>
-    <span class="k">def</span> <span class="nf">max_lags</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+    <span class="k">def</span> <span class="nf">max_lags</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]:</span>
 <span class="w">        </span><span class="sd">&quot;&quot;&quot;The maximum number of lags used in the lag-length selection.&quot;&quot;&quot;</span>
         <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_adf</span><span class="o">.</span><span class="n">max_lags</span>
 
@@ -720,7 +736,7 @@ <h1>Source code for arch.unitroot._engle_granger</h1><div class="highlight"><pre
 
     Created using
     <a href="https://www.sphinx-doc.org/" target="_blank" rel="noopener">Sphinx</a>
-    7.2.6.
+    8.1.3.
      and
     <a href="https://github.com/jbms/sphinx-immaterial/" target="_blank" rel="noopener">Sphinx-Immaterial</a>