Added some discussion.

pairs_trading.ipynb

@@ -197,7 +197,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 5,
    "metadata": {
     "pycharm": {
      "name": "#%%\n"
@@ -392,7 +392,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 6,
    "metadata": {
     "pycharm": {
      "name": "#%%\n"
@@ -449,14 +449,20 @@
     "Correlation\n",
     "</h3>\n",
     "<p>\n",
-    "\n",
+    "In selecting pairs for trading, the selection attempts to find pairs that have similar market price behavior and mean reversion.\n",
+    "One measure of similar market price behavior is correlation.  This section examines the correlation distribution for the\n",
+    "S&P 500 sector pairs.\n",
+    "</p>\n",
+    "<p>\n",
+    "The correlation is performed on the natural log of the close prices.  The correlation period consists of one year of trading\n",
+    "days.\n",
     "</p>\n"
    ],
    "outputs": []
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "outputs": [],
    "source": [
     "\n",
@@ -489,14 +495,22 @@
     "    return pairs_list\n",
     "\n",
     "\n",
-    "def calc_pairs_correlation(stock_close_df: pd.DataFrame, pair: Tuple, window: int, all_cor_v: np.array) -> np.array:\n",
+    "def calc_pairs_correlation(stock_close_df: pd.DataFrame, pair: Tuple, window: int) -> np.array:\n",
+    "    \"\"\"\n",
+    "    Calculate the windowed correlations for a stock pair over the entire data set.\n",
+    "    :param stock_close_df: A data frame containing the stock close prices\n",
+    "    :param pair: the stock pair\n",
+    "    :param window: The data window\n",
+    "    :return: a numpy array of windowed correlations for the pair over the entire time period.\n",
+    "    \"\"\"\n",
     "    cor_v = np.zeros(0)\n",
     "    stock_a = pair[0]\n",
     "    stock_b = pair[1]\n",
     "    a_close = stock_close_df[stock_a]\n",
     "    b_close = stock_close_df[stock_b]\n",
     "    a_log_close = log(a_close)\n",
     "    b_log_close = log(b_close)\n",
+    "\n",
     "    assert len(a_log_close) == len(b_log_close)\n",
     "    for i in range(0, len(a_log_close), window):\n",
     "        sec_a = a_log_close[i:i + window]\n",
@@ -507,9 +521,15 @@
     "\n",
     "\n",
     "def calc_yearly_correlation(stock_close_df: pd.DataFrame, pairs_list: List[Tuple]) -> np.array:\n",
+    "    \"\"\"\n",
+    "    Calculate the yearly pairs correlation over the entire time period\n",
+    "    :param stock_close_df: A data frame containing the stock close prices. The columns are the stock tickers.\n",
+    "    :param pairs_list: A list of the pairs formed from the S&P 500 sectors.\n",
+    "    :return: A numpy array with the correlcations.\n",
+    "    \"\"\"\n",
     "    all_cor_v = np.zeros(0)\n",
     "    for pair in pairs_list:\n",
-    "        cor_v: np.array = calc_pairs_correlation(stock_close_df, pair, trading_days, all_cor_v)\n",
+    "        cor_v: np.array = calc_pairs_correlation(stock_close_df, pair, trading_days)\n",
     "        all_cor_v = np.append(all_cor_v, cor_v)\n",
     "    return all_cor_v\n",
     "\n",
@@ -551,8 +571,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "outputs": [],
+   "execution_count": 8,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "<Figure size 720x576 with 1 Axes>",
+      "image/png": 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\n"
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "\n",
     "\n",
@@ -565,6 +596,44 @@
     }
    }
   },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "\n",
+    "<p>\n",
+    "The lookback period for pairs selection is one year (254 trading days). As a first step, all of the S&P 500 sector\n",
+    "pairs will be tested for correlation over the past year. The pairs that have a correlation of 0.75 or more will be\n",
+    "tested for mean reversion.\n",
+    "</p>"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "pycharm": {
+     "name": "#%% md\n"
+    }
+   },
+   "outputs": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "outputs": [],
+   "source": [
+    "#\n",
+    "# At this point we have close_prices_df which is a DataFrame containing the close prices for the S&P 500 stocks over\n",
+    "# the backtest time period.\n",
+    "#\n",
+    "# pairs_list contains the list of pairs formed from the S&P 500 sectors.\n",
+    "#\n",
+    "\n"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "pycharm": {
+     "name": "#%%\n"
+    }
+   }
+  },
   {
    "cell_type": "markdown",
    "source": [