theory-autocorrelation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Theory: Autocorrelation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import utils\n",
    "import pandas as pd \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.graphics.tsaplots as sgt \n",
    "import statsmodels.tsa.stattools as sts \n",
    "from statsmodels.tsa.seasonal import seasonal_decompose\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "import importlib\n",
    "importlib.reload(utils);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Correlation is a quantity for measuring the statistical relationship between two stochastic processes.\n",
    "\n",
    "The correlation between two stochastic variables $\\mathbf{X}$ and $\\mathbf{Y}$, denoted $r_{xy}$ is given by:\n",
    "\n",
    "\\begin{align}\n",
    "r_{xy} = \\mathbb{E}[\\mathbf{X}  \\mathbf{Y}]\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Covariance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Covariance is a measure of the linear relationship between two random variables. If the relationship between the random variables\n",
    "is nonlinear, the covariance may not reflect the strength of this relationship."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlation Coefficient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most commonly used linear correlation coefficient is known as the Pearson product moment correlation coefficient [(#)](https://www.geo.fu-berlin.de/en/v/soga/Basics-of-statistics/Descriptive-Statistics/Measures-of-Relation-Between-Variables/Correlation/index.html). Person's correlation coefficient assumes that the two random variables follow a Gaussian distribution.\n",
    "\n",
    "The correlation coefficient between two stochastic variables $\\mathbf{X}$ and $\\mathbf{Y}$, denoted $\\rho_{xy}$ is given by:\n",
    "\n",
    "\\begin{align}\n",
    "\\rho_{xy} = \n",
    "\\frac{\n",
    "  \\text{cov}(\\mathbf{X}, \\mathbf{Y})\n",
    "}{\n",
    "  \\sigma_x \\sigma_y\n",
    "}\n",
    "\\end{align}\n",
    "\n",
    "The correlation coefficient can only take values in the range $-1 \\leq \\rho_{xy} \\leq 1$:\n",
    "- $\\rho_{xy}$ close to 1 indicates a positive correlation\n",
    "- $\\rho_{xy}$ close to -1 indicates a negative correlation\n",
    "- $\\rho_{xy}$ around zero indicates no correlation.\n",
    "\n",
    "The correlation coefficient is a useful quantity for measuring both the direction and the strength of the linear relationship between two random variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"figures/linear-correlation-examples.png\" width=\"600\" />\n",
    "\n",
    "[Source](https://www.geo.fu-berlin.de/en/v/soga/Basics-of-statistics/Descriptive-Statistics/Measures-of-Relation-Between-Variables/Correlation/index.html)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Autocorrelation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Autocorrelation is the correlation between a signal $x[n]$ and a delayed/shifted/lagged version of the signal itself $x[n - \\ell]$. It provides a measure of the linear dependence between the signal at two different times; $n$ and $n-\\ell$. Informally, it describes how well the present value of the series is related with its past values. \n",
    "\n",
    "The autocorrelation function ACF computes the autocorrelation for a number of lags. \n",
    "\n",
    "<img src=\"figures/autocorrelation-example.png\" width=\"350\" />\n",
    "\n",
    "[Source Wikipedia](https://en.wikipedia.org/wiki/Autocorrelation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### AFC of S&P 500 Prices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us compute the autocorrelation sequence for S&P 500 closing prices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(14, 5))\n",
    "sgt.plot_acf(utils.load_sp500_data(), lags=30, zero=False, ax=ax);\n",
    "ax.set_ylabel('Correlation Coefficient')\n",
    "ax.set_xlabel('Lag $\\ell$')\n",
    "ax.set_title('Autocorrelation Sequence of S&P 500 Closing Prices');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot known as correlogram or autocorrelation plot gives us two types of information:\n",
    "\n",
    "1. The **stem plot** represents the correlation coefficient for each lag $\\ell$\n",
    "2. The **confidence band** (the blue cone around the x-axis) represents statistical significance (default 95% confidence interval):\n",
    "  - When a coefficient value at lag $\\ell$ is inside the blue area, it is not significantly different from zero. In other words, we have no evidence to indicate that it is no different than zero i.e., no statistical significance.\n",
    "  - When a coefficient value at lag $\\ell$ is situated outside the blue area, then it is significantly different from zero suggesting that the correlation exists and is not a statistical fluke.\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the figure above, we observe that the blue area expands as the lag values increase. The greater the distance in time, the more unlikely it is that this autocorrelation persists. For example, today's closing price is closer to yesterday's price than the closing price 30 days ago. Therefore, we need to make sure that the autocorrelation coefficient in higher lags is sufficiently greater to be significantly different from zero. \n",
    "\n",
    "All the autocorrelation coefficients are outside the confidence band. This suggests **time dependence** in the data. We also observe that the autocorrelation coefficient does not diminish as the lags increase. This suggests that the closing price 30 days in the past can still serve as decent estimator of the future prices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### AFC of Random Walk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data generated by a random walk process is very much like the stock market price data.\n",
    "Now, let us compare the autocorrelation of a random walk."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(14, 5))\n",
    "sgt.plot_acf(utils.load_random_walk_data(), lags=30, zero=False, ax=ax);\n",
    "ax.set_ylabel('Correlation Coefficient')\n",
    "ax.set_xlabel('Lag $\\ell$')\n",
    "ax.set_title('Autocorrelation Sequence of Random Walk');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ACF of White Noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Being able to distinguish white noise from regular signal is very important. \n",
    "White noise has no correlation between its values at different times.\n",
    "To confirm this knowledge, let us compute the autocorrelation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(14, 5))\n",
    "sgt.plot_acf(utils.generate_white_noise(), zero=False, ax=ax);\n",
    "ax.set_ylabel('Correlation Coefficient')\n",
    "ax.set_xlabel('Lag $\\ell$')\n",
    "ax.set_title('Autocorrelation Sequence of White Noise');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The autocorrelation of white noise contains both positive and negative coefficients. \n",
    "All the coefficients fall within the blue area, which means that the coefficients are not significant. Since the coefficients are effectively zero, the sign of each coefficient is rather arbitrary.\n",
    "This suggests that there is no correlation for any lag.\n",
    "This is in line of what we already know. White noise does not have any autocorrelation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Partial Autocorrelation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main difference between autocorrelation and partial autocorrelation is that the ACF measures the accumulated effects past lags have on the current value, while the PACF measures the direct effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(14, 5))\n",
    "sgt.plot_pacf(utils.load_sp500_data(), zero=False, lags=40, method=('ols'), ax=ax);\n",
    "ax.set_ylabel('Correlation coefficient')\n",
    "ax.set_xlabel('Lag')\n",
    "ax.set_title('Partial Autocorrelation of S&P 500 closing prices');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The only correlation coefficient of first lag is significantly different from zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Q/fpnlXt7jQ5CHo/xSxA6/lywD/21Hz22Hz22Hz22Hz22F/21Hz22X7D0mFPjAAAAAIQcghAAAACAkEMQAgAAABByCEIAAAAAQg5BCAAAAEDIsTUI5efnKykpSfv27Tvptu3bt2vw4MHq06eP7r//fpWWltpZCgAAAAB42RaENm/erD//+c9KT08/5e0TJkzQAw88oE8//VTGGKWmptpVSrXyeIw27TysD9bu0qadh4PmcoMAAABATWZbEEpNTdWDDz6ohISEk27bv3+/ioqK1L59e0nS4MGDtXz5crtKqTYej9GTCzfppaXbtHTNLr20dJueXLiJMAQAAABUM9v+oOpjjz1W7m2ZmZmKj4/3TsfHxysjI8OuUqrNlrRspR3IU7HLLUkqdrmVdiBPW9Ky1b7F2dVcHQAAABC6bAtCp+PxeORwOLzTxpgy02cqLi7ayrJOKz4+psKPyd50QCX/F4KOK3G5lZNfUqnlBTP6YT96bD96bD96bD96bC/6az96bL9g6XG1BKFGjRopKyvLO3348OFTnkLnS3Z2vl9OM4uPj1FW1tEKPy4uOlKREWHeI0KSFBkRpgbRkZVaXrCqbH9x5uix/eix/eix/eixveiv/eix/WpSj51Ox2kPnFTL5bObNGmiqKgoffvtt5KkpUuXqkePHtVRiq0Sm8ep+Tl1JY9LMkZREWFqfk5dJTaPq+7SAAAAgJDm1yA0atQobd26VZI0e/ZszZgxQ3379lVBQYGGDx/uz1L8wul06H9vbC8dWi1lf687B7TW/97YXk5nxU8DBAAAAGAd20+NW7Vqlff/8+bN8/6/VatWWrRokd1PX+2cToccx/ZJx/ZxgQQAAAAgQFTLqXEAAAAAUJ0IQgAAAABCDkEIAAAAQMghCAEAAAAIOQQhAAAAACGHIAQAAAAg5BCEAAAAAIQcghAAAACAkEMQAgAAABByCEIAAAAAQg5BCAAAAEDIIQgBAAAACDkEIQAAAAAhhyAEAAAAIOQQhAAAAACEHIIQAAAAgJBDEAIAAAAQcghCAAAAAEIOQQgAAABAyCEIAQAAAAg5BCEAAAAAIYcgBAAAACDkEIQAAAAAhByCEAAAAICQQxACAAAAEHIIQgAAAABCDkEIAAAAQMghCAEAAAAIOQQhAAAAACGHIAQAAAAg5BCEAAAAAIQcghAAAACAkEMQAgAAABByCEIAAAAAQg5BCAAAAEDIIQgBAAAACDkEIQAAAAAhhyAEAAAAIOQQhAAAAACEHFuD0LJly9SvXz/17t1bb7311km3b9u2Tddff72uu+463XnnncrLy7OzHAAAAACQZGMQysjI0Jw5c/T2229ryZIlWrhwoXbu3FnmPo899phSUlL0wQcfqFmzZnr11VftKgcAAAAAvGwLQuvWrVOXLl0UGxurOnXqqE+fPlq+fHmZ+3g8Hh07dkySVFhYqFq1atlVDgAAAAB4hdu14MzMTMXHx3unExIStGXLljL3mThxokaOHKnp06erdu3aSk1NrdBzxMVFW1LrmYiPj6n0YyMjw6u8jGBHb+xHj+1Hj+1Hj+1Hj+1Ff+1Hj+0XLD22LQh5PB45HA7vtDGmzHRRUZHuv/9+zZ8/X4mJiXrttdd033336eWXXz7j58jOzpfHYyyt+1Ti42OUlXW00o8vKSmVpCotI5hVtb/wjR7bjx7bjx7bjx7bi/7ajx7bryb12Ol0nPbAiW2nxjVq1EhZWVne6aysLCUkJHind+zYoaioKCUmJkqSbrzxRn3zzTd2lQMAAAAAXrYFoa5du2r9+vXKyclRYWGhVqxYoR49enhvb9q0qQ4dOqS0tDRJ0ueff662bdvaVQ4AAAAAeNl2alzDhg01fvx4DR8+XC6XS0OGDFFiYqJGjRqllJQUtW3bVjNmzNC4ceNkjFFcXJymT59uVzkAAAAA4GVbEJKk5ORkJScnl5k3b9487/979uypnj172lkCAAAAAJzE1j+oCgAAAACBiCAEAAAAIOQQhAAAAACEHIIQAAAAgJBDEAIAAAAQcghCAAAAAEIOQQgAAABAyCEIAQAAAAg5BCEAAAAAIYcgBAAAACDkEIQAAAAAhByCEAAAAICQQxACAAAAEHIIQgAAAABCjs8g9Pbbb5807+WXX7alGAAAAADwh/DybnjnnXdUVFSk+fPnq7i42Dvf5XLp3Xff1R133OGXAgEAAADAauUGofDwcO3YsUNFRUXasWOHd35YWJgmTpzol+IAAAAAwA7lBqGhQ4dq6NChWrlypa6++mp/1gQAAAAAtio3CB3Xvn17Pffcczpy5EiZ+VOmTLGtKAAAAACwk88gNGHCBNWqVUsXX3yxHA6HP2oCAAAAAFv5DEKHDh3SJ5984o9aAAAAAMAvfF4++5xzzlFBQYE/agEAAAAAv/B5RCghIUEDBw5Up06dVKtWLe98fiMEAAAAoKbyGYSaNGmiJk2a+KMWAAAAAPALn0Fo7NixKioq0u7du3XBBReouLhYtWvX9kdtAAAAAGALn78R2rx5s66++mrdeeedyszMVK9evfTdd9/5ozYAAAAAsIXPIPT4449r/vz5io2NVaNGjTRr1iw99thj/qgNAAAAAGzhMwgVFRWpRYsW3umePXvK7XbbWhQAAAAA2MlnEAoPD1dubq73j6mmpaXZXhQAAAAA2MnnxRJGjx6tW265RYcPH9bdd9+ttWvX6pFHHvFHbQAAAABgC59B6Morr9T555+vtWvXyuPxaMyYMTr//PP9URsAAAAA2KLcU+N++eUXSdK2bduUn5+vdu3aqUOHDioqKtK2bdv8ViAAAAAAWK3cI0KzZs3SSy+9pL/97W8n3eZwOPT555/bWhgAAAAA2KXcIPTSSy9JklatWqX8/HxFR0eruLhY+fn5iouL81uBAAAAAGA1n1eN+/jjjzV48GBJ0oEDB5SUlKRVq1bZXhgAAAAA2MVnEHrxxRe1YMECSVKzZs20ePFizZ071/bCAAAAAMAuPoOQx+NRo0aNvNONGzeWx+OxtSgAAAAAsJPPINSgQQO9++67Ki0tldvt1qJFi3T22Wf7ozYAAAAAsIXPIPTwww8rNTVViYmJSkxMVGpqqh588EF/1AYAAAAAtvD5B1WP/y4oNzdXYWFhio6OPuOFL1u2TP/4xz9UWlqqESNG6Oabby5ze1pamh588EHl5uYqPj5eTz31lOrVq1fxVwEAAAAAFVBuEJo3b55GjRqladOmyeFwnHT7lClTTrvgjIwMzZkzR4sXL1ZkZKSGDRumzp07q0WLFpIkY4zuuusu3X///erRo4dmz56tl19+WRMmTKjiSwIAAACA0ys3CMXExEiS6tevX6kFr1u3Tl26dFFsbKwkqU+fPlq+fLnGjh0rSdq2bZvq1KmjHj16SJJGjx6tvLy8Sj0XAAAAAFREuUFo8eLFGjZsmAoLCyt1lCYzM1Px8fHe6YSEBG3ZssU7vWfPHp199tmaPHmytm/frubNm2vq1KkVeo64uDM/Ta+q4uNjKv3YyMjwKi8j2NEb+9Fj+9Fj+9Fj+9Fje9Ff+9Fj+wVLj8sNQocPH9aLL76oDz/88JRXibvttttOu2CPx1PmlDpjTJnp0tJSffPNN3rzzTfVtm1bPf3005o5c6Zmzpx5xsVnZ+fL4zFnfP/Kio+PUVbW0Uo/vqSkVJKqtIxgVtX+wjd6bD96bD96bD96bC/6az96bL+a1GOn03HaAyflBqFp06bpo48+UlFRkXbs2FHhJ27UqJE2btzonc7KylJCQoJ3Oj4+Xk2bNlXbtm0lSUlJSUpJSanw8wAAAABARZUbhF577TW98sorevXVV/U///M/FV5w165dNXfuXOXk5Kh27dpasWKFpk2b5r29Q4cOysnJ0Y8//qhWrVpp1apVat26deVeBQAAAABUQLlB6JdfftGyZcv0zjvv6LzzzpMxZU9B692792kX3LBhQ40fP17Dhw+Xy+XSkCFDlJiYqFGjRiklJUVt27bV888/rylTpqiwsFCNGjXSrFmzrHlVAAAAAHAa5QahlJQULVq0SNnZ2VqwYEGZ2xwOh88gJEnJyclKTk4uM2/evHne/7dr106LFi2qaM0AAAAAUCXlBqFBgwZp0KBBmjFjhiZNmuTPmgAAAADAVk5fd7j33nv16quvauLEicrPz9dLL70kt9vtj9oAAAAAwBY+g9ATTzyhn376SZs3b5YxRmvWrNGMGTP8URsAAAAA2MJnEFq/fr1mzpypqKgoxcTE6J///KfWrl3rj9oAAAAAwBY+g1B4eLiczv/eLTIyUuHh5f60CAAAAAACns9Ec+GFF+qtt96S2+1WWlqa5s+fr1atWvmjNgAAAACwhc8jQvfff7+2bdum7Oxs/fnPf9axY8c0efJkf9QGAAAAALbweUQoOjpa06dPV2lpqYwxioiI8EddAAAAAGAbn0eEDh8+rNtvv13t27dXYmKihg8froyMDH/UBgAAAAC28BmEpk2bpvbt22vdunVat26dLr30Uj300EN+KA0AAAAA7OEzCKWnp2vs2LGqW7eu6tevr5SUFO3Zs8cftQEAAACALXwGodLSUhUXF3unCwsL5XA4bC0KAAAAAOzk82IJ/fr101/+8hcNHjxYDodD7733nvr06eOP2gAAAADAFj6D0JgxY9S4cWN99dVX8ng8Gjx4sIYMGeKP2gAAAADAFj6DUH5+vrKysvT0009r//79mj9/vgoLC1WnTh1/1AcAAAAAlvP5G6FJkybpyJEjkqS6devK4XBo6tSpthcGAAAAAHY5o6vG3XfffZKkmJgYTZ48WT///LPthQEAAACAXc7oqnH5+fne6WPHjskYY2tRAAAAAGAnn78RGjhwoIYOHaq+ffvK4XDos88+0+DBg/1RGwAAAADYwmcQuvPOO9WiRQutX79e4eHhuueee9SzZ09/1AYAAAAAtvAZhCTpqquu0lVXXWV3LQAAAADgFz5/IwQAAAAAwYYgBAAAACDkEIQAAAAAhByfvxFKS0vTvHnzdOTIkTKXzX7xxRdtLQwAAAAA7OIzCE2cOFGJiYnq2LGjHA6HP2oCAAAAAFv5DEKFhYWaMmWKP2oBAAAAAL/w+Ruhpk2bKjMz0x+1AAAAAIBf+Dwi5PF4lJSUpNatWysqKso7n98IAQAAAKipfAaha665Rtdcc40/agEAAAAAv/AZhAYNGqT9+/frm2++UWlpqTp16qSmTZv6ozYAAAAAsIXP3witWbNG119/vVauXKnPP/9cQ4YM0cqVK/1RGwAAAADYwucRoWeeeUZvvvmmWrRoIUn6+eefNWHCBF199dW2FwcAAAAAdvB5RMjlcnlDkCRdcMEFcrvdthYFAAAAAHbyGYRq1aqlrVu3eqe3bt2q2rVr21oUAAAAANjJ56lxEyZM0OjRo70XSNi1a5eeeeYZ2wsDAAAAALv4DEKXXnqpPvroI23evFkej0ft27dX/fr1/VEbAAAAANii3CC0dOlSDRgwQK+99lqZ+enp6ZKk2267zdbCAAAAAMAu5Qah3bt3S5J27Njht2IAAAAAwB/KDUIpKSmSpKuuuuqkS2UvWbLkjBa+bNky/eMf/1BpaalGjBihm2+++ZT3W716tR555BGtWrXqTOsGAAAAgEorNwitWrVKpaWlmjVrlowxMsZIkkpLSzV37lwNHDjwtAvOyMjQnDlztHjxYkVGRmrYsGHq3LlzmUtxS9Lhw4f1+OOPW/BSAAAAAODMlBuEtm/frq+//lrZ2dlasGDBfx8QHq6//OUvPhe8bt06denSRbGxsZKkPn36aPny5Ro7dmyZ+02ZMkVjx47Vk08+WcmXAAAAAAAVU24QGjNmjMaMGaO33nqr3FPaTiczM1Px8fHe6YSEBG3ZsqXMfRYsWKCLL75Y7dq1q/DyJSkuLrpSj6uM+PiYSj82MjK8yssIdvTGfvTYfvTYfvTYfvTYXvTXfvTYfsHSY5+Xzx46dKg+++wzHTt2TJLkdru1Z88ejR8//rSP83g8cjgc3mljTJnpHTt2aMWKFZo/f74OHTpUqeKzs/Pl8ZhKPbYi4uNjlJV1tNKPLykplaQqLSOYVbW/8I0e248e248e248e24v+2o8e268m9djpdGQhhoUAAByYSURBVJz2wInPIDR+/Hjt3btXWVlZuvjii7V582Z16tTJ5xM3atRIGzdu9E5nZWUpISHBO718+XJlZWXp+uuvl8vlUmZmpm666Sa9/fbbPpcNAAAAAFXh9HWH7du3a/Hixbrqqqs0efJkvfPOO8rNzfW54K5du2r9+vXKyclRYWGhVqxYoR49enhvT0lJ0aeffqqlS5fq5ZdfVkJCAiEIAAAAgF/4DEIJCQkKDw/XH//4R+3YsUMXXHCBjh71fTisYcOGGj9+vIYPH66BAwcqKSlJiYmJGjVqlLZu3WpJ8QAAAABQGT5PjatTp46WLVumVq1aKTU1Vc2bN1dBQcEZLTw5OVnJycll5s2bN++k+/3hD3/gbwgBAAAA8BufR4SmTp2q7du3q1u3bnI6nbrllls0cuRIf9QGAAAAALbweUSoWbNmuvfeeyVJTz/9tO0FAQAAAIDdyg1Cvz+l7feWLVtmeTEAAAAA4A/lBqGpU6f6sw4AAAAA8JtyfyPUqVMn779atWopLS1N7du3V0RExBn9HSEAAAAACFQ+L5awePFiTZo0Sa+88oqOHj2qv/71r0pNTfVHbQAAAABgC59B6I033tDChQsVHR2tuLg4LV68WK+//ro/agMAAAAAW/gMQk6nU9HR0d7pxo0bKywszNaiAAAAAMBOPoNQbGystm/fLofDIUn64IMPVK9ePdsLAwAAAAC7+Pw7QpMnT9bf//537dmzR927d1dUVJReeOEFf9QGAAAAALbwGYSKioq0dOlSpaeny+12q1mzZoqIiPBHbQAAAABgC5+nxt1zzz0KCwvT+eefrwsvvJAQBAAAAKDG8xmEWrZsqWXLlunAgQM6cuSI9x8AAAAA1FQ+T437/PPPtXz58jLzHA6Htm/fbltRAAAAAGAnn0HonXfeUZs2bfxRCwAAAAD4hc9T4yZMmOCPOgAAAADAb/iNEAAAAICQw2+EAAAAAIQcn0Fo69at/qgDAAAAAPzGZxDyeDx69dVX9dVXX6m0tFTdunXT6NGjFR7u86EAAAAAEJB8/kboySef1Ndff60RI0botttu0/fff6/HH3/cH7UBAAAAgC18HtZZs2aN3nvvPUVEREiSevXqpeuuu872wgAAAADALj6PCBljvCFIkiIjI8tMAwAAAEBN4zMItWrVStOnT9eePXu0d+9ezZgxQxdeeKE/agMAAAAAW/gMQg8++KDy8vI0bNgwDR06VDk5OZo6dao/agMAAAAAW/j8jVB0dLRmzpwpSSouLlZUVJTtRQEAAACAnco9IlRSUqL77rtPn332mXdeSkqKJk2apNLSUr8UBwAAAAB2KDcIPfvss8rPz9cll1zinffII48oNzdXc+fO9UtxAAAAAGCHcoPQ6tWr9eSTTyouLs47r2HDhpo1a5ZWrlzpl+IAAAAAwA7lBqGIiAjVqlXrpPnR0dGKjIy0tSgAAAAAsFO5QcjpdCo/P/+k+fn5+fxGCAAAAECNVm4QSkpK0pQpU1RQUOCdV1BQoClTpqh3795+KQ4AAAAA7FBuEBoxYoRiYmLUrVs33XDDDRoyZIi6deumunXrasyYMf6sEQAAAAAsVe7fEXI6nZo2bZpGjx6tbdu2yel0KjExUQkJCf6sDwAAAAAs5/MPqjZp0kRNmjTxRy0AAAAA4BflnhoHAAAAAMGKIAQAAAAg5BCEAAAAAIQcghAAAACAkGNrEFq2bJn69eun3r1766233jrp9pUrV2rAgAG67rrr9Ne//lW5ubl2lgMAAAAAkmwMQhkZGZozZ47efvttLVmyRAsXLtTOnTu9t+fn5+uhhx7Syy+/rA8++EAtW7bU3Llz7SoHAAAAALxsC0Lr1q1Tly5dFBsbqzp16qhPnz5avny593aXy6UHH3xQDRs2lCS1bNlSBw8etKscAAAAAPDy+XeEKiszM1Px8fHe6YSEBG3ZssU7Xb9+fV1zzTWSpKKiIr388su69dZbK/QccXHR1hR7BuLjYyr92MjI8CovI9jRG/vRY/vRY/vRY/vRY3vRX/vRY/sFS49tC0Iej0cOh8M7bYwpM33c0aNHNWbMGLVq1UqDBg2q0HNkZ+fL4zFVrtWX+PgYZWUdrfTjS0pKJalKywhmVe0vfKPH9qPH9qPH9qPH9qK/9qPH9qtJPXY6Hac9cGLbqXGNGjVSVlaWdzorK0sJCQll7pOZmambbrpJLVu21GOPPWZXKQAAAABQhm1BqGvXrlq/fr1ycnJUWFioFStWqEePHt7b3W63Ro8erWuvvVb333//KY8WAQAAAIAdbDs1rmHDhho/fryGDx8ul8ulIUOGKDExUaNGjVJKSooOHTqk//f//p/cbrc+/fRTSVKbNm04MgQAAADAdrYFIUlKTk5WcnJymXnz5s2TJLVt21Y//vijnU8PAAAAAKdk6x9UBQAAAIBARBACAAAAEHIIQgAAAABCDkEIAAAAQMghCAEAAAAIOQQhAAAAACGHIAQAAAAg5BCEAAAAAIQcghAAAACAkEMQAgAAABByCEIAAAAAQg5BCAAAAEDIIQgBAAAACDkEIQAAAAAhhyAEAAAAIOQQhAAAAACEHIIQAAAAgJBDEAIAAAAQcghCAAAAAEIOQQgAAABAyCEIAQAAAAg5BCEAAAAAIYcgBAAAACDkEIQAAAAAhByCEAAAAICQQxACAAAAEHIIQgAAAABCDkEIAAAAQMgJr+4CAKCiPB6jLWnZ2pNxVOc1jFFi8zg5nY7qLgsAANQgBCEANYrHY/Tkwk1KO5CnEpdbkRFhan5OXf3vje0JQwAA4IxxahyAGmVLWrbSDuSp2OWWkVTscivtQJ62pGVXd2kAAKAGIQgBqFH2ZBxVictdZl6Jy629GUerqSJreDxGm3Ye1gdrd2nTzsPyeEx1lwQAQFDj1DgANcp5DWMUGRGm4hPCUGREmM5tGFONVVUNp/uhuh3/3V32pgOKi47kd3cAQgJBCIDfWHGRg8TmcWp+Tl1t35UpOcIVFRmu5ufUVWLzOJuqtt+Jp/tJZU/3a9/ibL/Xw8UoQgtBHJXFewVqOoIQAL+warDldDr0vze21+3jJkuRcbpz9F9q/Ifv6U7383cQYlAcegItiAcaKwb7wXjELVjfKwh3oYUgBMAnKz4YrBxsOZ0OOY7tk47tC4qBWiCd7segOPQEUhAPNFYM9oM1MATje0WwriuUjyBkEbfHlBnEnMhjfvvRc0FxqT9LqjFy8orojc2q0mOPx+i5xVu1+1Ceil0eRUU41bRRXY0d3LZCHwy/7M89aR/57YMzVxeeG1vxugJsv6pKj1s0qaemjWL00+4syRGuWpFhatooRi2a1PP767N6PVnB4zHalp6jrK/3KL5elFr/sUG1DUqO17IvM19/SIiu1lqsqqdhgzqKjHCq2OXxzouMcCqhQZ2A2b+qy9a0bKUdyPX25vi+8J+fMtX2DE/HtWIZgciq9wqr96mqvBcH67qy2pn0OCoiTGE1IDwShCxS7HJrz6FTX7WqqOS3N4rybg91sUVuHTlSUN1lBLWq9Hjn/lztOpgnV+nxDwaPdh3M0+rv96tFk3pnvJyoiDBFhDu9y5GkiHCnIsPDKrVvBNp+VdXt+Lquf9Rj/14oZ6049R96g5o3rqt9mfkVXo7HY5R2ME+ZvxYqoX5tNW9ct0KDCqvXU1V5PEapq3fqYHaBXKUeRYQ71Tiujm7o1cLvASSQarGynphaEWrYoI52H/hVcoYrMiJMDRvUUUytiIDZv6rLtrScMgFR+u09cFtajurVifTbMgKRFe8VduxTVXkvDtZ1ZbUz6fF5jWJUJyrwYwaXzw4xHo/Rzv25WvfDIe3cn8sleoPc8fW9auPeSq/vzF8Ly3zQSZKr1KPMXwsrtJzmjeuqcVwdGbdLxhjvB17zxnUrXFMwcjod8hzdo9Ks79WiSb1KDQKODyqWrUvXv7ce1LJ16UpdvbNC6z3Q1lPawTzvIEn6bds7mF2gtIN5IV2LlfU4nQ7d0KuFSvatkufwd0ru+sdqC3eBJqF+bUWElx0qRYQ7lVC/tl+XcZxVn+FWLMeK94pA26esXFeoGWwNQsuWLVO/fv3Uu3dvvfXWWyfdvn37dg0ePFh9+vTR/fffr9LS0D4EbzcrBklW11PVQTrKd+L6XvmfPZVe31Z9MJw42CrN/JbBlg2sGFQE2nqyKogHWy1W13M8iHuyN1c6iFslkL6ws2Kwb9WXC1Z9hlu1HCveKwJtnwq0L4ICaV8IVrYFoYyMDM2ZM0dvv/22lixZooULF2rnzp1l7jNhwgQ98MAD+vTTT2WMUWpqql3lQIH1zYtVg3SrawqUb9qsYNX6tvKDwYqjHiifVYOKQFpPgfQNbSDVEoj1WPHeF2hf2Fkx2LfqiJtV7+lWjgWq+l4RaNuwlV8EVXV/CLR9IVg5jDG2dPT999/Xf/7zH02fPl2S9Pzzz8sYo7Fjx0qS9u/frxEjRmjlypWSpI0bN+rZZ5/VggULzvg5Hvvn1/o1r9j64n8nIjJMrpJTXwjhOLcxKi7nPum7dkiS/tjswkrXYIxRUYlbJaUeRYY7VSsyTA5HxXbM3GMlyjtWctL8umdFqt5Z/j33tbC4VNm5RTpx43NIiqtXS7Wr4ZxSY4yyjhSpxOWW+b9aIiPCFB9bq0J9tmo5VrByfRtjtHvvHjmcEUqIT6jU9necFfuDlcupquP7ZqnHKNzpqNbeWLlfBVJ/s44UqajEJckhp8NRbftUINViRz3pu3bI4XCo6R8vqHQtVX3vC7TPhuOs2B+q0l/Juvd0q8cCVemNHftUeLhTpb/7Qqiiqrq+rdgfAnFfqMjnXVRkmMKq4X3x9+rXjdL9I7uUe7ttnczMzFR8fLx3OiEhQVu2bCn39vj4eGVkZFToOcIjwhQRGVb1Ys+Ar+dxlHrkDj91pmxxQasqPbcxRoeyC1VY/H9vFE6HoiLC1CiuToXeKGpHhelogXRi9HU4fpsfHl6xg4PGGKXt2i05I9S4UYJqR4VXqJbSQqPfd8tIv+1cFaxFkn7Z+ZMk6fwWLSv8WEkqKHKppNTtrclIKil1y+X2qE6tCL8vR6r6a7JyfUtSi+bNKlXHScup4v5g5XKq2mOr9s3jqvqaosMilF/oUrHLLWN+W99REWGKrhNR4XqsWk9V7bEkNT67jgqLS71XLazo+42V9QRSLVbXU5V1btV7X6B9Nhxnxf5Q1WVY9Z5u+WdDFV9XoO1TUtVfkxX7Q6DtCxX9vAsPc1aqTquFR5x+/G5bEPJ4PGUaY4wpM+3r9jNxe7+L/HKIMD4+RllZp78CSkFxqW1X19m5P1fLstLlcPy2QRnz2+W6L7kgvkJX7bLq6izHl+OIiJGc4crJK1bjuDDd0Ov8M17Ozv25WrYu/aSrzVzZoUmFXtNxD694UpI09H/6VfixkrTuh0PKyCl7+pAx0gVNYtW1TSO/L8fjMXps/b/krBWnDi26VfjKX8eXEUhXuApEVd1urNo3rVTVq8ZZrao9PlFsbJ0qX2HSynqqKpBqOa6yPbbqvS/QPhusVpVt2OrP8GD8bHh4xZMKDw+r9vVtxf4QaPtCRT/vAuWqcb62adsqbNSokTZu3OidzsrKUkJCQpnbs7KyvNOHDx8uczv+63Tn/VdkZzh+7mtVB0nHzy92hEV4azl+fvGZ1nP8dye/fyOurh8kHj9P+fdvOBU9T9mK5Rz/kIr8w5WSM1zL1qVX6kPqxPWdV1SqurXCq31QHGys2jet5HQ61KJJvWp7foQmq95DA+2zIZBY9Rlu1XJQPiv2h0DbFwLx884KtgWhrl27au7cucrJyVHt2rW1YsUKTZs2zXt7kyZNFBUVpW+//VZ/+tOftHTpUvXo0cOucmo0qz5gJGsGSVbsDIE2SLfqDceK5VgRNI87vr6t+CY92Hg8Rs6Y8+SsFaed+3Mrtf1ZuW8GIyt6HMz1BBOr3kOtHKQH4/q26osOvjCxlxX7Q6AF1mD9vLMtCDVs2FDjx4/X8OHD5XK5NGTIECUmJmrUqFFKSUlR27ZtNXv2bE2ZMkX5+flq3bq1hg8fblc5NVqgfStg1c4QSIP0QPqmLVi/dQkkVh11C7R9M5BY1eNgrieYBulWDtqsGKQH2vpGaLFyTBEogTVYP+9sPXkvOTlZycnJZebNmzfP+/9WrVpp0aJFdpYQFALtW4FA2xmsGlAEyjdtwfqtSyCx6qhboB3ZDCRWHtkMtnqCdZAeSIO2QFrf8A/vWKDO2QHx5UIg7Q9WjJOC9fOu+n/FhDMSSDtUIAWzYBxQBFrQDEZWHnULpCObgSTQjmwGUj0M0u0XSOsb9gvGsYBVrOxNMH7eEYQsEhURpvMaxVR3GX71x3OsGZjH1K2turUqdxn0rWnZysgpO6DIyCnQ0SKX2jaPs6S+6nDPsA7alp6j/Vn5ahIfrdZ/bFClN/Oq9DgY5RaU6D8/ZqjY9d+BUlSEU62bN6j0fkyPywq0HttRT2VtS8855SC9pNRd7Z8jwbIdB9L6PlGw9DfQBOtYwAp29OZMtuMoH5etDhQEIYuEOR0BcZnAmqhB3VpyF7sq9diMnAKVuMoOKEpcHmXmFKjORQ2tKK/adL6ooWTRa6hKj4NRx5YJ+mrTAaUdyFOJy63IiDA1P6euOrZMqHTgpMdlBVqP7ainss5vUk9REWEqdv33j3BHRYSp+Tn1qv1zJFi240Ba3ycKlv4GmmAeC1SVHb0Jpu2YkTtqtPMaxijydwOKyIgwndswtI7OoWKcTof+98b22pKWrb0ZR3VuwxglNo8L+VMorBRoPQ6kehKbx6n5OXVPGqQnhvg311YKpPUN+zEWKB+9OT2CEGo0BhSoLKfTofYtzlb7FmdXdylBK9B6HCj1MEj3j0BZ37AfY4Hy0ZvTIwihRmNAAaAmYpAOWOfEsUBOfokaREcyFvg/jJNOjyCEGo8BBQAAoe34WCA+PkZZWUeru5yAwjipfM7qLgAAAAAA/I0gBAAAACDkEIQAAAAAhByCEAAAAICQQxACAAAAEHIIQgAAAABCTo2+fLY/r4HO9dbtRX/tR4/tR4/tR4/tR4/tRX/tR4/tV1N67KtOhzHG+KkWAAAAAAgInBoHAAAAIOQQhAAAAACEHIIQAAAAgJBDEAIAAAAQcghCAAAAAEIOQQgAAABAyCEIAQAAAAg5BCEAAAAAIYcgBAAAACDkEIROY9myZerXr5969+6tt956q7rLCUq33nqr+vfvrwEDBmjAgAHavHlzdZcUFPLz85WUlKR9+/ZJktatW6fk5GT17t1bc+bMqebqgsPvezxp0iT17t3buy1/9tln1Vxhzfbcc8+pf//+6t+/v2bNmiWJ7dhqp+ox27G1nnnmGfXr10/9+/fXa6+9Jont2Eqn6i/bsD0ef/xxTZw4UVKQbcMGp3To0CFzxRVXmF9//dUcO3bMJCcnm59//rm6ywoqHo/HdO/e3bhcruouJahs2rTJJCUlmdatW5u9e/eawsJC07NnT7Nnzx7jcrnMyJEjzerVq6u7zBrt9z02xpikpCSTkZFRzZUFh7Vr15obb7zRFBcXm5KSEjN8+HCzbNkytmMLnarHK1asYDu20IYNG8ywYcOMy+UyhYWF5oorrjDbt29nO7bIqfr7yy+/sA3bYN26daZz587mvvvuC7oxBUeEyrFu3Tp16dJFsbGxqlOnjvr06aPly5dXd1lBJS0tTZI0cuRIXXfddXrzzTeruaLgkJqaqgcffFAJCQmSpC1btqhp06Y699xzFR4eruTkZLblKvp9jwsLC3XgwAFNnjxZycnJevbZZ+XxeKq5yporPj5eEydOVGRkpCIiInT++ecrPT2d7dhCp+rxgQMH2I4t1KlTJy1YsEDh4eHKzs6W2+1WXl4e27FFTtXfWrVqsQ1b7MiRI5ozZ45Gjx4tKfjGFAShcmRmZio+Pt47nZCQoIyMjGqsKPjk5eXpsssu0/PPP6/58+fr3Xff1dq1a6u7rBrvscce06WXXuqdZlu23u97fPjwYXXp0kXTp09XamqqNm7cqEWLFlVjhTXbBRdcoPbt20uS0tPT9cknn8jhcLAdW+hUPb788svZji0WERGhZ599Vv3799dll13G+7HFft/f0tJStmGLPfDAAxo/frzq1q0rKfjGFAShcng8HjkcDu+0MabMNKquQ4cOmjVrlmJiYtSgQQMNGTJEX375ZXWXFXTYlu137rnn6vnnn1dCQoJq166tW2+9lW3ZAj///LNGjhype++9V+eeey7bsQ1O7HHz5s3Zjm2QkpKi9evX6+DBg0pPT2c7ttiJ/V2/fj3bsIX+9a9/qXHjxrrsssu884JtTBFe3QUEqkaNGmnjxo3e6aysLO9pMLDGxo0b5XK5vDuYMUbh4WySVmvUqJGysrK802zL1vvpp5+Unp6uPn36SGJbtsK3336rlJQUTZ48Wf3799c333zDdmyx3/eY7dhav/zyi0pKSnTRRRepdu3a6t27t5YvX66wsDDvfdiOK+9U/f34448VGxvLNmyRjz/+WFlZWRowYIByc3NVUFCg/fv3B9U2zBGhcnTt2lXr169XTk6OCgsLtWLFCvXo0aO6ywoqR48e1axZs1RcXKz8/Hy9//77uuaaa6q7rKDTrl077dq1S7t375bb7daHH37ItmwxY4ymT5+u3NxcuVwuLVy4kG25Cg4ePKgxY8Zo9uzZ6t+/vyS2Y6udqsdsx9bat2+fpkyZopKSEpWUlOjzzz/XsGHD2I4tcqr+duzYkW3YQq+99po+/PBDLV26VCkpKbryyiv1yiuvBNU2TEwuR8OGDTV+/HgNHz5cLpdLQ4YMUWJiYnWXFVSuuOIKbd68WQMHDpTH49FNN92kDh06VHdZQScqKkozZ87U3/72NxUXF6tnz57q27dvdZcVVFq1aqU77rhDf/7zn1VaWqrevXsrKSmpusuqsV599VUVFxdr5syZ3nnDhg1jO7ZQeT1mO7ZOz549tWXLFg0cOFBhYWHq3bu3+vfvrwYNGrAdW+BU/R07dqzq16/PNmyjYBtTOIwxprqLAAAAAAB/4tQ4AAAAACGHIAQAAAAg5BCEAAAAAIQcghAAAACAkEMQAgAAABByCEIAgBph3759XGIfAGAZghAAAACAkMMfVAUA1Gi7du3SI488omPHjikrK0utWrXS008/raioKH355ZeaPXu2nE6nLrroIq1bt05vv/22/vCHP1R32QCAasYRIQBAjZaamqqBAwcqNTVVK1as0L59+7R69Wr9+uuvuvfee/XEE09o6dKl6ty5szIyMqq7XABAgCAIAQBqtAkTJqhBgwaaN2+eHnroIWVmZqqgoEAbN27U+eefr1atWkmSBg0apOjo6GquFgAQKDg1DgBQo919991yu9269tpr1atXLx08eFDGGIWFhckYU+a+Tiff/wEAfsMnAgCgRvv3v/+tMWPGqF+/fpKkzZs3y+1265JLLlF6erp+/PFHSdKnn36qvLw8ORyO6iwXABAgOCIEAKgxCgoKTrqE9rhx4zRmzBjVqVNH0dHR6tixo/bs2aPY2Fg99dRTuu++++R0OtWmTRuFh4erdu3a1VQ9ACCQOMzvzxsAACAI5Ofn64UXXtDf/vY31a5dW9u2bdOdd96pNWvWcFQIAMARIQBAcIqOjlZERISGDBmi8PBwhYeH6+mnnyYEAQAkcUQIAAAAQAjiYgkAAAAAQg5BCAAAAEDIIQgBAAAACDkEIQAAAAAhhyAEAAAAIOQQhAAAAACEnP8PjUt+r16KIWkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(14, 5))\n",
    "sgt.plot_pacf(utils.load_random_walk_data(), zero=False, lags=40, method=('ols'), ax=ax);\n",
    "ax.set_ylabel('Correlation coefficient')\n",
    "ax.set_xlabel('Lag')\n",
    "ax.set_title('Partial Autocorrelation of Random Walk');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(14, 5))\n",
    "sgt.plot_pacf(utils.generate_white_noise(), zero=False, lags=40, method=('ols'), ax=ax);\n",
    "ax.set_ylabel('Correlation coefficient')\n",
    "ax.set_xlabel('Lag')\n",
    "ax.set_title('Partial Autocorrelation of White Noise');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}