Maximum_Likelihood_Estimation.ipynb

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    "colab": {
      "name": "Maximum Likelihood Estimation",
      "provenance": [],
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/TheHouseOfVermeulens/Financial-Engineering/blob/master/Maximum_Likelihood_Estimation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gup8OJkZSDq6",
        "colab_type": "text"
      },
      "source": [
        "##Normal Distribution MLE Estimators:\n",
        "\n",
        "\n",
        "##Exponential Distribution MLE Estimators:\n",
        "λ^=∑Tt=1xtT"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KjjWl2VkR06j",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Useful Libraries\n",
        "import pandas as pd\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import scipy\n",
        "import scipy.stats as stats"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FH62WK0_SeM7",
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      },
      "source": [
        "#1: Normal Distribution\n",
        "\n",
        "    Given the equations above, write down functions to calculate the MLE estimators μ^\n",
        "\n",
        "and σ^\n",
        "of the normal distribution.\n",
        "Given the sample normally distributed set, find the maximum likelihood μ^\n",
        "and σ^\n",
        ".\n",
        "Fit the data to a normal distribution using SciPy. Compare SciPy's calculated parameters with your calculated values of μ^\n",
        "and σ^\n",
        ".\n",
        "Plot a normal distribution PDF with your estimated parameters"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bOFVM5BhSRHC",
        "colab_type": "code",
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      "source": [
        "# Normal mean and standard deviation MLE estimators\n",
        "def normal_mu(X):\n",
        "    # Get the number of observations\n",
        "    T = len(X)\n",
        "    # Sum the observations\n",
        "    s = sum(X)\n",
        "    return 1.0/T * s\n",
        "\n",
        "def normal_sigma(X):\n",
        "    T = len(X)\n",
        "    # Get the mu MLE\n",
        "    mu = normal_mu(X)\n",
        "    # Sum the square of the differences\n",
        "    s = sum( np.power((X - mu), 2) )\n",
        "    # Compute sigma^2\n",
        "    sigma_squared = 1.0/T * s\n",
        "    return math.sqrt(sigma_squared)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gpBpavV3Sno9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "7e172920-c1c4-4e29-f327-4f01d0d19191"
      },
      "source": [
        "# Normal Distribution Sample Data\n",
        "TRUE_MEAN = 40\n",
        "TRUE_STD = 10\n",
        "X = np.random.normal(TRUE_MEAN, TRUE_STD, 10000000)\n",
        "\n",
        "# Use your functions to compute the MLE mu and sigma\n",
        "mu = normal_mu(X)\n",
        "std = normal_sigma(X)\n",
        "\n",
        "print ('Maximum likelihood value of mu:', mu)\n",
        "print ('Maximum likelihood value for sigma:', std)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Maximum likelihood value of mu: 40.00628052260704\n",
            "Maximum likelihood value for sigma: 9.999450198075902\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U-nJ9icISvZt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "60a0f447-93d8-4812-b0b7-9825fd4e2024"
      },
      "source": [
        "# Fit the distribution using SciPy and compare those parameters with yours \n",
        "scipy_mu, scipy_std = scipy.stats.norm.fit(X)\n",
        "print ('Scipy Maximum likelihood value of mu:', scipy_mu)\n",
        "print ('Scipy Maximum likelihood value for sigma:', scipy_std)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Scipy Maximum likelihood value of mu: 40.006280522610176\n",
            "Scipy Maximum likelihood value for sigma: 9.999450198076236\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J-rBodsjS9Js",
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        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 331
        },
        "outputId": "82a40c0a-32b7-4282-e9cb-1715b1ebf56c"
      },
      "source": [
        "# Get the PDF, fill it with your calculated parameters, and plot it along x\n",
        "x = np.linspace(0, 80, 80)\n",
        "\n",
        "plt.hist(X, bins=x, normed='true')\n",
        "plt.plot(scipy.stats.norm.pdf(x, loc=mu, scale=std), color='red')\n",
        "plt.xlabel('Value')\n",
        "plt.ylabel('Observed Frequency')\n",
        "plt.legend(['Fitted Distribution PDF', 'Observed Data', ]);"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:3: MatplotlibDeprecationWarning: \n",
            "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
            "  This is separate from the ipykernel package so we can avoid doing imports until\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
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xQNa2gowyqnpGRI4C1XGuONINB9ao6qlM+94TkVTgc+C57KZ8F5HRwGiAhg0b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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YCs7mmcTTGYs",
        "colab_type": "text"
      },
      "source": [
        "2: Exponential Distribution\n",
        "\n",
        "    Given the equations above, write down functions to calculate the MLE estimator λ^\n",
        "\n",
        "of the exponential distribution\n",
        "Given the sample exponentially distributed set, find the maximum likelihood\n",
        "Fit the data to an exponential distribution using SciPy. Compare SciPy's calculated parameter with your calculated values of λ^\n",
        "Plot an exponential distribution PDF with your estimated parameter"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3J99hutVTB5j",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Exponential lambda MLE estimator\n",
        "def exp_lambda(X):\n",
        "    T = len(X)\n",
        "    s = sum(X)\n",
        "    return s/T"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1T3m5TldTNpi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "6b5640dc-4c13-45b4-d90e-48579f9024da"
      },
      "source": [
        "# Exponential distribution sample data\n",
        "TRUE_LAMBDA = 5\n",
        "X = np.random.exponential(TRUE_LAMBDA, 1000)\n",
        "\n",
        "# Use your functions to compute the MLE lambda\n",
        "lam = exp_lambda(X)\n",
        "print (\"Lambda estimate: \", lam)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Lambda estimate:  4.880678279193443\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HGuHleVUTQ0h",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "2ff725c8-1dea-4dbf-e8b2-e95a0bdfdb4e"
      },
      "source": [
        "# Fit the distribution using SciPy and compare that parameter with yours \n",
        "_, l = scipy.stats.expon.fit(X)\n",
        "print ('Scipy lambds estimate: ', l)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Scipy lambds estimate:  4.8773758564994685\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xnDluUJXTXcN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 331
        },
        "outputId": "ba803033-28e5-4f13-e131-5971104df5ec"
      },
      "source": [
        "# Get the PDF, fill it with your calculated parameter, and plot it along x\n",
        "x = range(0, 80)\n",
        "\n",
        "plt.hist(X, bins=x, normed='true')\n",
        "plt.plot(scipy.stats.expon.pdf(x, scale=l), color = 'red')\n",
        "plt.xlabel('Value')\n",
        "plt.ylabel('Observed Frequency')\n",
        "plt.legend(['Fitted Distribution PDF', 'Observed Data', ]);"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:3: MatplotlibDeprecationWarning: \n",
            "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
            "  This is separate from the ipykernel package so we can avoid doing imports until\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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F1gEf1O4j14P0dAB7lKwxplGqcYxDRLrhXALbQVV7ichpOOMej9a0r6ouABZU\naHswaH4ZR3Y9BW/3MvByJe1ZQK+a3ttX7pVVPbbk8WlKus/BGGNM3fLSVfUCcB9QAuBePjs6lEE1\neAkJkJxM92I74zDGND5eEkcLVf2yQltpKIJpVNLS6LElz+8ojDGmznlJHFtF5GTcZ3K4pUE2hzSq\nxiA9nZO3F9Cs9KDfkRhjTJ3ykjhuAZ4HThWRQuAO4KaQRtUYpKcTU3aIbsU/+B2JMcbUKS83AP6g\nqheIyAlAE1W1x9t5ccYZAPTZtJpvO3b1ORhjjKk7Xs441ovIdOBMYHeI42k8TjyRTS3bkVG4yu9I\njDGmTnlJHKcCH+J0Wa0Xkaki8uvQhtU4ZCd1J6PAEocxpnHxcgPgXlV9U1UvA04HWgFLQx5ZI5Cd\n1J2kXcV03FmPRRaNMSbEvIxxICLnAaNwnn2RhVOCxFQiuLBh76TuAPQpXM38Vol+hWSMMXWqxjMO\nEcnHuZLqE6C3qv5WVd8OdWCNwar2qeyNaUZm4Uq/QzHGmDpT7RmH+xS/l1X14XqKp1EpjYrm647d\n6FO42u9QjDGmzlR7xqGqh4Bh9RRLo5Sd1J2eW9bR/OB+v0Mxxpg64WWM41MRmQrMJug5HKqaE7Ko\nGpGspO5EaxlpP37ndyjGGFMnvCSOQHnX4O4qBc6v+3Aan686nQpg3VXGmEajxsShqgPqI5DGakfz\nlnyfcCKZBTZAboxpHLxcVdVBRF4SkQ/c5R4icl3oQ2s8spK602fTaigr8zsUY4w5bl7uHJ+B8xS/\nTu7ydziX59ZIRIaIyBoRWSsiEytZ30xEZrvrvxCRFLd9rIgsD5rKRCTdXbfEPWZgXXsvsfgpJ6k7\nbfbvhjVr/A7FGGOOm5fE0U5V3wTKoPyRsIdq2sm9lHcacBHQAxgjIj0qbHYd8JOqdgGmAE+47zFT\nVdNVNR24GlivqsuD9hsbWK+qRR4+g6+y3RsB+fRTfwMxxpg64CVx7BGRBA4/j+NMYIeH/foBa1U1\nT1UPArOAERW2GQH83Z2fAwwUEamwzRh33wYrLz6J7c1bwWef+R2KMcYcNy+J4y5gHnCyiHwKvArc\n6mG/JGBj0HKB21bpNu6ZzA4gocI2o4A3KrS94nZT/amSRAOAiNwgIlkiklVc7HOtKBGyk061Mw5j\nTKPgpchhDnAe8CvgRqCn+9zxkBORM4C9qroiqHmsqvYGznGnqyvbV1Wnq2qmqmYmJvpfJyo7qQd8\n9x38+KPfoRhjzHHxclXVFUBzVc0FLgVmi0gfD8cuBE4MWk522yrdRkSigdbAtqD1o6lwtqGqhe7r\nLuB1nC6xsPevFPd2mEWL/E0R5YAAABQ+SURBVA3EGGOOk5euqj+p6i73GRwDgZeA5zzstwzoKiKp\nItIUJwnMq7DNPOBad34k8JGqBsZSmuBU4S0f3xCRaBFp587H4JRDWUEDkNvhJEhMhIUL/Q7FGGOO\ni5fEEbiCaijwgqrOB5rWtJM7ZjEB51LeVcCbqporIg+LyHB3s5eABBFZizOWEnzJ7rnARlXNC2pr\nBiwUkW+A5ThnLC94+Ay+U2kCF17oJA67n8MY04B5KTlSKCLPA4OAJ0SkGd4SDqq6AFhQoe3BoPn9\nwBVV7LsE53G1wW17gAwv7x2WhgyBmTMhJwcyM/2OxhhjjomXBPBbnLOGwar6MxAP3BPSqBqrCy90\nXq27yhjTgHl6dCyQD1wkIrcCHVX1/0IdWKPUvj306QP/+IffkRhjzDHzclXVgzg36SUA7XDuoXgg\n1IE1RikT5zO1WRdKP/2M3ne+6Xc4xhhzTLx0VY0F+qrqQ6r6EM64Q6X3TpiafZzah2gt41f5X/sd\nijHGHBMviWMTEBu03Iyj78cwHuV0OpVdTZtz3np7DpYxpmGq8qoqEfkrTn2qHUCuiCxylwcBX9ZP\neI1PaVQ0n6akc+76bFCFyiumGGNM2Kructws9zUbmBvUviRk0USIj1P7MOS7f8Pq1dC9u9/hGGNM\nrVSZOFT17wAiEgt0cZvXuvdemOPwcapbsWXhQkscxpgGp8oxDre8x3/jVLX9O05V3I0i8t9uuQ9z\njApad2BdfLJdlmuMaZCqGxx/Eudmv1RVzVDVPsDJQBvgqfoIrjFbfFIGLF4MO7w82sQYY8JHdYlj\nGHC9W4UWAFXdCdwMXBzqwBq7+aeeAwcPwnvv+R2KMcbUSnWJQwOVais0HsJ9GqA5dl91OgU6d4ZZ\nDfrhhsaYCFRd4lgpItdUbBSRq4DVoQspQojA6NHO8zm2bvU7GmOM8ay6xHELcIuILBGRv7jTUuA2\nnO4qc7xGj4bSUnjnHb8jMcYYz6pMHKpaqKpnAA/jFDnMBx5W1X6Bp/CZ45SWBqecYt1VxpgGpcbn\ncajqR8BH9RBL5Al0Vz38MGzeDB07+h2RMcbUyNMDmY6ViAwRkTUislZEJlayvpmIzHbXfyEiKW57\niojsE5Hl7vS3oH0yRORbd59nRRp4zY5Ro5zSI2+95XckxhjjScgSh4hEAdOAi4AewBgR6VFhs+uA\nn1S1CzAFeCJo3TpVTXenm4LanwOuB7q605BQfYZ60b2702Vl3VXGmAYilGcc/XBKlOSp6kFgFjCi\nwjYjcO5KB5gDDKzuDEJEOgKtVPVz91LhV4FL6z70ejZ6NPz735Cf73ckxhhTo1AmjiRgY9BygdtW\n6TaqWopTiTfBXZcqIl+JyFIROSdo+4IajgmAiNwgIlkiklVcXHx8nyTURo1yXt+0hzsZY8JfSMc4\njsNm4JeqejpwF/C6iLSqzQFUdbqqZqpqZmJiYkiCrDOpqXDGGfDqq854hzHGhLFQJo5C4MSg5WSO\nfgBU+TYiEg20Brap6gFV3QagqtnAOqCbu31yDcdsmG68EXJz4eOP/Y7EGGOqFcrEsQzoKiKpItIU\nGA3Mq7DNPOBad34k8JGqqogkuoPriMhJOIPgeaq6GdgpIme6YyHXAI2j2NPo0RAfD1On+h2JMcZU\nK2SJwx2zmAAsBFYBb6pqrog8LCLD3c1eAhJEZC1Ol1Tgkt1zgW9EZDnOoPlNqrrdXTceeBFYi3Mm\n8kGoPkO9at4crrsO5s6FgoKatzfGGJ9IJXUMG53MzEzNysqqecNKpEycX8fRHJY/eeiRDevXw8kn\nw/33wyOPhOx9jTHGCxHJVtXMiu3hOjgemVJTYdgwmD4dDhzwOxpjjKmUJY5wM2ECFBXBnDl+R2KM\nMZWyxBFuLrgAunaFadP8jsQYYypVY5FDEzoVx0/yJw+FJk3gllvgjjsgOxsyMnyKzhhjKmdnHOFo\n3Dg44QSYMsXvSIwx5iiWOMJR69Ywfjy8/jqsXOl3NMYYcwTrqgojwV1XbQ6czvK4OHjoISu5bowJ\nK3bGEaZ+bt4K7rzTubrqq6/8DscYY8pZ4ghnd90FbdvCn/7kdyTGGFPOEkc4a90a/vhHmD/feV6H\nMcaEAUsc4e7WW6F9e3jgAb8jMcYYwBJHWEuZOJ+UR5YwqfcI+Ogj+PBDv0MyxhhLHA3B6+kXsaF1\nB6ccidWwMsb4zBJHA3AguikPXDge1qzhmfN/55yJhLBqrzHGVMcSRwPx8UkZzO3Rn5s/f4uuxT/4\nHY4xJoJZ4mhAHhl4PbubteC/Fk5FtMzvcIwxESqkiUNEhojIGhFZKyITK1nfTERmu+u/EJEUt32Q\niGSLyLfu6/lB+yxxj7ncndqH8jOEk+0tWvPo+deRWbiKscv/4Xc4xpgIFbLE4T4zfBpwEdADGCMi\nPSpsdh3wk6p2AaYAT7jtW4FLVLU3zjPJX6uw31hVTXenolB9hnD0Ts/z+aRzOvcueQU2bvQ7HGNM\nBArlGUc/YK2q5qnqQWAWMKLCNiOAv7vzc4CBIiKq+pWqbnLbc4HmItIshLE2HCLcP/gWBGDUKDh4\n0O+IjDERJpSJIwkI/pO4wG2rdBtVLQV2AAkVtrkcyFHV4OtQX3G7qf4kIlK3YYe/DW078seLbnfu\nJr/7br/DMcZEmLAeHBeRnjjdVzcGNY91u7DOcaerq9j3BhHJEpGs4uLi0Adbzxac+msnaUydCjNn\n+h2OMSaChDJxFAInBi0nu22VbiMi0UBrYJu7nAzMBa5R1XWBHVS10H3dBbyO0yV2FFWdrqqZqpqZ\nmJhYJx8o7EyeDOeeC9dfD99843c0xpgIEcrEsQzoKiKpItIUGA3Mq7DNPJzBb4CRwEeqqiLSBpgP\nTFTVTwMbi0i0iLRz52OAYcCKEH6G8BYdDbNnQ5s2cPnlsG2b3xEZYyJAyBKHO2YxAVgIrALeVNVc\nEXlYRIa7m70EJIjIWuAuIHDJ7gSgC/BghctumwELReQbYDnOGcsLofoM4S5l4nxSns7msvPvcq6w\nGjwYduzwOyxjTCMnqup3DCGXmZmpWVlZx7RvQyntkX8O8JvfQN++sHAhxMX5HZIxpoETkWxVzazY\nHtaD46YWhg51nlH++ecwYgTs2+d3RMaYRsoSR2MyciTMmAGLFztjHnv3+h2RMaYRivY7AFM3Dnep\nxTP6wluY/I9pcN55MG8edOzoa2zGmMbFzjgaoVnpQ7jusgfY8/UKCk9J46Lf/9XvkIwxjYgljkbq\nn13O4Ldjn6CJlvHWzHvh/ff9DskY00hY4mjEcjuczKXX/IX8tp3gkkvgttts3MMYc9wscTRyW1q2\n4/Kx/w233w5//Sv06QPHeGmyMcaAJY6IcCCmGSmxgxg76lE2bdpGyRlnwv33w+7dfodmjGmALHFE\nkE9T0hny+6nM634uPP44dOsGr7wCZfY0QWOMd5Y4IszO2DjuHnY3l131JDnSCn7/e1Z06gYffAAR\nUEXAGHP8LHFEqJyk7lx21VPcesk9tNm3Ey6+GNLS4H/+B0pK/A7PGBPGLHFEMhH+t8d5DLhhOncN\nvZM1m3fA1VdTmJAEjz4KGzb4HaExJgxZ4jCURMXwTq+BDP79NMaNfIj18Z3gT3+irHMK/0pJ585h\nd1vVXWNMOauOW4OGUh23riXv2MJvVnzEyBX/pPPPPzrP/ujfH4YPd+4JSUnxO0RjTIhVVR3XEkcN\nIjVxlFOlT+Fq3kne6tS9WrUKgA2tO/D5L3vzxYm9+cvUW51E4j7+veLPLH/y0PqO2hhTB6pKHFbk\n0FRPhJzk7qQADD+HlF8XMiAvizM2rmDQ91/w228/hJOmQEICZGZCRgYXrS7ju3ad+aFtR0qj7Ctm\nTGNjZxw1iPgzjmqIltFt6wYW9o1y7kbPyoIVK+DQIQAONolmfXwn1scn8UObjmxs8ws2tO7Aq5Ou\ngBNPtIdNGRPmfDnjEJEhwDNAFPCiqk6usL4Z8CqQAWwDRqlqvrvuPuA64BBwm6ou9HJMU39UmrAm\nMQVuCuqK2rePoTdPp+u2jXTduoFuWzdw8rYCBqzLotkh9zLftx5yXlu3huRk+MUvoEMHZ2rf3jl7\nSUiA+HhnatPG2bZlS2hi13MY47eQJQ4RiQKmAYOAAmCZiMxT1ZVBm10H/KSqXURkNPAEMEpEegCj\ngZ5AJ+BDEenm7lPTMY2fmjcn9xddyP1FlyOaRctov3s7nX/+kTcvTobCQigocKYff3SeXFhUVH0Z\nFBF2xcSyp2nz8um0bp3ghBOgRQtnat4cYmMPT82aOVPTpodfY2IOv8bEOAP/gdfoaIiKOvwaPDVp\ncvi14nyTJs4YT/B8YDkwX93kfr4jlo0JU6E84+gHrFXVPAARmQWMAIL/kx8B/NmdnwNMFRFx22ep\n6gFgvYisdY+Hh2OaMKTShC0t27GlZTtSvgVoAy16QjfIfyfojGXvXs78w1u03b+TNvt20WbfLloe\n2EvLA3todWAPLQ/spUXJfuIO7qPFQffxuFu3OlV/9+51Hpm7f//hqYErw0kiTZoEJZfg14CK7VWt\nr0xttvWyfyhZUq297GynvFAdCmXiSAI2Bi0XAGdUtY2qlorIDiDBbf+8wr5J7nxNxwRARG4AbnAX\nd4vImmP4DADtgK3HuG+ohUVs8sRRTbWKq5L9vcur9R5h8TOrRBVxuWOQZb6ORTawn1lYCJ/YTjkl\neKm2cXWurLHRXvKiqtOB6cd7HBHJqmxwKByEa2zhGheEb2zhGheEb2zhGheEb2x1FVcoRxoLgROD\nlpPdtkq3EZFooDXOIHlV+3o5pjHGmBAKZeJYBnQVkVQRaYoz2D2vwjbzgGvd+ZHAR+pcHzwPGC0i\nzUQkFegKfOnxmMYYY0IoZF1V7pjFBGAhzqWzL6tqrog8DGSp6jzgJeA1d/B7O04iwN3uTZxB71Lg\nFlU9BFDZMUP1GVzH3d0VQuEaW7jGBeEbW7jGBeEbW7jGBeEbW53EFRE3ABpjjKk7djeVMcaYWrHE\nYYwxplYscVRDRIaIyBoRWSsiE32M42URKRKRFUFt8SKySES+d1/b+hTbiSKyWERWikiuiNweDvGJ\nSKyIfCkiX7txTXLbU0XkC/d3Otu9yKLeiUiUiHwlIu+HWVz5IvKtiCwXkSy3LVy+a21EZI6IrBaR\nVSJylt+xicgp7s8qMO0UkTv8jisovjvd7/8KEXnD/Xdx3N81SxxVCCqZchHQAxjjlkLxwwxgSIW2\nicA/VbUr8E932Q+lwN2q2gM4E7jF/Tn5Hd8B4HxVTQPSgSEiciZOWZspqtoF+Amn7I0fbgdWBS2H\nS1wAA1Q1Peh6f79/lwHPAP9Q1VOBNJyfn6+xqeoa92eVjlNzby8w1++4AEQkCbgNyFTVXjgXFAVK\nOx3fd01VbapkAs4CFgYt3wfc52M8KcCKoOU1QEd3viOwxu+fmRvLezi1xMImPqAFkINTZWArEF3Z\n77ge40nG+c/kfOB9QMIhLve984F2Fdp8/13i3OO1HveCnnCKLSiWC4FPwyUuDlfmiMe5gvZ9YHBd\nfNfsjKNqlZVMSapiWz90UNXN7vyPQAc/gwEQkRTgdOALwiA+tztoOVAELALWAT+raqm7iV+/06eB\nPwJl7nJCmMQFTo2T/xORbLdsD4TB7xJIBYqBV9wuvhdF5IQwiS1gNPCGO+97XKpaCDwFbAA2AzuA\nbOrgu2aJoxFQ508HX6+rFpE44G3gDlXdGbzOr/hU9ZA6XQjJOEUyT63vGCoSkWFAkapm+x1LFX6t\nqn1wumhvEZFzg1f6+F2LBvoAz6nq6cAeKnT/+PnvwB0nGA68VXGdX3G54yojcJJuJ+AEju7yPiaW\nOKoW7uVNtohIRwD3tcivQEQkBidpzFTVd8ItPlX9GViMc1rexi1vA/78Ts8GhotIPjALp7vqmTCI\nCyj/KxVVLcLpq+9HePwuC4ACVf3CXZ6Dk0jCITZwEm2Oqm5xl8MhrguA9aparKolwDs437/j/q5Z\n4qhauJc3CS7Xci3O2EK9ExHBqQCwSlX/X9AqX+MTkUQRaePON8cZd1mFk0BG+hWXqt6nqsmqmoLz\nnfpIVcf6HReAiJwgIi0D8zh99isIg++aqv4IbBSRQKnXgTiVJXyPzTWGw91UEB5xbQDOFJEW7r/T\nwM/s+L9rfg0kNYQJuBj4Dqdv/H4f43gDp4+yBOcvr+tw+sX/CXwPfAjE+xTbr3FOw78BlrvTxX7H\nB5wGfOXGtQJ40G0/Cafu2VqcboVmPv5e+wPvh0tcbgxfu1Nu4Dvv9+8yKL50IMv9nb4LtA2H2HC6\ngLYBrYPafI/LjWMSsNr9N/Aa0KwuvmtWcsQYY0ytWFeVMcaYWrHEYYwxplYscRhjjKkVSxzGGGNq\nxRKHMcaYWrHEYUwdcCsED67QdoeIPFfNPrtDH5kxdc8ShzF14w3cRx8HCa5dZEyjYYnDmLoxBxga\neLaBW/CxE/CViPxTRHLc51yMqLijiPQPPJfDXZ4qIuPc+QwRWeoWHVwYKGNhjJ8scRhTB1R1O87d\nuBe5TaOBN4F9wG/UKRw4APiLW/6hRm4NsL8CI1U1A3gZeKyuYzemtqJr3sQY41Ggu+o99/U6nGdt\nPO5WmS3DKWHdAafUdk1OAXoBi9xcE4VTesYYX1niMKbuvAdMEZE+QAtVzXa7nBKBDFUtcavixlbY\nr5Qjz/4D6wXIVdWzQhu2MbVjXVXG1BFV3Y1TefRlDg+Kt8Z5/kaJiAwAOley6w9ADxFp5lb0Hei2\nrwESReQscLquRKRnSD+EMR7YGYcxdesNnOdYBK6wmgn8r4h8i1PZdXXFHVR1o4i8iVPBdD1OVV9U\n9aCIjASeFZHWOP9en8apXGuMb6w6rjHGmFqxripjjDG1YonDGGNMrVjiMMYYUyuWOIwxxtSKJQ5j\njDG1YonDGGNMrVjiMMYYUyv/P4557aHOQSmNAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "30MujfVlTelA",
        "colab_type": "text"
      },
      "source": [
        "3 : Fitting Data Using MLE\n",
        "\n",
        "    Using the MLE estimators laid out in the lecture, fit the returns for SPY from 2014 to 2015 to a normal distribution.\n",
        "    Check for normality using the Jarque-Bera test\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "37y2eppETbEo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "prices = get_pricing('SPY', \n",
        "                     fields='price', \n",
        "                     start_date='2016-01-04', \n",
        "                     end_date='2016-01-05', \n",
        "                     frequency = 'minute')\n",
        "returns = prices.pct_change()[1:]\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5cxpYr6CTfdG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "mu = normal_mu(returns)\n",
        "std = normal_sigma(returns)\n",
        "\n",
        "x = np.linspace(returns.min(), returns.max(), num=1000)\n",
        "h = plt.hist(returns, bins=50, normed='true')\n",
        "l = plt.plot(x, scipy.stats.norm.pdf(x, loc=mu, scale=std), color = 'red')\n",
        "plt.show(h, l);"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xL-cUm3xTup_",
        "colab_type": "text"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GojkK1rhT0Lk",
        "colab_type": "text"
      },
      "source": [
        "Recall that this fit only makes sense if we have normally distributed data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6PaOVXbeTn49",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "alpha = 0.05\n",
        "stat, pval = scipy.stats.mstats.normaltest(returns)\n",
        "print (pval)\n",
        "\n",
        "if pval > alpha: \n",
        "    print ('Accept our null hypothesis')\n",
        "if pval < alpha: \n",
        "    print ('Reject our null hypothesis')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rRIAV1_qUBtW",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "```\n",
        "0.000572927470337\n",
        "Reject our null hypothesis\n",
        "```\n",
        "\n"
      ]
    }
  ]
}