ml-finance-python

notebook.ipynb

(122258B)

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     "# Exercises: Maximum Likelihood Estimation - Answer Key\n",
     "By Christopher van Hoecke, Max Margenot, and Delaney Mackenzie\n",
     "\n",
     "## Lecture Link : \n",
     "https://www.quantopian.com/lectures/maximum-likelihood-estimation\n",
     "\n",
     "### IMPORTANT NOTE: \n",
     "This lecture corresponds to the Maximum Likelihood Estimation lecture, which is part of the Quantopian lecture series. This homework expects you to rely heavily on the code presented in the corresponding lecture. Please copy and paste regularly from that lecture when starting to work on the problems, as trying to do them from scratch will likely be too difficult.\n",
     "\n",
     "Part of the Quantopian Lecture Series:\n",
     "\n",
     "* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n",
     "* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n",
     "\n",
     "Notebook released under the Creative Commons Attribution 4.0 License.\n",
     "\n",
     "----"
    ]
   },
   {
    "cell_type": "markdown",
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    "source": [
     "## Key Concepts\n",
     "Normal Distribution MLE Estimators: \n",
     "\n",
     "$$\n",
     "\\hat\\mu = \\frac{1}{T}\\sum_{t=1}^{T} x_t \\\\\\qquad \\hat\\sigma = \\sqrt{\\frac{1}{T}\\sum_{t=1}^{T}{(x_t - \\hat\\mu)^2}}\n",
     "$$\n",
     "\n",
     "\n",
     "\n",
     "Exponential Distribution MLE Estimators: \n",
     "$$\\hat\\lambda = \\frac{\\sum_{t=1}^{T} x_t}{T}$$"
    ]
   },
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    "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"
    ]
   },
   {
    "cell_type": "markdown",
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    "source": [
     "----"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {
     "deletable": true,
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    },
    "source": [
     "# Exercise 1: Normal Distribution\n",
     "- Given the equations above, write down functions to calculate the MLE estimators $\\hat{\\mu}$ and $\\hat{\\sigma}$ of the normal distribution. \n",
     "- Given the sample normally distributed set, find the maximum likelihood $\\hat{\\mu}$ and $\\hat{\\sigma}$.\n",
     "- Fit the data to a normal distribution using SciPy. Compare SciPy's calculated parameters with your calculated values of $\\hat{\\mu}$ and $\\hat{\\sigma}$.\n",
     "- Plot a normal distribution PDF with your estimated parameters"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 2,
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    "outputs": [],
    "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)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 3,
    "metadata": {
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    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Maximum likelihood value of mu: 39.9907086081\n",
       "Maximum likelihood value for sigma: 10.003042353\n"
      ]
     }
    ],
    "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"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 4,
    "metadata": {
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    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Scipy Maximum likelihood value of mu: 39.9907086081\n",
       "Scipy Maximum likelihood value for sigma: 10.003042353\n"
      ]
     }
    ],
    "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"
    ]
   },
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    "execution_count": 5,
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IlHO5X32FzXffkeHvT0JwMBw9ess+sbGxBiS7M+lVXJjXZwIzvpvJv7Z+yYnorrfd38fH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\nrkJggg==\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7f3ca1a325d0>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "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', ]);"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {
     "deletable": true,
     "editable": true
    },
    "source": [
     "------"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {
     "deletable": true,
     "editable": true
    },
    "source": [
     "# Exercise 2: Exponential Distribution\n",
     "- Given the equations above, write down functions to calculate the MLE estimator $\\hat{\\lambda}$ 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  $\\hat{\\lambda}$\n",
     "- Plot an exponential distribution PDF with your estimated parameter"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 6,
    "metadata": {
     "collapsed": true,
     "deletable": true,
     "editable": true
    },
    "outputs": [],
    "source": [
     "# Exponential lambda MLE estimator\n",
     "def exp_lambda(X):\n",
     "    T = len(X)\n",
     "    s = sum(X)\n",
     "    return s/T"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 7,
    "metadata": {
     "collapsed": false,
     "deletable": true,
     "editable": true
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Lambda estimate:  5.04104991618\n"
      ]
     }
    ],
    "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"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 8,
    "metadata": {
     "collapsed": false,
     "deletable": true,
     "editable": true
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Scipy lambds estimate:  5.03179059849\n"
      ]
     }
    ],
    "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"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 9,
    "metadata": {
     "collapsed": false,
     "deletable": true,
     "editable": true
    },
    "outputs": [
     {
      "data": {
       "image/png": 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+/fXee+9p9uzZzs5nuD3sfAcAAAD4HH9HL/jzn/+s77//XgMHDtS0adPUrl07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\nJRERERERkQb+H88lnJr0HSmoAAAAAElFTkSuQmCC\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7f3ca1110c10>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "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', ]);"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {
     "deletable": true,
     "editable": true
    },
    "source": [
     "----"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {
     "deletable": true,
     "editable": true
    },
    "source": [
     "# Exercise 3 : Fitting Data Using MLE\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"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 10,
    "metadata": {
     "collapsed": true,
     "deletable": true,
     "editable": true
    },
    "outputs": [],
    "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:]"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 11,
    "metadata": {
     "collapsed": false,
     "deletable": true,
     "editable": true
    },
    "outputs": [
     {
      "data": {
       "image/png": 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XaN8LL+i0u8bokWVP6b4R/9T+yNiT7lZ+MF+TZhQoLCqrTm9XVpyn2ZNHKCEhwdXEAOBT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\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7f3cdea793d0>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "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);"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {
     "deletable": true,
     "editable": true
    },
    "source": [
     "Recall that this fit **only** makes sense **if** we have normally distributed data."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 12,
    "metadata": {
     "collapsed": false,
     "deletable": true,
     "editable": true
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "0.000572927470337\n",
       "Reject our null hypothesis\n"
      ]
     }
    ],
    "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'"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {
     "deletable": true,
     "editable": true
    },
    "source": [
     "---\n",
     "\n",
     "Congratulations on completing the Maximum Likelihood Estimation exercises!\n",
     "\n",
     "As you learn more about writing trading models and the Quantopian platform, enter the daily [Quantopian Contest](https://www.quantopian.com/contest). Your strategy will be evaluated for a cash prize every day.\n",
     "\n",
     "Start by going through the [Writing a Contest Algorithm](https://www.quantopian.com/tutorials/contest) tutorial."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {
     "deletable": true,
     "editable": true
    },
    "source": [
     "*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company.  In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*"
    ]
   }
  ],
  "metadata": {
   "kernelspec": {
    "display_name": "Python 2",
    "language": "python",
    "name": "python2"
   },
   "language_info": {
    "codemirror_mode": {
     "name": "ipython",
     "version": 2
    },
    "file_extension": ".py",
    "mimetype": "text/x-python",
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython2",
    "version": "2.7.12"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 2
 }