StockData.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stock Data \n",
    "\n",
    "We  considered  a  five-dimensional  set  of  data  (oil,  S&P  500,  usd/eur,  usd/yuan)  ,i.e.   toknow the dependence structure between oil price, the S& P 500 index and some currencyexchange rates w.r.t USD. The time series data consists of 1000 daily log-returns from May 2016 to April 2020"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "IbyHLa6QdFYs",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     "output_type": "stream",
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     ]
    }
   ],
   "source": [
    "!pip install seaborn\n",
    "!pip install yfinance\n",
    "!pip install matplotlib\n",
    "!pip install copulas\n",
    "!pip install ambhas\n",
    "!pip install copulae\n",
    "!pip install factor_analyzer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "B8-rRyhXi3p6"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "from scipy.stats import invgamma, chi2, t\n",
    "import math\n",
    "import yfinance as yf\n",
    "import seaborn\n",
    "import seaborn as sns; sns.set()\n",
    "from pandas.plotting import register_matplotlib_converters\n",
    "register_matplotlib_converters()\n",
    "from sklearn.datasets import load_iris\n",
    "from factor_analyzer import FactorAnalyzer\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import fmin\n",
    "from scipy.optimize import minimize\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating Test statistic "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "I5AkhOAQmaRN"
   },
   "outputs": [],
   "source": [
    "# Defines required functions \n",
    "\n",
    "# Student T distribution Multivariate random function\n",
    "# Sig - Covariance Matrix for T copula\n",
    "# df - degrees of freedom for T copula\n",
    "# Size - No of samples to be generated\n",
    "def tMultivariate_rand(Sig, df, size):\n",
    "    (m,n) = Sig.shape\n",
    "    s = np.diag(Sig)\n",
    "    s_not_1 = s != 1\n",
    "    if any(s_not_1):\n",
    "        Sig = Sig/np.sqrt(s*s.T)\n",
    "    T = np.linalg.cholesky(Sig)\n",
    "        \n",
    "    ra = np.dot(np.random.randn(size,len(T)),T)\n",
    "    x = np.sqrt(nu/chi2.rvs(df, size=size)[:, np.newaxis])\n",
    "    ra = ra*x    # No need the ./x(:,ones(n,1)) as Python does elem by elem operations\n",
    "    if(df>2):\n",
    "        ra=ra*(df/(df-2))\n",
    "    return ra\n",
    "\n",
    "# This function generates random Student T Copula \n",
    "def tCopula_rand(Rho, nu, d, n):\n",
    "    multiVar = tMultivariate_rand(Rho, d, n)\n",
    "    u = stats.t.cdf(multiVar,nu)\n",
    "    return u\n",
    "\n",
    "# takes i,j and returns index of it in the vectorize function\n",
    "# is used in correlation estimator matrix\n",
    "def indexMappingFunc(i, j):\n",
    "    index = -1\n",
    "    for k in range(1,i):\n",
    "        for l in range(0,k):\n",
    "            index = index+1\n",
    "        \n",
    "    for m in range(0,j+1):\n",
    "        index = index+1\n",
    "    return index\n",
    "\n",
    "# for given i, j get kendalls tau value\n",
    "def kendalls_tau(U, i, j, k, l):\n",
    "    n,d = U.shape\n",
    "    snij = 0\n",
    "    snkl = 0\n",
    "    snijkl = 0 \n",
    "    for p in range(0, n-1):\n",
    "        for q in range(0,p-1):\n",
    "            snij = snij + np.sign((U[p][i]-U[q][i])*(U[p][j]-U[q][j]))\n",
    "            snkl = snkl + np.sign((U[p][k]-U[q][k])*(U[p][l]-U[q][l]))\n",
    "        snijkl = snijkl + (snij*snkl)\n",
    "\n",
    "    snijkl = (snijkl/(n*(n-1)*(n-1)))\n",
    "    snij = ((snij*2)/(n*(n-1)))\n",
    "    snkl = ((snkl*2)/(n*(n-1)))\n",
    "    return snij, snkl, snijkl\n",
    "\n",
    "# Given a multivariate Copula matrix\n",
    "# Generates kendalls estimators\n",
    "def Kendalls_estimators(U):\n",
    "    n,d = U.shape\n",
    "    t = np.identity(d)\n",
    "    dim = int((d*(d-1)/2))\n",
    "    T = np.identity(dim)\n",
    "    snij = 0 \n",
    "    snkl = 0\n",
    "    snijkl = 0\n",
    "    for i in range(1,d):\n",
    "        for j in range(0,i):\n",
    "            for k in range(1,d):\n",
    "                for l in range(0,k):\n",
    "                    snij, snkl, snijkl = kendalls_tau(U, i, j, k, l)\n",
    "                    #print(i, j , k , l)\n",
    "                    t[i][j] = snij\n",
    "                    t[j][i] = snij\n",
    "                    t[k][l] = snkl\n",
    "                    t[l][k] = snkl\n",
    "                    a = indexMappingFunc(i,j)\n",
    "                    b = indexMappingFunc(k,l)\n",
    "                    T[a][b] = snijkl\n",
    "                    T[b][a] = snijkl\n",
    "    return t, T\n",
    "\n",
    "#Vectorize the correlation matrix to a vector with non repeating elements\n",
    "def vectorize(C):\n",
    "    n,n = C.shape\n",
    "    vec = []\n",
    "    for i in range(1,n):\n",
    "        for j in range(0,i):\n",
    "            vec.append(C[i][j])\n",
    "    return vec\n",
    "\n",
    "#Devectorizes a vector to the correlation matrix with non repeating elements\n",
    "def devectorize(arr):\n",
    "    n = len(arr)\n",
    "    d = int(np.sqrt(n*2))+1\n",
    "    C = np.identity(d)\n",
    "    c = 0 \n",
    "    for i in range(1,d):\n",
    "        for j in range(0,i):\n",
    "            C[i][j] = arr[c]\n",
    "            C[j][i] = arr[c]\n",
    "            c = c+1\n",
    "    return C\n",
    "\n",
    "#Generate Kendalls T matrix estimate\n",
    "#Returns a matrix\n",
    "def Kendalls_tau_matrix(T, t, d):\n",
    "    n, n = T.shape\n",
    "    Testimate = np.identity(n)\n",
    "    for i in range(1,d):\n",
    "        for j in range(0,i):\n",
    "            for k in range(1,d):\n",
    "                for l in range(0,k):\n",
    "                    a = indexMappingFunc(i,j)\n",
    "                    b = indexMappingFunc(k,l)\n",
    "                    #print(i,j,k,l,a,b)\n",
    "                    Tval = T[a][b]\n",
    "                    stat = (math.pi*math.pi)*math.cos(math.pi*float(t[i][j])*0.5)*math.cos(math.pi*float(t[k][l])*0.5)*(Tval - t[i][j]*t[k][l])\n",
    "                    Testimate[a][b] = stat\n",
    "                    Testimate[b][a] = stat\n",
    "                    \n",
    "    return Testimate\n",
    "\n",
    "\n",
    "def generateTestStatisticTau(U):\n",
    "    #Estimate kendalls tau and Kendalls estimator matrix\n",
    "    #t -> Kendalls tau matrix\n",
    "    #T -> Kendalls Tau based correlation estimator\n",
    "    t, T = Kendalls_estimators(U)\n",
    "    d, d = t.shape \n",
    "    # Calculate the optimized test statistic\n",
    "    # the Kendalls tau related correlation estimator\n",
    "    # r = sin(pi/2*T) where T is kendals tau matrix\n",
    "    tvec = vectorize(t)\n",
    "    RTau = [(math.pi)*float(i)*0.5 for i in tvec] \n",
    "    #RTau = math.sin((math.pi/2)*float(tvec))\n",
    "    \n",
    "    Testimate = Kendalls_tau_matrix(T, t, d)\n",
    "    TestInv = np.linalg.inv(Testimate)\n",
    "    # Quadratic descrepancy function\n",
    "    # D = ((r-RTau)^T)*(T^-1)*(r-RTau)\n",
    "    #print(len(r))\n",
    "\n",
    "    return RTau, TestInv\n",
    "\n",
    "def generateTestStatisticRho(U, r):\n",
    "    #Estimate kendalls tau and Kendalls estimator matrix\n",
    "    #t -> Kendalls tau matrix\n",
    "    #T -> Kendalls Tau based correlation estimator\n",
    "    t, T = Kendalls_estimators(U)\n",
    "    d, d = t.shape \n",
    "    # Calculate the optimized test statistic\n",
    "    # the Kendalls tau related correlation estimator\n",
    "    # r = sin(pi/2*T) where T is kendals tau matrix\n",
    "    tvec = vectorize(t)\n",
    "    RTau = [(math.pi)*float(i)*0.5 for i in tvec] \n",
    "    #RTau = math.sin((math.pi/2)*float(tvec))\n",
    "    \n",
    "    Testimate = Kendalls_tau_matrix(T, t, d)\n",
    "    TestInv = np.linalg.inv(Testimate)\n",
    "    # Quadratic descrepancy function\n",
    "    # D = ((r-RTau)^T)*(T^-1)*(r-RTau)\n",
    "    #print(len(r))\n",
    "\n",
    "    return r, TestInv\n",
    "\n",
    "\n",
    "def optimfunction(RTau, TestInv, rinit):\n",
    "    #if simulation - use r, otherwise r[i] - variable\n",
    "    \n",
    "    diff = np.array([rinit[i]-RTau[i] for i in range(0,len(rinit))])\n",
    "    return ((diff).transpose()*TestInv*(diff)).min()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stock Data \n",
    "\n",
    "We  considered  a  five-dimensional  set  of  data  (oil,  S&P  500,  usd/eur,  usd/yuan). \n",
    "Download the corresponding data from yahoo finance and get the log returns.\n",
    "Each security's data is downloade and plotted to understand the patterns in the last 5 years. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 548
    },
    "colab_type": "code",
    "id": "Wy6SAuk6HqHG",
    "outputId": "5037b021-3b0d-401a-9e4e-ae0dc1daf5fa"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/greeshmab/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:9: RuntimeWarning: invalid value encountered in log\n",
      "  if __name__ == '__main__':\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Get real data for oil, S&P500, eur and usd\n",
    "\n",
    "#Oil Prices\n",
    "oilt = yf.Ticker(\"CL=F\")\n",
    "#print(oilt.info)\n",
    "oilC = oilt.history(period=\"1500d\")['Close'].pct_change()\n",
    "oilLog = np.log(1+oilC).to_frame()\n",
    "\n",
    "#S&P500\n",
    "SnP500t = yf.Ticker(\"^GSPC\")\n",
    "#print(SnP500t.info)\n",
    "SnP500C = SnP500t.history(period=\"1500d\")['Close'].pct_change()\n",
    "SnP500Log = np.log(1+SnP500C).to_frame()\n",
    "\n",
    "\n",
    "#USD/EUR Exchange rate\n",
    "UsdEurt = yf.Ticker(\"USDEUR=X\")\n",
    "#print(UsdEurt.info)\n",
    "UsdEurC = UsdEurt.history(period=\"1500d\")['Close'].pct_change()\n",
    "UsdEurLog = np.log(1+UsdEurC).to_frame()\n",
    "\n",
    "#Gold Prices\n",
    "Goldt = yf.Ticker(\"GC=F\")\n",
    "#print(Goldt.info)\n",
    "GoldC = Goldt.history(period=\"1500d\")['Close'].pct_change()\n",
    "GoldLog = np.log(1+GoldC).to_frame()\n",
    "\n",
    "#USD Yuan exchange rate\n",
    "UsdYuant = yf.Ticker(\"USDCNY=X\")\n",
    "#print(UsdYuant.info)\n",
    "UsdYuanC = UsdYuant.history(period=\"1500d\")['Close'].pct_change()\n",
    "UsdYuanLog = np.log(1+UsdYuanC).to_frame()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data downloaded for each security is then converted into Dataframe in order to process. \n",
    "All the missing data with values NA is removed i.e all the data for 5 securities for the date on which the data is missing is deleted. \n",
    "\n",
    "We plotted data for last 3 months to understand COVID 19 effect. It can be clearly noticed that Gold is bullish where as oil and market are down. There aren't any significant pattern in exchange rates since all the major economies are affected similarly due to this pandemic. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 232
    },
    "colab_type": "code",
    "id": "U7t8Ytxf15FP",
    "outputId": "e8739d48-b515-4561-8f96-a89dd2f97607"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1002, 5)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Data is missing for some dates - hence merge it by date as key\n",
    "df = pd.concat([oilLog['Close'], SnP500Log['Close'], UsdEurLog['Close'], GoldLog['Close'], UsdYuanLog['Close']], axis=1)\n",
    "# Drop NA values\n",
    "df.dropna(inplace = True) \n",
    "#Returns (1223, 5)\n",
    "#Removing 223 days to get matrix of size 1000\n",
    "dfa = df.iloc[223:]\n",
    "dfa.columns = ['oil', 'SnP500', 'Usd/Eur', 'Gold', 'Usd/Yuan']\n",
    "#Convert the data into matrix for the analysis\n",
    "retDf = dfa.to_numpy()\n",
    "\n",
    "print(retDf.shape)  #Returns (1000, 5)\n",
    "#print(dfa.head)\n",
    "\n",
    "dfarecent = dfa[:][950:]\n",
    "\n",
    "plt.plot(dfa['oil'], '-b', label='oil')\n",
    "plt.plot(dfa['SnP500'], '-r', label='SnP')\n",
    "plt.plot(dfa['Usd/Eur'],'-g', label='Usd/Eur')\n",
    "plt.plot(dfa['Gold'], '-y', label='Gold')\n",
    "plt.plot(dfa['Usd/Yuan'], '-p', label='Usd/Yuan')\n",
    "fig = plt.figure()\n",
    "(dfarecent + 1).cumprod().plot()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Goodness of Fit test\n",
    "Before we apply our method to real life data, we must either verify or falsifying the assumption of an elliptical copula. For the parametric tests dependence structure of a data set is really app Information criteria, such as Akaike's informa about the power of the decision rule that is em been suggested by various researchers and we (2007) for discussions of existing methods. We tried to fit both normal and t-copula for the whole data set and tested goodness of fitGoodness of fit is done using Parametric bootstrap goodness-of-fit test with Kendall KStest and normal copula and t copula."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0uVfTVViH1NT"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian Copula Summary\n",
      "================================================================================\n",
      "Gaussian Copula with 5 dimensions\n",
      "\n",
      "\n",
      "Parameters\n",
      "--------------------------------------------------------------------------------\n",
      " Correlation Matrix \n",
      " 1.000000  0.134054 -0.012386  0.083699  0.000792\n",
      " 0.134054  1.000000 -0.057918 -0.126398 -0.010113\n",
      "-0.012386 -0.057918  1.000000 -0.033851  0.363483\n",
      " 0.083699 -0.126398 -0.033851  1.000000 -0.014861\n",
      " 0.000792 -0.010113  0.363483 -0.014861  1.000000\n",
      "\n",
      "\n",
      "\n",
      "                                  Fit Summary                                   \n",
      "================================================================================\n",
      "Log. Likelihood      : -94.1307355870704\n",
      "Variance Estimate    : Not Implemented Yet\n",
      "Method               : Maximum pseudo-likelihood\n",
      "Data Points          : 1002\n",
      "\n",
      "Optimization Setup\n",
      "--------------------------------------------------------------------------------\n",
      "\tbounds         : [(-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001)]\n",
      "\toptions        : {'maxiter': 20000, 'ftol': 1e-06, 'iprint': 1, 'disp': False, 'eps': 1.5e-08}\n",
      "\tmethod         : SLSQP\n",
      "\n",
      "Results\n",
      "--------------------------------------------------------------------------------\n",
      "\tx              : [ 0.13405411 -0.01238593  0.08369944  0.00079229 -0.05791786 -0.12639838\n",
      " -0.01011319 -0.03385062  0.36348308 -0.01486095]\n",
      "\tfun            : -94.1307355870704\n",
      "\tjac            : [ 0.0002558  -0.00040359 -0.00048885  0.00067359  0.00055328 -0.00049738\n",
      " -0.00116434 -0.00041117 -0.00016295  0.00082802]\n",
      "\tnit            : 14\n",
      "\tnfev           : 194\n",
      "\tnjev           : 14\n",
      "\tstatus         : 0\n",
      "\tmessage        : Optimization terminated successfully.\n",
      "\tsuccess        : True\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from copulae import NormalCopula\n",
    "from copulae import TCopula\n",
    "import numpy as np\n",
    "\n",
    "np.random.seed(8)\n",
    "#data = np.random.normal(size=(300, 8))\n",
    "cop = NormalCopula(5)\n",
    "cop.fit(retDf)\n",
    "\n",
    "cop.random(10)  # simulate random number\n",
    "\n",
    "# getting parameters\n",
    "p = cop.params\n",
    "# cop.params = ...  # you can override parameters too, even after it's fitted!  \n",
    "\n",
    "# get a summary of the copula. If it's fitted, fit details will be present too\n",
    "print(cop.summary())\n",
    "\n",
    "# overriding parameters, for Elliptical Copulae, you can override the correlation matrix\n",
    "cop[:] = np.eye(8)  # in this case, this will be equivalent to an Independent Copula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Student Copula Summary\n",
      "================================================================================\n",
      "Student Copula with 5 dimensions\n",
      "\n",
      "\n",
      "Parameters\n",
      "--------------------------------------------------------------------------------\n",
      " Degree of Freedom  : 8.223078185479086\n",
      "\n",
      " Correlation Matrix \n",
      " 1.000000  0.188386 -0.014565  0.075615  0.012343\n",
      " 0.188386  1.000000 -0.050432 -0.126084 -0.033721\n",
      "-0.014565 -0.050432  1.000000 -0.030203  0.359785\n",
      " 0.075615 -0.126084 -0.030203  1.000000 -0.003216\n",
      " 0.012343 -0.033721  0.359785 -0.003216  1.000000\n",
      "\n",
      "\n",
      "\n",
      "                                  Fit Summary                                   \n",
      "================================================================================\n",
      "Log. Likelihood      : -149.52314045577384\n",
      "Variance Estimate    : Not Implemented Yet\n",
      "Method               : Maximum pseudo-likelihood\n",
      "Data Points          : 1002\n",
      "\n",
      "Optimization Setup\n",
      "--------------------------------------------------------------------------------\n",
      "\tbounds         : [(0.0, inf), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001), (-1.000001, 1.000001)]\n",
      "\toptions        : {'maxiter': 20000, 'ftol': 1e-06, 'iprint': 1, 'disp': False, 'eps': 1.5e-08}\n",
      "\tmethod         : SLSQP\n",
      "\n",
      "Results\n",
      "--------------------------------------------------------------------------------\n",
      "\tx              : [ 8.22307819e+00  1.88386191e-01 -1.45649172e-02  7.56149233e-02\n",
      "  1.23427246e-02 -5.04317970e-02 -1.26084058e-01 -3.37213237e-02\n",
      " -3.02027442e-02  3.59784582e-01 -3.21592214e-03]\n",
      "\tfun            : -149.52314045577384\n",
      "\tjac            : [ 0.00023116 -0.00317944  0.00221689 -0.00020464 -0.00289712 -0.00226047\n",
      "  0.00022358  0.00283838  0.00150635 -0.00346366  0.00019706]\n",
      "\tnit            : 18\n",
      "\tnfev           : 262\n",
      "\tnjev           : 18\n",
      "\tstatus         : 0\n",
      "\tmessage        : Optimization terminated successfully.\n",
      "\tsuccess        : True\n",
      "\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(8)\n",
    "#data = np.random.normal(size=(300, 8))\n",
    "cop = TCopula(5)\n",
    "cop.fit(retDf)\n",
    "\n",
    "cop.random(10)  # simulate random number\n",
    "\n",
    "# getting parameters\n",
    "p = cop.params\n",
    "# cop.params = ...  # you can override parameters too, even after it's fitted!  \n",
    "\n",
    "# get a summary of the copula. If it's fitted, fit details will be present too\n",
    "print(cop.summary())\n",
    "\n",
    "# overriding parameters, for Elliptical Copulae, you can override the correlation matrix\n",
    "cop[:] = np.eye(8)  # in this case, this will be equivalent to an Independent Copula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from factor_analyzer.factor_analyzer import calculate_kmo\n",
    "from sklearn import decomposition\n",
    "from sklearn.decomposition import FactorAnalysis\n",
    "from scipy.stats import pearsonr\n",
    "import pandas as pd\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test Statistic Calculations\n",
    "In order to calculate the optimal min value of test statistic, we used python SciPyoptimize and fmin() function. It uses a Nelder-Mead simplex algorithm to find theminimum of function of one or more variables.•For the initial value, we used Factor Analysis from sklearn.  decomposition FactorAnalysis which is a simple linear generative model with Gaussian Latent Variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigen values are :\n",
      "[1.36185594 1.17395184 0.96206576 0.87021357 0.63191289]\n",
      "Corellation matrix is: \n",
      "               oil    SnP500   Usd/Eur      Gold  Usd/Yuan\n",
      "oil       1.000000 -0.093590  0.020592  0.114331 -0.010169\n",
      "SnP500   -0.093590  1.000000 -0.068356 -0.045525  0.037782\n",
      "Usd/Eur   0.020592 -0.068356  1.000000 -0.055147  0.350542\n",
      "Gold      0.114331 -0.045525 -0.055147  1.000000 -0.032148\n",
      "Usd/Yuan -0.010169  0.037782  0.350542 -0.032148  1.000000\n",
      "(1002, 5)\n"
     ]
    }
   ],
   "source": [
    "fa = FactorAnalyzer()\n",
    "fa.fit(retDf)\n",
    "#fa.analyze(df, 25, rotation=None)\n",
    "# Check Eigenvalues\n",
    "ev, v = fa.get_eigenvalues()\n",
    "print(\"Eigen values are :\")\n",
    "print(ev)\n",
    "\n",
    "\n",
    "print(\"Corellation matrix is: \")\n",
    "#Sklearn function does not standarize your data while R facanal() does\n",
    "r = dfa.corr(method='pearson')\n",
    "\n",
    "print(r)\n",
    "print(retDf.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/greeshmab/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:7: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  import sys\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "10\n",
      "(10, 10)\n",
      "T tau value is\n",
      "9.039817759341588\n",
      "T rho value is\n",
      "7.813051044949247\n"
     ]
    }
   ],
   "source": [
    "factor = decomposition.FactorAnalysis(n_components=2)\n",
    "factor.fit(retDf)\n",
    "L = factor.components_\n",
    "R = L.transpose().dot(L)\n",
    "\n",
    "#Rvec is the vectorized version of correlation matrix\n",
    "rvec = vectorize(r.as_matrix())\n",
    "\n",
    "#rinit is the inintializer of loadings that are derived from standard factor analysis\n",
    "#using  sklearn.decomposition import FactorAnalysis\n",
    "\n",
    "rinit = vectorize(R)\n",
    "Rtau, Testinv = generateTestStatisticTau(retDf)\n",
    "\n",
    "RRho, Testinv = generateTestStatisticRho(retDf, rvec)\n",
    "\n",
    "#Use optim function to minimize the T statistic and optimize the R(v) values\n",
    "#We get factor loadings by building back R matrix and doing choleskey decomposition\n",
    "\n",
    "print(len(Rtau))\n",
    "print(len(rvec))\n",
    "print(Testinv.shape)\n",
    "\n",
    "print(\"T tau value is\")\n",
    "print(-1000*optimfunction(Rtau, Testinv, rinit))\n",
    "\n",
    "restau = fmin(optimfunction, rinit, args=(Rtau, Testinv), full_output=True,disp=False)\n",
    " \n",
    "print(\"T rho value is\")\n",
    "\n",
    "\n",
    "print(-1000*optimfunction(rvec, Testinv, rinit))\n",
    "\n",
    "resrho = fmin(optimfunction, rinit, args=(rvec, Testinv), full_output=True,disp=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([-4.31133600e-05,  3.91897053e-06, -2.80073395e-06,  3.16307833e-05,\n",
      "       -5.93361490e-06, -1.83784998e-06, -2.21627370e-06, -3.70247077e-07,\n",
      "        4.36199603e-06, -1.28794459e-06]), -0.0012430295172522223, 1, 11, 0)\n",
      "(array([-4.31133600e-05,  3.91897053e-06, -2.80073395e-06,  3.16307833e-05,\n",
      "       -5.93361490e-06, -1.92974248e-06, -2.21627370e-06, -3.52616264e-07,\n",
      "        4.36199603e-06, -1.28794459e-06]), -0.002152727500441127, 1, 11, 0)\n",
      "[[ 1.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00]\n",
      " [-4.31133600e-05  9.99999999e-01  0.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00]\n",
      " [ 3.91897053e-06 -2.80056499e-06  1.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00]\n",
      " [ 3.16307833e-05 -5.93225120e-06 -1.83799056e-06  9.99999999e-01\n",
      "   0.00000000e+00]\n",
      " [-2.21627370e-06 -3.70342628e-07  4.36200367e-06 -1.28786867e-06\n",
      "   1.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "print(restau)\n",
    "print(resrho)\n",
    "\n",
    "LLt = devectorize(restau[0])\n",
    "L = np.linalg.cholesky(LLt)\n",
    "print(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/greeshmab/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:7: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  import sys\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "10\n",
      "(10, 10)\n",
      "T tau value is\n",
      "9.039816973853851\n",
      "T rho value is\n",
      "7.813050314702046\n"
     ]
    }
   ],
   "source": [
    "factor = decomposition.FactorAnalysis(n_components=3)\n",
    "factor.fit(retDf)\n",
    "L = factor.components_\n",
    "R = L.transpose().dot(L)\n",
    "\n",
    "#Rvec is the vectorized version of correlation matrix\n",
    "rvec = vectorize(r.as_matrix())\n",
    "\n",
    "#rinit is the inintializer of loadings that are derived from standard factor analysis\n",
    "#using  sklearn.decomposition import FactorAnalysis\n",
    "\n",
    "rinit = vectorize(R)\n",
    "Rtau, Testinv = generateTestStatisticTau(retDf)\n",
    "\n",
    "RRho, Testinv = generateTestStatisticRho(retDf, rvec)\n",
    "\n",
    "#Use optim function to minimize the T statistic and optimize the R(v) values\n",
    "#We get factor loadings by building back R matrix and doing choleskey decomposition\n",
    "\n",
    "print(len(Rtau))\n",
    "print(len(rvec))\n",
    "print(Testinv.shape)\n",
    "\n",
    "print(\"T tau value is\")\n",
    "print(-1000*optimfunction(Rtau, Testinv, rinit))\n",
    "\n",
    "restau2 = fmin(optimfunction, rinit, args=(Rtau, Testinv), full_output=True,disp=False)\n",
    " \n",
    "print(\"T rho value is\")\n",
    "\n",
    "\n",
    "print(-1000*optimfunction(rvec, Testinv, rinit))\n",
    "\n",
    "resrho2 = fmin(optimfunction, rinit, args=(rvec, Testinv), full_output=True,disp=False)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get optimal vec(R) value. We need to devectorize to get the R - correlation matrix. We then do the SVD decomposition to get the Factor loadings and plot them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loadings for factor 1 \n",
      "[-0.6875042   0.57216751 -0.05854416 -0.4423809   0.02887962]\n",
      "Loadings for factor 2 \n",
      "[ 0.00074961 -0.14855539  0.70427659 -0.24408106  0.64988434]\n",
      "Eigen values for SVD decomposition\n",
      "[[1.00005666 0.         0.         0.         0.        ]\n",
      " [0.         1.00000529 0.         0.         0.        ]\n",
      " [0.         0.         0.99999627 0.         0.        ]\n",
      " [0.         0.         0.         0.99999265 0.        ]\n",
      " [0.         0.         0.         0.         0.99994913]]\n"
     ]
    }
   ],
   "source": [
    "#Gets the spearmans correlation estimator and SVD analysis gives factor loadings\n",
    "temp = devectorize(resrho[0])\n",
    "u,s,vh = np.linalg.svd(temp)\n",
    "\n",
    "print(\"Loadings for factor 1 \")\n",
    "print(u[:,0])\n",
    "\n",
    "print(\"Loadings for factor 2 \")\n",
    "print(u[:,1])\n",
    "\n",
    "print(\"Eigen values for SVD decomposition\")\n",
    "print(np.diag(s))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loadings for factor 1 \n",
      "[ 0.68747374 -0.57213162  0.05927117  0.44239325 -0.02864281]\n",
      "Loadings for factor 2 \n",
      "[-1.95479812e-04 -1.46594498e-01  7.03217077e-01 -2.41249587e-01\n",
      "  6.52529229e-01]\n",
      "Eigen values for SVD decomposition\n",
      "[[1.00005666 0.         0.         0.         0.        ]\n",
      " [0.         1.00000526 0.         0.         0.        ]\n",
      " [0.         0.         0.99999623 0.         0.        ]\n",
      " [0.         0.         0.         0.99999271 0.        ]\n",
      " [0.         0.         0.         0.         0.99994913]]\n"
     ]
    }
   ],
   "source": [
    "#Gets the Kendalls correlation estimator and SVD analysis gives factor loadings\n",
    "\n",
    "temp = devectorize(restau[0])\n",
    "u,s,vh = np.linalg.svd(temp)\n",
    "\n",
    "print(\"Loadings for factor 1 \")\n",
    "print(u[:,0])\n",
    "\n",
    "print(\"Loadings for factor 2 \")\n",
    "print(u[:,1])\n",
    "\n",
    "print(\"Eigen values for SVD decomposition\")\n",
    "print(np.diag(s))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the initial value, we used Factor Analysis from sklearn.  decomposition FactorAnalysis which is a simple linear generative model with Gaussian Latent Variables.\n",
    "* For Factor 1 : We can observe that both exchange currency rates are near zero. But oil,gold are negative. S&P500 which is a benchmark index is positive. We can interpretthis as a commodity factor\n",
    "* For Factor 2: We see that both exchange rates are negative , near to -1. Whereasthe oil, SnP500 and gold are near zero. This is a factor which is not even tracked bybenchmark. We can call this as currency factor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Factor 1\n",
    "df1 = pd.DataFrame({\"stock\": ['oil', 'SnP500','Usd/Eur','Gold','Usd/Yuan'],\n",
    "                   \"Tau\" : [-0.68894582, 0.48562668, -0.06074125, -0.53442184, 0.01497244],\n",
    "                   \"Rho\" : [-0.68900362, 0.48564336, -0.05955055, -0.53446329, 0.01507526] })\n",
    "df2 = pd.DataFrame({\"stock\": ['oil', 'SnP500','Usd/Eur','Gold','Usd/Yuan'],\n",
    "                   \"Tau\" : [0.00230484, 0.2025604, -0.73951464, 0.2485645,  -0.59185957],\n",
    "                   \"Rho\" : [0.00124429,  0.20623856, -0.74066372,  0.25174185, -0.58779877] })\n",
    "df1.plot(x=\"stock\", y=[\"Tau\", \"Rho\"], style='-o', title = \"Factor 1\")\n",
    "plt.show()\n",
    "df2.plot(x=\"stock\", y=[\"Tau\", \"Rho\"], style='-o', title = \"Factor 2\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "machine_shape": "hm",
   "name": "517Project_Stockdata.ipynb",
   "provenance": []
  },
  "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}