180214_Test_model_data-Copy1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TEST INPUT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from pandas import DataFrame as df\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from pylab import rcParams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "filename = 'fed_data.xlsx'\n",
    "xls = pd.ExcelFile(filename)\n",
    "CA_raw = pd.read_excel(xls, 'CA')\n",
    "DM_raw = pd.read_excel(xls, 'DM')\n",
    "JA_raw = pd.read_excel(xls, 'JA')\n",
    "UK_raw = pd.read_excel(xls, 'UK')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def T3(dum_data, Table3_Currency_Vol, row):\n",
    "    returns = 100*np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "    subperiod = 4\n",
    "    Table3_Currency_Vol.loc[row,'Entire'] = float(np.std(returns))\n",
    "    for i in range(0,subperiod):\n",
    "        sub_data = dum_data['Column2']\n",
    "        #print('i = ' + str(i))\n",
    "        #print('from : ',int(np.floor(i*len(returns)/subperiod)))\n",
    "        #print('to   : ',int(np.floor((i+1)*len(returns)/subperiod)))\n",
    "        sub_data = sub_data.iloc[int(np.floor(i*len(returns)/subperiod)):int(np.floor((i+1)*len(returns)/subperiod))]\n",
    "        returns2 = 100*np.log(1+sub_data.pct_change().dropna())\n",
    "        Table3_Currency_Vol.iloc[row,i+1] = float(np.std(returns2))\n",
    "        \n",
    "    return Table3_Currency_Vol\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Table3_Currency_Vol = df()\n",
    "Table3_Currency_Vol['Entire']=[]\n",
    "Table3_Currency_Vol['Sub1']=[]\n",
    "Table3_Currency_Vol['Sub2']=[]\n",
    "Table3_Currency_Vol['Sub3']=[]\n",
    "Table3_Currency_Vol['Sub4']=[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Entire</th>\n",
       "      <th>Sub1</th>\n",
       "      <th>Sub2</th>\n",
       "      <th>Sub3</th>\n",
       "      <th>Sub4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.664101</td>\n",
       "      <td>0.586819</td>\n",
       "      <td>0.716642</td>\n",
       "      <td>0.708206</td>\n",
       "      <td>0.635449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.656566</td>\n",
       "      <td>0.544619</td>\n",
       "      <td>0.639886</td>\n",
       "      <td>0.645119</td>\n",
       "      <td>0.775137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.606847</td>\n",
       "      <td>0.485806</td>\n",
       "      <td>0.724471</td>\n",
       "      <td>0.699407</td>\n",
       "      <td>0.472817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.274376</td>\n",
       "      <td>0.220132</td>\n",
       "      <td>0.254553</td>\n",
       "      <td>0.284356</td>\n",
       "      <td>0.326698</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Entire      Sub1      Sub2      Sub3      Sub4\n",
       "0  0.664101  0.586819  0.716642  0.708206  0.635449\n",
       "1  0.656566  0.544619  0.639886  0.645119  0.775137\n",
       "2  0.606847  0.485806  0.724471  0.699407  0.472817\n",
       "3  0.274376  0.220132  0.254553  0.284356  0.326698"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw = [DM_raw, JA_raw, UK_raw, CA_raw]\n",
    "for row in range(0, len(raw)):\n",
    "    Table3_Currency_Vol = T3(raw[row], Table3_Currency_Vol, row)\n",
    "Table3_Currency_Vol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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WPzecu89sg6+vPsK6GdS4djXGXti52Pt/7of1Ppff979VnP2fBT7XWWzVUx97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\n2DbHvLb/QHKzYeaD7o2AhjwJ854vnI4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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fa47d7da90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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aew8A+znnBznnpQC+BXCjCe0SBEEQOjBDsDcCICyikO/eRhAEQVhAyJynjLGx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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fa481cd630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Tz/tz8dR3+/DPnw9oO5DM76Een96MU4W6Xdi+21l9oSmrqMLbqw973V/t8ody74J9eWVF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\njdcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fa48223a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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D4QseJ/U9/Pku/WzQ6Lcsr+CYtlT6uIephD2AlN2JxKkrUFDsnB2y888r2Jl9pcp7Gw9f\nxEoZmRG/HlGWXWMrbqUFq/d7P81uccYZPPz5LnvWjZTLbubyg5i79qih9X68gRmLhF0pLMEzi7Lc\nVkq8dOMWEqeuwC7BPbE44wz+/kUGFmt4vUrF9iyZvmy/Jtf4kfMF+G6n9EwlUwm7GS4pNdX8pJB/\ns1R24aELEmO+D3+xC49/84cSs2TxnYYV6yZ8/Ydm2TWcc0klFxwzPqRcd1/8lg0AHntJt8qqXzjx\nxq0y3Lil31yCd9YdxdLMXCzZ7XrW9a4/LYK+YEtlieSz1yz3Te41bcdMikvLPX5foae+5sAFN1vq\ng6mE3Qws33MWx3Sc/pw2cy1G/Os3WfvIjbnm3yzF2gPGlQgWo6KC41pRCeZvPuG0ipOamuc28m+W\nImnaSnwqYRq+noiVN1AbM//q92zF+y7YKq0WvA0lzlXKy2uQ8vIaBXtqj1BQ7READQYtPt18EuP/\nkwEAuPP9rR6/r9ED5tVe2MV+gLfW6Fu86NA51xNsrhaWYOS/RMrZyrhSnvouE+O/2o2HP1c+Q3X4\nh9swaaG83sutsqrT/csruD3c8a9Nx9H+lXWis2kDA9T31dJmrgUALNplTP1rd9h+uVtl5ZJq8jv+\n1C/9dEDRcQuKS/Hqfw9K3j7napGsipGJU1dgiof5EG+sdv69lXKlsASLRX7fjzadwP8Keqq2XrFN\n14V+wwcbjuG+T7fLPvaslYew1jqZ6/jFGx63NzrBwFTCLgzvGfnEMyLMmDh1BVJeXoNlmblO077l\nctrqNW5UGEMHLIOrP2WdlbVPyxmr0X125YIeL/+8H2kz16K4tNx+U4gRFOC9y3CbyBqfcuLKtpo9\njqzYew4bDrvvcr+1+ggmfL0bv51wtuHxb7SN3a8/eAGp/1wrax+53j3geblFLVOY560/hik/7MUJ\nh9/A8eGRNnMthr63BTZ/QejFz117FL+duCzruN6qe7/t+CUs/UObIn9BmrTiw5hprOjGrTKcvOTC\nGzCToW64LKg0+FOm5cFQ4iH7ZmlmDganNNDVLgD47fgl3P+ZulUbObcUJ4urVaPK+7bVl1xRUlaB\nz6zCmS9SX37lvkpPXgufRkmd8UCV19jKfecwNDVOVRtSkJLNdTKv0P7AVhvp6zd3k+j75/JvIufq\nTXROjAHnHGUVHMHWeQBCx9Q27lNWXoEV+87h7rSGos6E7doc2THe6TO5P42pPHYhO/+84nkjDTA6\nFubIvlwXYRoZhkotQfzofzI8lrx1t1jC2Ws3Ue7mrimQOKA2c7n0cIFSZq88hOV75fVAXPH5tmwk\nTl2Bw+el16wRVqr0xiWXfVm+lxmoMofdGwP3nhDeJnJD7AfPXhd96LpiwNxfMerj31FRwTH9x/1I\nnr7K3msT9hJ+zDqLnKtF+Gzrn5i0MAvLvLCAuGmF/dejeYZN79ZyFuRLP+5H+1ekd4nFsjr0XMpu\nv8jycsLCWO4WS8gruIU3JcZQPZ3RP05pU47Y1T38yeaTLrN55P7aq6zpa9uOXwbn3OPDkXMgSGRG\npy0baF+Otkv8AUCRgjkOjh67WMjIE+UV3GXm0P+ttVxLvxy6oCqLZvPRPGw5lmfxkh28d2HIz3bt\nSs0lH/reFoz6RHpig21C5Ycbj+PbHZZUxL9/YRlgdTxkrzc2Ys4qy71yRUb9/J/3nFV0fZhW2AHt\nJ2oUlZQhbebaKjPN9I5wfLX9FK7J8ALEPOC7Ptiqu6Fnr920x1g7z1rvYetKpMzak+IxeQplAMpP\nQc5V98Irt90zVyze97qD55E0bSV6v7nR4z5BDgPEO/+8gvTX1mPm8gOW39cEOM4j+WaH/AqPkxdl\nofU/Vot+9v6G4zh1uRCPfJmB5xZXDrrOWXUYP2VJ92JfX3kYDy7YiU82n0Tz6atk2+iOoxc8D4w6\nolW1UTGe+i5T0fVRrWLsJ/MKkX+zFG+uPoL2CdEAxEXH2+FsodfsMrKhc8zo71/swuHzBWgSEy5r\nv7IKjhu3yvBnnvuu/0kNBqDEehdOx8mzLB9oi2HmXC1CrzfcC6/SU7v9pPRwoWPmj+27fL4t261B\ncrw7wOLNHnSTdeWODzaqX6N0+R734a5C68LewlDRx79aBliHt28k61hSJ8oxMEz9YS+2CXoget7i\nc9cc0bSOEiBfk0wt7FoXhlIr2EUlZRj9yXbMHpmqmW17c67h7g8q0xvdpULqiW2xiketubpyeOzL\nDPx+0nWmwf2fbddkMYx/SEz7233qKmrWCEaL+lH460eeu9andV5aj4M7DfhJvRYzsuWNNT3k44uw\nlFdwvLL8AB7t3RQJHpyMEx6cCRtFJWVY6JAm6fgsT56uejVPO54ekN6Y3WvqUEyebgvNVv6sYufY\n1XnPPH0N+3LzMWvFIbdhIrHYnytGffy7pO0On3eeNFVQXCprAM8dahbJ3n36qtvP97saENaJez7+\n3b4U24Xrnq+hix4WHZETJhCFA91nb5C8+S+HK8NbE7/Vdya0O1bsPYfTInVztOT2d36t8veenGv4\n8vdTsudQuOM/EhbwLi03NotC9TXmgKmFveecDZoOoIp52XL0TMpz9u21R5A0bSWaT1/lNjtl3np5\n6Whi8c6J32bal4/bfcq9uLri0o1byL9ZikIJg21yBrykPtj0RKtFrpWkDrrjxq0yt72ETYL5B0Yv\nOPO6TtUHbTjGtG0OhvBbf7PDszDLRanPrEdO+8WCYvvAqlaYWtgBoKzC+wIhzCkWw93N9t6Gym5Y\nfxf5r4BlsoWW7FW4yPVLPx1Al1nrXS5DJ2S42CCOi1PRR8KAot5IGdSUwimNvdYpS/aKx9ZFMNqT\nXH3gvG51YNz1EoXCq0HFCedjK9zv6cXaLy7TY/YGjw8auaFf0wu7XgswXLUOSrkKu4gO1Jl4jpBY\nOp1UbknsFbmMaTrcJTduleFsvraFl3wZOdP0zch8wWIQm45cROLUFZrUU/J2iE4ORSVlmLZ0Hx5c\nUHVCW6bIrPDVMusyvfrfg1iWWTnDtKyCax53N0zYn1mU5ZSfeT7fczz0SmEJEqeuUFUYCaj8MVw5\nDe7ygM02qQkAQry0QMLX2z13i+fqXGuH8C5/nLpqjwHbavHcZh3DUIOnGclGUVxajrlrjuK7naex\n5Zj8XH4pPL2oao2dXI3r/Bsi7KXlFViameuUn/mDhDoJuVctJ+Clnw6Ac47Tl4uq5H7vOHnZZYqY\n2oeisPegRU9i8sJMyd6yO5745g+v1VuZ8eP+Kn+fvFTodIO6q5tN+B5bj1/CpIXahCBs2UFiyQCA\n95ym5753Xbys1Uur8e9t8uvmaEX/uZvw8k9V7zO5Y2imD8U4Tr8VxreTpq1En7c2VhmIHD1/O+79\nxJJpUl7BRWuZq714tLr2fpRZZMsVK/adw7NuLlSCMAvDPxSpXCrAdm+ZccEPb/HnpUJ86ZDJIzfc\nYwphr6jg2Oqiy/PO+qMeR+a3n7yM/bn59sEYW1nNN9ccRtfXf8HFAou4i10rrsq8ekqDNDpbwcxo\nPdhImIOpP+yVVLJWKddFVgojlGG4sG8+moemL67EAwvEq+7lFdyqMngj5m3vyr6KO9/f6pRpsNGa\nD+wYmhGK8r7cfNGMErddH9J0t+zwUgE3wrss3HUGxzQU9ssO81RKyyowc7llEprS9F1/QphVt/mo\nvBLchgu7ljPlXvGwqICruLhw5qcNsbzS6ts5JAjtGf+Vcw16YabMVxIG6v0ZqVVaxTB1SQEhwvof\nUnFV0EdJoZ8qtpDLThCa45iJ9tKP+3GTBuIVYbjHLhWbGJdLHPlcLyjfafPUVWfFCBoQ8/IfU1Bn\nhSAIC4UiIi62lCLhGUM8diVZKXvOXEP+zVKskTg67FjMSsuBGVf2r3Oz/BtBEO4xsi6Ov2GIsJ+6\nUoTaMveZ8sNexcfLOnMVd8zbh2dvayFrv8SpK7BqUm+0jqsJwGdWpyMIn0TPjJvqhs+EYtSwxzrD\nVe4itoD4QhIUYScIwsxUC2G31XdQMjlTLOxSYcaaAgRBEFYMEXY1tb+VYFu8wnHpLym8Jah7Yttb\nj2pzBEEQWmGIsGtRH0UJWk1TriBlJwjCxFSLUIwNubO3bHDOMXP5AfusO7EFpwmCIMyCJlkxjLHB\nAN4FEAjgM875HC3aNQu5125WKVegdLFggiAIb6DaY2eMBQL4EMAQAG0AjGWMtVHbrpnwtMo9QRCE\nmdAiFNMFwHHO+UnOeQmAhQCGa9AuQRAEoQAthL0RAGHt2xzrewRBEIQBeG3wlDE2njGWwRijgioE\nQRA6ooWw5wJIEPwdb32vCpzz+ZzzdM55ugbHJAiCIFyghbDvApDMGEtijIUAGAPgZw3aNQ19WsTa\nX//4RE8s/p/uaBRdw0CLCIIgXKNa2DnnZQAmAlgD4BCAxZzzA2rbNRNfPtwZj/RKwrePdUX7hGh0\nSYrBiA40jEAQhDnRJI+dc74SwEot2jIbnz6UDsYYXrqzagbnxAHN8cHG4wZZRRAE4ZpqNfNUCa7q\n2lAJX4IgzAoJuweoeABBEL4GCbsHXBWidLUwNkEQhNFUG2Ef3r4h4msryWQhn50gCN+i2gh7j2Z1\nMFJBJotLj50cdoIgvMjb96ZJ3rbaCLvS0Ikrf510nSAIb3JH2waSt602wi6XWjWCAbj22NWy/pm+\n+jRMED5IVJgmmdd+jRwpImEHEBbsfBp6Na8LAOAuTqfa1Zjq1wxVtT9B+BPUAxZndHqC541EqDbC\nHhMRIi8wbt3UdVaMOmoEB6psgSCqBzPvbmu0CYbxxj3tFO3nM8L+5j3tcE+nePvft7epL2v/ga3r\nSd62RnCgXbj1iMREhAQiKNBnTj1B6E5AQKWrlFQ3wv66aWwExvVINMAi8+FqsqQYhqiL8IeTyr3p\nCeiSFGP/u1vTOpL3DQpgYMz18KnY+bKFWpTOPJ07yvUI9n8e6ep+Z4IwOWqK4ImFIetEhNhfx9UK\ns7+23WbBgdoGa1rH1fS4zZyRqZoe05sYIuwBCuPTjoW3HuzWBACQEOP6IntvbAccf32o7GN5stBT\njF3YuxCSWCccnZrUlm0PQZiNe9PFr3FPdG9aBw1qhlV5b/KgFvbXH97X0f7adp9Fhmo3uPrsbS3w\n4xM93G6zZEJ3pDSqpaj9+7s2VrSfJ0w/eCo2WCmF4MAA/E3QLXv1LynInjMMW6YMUGWPmEbb3qvQ\nOC1G+EDo2DhadXvP3NYCTeqEq26H0J8APxshfPOeNHRQcA0nxDhfryFBlZpQW+C927grraHs44gR\nHR6MJwcmIzTI/RhXemKM4oy4+Nry7kc9MoIM89h/fb4fkupGYGL/5kaY4BF7jF2Frj/Qzf2T+/k7\nWilv3MpTA5NRL4oybHyBAzMHG22CaZDaabdtFqjyqbhlSn/sfHEgfn2+v+R9kutHokX9SNmJDq4y\n6VyxenIfSduFy7DDsBG8JnUisPG5fnjujpa6HkcYI3d1MbmPsSs/tmOpX3c8NTBZ0naJIt451a3x\nDWqEUCaUK2zzRhxRmlXsGBVIiAlHvZphLo8j3kYg1j7dF50FY3tSkKsZ0RJtkpNwYerUjOb1Ir1y\nHNFQjPV/NYEYOYI7prO0fNUAEc8lLjpMZEvCkffGdnB676tHuhhgie9TO0K6QEohKiwIv00dgN+n\nVQ2rKnVamsVWake/lrGi2xx5rbIH1VWmeLtjlIyxh4a1whCh4fiBDVMIu7tu1uRByZJFTwylE4mm\nDW2NezrF4852cbL3bSNhxF2Iu4tKSjbAa39JkXU8LdDyRvAWd4vEadvFRyPED1NPtYrnd04UH+hf\nMK6zy33cJTMA4h5t24a10DC6BuJqab/kpKvf11Oc3cZD1iQNIUsmdHe5fb0o6Y5W/1au07DV/Iam\nuKLbxYuPPnPOMXlQC8z5q7IkfVsbnrdxfi82KhRzR6UhTMFEopWTegPwXqGwiBDtnviBAQzhEkIG\nPZrVdXqvTVxNzPbhFDGjUOI8eELtzGgbwt/T5kAMbtsA9Wtq10t0l0zh7mtIHVBtLDJY64g7lRjU\npj6y5wxD9pxh9vfSE2Ps2TuhQdrL6Duj07BORdkRUxdo0HpykKtunV4CrEeztja/ebSrLl24JRO6\n47H/7Eb+cSO4AAAXEUlEQVRRSbnsfW0PtGlL92ltlma0T4hG1plrqtpoWjcCJy8VqrZl0fhuOH2l\nCKPSE/DfvStUtydEzmQWKTSNjcAD3ZogLDgQt7mZHJiWEI0rhbdUH2/BuHQ88mUG/ulm1mnv5LpY\nvues6Gd1Iy0JBc/f0RKP9W7q8Xi23PkXh7aSnNUyrF0catXoisS64ej1xkZJ+0hlRIfKcM7OFwfi\nxq0yWfubwmN35OW7pA862lj7tLSRZTH0KvQlfqzKg0kZPWdgaCoyoat+zVC0T7Ckmmn5YLLcEOpO\nyCvDjZsC3jS28lztmj7I6fO/uphf4C16Nq+cWNe1aR2MEqkFMixVew9eKSVllmvBFs64p1O82wHI\nbhJDdJ4u2YGtLV6yu4mI97qpozJvdHvMGpGCJ/o3r5JK6YpZI1Ixb3R7jO/TDENlnP9eyXVlpzcC\nllRtqdSrGYamsfLGG00p7L2TrYMdbvTF8aMW9aN0s0cpYt1hJV1kb2VTTBqYjISY8CoPulEGC6Fc\nUhpWhvViJaaBij1g9RpDkOJEfHh/R5ef1Q7XdtDSE0l1IxBXKwzTh7WWvI9cR0kPx6p2RAju7+oc\nG3dFZGgQ/iJxvQZNUrTdfGkpoVBPmELYHaXO24tYNFQxPVoNUkb8Xxsh/mR3vC7GdW8imvUhB9sK\nU1Lus1o1TB3FU83C8d3wWO8kzdtVK2JPDpCWFqtFjD2pbgRqhATi92kDK50tDdAiJu1O/NbJ6L2P\n6hQvKy05e84wtynaYgP0wl6kFLR40JlC2B2/R2KdCAxv3xDv36dMqCJDgzBYpCi92LU+e2QqBsko\nECYHsVurbcPKjBlPoZh6UaFVupsv3dnGZS9g5vAU0YtKDjZrhINNFS5MfLB7out2TLSaoNKMIcYY\npg9zfcPXtM4WlHrt3NHWEpeWO3mlVYOqPVGpE3XUxNhtE96kLCX5wuBWYMyy9CQAgHnuPTvOLJXy\nDHL8Ou4GFpNl9N7fGpWGR3pp9wB3/H12vDgQyyf2ct7Q4Uu7KkGiFFMIuyOBAQzvjumAtg2V1WoI\nCQpAsESvoKdIdoeevCGS4cOYtItbj/BAcCCzx31jwi033L//VpnKFhLkbFiPZnWcLmBXs19njUjB\n5EHSvEwtcJSzB0RS1bTA9v37tpQm7ErzsaO9EHoRxqAHtKqH8X0sg43J9TwLZLemdfDn7GFo1cDq\nsHDg3THtnabJ35sej9WTe2PK4JYY0zmhioOi5BmkpgiZHthKnTgO1Nav6Zynvnpyb6f9AwXn47Nx\n6artMaWwq0WOt8LBNUsNc0SsWbHpyZxLu7jl3gCPSvBEGBi+eLgLPrq/o720cYzAo3pUQkbBzhcH\nYuNz/ZzeDw5kuL9rE0npmJ//zXVetJ4o+enjY8IrrxmJP4rMzSXz5ABtS3J89pB6UYkKC7Y7TLaw\nS7emddCqQU083q85ggID3GbWiGH2NYb/eXdbZM8ZhjYNxeewCB9E9oegAFtPbs7IVPRsrt7Z9E9h\nB9A6zuJteDt+/sdLt9lfi4dN5LepZJ8uSTF4YYi0WjTBgQEYkhonaq9YPNRRnKLDQ6p4JbYH69gu\nMqrcmfzGFfL+2A5Its6KDpY5uUlLXa8RHIgmdZzjt4v/x/XkGU8IZzbLDRsBkPw7zhjWGlumSK/b\n4mu8eU+7KnMAtk11X6hwfJ+miK9dA4NkPvBc4bMjYO6uH86BCX2aoWezukhLiHa7DwPD/V0bY/7m\nk5rYFSNSmc4TSoTb0y3HoK1WhgQFoKSsQtY+no4fGMBQbgviS9CQlvWjcORCgdttOOd4amCyyxmT\nWlCrRjDmP5SO/bn5uFZUCgAYktIAq/af1/xYSjz8LipDdkp6sLYaRs3qSkvLCwoMsE9ykmKvmcZt\npCCWijl1SCuXod/m9aKw9QV1VWqF+KfHzjkCAlgVUXeHmNcjhZNK6rwLbhpb3NVVfXpbDu+7Yzrg\nnk7xaB0X5XXHVuwmd/TkvNVN7t5M2uIqz9zWwnUWh0yFOPjKHaLv16oRXKXL7OkcyD1HShwEoHKQ\nVg1KBl6HpMZh2eM9nOqkuAtBhQQFYPXk3vj4gU5KzPQ5JvRthlQXs+y1xi+F/dnb9a0YaUOsIJcc\nuiTFYFz3Ji5XW7ItCdYsNhJzR6UhKDDAXhhNSilRLcYOxG5yT6lvrmShbqQbsfLyE6t+zVC0iauJ\niJAgt1qvdeXMJIlOxE9P9MS80e2dBF7rGaXukPvdOzSubb/mpI4ptGpQU9UM6s8f7oxVk5wHI6s7\nfinsRqyRmFwvEssed78qiyOBAZY0xYbRNSR7dHNHpeGrR7qILlbgLf63bzNJ2zk+WP7SvuoEEG+K\nlCODWtfHykm9Vdf57tW8LuJr18ATEietTLJmCImVXxaSEBOOv3RohOhwZZ671Al7whnbT/Sv+rsq\nirE7YBd4jdpxpH/LepKWuTMbbaxjgGrDZq7w2Ri7GJ89lI7jeTcMOXa9mqHo0FjbuK7YxRwRGiR5\nsogkyZKpa3UiQpx6Ko5NuNPrbx/rin05+Zi96rC8A0tE7NDvj+3gtMqU8Ny2jquJfbn5ou15euDW\nCg+WFRuNqxWG5+9oqbjwF2MMzWIjcCKvsDJ3XIDt3H/zaFccOleABxbscNue8AFgm/ykZZZY+4Ro\nbD95BUl1tXNE/GElqk5NYrBz+kBZlSDl4HMeu23ab1+RGsuD2tTHBDfepJ6x4Oqy2IWUc2jzgsW8\n4R7N6uLhns5pmFLOnhQPv77IjXJXWkO0i7eMt4i14I2a7LbrgzGGJ/o3lzGuU9Vizrm9t3a7SDzd\ntnWdyFD0SvbuHA0xHuyWiA3P9kWnJuo8U9tPP21IKxx+dYgGlhmPXqIO+KCwt0+IRvacYVUK6ZsB\ntQ8NraMSniY9HX7V/TJtozrFo15UKBrWqoGRHRth/oOWAS53q03ZGN05AX/rkWifmGTzlpu5WThF\n6tcXlk618eMTPbHiqV54Z3QapgyWNr4ifBArDXfIwsP1oWcWj1K0uiblFrByR3BggKSiXtUdvwrF\nGEGdiBBcLizRrL36NUNRLyoM+3LzDe0DvCUY0H373vbIK5BeijUsOLBKudXb2zbAssd7OFWj1OpZ\nZmtX6UxlwFKCdfPRPBQUVy2PKueBXTcyBJduKLsWxnZpjF3ZVyVt686k+jWrzgB+46+pKCguw2sr\nDimyy2z4WNajYdCjTyVvjVK+CIgYDAyDUyx1bhrUUt5VY2CSYqVyHx7ulhF0R5WMCYfP4mqFSWpD\nrxnCAPDhfR1Fi6jJCbFJqfvtCkVzGURUroHDAhijOzfGaIUrkJlptqeZbPEFqpXHrocwBAVo82wU\nmvZ4v2a4v2tjXUMEtvi31NrfttLB7upjK2Hb1AGIDA1C5mnP3qoWWTRumxD5TDhM8OxtLdDNTS69\nt8RHeB23lzBXQ+l1b6ZJQWayxReoVsJuo1OT2jifX4zcazdVt6XH9cYY0z3uGxwYgN0zBqGmxBXS\nI0OD8MuzfUWLL8nVDZvQcK6+mNPPE3sq2k+qzcKV4Z8cqLyYmdRT5FhR0ZOgNa8Xiew5w5A4VfkK\nTE5lsxW3pD9mts1MVMtQTNekGOrawZI5IafWSbPYSEVrwDqi5alv2UD/BVY6NJY2g1mLzKj0Jt4f\nRCVn2P9Q5bEzxt4CcBeAEgAnADzMOVe1oKSUGtBqEV7IJPDq0TP2LcQoAVoyoYe0RdHdWCj1HDm2\n4HjYga3rY/OxS6KfAeKF1/zpEqeHkDTUeuzrAKRwztsBOApgmpJGosIqwwF6xtJsC9Y2VDEoKZcO\njaNdlgyortg0znERCW+gJE4fGMCqhGSMYnR6AhJiwt0KdZ1IacsBumNwSgOEBQfgvq4yqnPqDDlg\n8lB1tXLO13LObflh2wEoWgbknXvTMK67PgsiCBnRoREWjEvH/V2b4OMHOmFkh0a6l/Vd9nhPzVdH\nkYI3boSP7u+oKP+aMYbvHuuGbx/rJm8/2UeS15YWU+gB4EGdFvew/aa2Wubu5gWI7SeVhtE1cPjV\nIaZaR1jq81hsAfPqiJaDp38HsEjJjnUiQ/Fo76b48vdTGprjDGMMA1tbboqURrXw9uj2ots91EP6\njVmdHYkhqXEYImNFdyGOlRqlhCrE7m0zzvgNC3b2lzxZKed7jO6cgLvbN0S4hAVMpGC+M+gaT7ZK\nXcDc3/HosTPG1jPG9ov8Gy7YZjqAMgDfuGlnPGMsgzGWkZeXJ/K55X8jC0PZmDpY2gIVhPFo5WUb\nje36d1XCueq2TJaoOz405CzeTPgmHoWdcz6Ic54i8u8nAGCM/Q3AnQDu525UmXM+n3OezjlPj411\nrvPirQE4KZjJFqX42ldIsS4pJiVs9dH9HRUfx6jHgKffY0hKHB7o1hgzhrXW3RbHxZv1SdnVoVG4\ntnX15N7YJLI8Y3VFVYydMTYYwBQAd3POi7QxiaiO1IkMRfacYegnUtzNkSGpcQgOVKccoguIWFWj\nvwQbxFDT2QwJCsBrf0l1GvzUsnSuP9OqQU0k1lW2YI4/onao/wMAUQDWMcayGGMfqzXIPzrWytEr\ntOCp6JdZCDFB9olatOzxCStkemq2Wax0YZs9MtXJc/cFqsEzShNUjb5wzjVbIj3aOgNSbK3A6oDe\ng4BaTCzyBgNb18fkQclYvf88Dp8vwMLx3TBm/nan7SznS9uHoFZ6LBaRVNr0lDtaYXFGDsoruNse\nQcaMQYiQEXcX5rvrceU92rsp1hy4oNtCEoR7TOMeRYQG4disIfZSr76G2jFffxkEVEtgAMPkQS08\nljrQ43yp/Q31CHnUjgjBq8NTPG5XNzLUXs/HDHRsXBsnXh9KWSoGYRphByz1S/xh4FINWnnucrw3\nM9LJOrVeKAxaJExJaUOPollaXNdKm/CnW4rcH2mYSth9GbPcPLZUtro+7ik9d3tLrHu6j8sFVcyY\nv25DTMRHqZikpndvLtxEnj6hDSTsfkaon6wuExjAkKzDzMc70+KQEFPD6wue92iuxTJ1yh5mnh6C\n30/ogalDWvnEOIx5H+fmwj9UwI+gWLtragni7q2sq7zL9dzrRYVhy5QBSBJJjVMb6hnRsRFa1o/C\nQ7qVx9Dn2mheL9LtWsGE7+HbgVg/wpuhBallaM3GkwMrk7D+8/cuOHSuQJf1L5X+EvWiwrDm6T6a\n2qIFZgkTEt6DPHaNMEElBADSfLpljytbnMJoQoMqQwXR4SFO9Wb8H1JoQhrksatEs9xnCsEYTp8W\nsfhrx3g8c3sLo02pglmcBiN5vH8znLlShHvSvV8p1RchYTcZakMy5NMpJyQoAP93L9XONyP1osKw\n4G+djTbDZ6BQjJU0CYsCewPy3AlHKEZOyIWE3cpPTxgbdzZzXjYhn+UTe+H9sR00aUvLUMyXf++i\nXWOEaSFh9zPI3zcHqfG1cFdaQ03bVOq5Cxcs79tCWeVKwregGLtGmC2EIqYB657uY6p6IoQ0zHVl\nEb4ACXs1Qo+ZnARBmA8KxWgExcgJvaAri5ALeewmoWYNy08xWmU9+pphlnZqh4eotolQz9YX+iMo\nQJ3/RKEYQi4k7CYhPMRSjz4oQJ1/dle7higoLsMomshhCuJrh2vWFnnuhFRI2E1EsAbLwgUEMDzQ\nTa8iVMbRKLqG0SYYRmykpffVsBqfA0IeJOwaYbasGH9i6wv9Pa6o5M/c0bYBPn6gEwa1rme0KYSP\nQMKuEho01R8twxm+CGMMg1MaGG0G4UNQVgxBEISfQcJOEAThZ5CwEwRB+Bkk7F4ivjZlNBAE4R1o\n8NRLrHiqN/KLSo02gyCIagAJu4DvJ3TXbcZmrRrBVRZjJghv8sF9Hap9dlF1goRdQOfEGKNNIAhd\nuLOdtiWECXNDMXaCIAg/g4SdIAjCzyBhJwiC8DNI2AmCIPwMEnaN0HLBYYIgCDWQsKtE6QLDBEEQ\nekHCThAE4WeQsBMEQfgZJOwEQRB+Bgk7QRCEn0HCrpLGMZb6GwNa0bJlBEGYA01qxTDGngUwF0As\n5/ySFm36Cgkx4djzj9tRs4Y5y+7MGZmK5PpRRptBEIQXUa1GjLEEALcDOK3eHN+kVrh5qzaO6dLY\naBMIgvAyWoRi3gEwBQBN0SEIgjABqoSdMTYcQC7nfI9G9hAEQRAq8RiKYYytB9BA5KPpAF6EJQzj\nEcbYeADjAaBxYwoPEARB6AXjCoucMMZSAfwCoMj6VjyAswC6cM7Pu9s3PT2dZ2RkKDouQRBEdYUx\ntptznu5pO8WDp5zzfQDsOX6MsWwA6dUtK4YgCMJsUB47QRCEn6FZ8jXnPFGrtgiCIAjlkMdOEATh\nZygePFV1UMYKABzx+oHVUxeAL44hkN3ewxdtBshub6PU7iac81hPGxk1D/6IlJFds8EYyyC7vYcv\n2u2LNgNkt7fR224KxRAEQfgZJOwEQRB+hlHCPt+g46qF7PYuvmi3L9oMkN3eRle7DRk8JQiCIPSD\nQjEEQRB+hleFnTE2mDF2hDF2nDE21ZvHdmHPvxljFxlj+wXvxTDG1jHGjln/ry34bJrV9iOMsTsE\n73dijO2zfvYeY4zpbHcCY2wjY+wgY+wAY2ySL9jOGAtjjO1kjO2x2j3TF+y2Hi+QMZbJGPuvD9mc\nbT1eFmMsw4fsjmaMLWGMHWaMHWKMdTe73YyxltbzbPt3nTE22TC7Oede+QcgEMAJAE0BhADYA6CN\nt47vwqY+ADoC2C94700AU62vpwJ4w/q6jdXmUABJ1u8SaP1sJ4BuABiAVQCG6Gx3HICO1tdRAI5a\n7TO17dZjRFpfBwPYYT22qe22Hu8ZAN8C+K8PXSfZAOo6vOcLdn8J4FHr6xAA0b5gt8D+QADnATQx\nym7dv6Tgy3YHsEbw9zQA07x1fDd2JaKqsB8BEGd9HQdLzr2TvQDWWL9THIDDgvfHAvjEy9/hJwC3\n+ZLtAMIB/AGgq9nthqVy6S8ABqBS2E1ts/UY2XAWdlPbDaAWgD9hHf/zFbsdbL0dwDYj7fZmKKYR\ngDOCv3Os75mN+pzzc9bX5wHUt752ZX8j62vH970CYywRQAdYvF/T224NaWQBuAhgHefcF+yeB8sq\nYRWC98xuM2BZ1Ww9Y2w3s6yHAJjf7iQAeQA+t4a+PmOMRfiA3ULGAPjO+toQu2nw1A3c8sg0bdoQ\nYywSwA8AJnPOrws/M6vtnPNyznl7WLzgLoyxFIfPTWU3Y+xOABc557tdbWM2mwX0sp7rIQCeYIz1\nEX5oUruDYAmPfsQ57wCgEJYQhh2T2g0AYIyFALgbwPeOn3nTbm8Key6ABMHf8db3zMYFxlgcAFj/\nv2h935X9udbXju/rCmMsGBZR/4ZzvtT6tk/YDgCc82sANgIYDHPb3RPA3cyy3sBCAAMYY1+b3GYA\nAOc81/r/RQDLAHTxAbtzAORYe3IAsAQWoTe73TaGAPiDc37B+rchdntT2HcBSGaMJVmfamMA/OzF\n40vlZwDjrK/HwRK/tr0/hjEWyhhLApAMYKe1m3WdMdbNOnr9kGAfXbAeZwGAQ5zzt33FdsZYLGMs\n2vq6BizjAofNbDfnfBrnPJ5bylKPAbCBc/6AmW0GAMZYBGMsyvYalrjvfrPbzS2rr51hjLW0vjUQ\nwEGz2y1gLCrDMDb7vG+3NwYTBAMBQ2HJ4DgBYLo3j+3Cnu8AnANQCoun8AiAOrAMlB0DsB5AjGD7\n6Vbbj0AwUg0gHZab5gSAD+Aw8KOD3b1g6dLtBZBl/TfU7LYDaAcg02r3fgD/sL5varsFx+yHysFT\nU9sMS/bZHuu/A7b7zex2W4/XHkCG9Tr5EUBtH7E7AsBlALUE7xliN808JQiC8DNo8JQgCMLPIGEn\nCILwM0jYCYIg/AwSdoIgCD+DhJ0gCMLPIGEnCILwM0jYCYIg/AwSdoIgCD/j/wG0ZKGzXw6MKgAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fa48223240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7TmgyYd34wTJ888/ulshrJGX0rSrRxEZQm0mtD6d4FOnvFPSUhXUDTkoJbidm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\nCZlNT5MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fa47629cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# rcParams['figure.figsize'] = 5, 10\n",
    "\n",
    "for row in range(0, len(raw)):\n",
    "    dum_data = raw[row]\n",
    "    returns = 100*np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "    a = returns.to_frame()\n",
    "    a.plot()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from pandas import DataFrame as df\n",
    "from MSM_util import *\n",
    "from lmfit import minimize, Minimizer, Parameters, Parameter, report_fit\n",
    "import sys, scipy, numpy\n",
    "\n",
    "# print(scipy.__version__, numpy.__version__, sys.version_info)\n",
    "\n",
    "# Hyper parameters\n",
    "\n",
    "# How much period taken into calculation and prediction\n",
    "m = 20\n",
    "# number of days prediction\n",
    "RVn = 22\n",
    "# kbar\n",
    "kbar = 3\n",
    "vary = \"k\"\n",
    "kbar_start = 3\n",
    "kbar_max = 9\n",
    "\n",
    "xls_data = pd.read_excel('data_GVZ_GLD.xlsx')\n",
    "date_GLD = xls_data.iloc[:,3]\n",
    "GLD = xls_data.loc[:,'GLD']\n",
    "\n",
    "GLD2 = GLD.shift(1)\n",
    "GLD2[0] = GLD[0]\n",
    "GLD_r = np.log(GLD/GLD2)\n",
    "\n",
    "GLD_d = GLD_r - np.mean(GLD_r)\n",
    "plt.plot(date_GLD,GLD)\n",
    "plt.title('de-mean data')\n",
    "plt.plot(date_GLD,200*GLD_r)\n",
    "\n",
    "data = GLD_d[::-1]\n",
    "\n",
    "\n",
    "startingvals = []#[1.2, 1.2, 0.5 , 1.2 ]\n",
    "LB = [1, 1, 0.001, 0.0001]\n",
    "UB = [1.99, 50, 0.99999, 50]\n",
    "op_methods = 'slsqp'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ===== STOP HERE ====="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=====kbar = 3\n",
      "round0\n",
      "==========init params=========\n",
      "m0 =   1.8000\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.0122\n",
      "round1\n",
      "==========init params=========\n",
      "m0 =   1.8000\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.0122\n",
      "round2\n",
      "==========init params=========\n",
      "m0 =   1.8000\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.0122\n",
      "round3\n",
      "==========init params=========\n",
      "m0 =   1.8000\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.0122\n",
      "round4\n",
      "==========init params=========\n",
      "m0 =   1.8000\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.0121\n"
     ]
    }
   ],
   "source": [
    "RV, m0, b, gamma_k, sigma = msm_vary_k_cal(data, vary, kbar_start, kbar_max, LB, UB, op_methods, startingvals, m, RVn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "output = df()\n",
    "output[\"m0\"] = []\n",
    "output[\"b\"] = []\n",
    "output[\"gamma_k\"]=[]\n",
    "output[\"sigma\"] = []\n",
    "output[\"LL\"] = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DM (SLSQP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==========init params=========\n",
      "m0 =   1.6642\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6642\n",
      "==========init params=========\n",
      "m0 =   1.5790\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6642\n",
      "==========init params=========\n",
      "m0 =   1.5108\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6642\n",
      "==========init params=========\n",
      "m0 =   1.4471\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6642\n",
      "==========init params=========\n",
      "m0 =   1.4134\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6642\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "      <th>LL</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.654133</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.074717</td>\n",
       "      <td>0.681917</td>\n",
       "      <td>5920.855214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.589899</td>\n",
       "      <td>8.016190</td>\n",
       "      <td>0.106829</td>\n",
       "      <td>0.650574</td>\n",
       "      <td>5782.955933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.554626</td>\n",
       "      <td>21.914101</td>\n",
       "      <td>0.672520</td>\n",
       "      <td>0.600249</td>\n",
       "      <td>5731.776138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.524582</td>\n",
       "      <td>14.488014</td>\n",
       "      <td>0.619396</td>\n",
       "      <td>0.509316</td>\n",
       "      <td>5716.837059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.461940</td>\n",
       "      <td>7.886241</td>\n",
       "      <td>0.750577</td>\n",
       "      <td>0.511678</td>\n",
       "      <td>5708.240226</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         m0          b   gamma_k     sigma           LL\n",
       "0  1.654133   1.500000  0.074717  0.681917  5920.855214\n",
       "1  1.589899   8.016190  0.106829  0.650574  5782.955933\n",
       "2  1.554626  21.914101  0.672520  0.600249  5731.776138\n",
       "3  1.524582  14.488014  0.619396  0.509316  5716.837059\n",
       "4  1.461940   7.886241  0.750577  0.511678  5708.240226"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "op_methods = 'slsqp'\n",
    "row = 0\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "data2 = data[::-1]\n",
    "\n",
    "for i in range(0,5):\n",
    "    kbar = i+1\n",
    "    result = MSM_fitdata(data, kbar, LB ,UB,op_methods, startingvals)\n",
    "    re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data)\n",
    "    output.loc[i,\"LL\"] = re2\n",
    "    for element in result.params:\n",
    "        output.loc[i,element] = result.params[element].value\n",
    "        \n",
    "output  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## JPY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==========init params=========\n",
      "m0 =   1.7514\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6566\n",
      "==========init params=========\n",
      "m0 =   1.6996\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6566\n",
      "==========init params=========\n",
      "m0 =   1.7212\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6566\n",
      "==========init params=========\n",
      "m0 =   1.6102\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6566\n",
      "==========init params=========\n",
      "m0 =   1.6013\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6566\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "      <th>LL</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.796889</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.198939</td>\n",
       "      <td>0.629831</td>\n",
       "      <td>6451.792036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.776115</td>\n",
       "      <td>49.999999</td>\n",
       "      <td>0.326069</td>\n",
       "      <td>0.542970</td>\n",
       "      <td>6106.053752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.693019</td>\n",
       "      <td>12.457144</td>\n",
       "      <td>0.311948</td>\n",
       "      <td>0.565600</td>\n",
       "      <td>5959.710137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.654031</td>\n",
       "      <td>15.584092</td>\n",
       "      <td>0.697346</td>\n",
       "      <td>0.461886</td>\n",
       "      <td>5900.663844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.640454</td>\n",
       "      <td>16.034262</td>\n",
       "      <td>0.777633</td>\n",
       "      <td>0.708564</td>\n",
       "      <td>5882.924358</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         m0          b   gamma_k     sigma           LL\n",
       "0  1.796889   1.500000  0.198939  0.629831  6451.792036\n",
       "1  1.776115  49.999999  0.326069  0.542970  6106.053752\n",
       "2  1.693019  12.457144  0.311948  0.565600  5959.710137\n",
       "3  1.654031  15.584092  0.697346  0.461886  5900.663844\n",
       "4  1.640454  16.034262  0.777633  0.708564  5882.924358"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "op_methods = 'slsqp'\n",
    "row = 1\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "data2 = data[::-1]\n",
    "\n",
    "for i in range(0,5):\n",
    "    kbar = i+1\n",
    "    result = MSM_fitdata(data, kbar, LB ,UB,op_methods, startingvals)\n",
    "    re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data)\n",
    "    output.loc[i,\"LL\"] = re2\n",
    "    for element in result.params:\n",
    "        output.loc[i,element] = result.params[element].value\n",
    "        \n",
    "output  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GBP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==========init params=========\n",
      "m0 =   1.7109\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6069\n",
      "==========init params=========\n",
      "m0 =   1.6529\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6069\n",
      "==========init params=========\n",
      "m0 =   1.6041\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6069\n",
      "==========init params=========\n",
      "m0 =   1.5604\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6069\n",
      "==========init params=========\n",
      "m0 =   1.5247\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6069\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "      <th>LL</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.715749</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.109946</td>\n",
       "      <td>0.608671</td>\n",
       "      <td>5960.169424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.671453</td>\n",
       "      <td>19.905256</td>\n",
       "      <td>0.222166</td>\n",
       "      <td>0.589501</td>\n",
       "      <td>5724.358738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.647746</td>\n",
       "      <td>14.287636</td>\n",
       "      <td>0.278009</td>\n",
       "      <td>0.513386</td>\n",
       "      <td>5622.725978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.609150</td>\n",
       "      <td>12.504412</td>\n",
       "      <td>0.644876</td>\n",
       "      <td>0.467192</td>\n",
       "      <td>5570.014434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.578922</td>\n",
       "      <td>11.018658</td>\n",
       "      <td>0.637156</td>\n",
       "      <td>0.421255</td>\n",
       "      <td>5537.792457</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         m0          b   gamma_k     sigma           LL\n",
       "0  1.715749   1.500000  0.109946  0.608671  5960.169424\n",
       "1  1.671453  19.905256  0.222166  0.589501  5724.358738\n",
       "2  1.647746  14.287636  0.278009  0.513386  5622.725978\n",
       "3  1.609150  12.504412  0.644876  0.467192  5570.014434\n",
       "4  1.578922  11.018658  0.637156  0.421255  5537.792457"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "op_methods = 'slsqp'\n",
    "row = 2\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "data2 = data[::-1]\n",
    "\n",
    "for i in range(0,5):\n",
    "    kbar = i+1\n",
    "    result = MSM_fitdata(data, kbar, LB ,UB,op_methods, startingvals)\n",
    "    re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data)\n",
    "    output.loc[i,\"LL\"] = re2\n",
    "    for element in result.params:\n",
    "        output.loc[i,element] = result.params[element].value\n",
    "        \n",
    "output  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CAD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==========init params=========\n",
      "m0 =   1.6606\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.2744\n",
      "==========init params=========\n",
      "m0 =   1.5457\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.2744\n",
      "==========init params=========\n",
      "m0 =   1.4564\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.2744\n",
      "==========init params=========\n",
      "m0 =   1.4105\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.2744\n",
      "==========init params=========\n",
      "m0 =   1.3644\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.2744\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "      <th>LL</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.645899</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.063753</td>\n",
       "      <td>0.279947</td>\n",
       "      <td>271.002919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.555996</td>\n",
       "      <td>10.923537</td>\n",
       "      <td>0.109376</td>\n",
       "      <td>0.277509</td>\n",
       "      <td>129.793835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.473896</td>\n",
       "      <td>4.759149</td>\n",
       "      <td>0.128984</td>\n",
       "      <td>0.292866</td>\n",
       "      <td>105.152252</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.435084</td>\n",
       "      <td>3.948476</td>\n",
       "      <td>0.170709</td>\n",
       "      <td>0.263495</td>\n",
       "      <td>91.314827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.386468</td>\n",
       "      <td>4.022490</td>\n",
       "      <td>0.441396</td>\n",
       "      <td>0.251033</td>\n",
       "      <td>88.401337</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         m0          b   gamma_k     sigma          LL\n",
       "0  1.645899   1.500000  0.063753  0.279947  271.002919\n",
       "1  1.555996  10.923537  0.109376  0.277509  129.793835\n",
       "2  1.473896   4.759149  0.128984  0.292866  105.152252\n",
       "3  1.435084   3.948476  0.170709  0.263495   91.314827\n",
       "4  1.386468   4.022490  0.441396  0.251033   88.401337"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "op_methods = 'slsqp'\n",
    "row = 3\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "data2 = data[::-1]\n",
    "\n",
    "for i in range(0,5):\n",
    "    kbar = i+1\n",
    "    result = MSM_fitdata(data, kbar, LB ,UB,op_methods, startingvals)\n",
    "    re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data)\n",
    "    output.loc[i,\"LL\"] = re2\n",
    "    for element in result.params:\n",
    "        output.loc[i,element] = result.params[element].value\n",
    "        \n",
    "output  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TEST MSM_likelihood_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5782.9562468040886"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "op_methods = 'lbfgsb'\n",
    "row = 0\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "returns = returns\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']\n",
    "\n",
    "MSM_likelihood_new(1.590,8.01,0.107,0.651, 2, data*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==========init params=========\n",
      "m0 =   1.3232\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6642\n"
     ]
    }
   ],
   "source": [
    "op_methods = 'slsqp'\n",
    "predict_period = 1\n",
    "kbar = 10\n",
    "row = 0\n",
    "starting_index = 3000\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "\n",
    "data_fit = data#[:starting_index]\n",
    "\n",
    "# fit params\n",
    "result = MSM_fitdata(data_fit, kbar, LB ,UB,op_methods, startingvals)\n",
    "print(op_methods)\n",
    "re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data_fit)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "print(result.params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-23-9c691a1d831f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mstarting_index\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m     \u001b[0mPdict\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"index\"\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 9\u001b[1;33m     \u001b[0mPdict\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"vol\"\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mMSM_likelihood_new\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m  \u001b[0mkbar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpredict_period\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     10\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Users\\lawof\\Documents\\Fractals\\Thanasarn_MSM\\GIT_MSM\\MSM_util.py\u001b[0m in \u001b[0;36mMSM_likelihood_new\u001b[1;34m(*args)\u001b[0m\n\u001b[0;32m    193\u001b[0m     \u001b[0mw_t\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmatlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrepmat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mk2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    194\u001b[0m     \u001b[0mw_t\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdivide\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpa\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0me\u001b[0m \u001b[1;33m**\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m0.5\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpower\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdivide\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mw_t\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 195\u001b[1;33m     \u001b[0mw_t\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mw_t\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m10\u001b[0m \u001b[1;33m**\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m16\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    196\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    197\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mT\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# df for OLS\n",
    "Pdict = df()\n",
    "Pdict[\"index\"] = []\n",
    "Pdict[\"vol\"] = []\n",
    "\n",
    "\n",
    "for i in range (starting_index,len(data)):\n",
    "    Pdict[\"index\"] = i\n",
    "    Pdict[\"vol\"] = MSM_likelihood_new(result.params,  kbar, data[:i], predict_period).sum()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.64652583591045154"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MSM_likelihood_new(result.params,  kbar, data[:i], predict_period).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Parameters([('m0', <Parameter 'm0', 1.3534521193284004, bounds=[1:1.99]>),\n",
       "            ('b', <Parameter 'b', 1.7570908024867271, bounds=[1:50]>),\n",
       "            ('gamma_k',\n",
       "             <Parameter 'gamma_k', 0.32315329524110031, bounds=[0.001:0.99999]>),\n",
       "            ('sigma',\n",
       "             <Parameter 'sigma', 0.65595311973894799, bounds=[0.0001:50]>)])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5705.0863252038516"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MSM_likelihood_new(1.326,2.70,0.959,0.643, 10, data*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pickle\n",
    "\n",
    "# obj0, obj1, obj2 are created here...\n",
    "\n",
    "# Saving the objects:\n",
    "with open('objs2.pkl', 'wb') as f:  # Python 3: open(..., 'wb')\n",
    "    pickle.dump(result.params, f)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# save load params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pickle\n",
    "# Getting back the objects:\n",
    "with open('objs.pkl', 'rb') as f:  # Python 3: open(..., 'rb')\n",
    "    rez = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Parameters([('m0', <Parameter 'm0', 1.412890686515486, bounds=[1:1.99]>),\n",
       "            ('b', <Parameter 'b', 5.1996491414955583, bounds=[1:50]>),\n",
       "            ('gamma_k',\n",
       "             <Parameter 'gamma_k', 0.86214719171172072, bounds=[0.001:0.99999]>),\n",
       "            ('sigma',\n",
       "             <Parameter 'sigma', 0.64652583591045187, bounds=[0.0001:50]>)])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rez"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# new forecast functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "code_folding": [
     31,
     78
    ],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def MSM_likelihood_wantto_forecast(*args):\n",
    "    \"\"\"\n",
    "    calculate LL for 3 cases (depend on number of input)\n",
    "    :param args:\n",
    "    :return:\n",
    "    \"\"\"\n",
    "\n",
    "    if len(args) ==3 :\n",
    "        # choose starting val\n",
    "        inp = args[0]\n",
    "        kbar = args[1]\n",
    "        data = args[2]\n",
    "        m0 = inp['m0'].value\n",
    "        b = inp['b'].value\n",
    "        gamma_k = inp['gamma_k'].value\n",
    "        sigma = inp['sigma'].value\n",
    "\n",
    "    elif len(args) == 4 :\n",
    "        # prediction\n",
    "        inp = args[0]\n",
    "        kbar = args[1]\n",
    "        data = args[2]\n",
    "        m0 = inp['m0'].value\n",
    "        b = inp['b'].value\n",
    "        gamma_k = inp['gamma_k'].value\n",
    "        sigma = inp['sigma'].value\n",
    "        \n",
    "\n",
    "    A_temp = T_mat_temp(kbar)\n",
    "    k2 = 2 ** kbar\n",
    "\n",
    "    def transition_mat(A_temp, b, gamma_k, kbar):\n",
    "        A = A_temp\n",
    "\n",
    "        gamma = np.zeros((kbar, 1))\n",
    "        gamma[0] = 1 - (1 - gamma_k) ** (1 / (b ** (kbar - 1)))\n",
    "\n",
    "        def bitget(number, position):\n",
    "\n",
    "            bi_number = bin(number)\n",
    "            bi_number = bi_number[2:]\n",
    "            if len(bi_number) >= position:\n",
    "\n",
    "                fn_output = bi_number[-position]\n",
    "            else:\n",
    "                fn_output = 0\n",
    "\n",
    "            return fn_output\n",
    "\n",
    "        for i in range(1, kbar):\n",
    "            gamma[i, 0] = 1 - (1 - gamma[0]) ** (b ** i)\n",
    "\n",
    "        gamma = gamma / 2\n",
    "        gamma = np.append(gamma, gamma, axis=1)\n",
    "        gamma[:, 0] = 1 - gamma[:, 0]\n",
    "\n",
    "        kbar1 = kbar + 1\n",
    "        kbar2 = 2 ** kbar\n",
    "\n",
    "        prob = np.ones((kbar2, 1))\n",
    "\n",
    "        for i in range(0, kbar2):\n",
    "            for m in range(1, kbar + 1):\n",
    "                prob[i, 0] = prob[i, 0] * gamma[kbar1 - m - 1, int(bitget(i, m))]\n",
    "\n",
    "        for i in range(0, 2 ** (kbar - 1)):\n",
    "            for j in range(i, 2 ** (kbar - 1)):\n",
    "                A[kbar2 - i - 1, j] = prob[kbar2 - int(A[i, j]) - 1, 0]\n",
    "                A[kbar2 - j - 1, i] = A[kbar2 - i - 1, j]\n",
    "                A[j, kbar2 - i - 1] = A[kbar2 - i - 1, j]\n",
    "                A[i, kbar2 - j - 1] = A[kbar2 - i - 1, j]\n",
    "\n",
    "                A[i, j] = prob[int(A[i, j]), 0]\n",
    "                A[j, i] = A[i, j]\n",
    "                A[kbar2 - i - 1, kbar2 - j - 1] = A[i, j]\n",
    "                A[kbar2 - j - 1, kbar2 - i - 1] = A[i, j]\n",
    "        return A\n",
    "\n",
    "    def gofm(m0, kbar):\n",
    "\n",
    "        m1 = 2 - m0\n",
    "        kbar2 = 2 ** kbar\n",
    "        g_m1 = list(range(0, kbar2))\n",
    "        for i in range(0, kbar2):\n",
    "            g = 1\n",
    "            for j in range(0, kbar):  # not req -1\n",
    "                if g_m1[i] & 2 ** j != 0:\n",
    "                    g = g * m1\n",
    "                else:\n",
    "                    g = g * m0\n",
    "            g_m1[i] = g\n",
    "\n",
    "        g_m = np.sqrt(g_m1)\n",
    "        return g_m\n",
    "\n",
    "    A = transition_mat(A_temp, b, gamma_k, kbar)\n",
    "    g_m = gofm(m0, kbar)\n",
    "    T = len(data)\n",
    "    pi_mat = np.zeros((T + 1, k2))\n",
    "    LLs = np.zeros((T,1))\n",
    "    pi_mat[0, :] = (1 / k2) * np.ones((1, k2))\n",
    "\n",
    "    # Likelihood Algorithm\n",
    "\n",
    "    pa = (2 * np.pi) ** (-0.5)\n",
    "\n",
    "    # g_m is binomial measure ?\n",
    "    g_m = np.array(g_m).reshape((1, len(g_m)))\n",
    "    s = np.matlib.repmat(sigma * g_m, T, 1)\n",
    "\n",
    "\n",
    "    data2 = np.array(data).reshape((len(data), 1))\n",
    "\n",
    "    w_t = np.matlib.repmat(data2, 1, k2)\n",
    "    w_t = np.divide(pa * np.e ** (-0.5 * np.power(np.divide(w_t, s), 2)), s)\n",
    "    w_t = w_t + 10 ** -16\n",
    "\n",
    "    for t in range(0, T):\n",
    "        piA = np.matmul(pi_mat[t, :], A)\n",
    "        C = np.multiply(w_t[t, :], piA)\n",
    "        ft = sum(C)\n",
    "\n",
    "        # stop div by zero if prob are too low\n",
    "        if ft == 0:\n",
    "            pi_mat[t + 1, :] = (1 / k2) * np.ones((1, k2))\n",
    "            print(\"!!!!!\")\n",
    "        else:\n",
    "            pi_mat[t + 1, :] = np.divide(C, ft)\n",
    "\n",
    "        LLs[t] = np.log(np.dot(w_t[t, :], piA))\n",
    "\n",
    "    LL = -sum(LLs)\n",
    "\n",
    "    if np.isinf(LL):\n",
    "        print('Log-likelihood is inf. Probably due to all zeros in pi_mat.')\n",
    "\n",
    "    if len(args) == 4:\n",
    "\n",
    "        # provide ingrdents for forecast\n",
    "        \n",
    "        return pi_mat, A, sigma\n",
    "\n",
    "    else:\n",
    "        return sum(LL)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TRY predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "op_methods = 'slsqp'\n",
    "predict_period = 1\n",
    "kbar = 10\n",
    "row = 0\n",
    "starting_index = 3000\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "\n",
    "pi_mat, A, sigma = MSM_likelihood_wantto_forecast(rez, kbar, data, predict_period)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6420"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(pi_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "setting an array element with a sequence.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-29-6c4cc5e07a91>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     10\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mpredict_period\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 12\u001b[1;33m         \u001b[0mvol\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstate_now\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmatrix_power\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mA\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mt\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0msigma\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     13\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     14\u001b[0m     \u001b[0mPdict\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mstarting_index\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m\"vol\"\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvol\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: setting an array element with a sequence."
     ]
    }
   ],
   "source": [
    "# df for OLS\n",
    "Pdict = df()\n",
    "Pdict[\"vol\"] = []\n",
    "\n",
    "vol = np.ones((predict_period,1))\n",
    "vol = vol.astype(float)\n",
    "\n",
    "for i in range(starting_index,len(pi_mat)):\n",
    "    state_now = pi_mat[i , :]\n",
    "    for t in range(0,predict_period):\n",
    "        \n",
    "        vol[t,0] = sum(np.matmul(state_now, np.linalg.matrix_power(A, t+1)))*sigma\n",
    "        \n",
    "    Pdict.loc[i-starting_index,\"vol\"] = sum(vol)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  9.76562500e-04,   9.76562500e-04,   9.76562500e-04, ...,\n",
       "          9.76562500e-04,   9.76562500e-04,   9.76562500e-04],\n",
       "       [  1.85710003e-02,   1.96005736e-02,   1.96005736e-02, ...,\n",
       "          2.22829362e-17,   2.22829362e-17,   2.22829362e-17],\n",
       "       [  5.94619336e-03,   9.17009574e-03,   8.21343008e-03, ...,\n",
       "          1.86213233e-15,   5.12245735e-16,   5.43238814e-17],\n",
       "       ..., \n",
       "       [  5.01378367e-07,   7.75596883e-07,   1.27806119e-06, ...,\n",
       "          2.51259230e-34,   8.31133819e-35,   6.69496793e-35],\n",
       "       [  2.71984962e-07,   4.40526281e-07,   7.19433070e-07, ...,\n",
       "          1.02239294e-24,   3.30937870e-25,   1.54929166e-34],\n",
       "       [  1.32241301e-07,   2.18303069e-07,   3.72674308e-07, ...,\n",
       "          9.17565002e-18,   3.55559570e-18,   4.35776987e-19]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state_now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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