abc.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## 12.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "library(TSA)\n",
    "data(CREF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "options(repr.plot.width = 8, repr.plot.height = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6lZ7Tz83KnjzLhCYFkEHqWKfkFaX4D5Ao6/qED5xz4iIbCdCCzjAswh9CtSfvll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\nbKxRAq1WNBmsAXuAOqwJWpHGNjT0eilZwe+s6aB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A61W/Tbx7/fdSAbZaX9fz3uCdvqyty8sn7dnXwOsyV2l0Yx2xwXquVfpGcan4ByKx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\nAAECBAgQIECAAAECBAgQIECAAIGhC/wFjMMqqTuI39QAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r.chef=diff(log(CREF))*100\n",
    "x11(width=4.875,height=2.5,pointsize=8)\n",
    "plot(abs(r.chef))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vVvf/l/jP9E+mnV1u8o5F+f+5j0JOkr0hHSz6RJjG/DvaDH1TM3LkPuh0AIhEAI\nhEAIhMAiEfB5xeEkj/mSCv+N9L5JKknZNUXA887hQp23AzxL3wDTXtqOLxRbAQQmcYDp3sMk\n/tn8e3Ehe0qlDyv8PgkzZnzb+wfS4dJF0t9LL5V2k66X3iDR7qdLH5L62n4q+C1pkm/Y+z47\n5UIgBEIgBEIgBEKgCwF/e9XGARlXL2eq8s/jxuXP/ZVLgN8A5cujd0zYBc87hwtVZ9+lrwNM\neb7EsyO90LPG3fO6IV8ZH1cu95eZgCdRn2bgJPJ/dvEN6nm1CnasXc/K5T5qyFkS/1UT9tcS\nTjHOr+2ziuzii57huSp3F6nt4nqx8vLr17EQCIEQCIEQCIEQWGoCdjwcTvJ8zj9tfpV1kmek\n7GwQeISa8SppUgfYzmObeeMvl3CA+/gxnM1xgPuUVbF5VtbhPszLkIvZJFAOXNcWnqQCfyi9\npWvBZczPt7s7SydKn6z0FYW2/RV5qvRIJ0wQ8msQbX8Vgr+ljoVACIRACIRACITAchDw4X1a\nDvA06lkODnlmNwI4rHftVqQxt+eLw8ZMVaJ9l77f4lJ+Wg6w1w1NK+NVUxPMKgH/FKVP+36i\nQhv6FFzGMrfp2fwN8Lul51btuKYKcXr5Zvij0oVVWoIQCIEQCIEQCIEQWO0E7Hg4nKS/+QZ4\nEnorqyzzhfGe1Dzv2nwD7N+u7Psr0Iv1DbD7MCmLlF8CAv4pSttH4TDzK8PY30n8IwfnSD+Q\nmIg2/oGpWf1W85/Utn+T6gv2h0o7SNogxUIgBEIgBEIgBEJgrRDwt1dtHJBxTKgjzsA4Sqvj\nPuM8jW+APf/azJtJHGD8mG2kvt8e10fN7Sa9jNfz5XrGCHR1gB+k9n+j1ocv1665fI70kYb0\nWUnCQUelXVFeJB4CIRACIRACIRACa4SAHQ+HfbuNg4EjMA1Hum8b1kq5deoo/2YNf963XMY4\nM96M+60TNMLzrs28mcQBdtlp/Qp06UfFAZ5gAix10XLg2jz7NGXau0XGjS3yJEsIhEAIhEAI\nhEAIhMDyE/Dh3Y5I3xb5t+vaODJ9n5FyQwKvUXCM9OhlBOL5wrfAN0zQDtfjcKGq7Lv0+RZ3\nkrJNbfK64V4Zb8qbtBkiwE9suhi/5nxBocsVZ7MjbZN0/yrO3wfHQiAEQiAEQiAEQiAEZp+A\nHQ+HfVtsB3jSevo+fy2Vw+mcxq8fT8LM4+xx71uX62nzgxN/i9vnb4BddjG+AXYf+jJIuSUk\n0NUBLpu2ry74298XVon8X8Dvlz5RXScIgRAIgRAIgRAIgRCYfQL+9mrSQ7wdGIez3/OV20IY\nLzdnP39SR7zL/LMT28cBzjfAK3e+T7XlkzjAv6CWfFx6c9WiixXOSbtKD5BiIRACIRACIRAC\nIRACs0/Ajq8dmr4t9jeBrq9vPSk3ngBjZd7jcy9ODo/zpO1wPQ4Xaq0dYP6rUccXyl/ec/7F\n+AbYTnz5vMRnlMAkDvDh6tO3av3ipzGkHVtLz2UIhEAIhEAIhEAILAeBe+qhOy7Hg1fQM314\nb+OALNQtO0KTOtILPSP3hgRgvNycPV8m/QbY9bTpD04s/9PMLZIdWkVb2WJ8A0w7aI/XEA3Z\niY/Y7BKYxAE+Rd36dWn3onuHKM43w98t0hINgRAIgRAIgRAIgS4EfCDuUmZU3nfpxjtG3Uz6\ngIB5O+yLxQ7wpPX0ff5aKgfjNg7jYjLx8z3ufZ/l+eJwoXpwYnE6+zjAdpin+Q0wzi/fRrvt\n+yjOPwZ8Hyk2owQmcYD/Wn3ivw7iV5/PkC6U+KfY/146WYqFQAiEQAiEQAiEQFcC61XgamnS\nQ7Wfy7e/9/BFwkYC/vbKh/jGTC0S7RA5bFEkWXoSgPFyc/Z8mfQbYM+/Nv3Bie3rAC/GN8A4\nv/wGrPvAt7/4V/zbSLEZJeCJ0Kd5/D+6z5D4v4GPlG6Tvinl219BiIVACITAMhLYQc8+Qjpl\nGduQR4dAXwL3VUEO1DiuP+tbSVFuWo50UeWqi9qRcdi3g2Y9aT19n7+WyuEsmvdy9dvjPGk7\nXI/DhfqDA9z3V6Api037G+DyV6D9wwCHwyfmc6YITOIA0xF+AvONSlzHQiAEQiAElp/AiWrC\nu6X8HdLyj0Va0J0AP8DBpnWAnPRwPmzN6v70t1dtvoFbiIRZT1rPQs/IvSEBGC83Zz9/0rVq\nx9f1jRrjnXVjFr8BbnKAvY+N6kvSl5HAJL8CParZ/J0N/0BWLAS6EuAF/O/Sbl0LJn8IhMA8\nAji+efnOQ5KLFUTgblVbJz1Uu8s4ZXbMnJZwPgE7IA7n321/Zc7jHJn2NSbnKAIw5ty0zagM\nS5Du+eJxH/dI3ksPbMjkehw2ZBn8G0M/1I1pOcCTfglIG6mj/jfA3rccki82YwQWwwF+pPqY\nP/yesYFeIc3hX+p8ojS3QtqbZobAchNgr31mQyP42yMOEouxxzc8LkkhMFUC/uHNtA6QHM7j\nkC08RP4GeCEHZOEahnfNedJ62jxrrecxa4fLwcPj3Hat8qeTn2xoqOtx2JDlDq9U4r0lnM6+\nfwNc/gq0403PapvGuqn/DbBZeB9rW1fyLSGBSQ5Hj1Y7j29o69FK+1xDepJCYBwBbxoOx+XP\n/RBY6wROEAD+QcK6+R/fyFqqk8n1SiCQb4CXfpTseDjs2wJ/E7icTlnftq+0ch4rM1+O9nuc\n27Zh1D9I5x/AuL56Xw5UAl+w4bfcXbID3PVbXOef9t8A4wS7D37vOtStqRqMPi/xbyXEehKY\nxAF+uZ751J7PXc5i/ETmTdIHpFdJXgyKDuyd+jy2iidYWgLeQBdr01ja3uRpIbD4BPh7qKb1\nYgfYa2rxW5InhMD0CNgBnmT+vlrNeWnVJOoZdbCeXqtXdk0+vNup6tsbj9mk9fR9/loq5znt\ncDn67nFueg81tYczOHnrv7btehzWy75MCZurRJxofu0YJ7jrt7jOjwPsuKKt7H8o1ytrOVk3\nOL9NDvBifQPMe/9Rkt/zisa6EpjEAf7/9LDjJH4iw68kMKGtrpNKRZfM/kJP+mWJf8X6rdLJ\nEr96aztGkfwNqmksbegXZ9uNdGlbl6eFwOwR4EXodVO2znta1lJJJfGVQsAHx0nm79PV2UdU\nHWaNNK2TlcJjKdppxwPHpP7FQJfnm/NyOmVd2ruS85qxw+Xoi+eNx31cG/jhFnPMP+RyfurB\nqR3Vl8fq3keqzPyXZv4GuKsfY/+kjwN8gp77gKoNDlgrtJv/BsksvG85dN5pha53Gv9C/rTa\ntOLqmWSTO169PUT6UkOvn6M0T9SG28uWxAJ9onSAdJ30GulD0iekJ0g4xdMwfjr125J/ojqu\nzvyjYUNCXtRtN9JxXHM/BFY7Af6xK17o/im0++ufDHtNOT1hCKwEAj4cTzJ/91JHr6o6yzuF\nA3NsNAH2EA7UsMIJ4VDfx+zA2BnoU0fKtCNg1g7blZos16dV/Pelr1TV+Nlt16rXNuH1VR0E\nzBeuR80b8l8sYZyx7QBzzTuw7fq234MDjLUti6O9v/Q9ChXmd+9SfgPsM/K0fJaiO2sn6onQ\np8fvUCH+m40mu7wpcQbSeCFuknB+MSbPSdKnpA9Jz5SmYfz0er00aiHXn7FHPWGNXntRt91I\n1yimdDsEthDgG2CMNcML2GYH2GvK6QlDYCUQ8CG577uAb5h4359VdZZ10HRAfqXSyftXVb61\nHNgBgRXxG3rC8J5jx6hnNSnWgoDPmGbeoshEWXACHy19ULID3LUN/u0O/o639BVwJK+WRs0b\n+rhRwuwA+4c0bZ1YypIXswOMH9S0NwwyFR97K04bvDf5FuVpR5MD3Hf/ct2jQtcbB3gUoRbp\nkzjAOJJoJdmP1FgW2VOkf5Vuk/i1Bf5Vui9I75G8mBXtbSxqfv2qrb1MGUf9MKFtHashnzdx\nL+7V0Kf0IQQWk4AdYNbOtcWD7ABnLRVQEl0xBHxI7jt/76OecpB2edZH0yH38Uq/VYoDPDwb\n4fTuIk1yDoI19eAo+NsxRWOLQMDOosNFeMS8KvlHl/AbvD65yVxhDXmtkbaQ2YF06LzUs9A3\nwDzTPkf5K9CUt1NLfJzRfp/9ydu27EFVxfV2e443OcAlJ4rzG1uflJ4kXSP1NbPOr0D3Jahy\nXX93foJHzUzRN6slvOz+V9EiJuITpCMqFbcSXUICXtS8QGMhEALjCdgB9tpxiTjAJpFwJRLw\nwbE+r9v2hW9/MerhgMpZp8lJwNnzWlF0TZsdECBM6gD7h3GT1LOmB6Nl5z2nHbYs1jvb7lXJ\ncl0yxox323Ob1zbfANtwSvlNDBzgUX3hmfz2Jl9a7Sjxrat/qNXWiVWRLb/y7G+P234ReCCF\nZXUHmPLURbs8383HoW4NbFd9PkxaN7zs/Um9PNN96F3RWi64Fh3gD2vA95H+vDbwV+r6KOnl\n0tm1e7lcGgLeQOubxtI8PU8JgZVHgJ8oY147w6uth/p6uu8nDIFZJuBDZt93gR1gynsNcDjl\nkF3afXThfzCuTF+LcX5QgAOC+SA/vOr2iQNjB3iUM9OtxuQeRYAxw5aKsx1gO7F+Nl8itV2r\nLus1Th3uBw7uqLlHH/mV359Ik34DjOPY1Xk+SGWw0nHnmrbz7W+bb4Ddd4eU72PsabCITUBg\nLTrA4GKintvAjUXxN9J3G+4lafEJeAN1uPhPnL0n8CtGvzB7zUqLZpRA0zfAvJD9gl3La2lG\nhyzNakFg0vlrB5h67ADz2LqjEAd462DgeNxQXdY5bc01PgZv/3rnKGdmfC3JMY5AOa/L+Lhy\nk9y3A+z3Cj9Q4htQxrttG+z4lo6k5wk/gHFc0S1G3fgrOH3MUb4BxoHt6sSqSO9vgA9S2csk\nt5+6MH8D3OQAm9Mw59ay9XTfbxtSPg5wW1oj8q1VB3gEjiQvMwFvoA6XuTlbHv9AxV635Wpx\nI49V9X+1uI9I7auEAIcP//pmuWacRjcnfdGuElTpxgoj4ENm3/lrB5jy5doo4/zaJL9BkW+A\nh5ODH5xN4xtgGOcb4CHTxfwsHcVJfmDRpY11B9htmPQbYNfD/Gvqi/cBnL7l+gb4QD37VMl7\nk6IDW45vgOERB7gagL5BHOC+5FJuMQj4cOLNbjGeUdb5Ql20Ofw8R/leXhZcxDg/Fa1vsIv4\nuFS9ggng6HoPL9eM5zT/ymWZvoK7mqavMQLeA/vOXxzgK6SFvgHmtydYP14viq5pwwmZtgNs\nx2ZNg12kzpeOYhlfpMcNqrUD7N/Q8HP5gYfPb+Oe77Xd5Rtg7wM4v2ipvwFmj+Dvd5scYH8D\nfKPue767vQ51a2Dm5tDpXUPqzT+A1ZVaLb8PT7XkXIbAshDwZuFwMRuB8/Be6fgWD1mvPOVm\n3aJI7yw8hw3VG2nvilJw1RPg2ytbefjwN8CX6WaZ7rwJQ2DWCfiA2PddgAN8lkT5cg2UcX79\nGeMQX6YPEpfhg2+SltN4vn8FepL3Dzz5RhCzgzS8yuc0CZRsy/g0n1Gvyw6w16XnyWr/Bni/\nCsRpCu3Am82ob4D5l6a9jzmvr83P6V1D9qt8A9yVWi1/HOAakFwuKwEfQhwuZmOOUuX8Cmkb\nx3YpHWBvrg4Xk8G4uh+nDEeMy5T7y0aAb7Cw+je9OMD8ewabpK4v2heoTMZcENaYcZA9cIb6\nzP7Ht0pd56+7gAP8w6p8WUfpKNgBpsxyfwvMWYz1yntpuYw5wKH6VsmOTZ+2wJuxwyapZ1hD\nPkcR8FzmG9GlODPRDhxgHDuvKY8vDnDbNvhsU569/MOfUX8D7OcxP/khDX3v8w9ZqVivvwHm\nH92i35dKrNWyr/4GuP43wE0/FLAD7FBV9TJ4xAHuhW5roTjAW1kktngEnqWqX9Siem9yDlsU\n6Z3loVXJchNuqoxfteEwxaZd/xdEm/JPmub2TLpBTtoOyv+u9OJpVJQ6FoUADjC/dsXBuXwh\n4wBfLfGC7LqWXqsyz5Ria4vA09Xdk2eoy+x/fX6AQxdYC/eV+Aa4/Dt5Xc5bJzjAHGox1sxy\nGu8ZRLuXy3BC2E+Qnas+baGsHeBJ6unz7LVUxmxh7fhi9393PeBSyecTP5c2LPSueZLuf13C\n7AA7JM2OdNu/AaZM338Eyw5rl39Ai3MZP2jgX6nGyraP+gb4KuUzp0Gholw93ffbhrCOA9yW\n1oh8cYBHgEnyVAlwuGpzqPYhfqGNdFoNe0hVUbmRNdV9iBI5RKFxeZvKd03zMxx2LT/N/BwQ\nl/tgOM3+rLa6dlaHNkt1R5cxu7pK95rSZStj3vmHMK0KJNOqIMCcmZW1zl7LO2BjFSroZPdX\nbuo4syq1U1G6XA+7KP2i6t5yfwOM84st59rDCeFbLH6jxA6Jop0NxjhEmB2k4VU+p0nAbGHt\n+DTrr9eF48iZ4BzJZzTPE9435drS5TzbW1cHVyk4f+T3XOed43pG/TdIfh5/94ojivV1gPnH\n7yjLN8gY/RpntBHnnG+fsfJ8Rnnq4gdH7gftbfoBnvsxDQc4fwMsyJNYHOBJ6KVsWwL3VkZ+\nhWSceQN1OC7/JPePrgp7Ex5V13rd8E8Kx+UdVUeXdG+sk26QXZ45Ki/fRiz3wXBU25I+/Bds\n+SkzL8JyzeDIcMCoO8ZKGmvMcc/BsZlXeQYONnwrym+ArHbDAeObjHIeLVef2ftwYJsOkG3a\n9GxlOkM6u8rMD4p8aC4dBQ7z50s4fdPe57qerfx+XIp3jLrbaOU3wD7IN2Yckwhj9qTSIRhT\nJLd7EPBcXioHeFe1kXl9ruTziecJbbBzp+jtjP0FUY599QqJ98wzpB9Irgcn03FFtxh184MZ\nfj3fTmhfB9gOq891OMTjjLaXDnC5Tkd9A8z+ZU6u3+/WhVg570Ih5Xm/xyYg0HWTnuBRKbqG\nCeAAs4GMM28KDsfl73t/HxXk8MMBqdzImupbr8TTqxtt+tBUR5c0t8cbZZey08zL3sC44UzF\nZpMAB3sc4LqjaweYQ2jXtcT88xxUdE0b3xweKx20Bih4b3O4nF32oXGjGtF1/tLuF0jvl+z0\nMo4cmnF0Swefd8CV0jXSNPe5N6s+nt/FZsEBxvGA0aSOK4ztANtJ68IiedsRsKN4nbKX87pd\n6e65dquK4AB7XboNrKGF2uB3yh5VHZcrJG1PaZ2EE4nhZDbNGZ5nh8/rGge2y7e4yj6wxfoG\nmLXjftBe3s3mNHiwPry3OXR61xDW5tG1bPJXBOIAZyosBYG2DjCLmp/w1TeNabfxaFW4STpN\nGudorleer0mYN/Hh1eJ8uj2TbpCTtm4XVcD+MO1vRiZtV8pvJWAHmMNmefjgMM+BhBdkma7L\nscb8W4p5PrYhM5DBziCO0mo399WO2HL213vgRjWi6/x9qMrsJ31Q8gFxJ8VZI3yDVB6uSwd4\nmvsch3wO9l3M3Jdz7U3rG2DGzLztIHVhkbztCDCXcbpwCMt53a5091z8/S/f9F4p+Yzm5/K+\ncZqitzPP6/tVd65QyDpfJ1EHcRxa1mzTnKFur2c7wDi/lMHafIs7zDn8BrprWdqPc86z+XcD\nvEcpOnB6GYe6A8wZs36O87VDyvexkkef8ikjAnGAMw2WggAOsF/wCz2PF+fV0kIb6ULl2967\nvzKeKbGheWMeVfYQ3fh6dXNc3lF1dEn3M8oNtkv5aeW9b1XRNL8ZmVbbUs+QgB1gDgblmuEw\nzzqqpw9Ljf5k/fHrYZ6Do3OujTves9aCA+y+2hFezhH24ZADZDmv27TpF5TpS9KFkg/KrBM7\nZKVDzQ/5NkqslWk6wDDsWp/5L+faw/HgED+Nb4D5YUP9Bw5Kik2RAI7jYnA+QPU+r6GdOMCX\nSrxXvEaZMziEfAtNfJRP4X3FDvCVystc9zmDPZZ5h+xUK7rFeB7PxW4YBgPnly9MsC4OMHm7\nfntMWzkv0lfaUZ7PeGfiULN2YMCfb9CHq6Ryv9HlFm5d9zXKlkZ59rTYBARGTdYJqkzREJhH\ngM2Gw4A3wHk3axcs6s1SfdOoZZv4ksMGP7FkQys3sqaKOSRdIrHptelDUx1d0tweh13KTjOv\nX0xdD3LTbMM06mL+fVTi5T1Lxg+FjpuwQRzsWS+8CMs1wzdeHOpJ7/Ki9eHboYqvafN6XwsO\nsPvqkIF/pLTrMswA732b9Owu85em7iedSkSGc8CB1d8Asx7KwzXjeqXEu2CaP+jj/dJ136QM\ntpxrz98AT+q4whjWODM4BLHFIQBnGE86XvXWPUMJb6kn6pp1dJXED5a8LhlfHD//sKl8Dyl5\ni3le2wG+QndY5+uqHJyzqIe+4EDiVJZGvXaA/azSieU939bssHb59pj2c17E6udG1o1/cETc\nbNi/6IuvFd3iAPsHCKT1sZJHn/IpIwJxgDMNFpsAh3Q2ARb8uPnGouZAX24Yupy6cdi4VmIj\n88bc9BDawwZPXn7CuVBe3Z6K+RmTbpCTNma1OMC8tHmhHzQpkCmXf6Hqe8+EdfpAUnd0OXz7\nG2DmcFvz3HPYttxqzWdn0GthtfaTfrmvdsRI+2vp+USW2Lz3cYDs+i6g/ddU7fW3NbyDWCOo\nXA+lA9zVYa0e0RjAsmt95r+ca8/OzKSOK4xhPW3HrBH2Gk5kvGCMynk9KRLWS7kPuD6vLRxR\nr0uccJ7PeGOj2uF5bQf4cuUlzXsrPxC2M6/ovB9Ucc3zmhzgLk4s9WA4y5Rz2bqzTZ660VY7\nwHwD7R/Skc8ONU5w3QHmvlkR997mkLQ+VvLoUz5lRGCcQxJIITApgV2qCnCC/ZIfVSeb51I4\nwBxOOCSxkXljVvR25pcAecc5y7cr3DPBG6vDntVMXIzDIQdIXhYLMZr4QWMqeK3uv3VMnoVu\n+yDqcKG8S3lvDz0MB3YS49BwlcTBoDx4lOnly3fcszzODsflX+33vV+xFmbd/kENfNgEjXRf\nHVIV34pOOkf7NIm9jznN/txl/vIs1jk/sLRRD32wQ1auE95NV0rs794fcCr+pzTJAZX3Bhx5\n57U1v2uWc+35G+BJHGDOlNQDb+rBQYotDoHS+ZwmZxxgr4ey5aSxVvgG1uuS9cI42zl1upLm\nmec17z1+XXizxDq3A8xapB6EUW9prEc/g30BK53YPt8Ac77hV6jblKX9nAExnl+ez5jvOL91\nB5h3M1buJY6P4jQsMf6T8uYxPndyNBKIA9yIJYlTJMBh3FYerpxWhixqNkY2vy6Hh7KONnEO\nGxyS2NDKjaxe1i8B5x3X/nr5Ptd+UXij7FPHNMrwYrqwqmiavx7YtW1HqQDqax7D5exDU9t3\nU6IPvU33x6Xx0t5XOk/isOkXKutmH+nHtXRdzjMcpl+cl7L1Bx2eg7Xba+7SHO6zAnp+gtp4\nxATt9N5WzknWzHKsG/Y+Dpkc8DyvFW1ltJ9Duo3Duh1g1okdBfLxntkoXS25n3sr/jrpAKmv\nwZKzledPm3rMvUuZNvV2yQMPDvE4IcT7mH/AwLeCqG89fZ69FGWerYc8Yyke1OIZdoDh7Hnd\notjYLDjAnIvqjiHvUs5CrEveM4w1z2W+sLYwj//wauun95c9lcSaZH0z19dJWN0BrvendPgo\nj+FIN/0N8H5Kfz8ZRhj98re/1DHNb4CZ796zrqqe72su4cq5c9LzHXWauaKxPgTiAPehljJd\nCOAA85M2zJvg8Or2n2yem6vkctO4fc7JUjhssJF7Ex5Vm50nDlRsWktxOGGDZFNfyDHX7UU3\nHOCzq6eYw6I/tOEBvIw5wPY1H2wdUs9TpP86okJe7KdJ60fcn1by7qqIF2/fOcVLnvVyhsSL\n0AcPDhjEGTsOKk5XdJ49WFcvnpeytS3LPfdqzZr4kp/Q9zE7JffpU3gJy3CgY28t53jXx3tv\ndshBjrkzSZ1d2+D8zD/2ZuYvZ5QuTpQP6So2MOpgD2GN4Ch4PXhMr1Qa+7v3OPfX93Wrs3ne\nuM42FbhM3/2gzTPG5ZnGN8B2XMzb1+OevVLuv0AN/YUZaSxsmdOL4QDTRc9J4hjzmbXCmsJw\n4libOMBOG3Vu87zeQ3lZ25yn2GvsCO6i+E0SfcHqa556/Qw7wDixdmR5771dwg6XGCevddJK\n472L44tRnv1znNF+2ozRfveHa38DDAfiZrCJmzL30fGNtTTSuxp9M4+uZZO/IrDWHOCHVJOG\nibOQnjnhDNlL5X8gndNSfzDh82a5OA7wZVUD6xtqvd1sHJurRG8i9TzTuGYjxwFmQys3snrd\ntBdnlHzXSQvl1e2JjRcam/M0NshJG1M6wD4UTlpnn/IcXid5vudcWcfTVOezRzSGlzIv0PuP\nuD+t5N2qipiLfWy9CnEYuVBiL/N62V9xXu4bpDJdl/MMHo+U4Guz48vLtc2hwOUcvkGRZ/hi\nRkL6CSe+2etqdgYncYa6PrNPfvrID27KOd61Hq8Th67LYdf6JsnPPOSQixOFeW4Pr27/eZKS\nnlgl037G28YaoD7qQuyxmMe07gDvNLy95X512SnwvOmyts19sd8xC3UEpwMnhIO8OZG/7oyQ\nNsrYOzBYU0+XspSbdWPe7LJEjdxVzzlggWcxRnaAzX2B7K1v+Z1Qn79cs7ZYmxjrkvGlDYw3\nNqodzGveS5wrKH+DZGONck5kviCsPm94FvkwP9/OLyHvsjdInJ+8hqmzyXi3uSxtosw4o/1u\nM6HflZSjPPWwdpoc4HL/whneKJVpuuxsJY/OhVNgSKDNwK8mVt9QZ35D+jPpl6RzpSYbld6U\ntyntMiX+D6m+iJvykvYIifasRmMTukhi4/PBYFQ/2Tw3VzdHbaSjynZJ9yEJx7bcyOp1sOHj\nKGPkHdf+QcYJPtyWK1SH467uWEX+UjrcCYscMl7fknjZwGG5jJdx+RPUru1w28uD/JwqGXWI\nGffy7Pr8UfntANOui0dlWiB9ve59v7rPwcDrBQeYX3/mhUz6qBctz+Ug8BTp7yWMl7yNOIed\nLvY8Zf669M9dCi1y3t1VPwzgdX7HZ7Her5NgxcGGA84smue2526fNjLe9M97nOt02KfOvmVY\n7xwy2Xswxm+hufhS3b9UOlliTpd5XQcHdA7qXiesf55B+tWS9wkzHLU/KOuCxjzxM1znggWq\nm34nlWuwTblp5qHtdkJ8dnmm0n5PYv20MfcdrtRVOtJtys96HubFUu0Dr9ezDpWeMAIKbGHM\nvJ4mZzvA/qGMH898Zm3ZEWVdug1lmvOXIfP6YokfRLLurpdsnLfheqlEf7B6f3iWn0F57JZh\nMAj9PmX9eg3TD55ZNzuspFMHewb2Kukc6dNc1Iz2u808vzyfsW6YE4g4bcVgdatUnl+Ib5IO\nkCaxksck9azpsmvNAWaw3y3tJ/2qdLy0GMYifm+Hivnp/Wp2gDeqfxwkfbgahYaX5+bqpjeR\nUXknSWdjv1aqb2T1Or3hk87mxyY4yjj8v0Z6+KgMLdJd/xXKW26aFN1fWi+Vmzfpi2X3VcW0\ng018OQ7B7hcvMR+qnNYldNvLw+g+qoAXbpP55e+wKc+kacztpnZ1qZe5cEZVoHR0mSdnV+kc\nQpvYsQ6ZR6dLT5dKB9gHAuYiY9/F5pT5gi4FliAvP4DD2PO7GpzOk46Q7iNdIs2i+cDnOdW1\njcwF5iRj5z3a66VvnW3bwDp8o/SbRQEOlziuzF9s3LuAscEJcJvZ220+NFMX8sGaMldWmco9\nziy538fMj7JuT5t6KMf88vPblJl2HpxeDvGwJI6xV+47iLX78H4D67KedqWXJtfb9ZjLpHf1\neBzzAkZLYTxroXnIGMG4nNfTaJffffX56x/SeE1xRqENnHdx9ODi8Vd0nvE+4X2DA8zavkHC\nOBdeLh0onS/RH8zzb3g13APIh1Eea3KAabvXkPf+QebqYw+FOLwuyw+K7Qf9muJfkj4t1Y32\ncwbEaHvpAPtMRv9pN/sVY3KbVL6bdTk4121UeCQXE5ifMUEVKXrHNYrgLer316RRh+A1imVe\nt7u89OYVrF3AeJPEoaQ8HNSyDS7ZPDdXN1jgi2V2gNnQWAOjnuV8tIONmk1wlD1XNw4ZdbNl\nuuvH8Sw3WIrDcRvJLyfSMDZ5Nu5pW+kA11+E034W9dE3VBovKp7NvBj1Yi3zN8Xddh/kqXNP\nibGtv2Qpb74OSZu27VZU6HYVSa2ihynXGVVOXrbmc4DiZ1fp9Zdvlbylj+9XwuOcqJD5Z6fA\nc7G4vSX6IMU4SJTGoQPWZd/K+8sV9zj2cYBhcG7V8IUOosvVNz/XB76+c8n78sWqkHWBuS6H\nw9Tpfx6lKn9Dch94wg4Sh0wfdEftz+TF2BvZB932a0iszHWwRsp1QpmNVZ6rFbqs+9t3vM2S\nqr33VI9ZMOD5l0gLrbsFK5jwJnsveyPODPLeCFf4t22X9yEcGeQfOCg6daPu5/So9TiVeXmP\ncvBhnsKk/q7qUd3YIjwHjTL6P23O1Mn6w+rzl2vWltcU84J5QhuwUe8b5gRO4oVkkrG2rx/E\nhs7vtYpvK+FAMvew+rzhWdSPUR6zE0u42yBl+P72XuK9v7p1h2MV4Rte+ofji1GWceX5+0v3\nlZqM+e82E5bns7LtxMu2wso8FR3cY98hzyQGU/OYpJ41XXatOsC8CN8gMRFjtydwoJLYKHa9\n/a3OKWzgm6TrJB8ymiphw+Olsrm66RdpU95J0ti42PDYdL2Rjnq5e8PneWx6o/LxEnisRH42\n+iZjUx633rypXqG8jruuXaqIQ6c/SpE/l9h4p2WMBWN1pcTh0IdCRRfN/kQ1/1mtdpj5oNG3\nDYwJ5vI4bmZVZ0k+vzQdkjZt272q8CqFbl+XZzA++0tnVIXYz/xCJf1HRXrTOvIB4ZvKxzxz\nX5nfl1VlR811br9L+s0qn4O5KuKDiNOXO/QBcr+iIb+m+FuL61FR1gCHNg5LfR2iUXVPM93j\n6TnetW47bZeooOOel33rbNsGHzhLvsxJ9mbmNea5Pby6/SdlGWe3mb3d5kMidXFQZ+1glNk4\niA0P9bwTmPNmWbanytYq8DuOd57b06Yg5eBP373ntSnXNQ/jeVRDId5hmJ0QX3v9tOVhvvAu\nHelB5VP+OF71fVhaaK9qeiT77yFSuSc05aunwYKx4R2/2OuCZ/M88+e6brBmTqOmfb6ev821\n5z95PZeJ02/2BtYWY8u3m6xL5gnjjJHe1A6PzwWDXEMH+voqzlnH65V66Avm+Te8Gj7La9kO\neOnErqsy8i5zH+rsGG/at6dk55k6GM8DJM4F3o8U3WL0fQfJbb5BcdapjfLUw9qhDri4rYTe\nv3g2Z0D2HerrazyD/crP6FvPmi837kC+5gGtUQD7qt8s+q4viCZcbEIcBq6TfLhqyudNYnN1\n09dcssF8RrofFxOaDyXXqB5vaN6g61XzAvDmTN5R7T9e96gDZrtITXaKEp/fdKNIow5eLE0b\npDfzev1s/DyXl/q0zC8BXk5wMrNp1d9UzyFKfGjthl9kJJfxWrYFL912h/sUuessucULFHM4\nvJru526qjjUB3z4HqYNUjhfgGRLGi5CXK2ms3bMljHT2eB9KScNgya+sncmFzHOH+Xf5IOX2\nh8o/VPrTqnu0v743mCvzset7xfOtqn6qgccRLrZjFeGLDaWvAABAAElEQVRboHHGemf9sx7b\nOgDj6uxy/1nK/MEWBTyH+q4R72sX61k+9LpO5gT772KZx94hz+Fw+ROJ+YuV74JhytZP8nKf\n/ZE1ziHU5RTdEudwXh7QWftXkkFGOrarZIZ9x9v8LlJd3nOoe5xR7lKJvXySw/G457xIGT7U\nkMkOB04I8p7hPbIcn4biW5IYC95hODJlPVsyjIm4Hc7GGjjMF7XQew77UVuDL/sdbfR+1rZs\nOSfMpW3ZPvmY08xvj0W9DtLhzPwdladeZty198urlLGcv+wR7OvXVBWwxpinPJdxxrjn9TNI\nqD7YQ7ALh8GWH27xDuJ9c12VTj2MC85kvT/MK69r9gbMTiwhTiFG+90G92VwQx97VZE5hTwD\noyzvTc4f2LphMO+TftL366vUugPMs9l3EHUxZmVbvZ4d8j5hT3WbFe1ksMD8jOFVPjsT6HpQ\n6fyAFFiRBHhBYHsPg4k+2cQ3SRwkfdBqqpADPMbmwqbuRU7agdJjpaO4mNB8QKE93tDYsJqM\nF4A3fDZpb+T1vCcq4bQqsXxJlvnmdHH/MqEhTjvoP+2qt8kvXHiW5udN44cDrteHnSuUcLXk\nw7Dvtw3Z5J/fMjNz7mCJA4qt7GvfNlCOF4XLzynOQZ8Xn9kpusX80nS45cYUI/T1Eom5VR4y\n2j7iEGW8shJlOACxXuYkXqqlA6zLLT+Vf7LirGkOCMz/yyVe2l7vzG/aBK/6XD9JaY+RMByF\n0qEkbU6iHGPexFXJjXaoUhkP2rQYxhyij/tInlu0f500ztivWPesA6+JcWWmef+XVNmjWlRo\ndp7jLYrMy+J9mXFwnLrYh7E+c3RYcvynx6GcMxwUb5A4pKLyXaDLeeZyrFfaybwuzYdl1gj9\n8XuG/XRjlfHSKqQOWPJM11vdah3Aj+ewPrtw473EnoDV194wdTqfrHXeFV4LrpV9A2Ot3CjZ\nEfUe3Hb+47h43hDWHRkljbSH6w4MynPpm3T9yhEl5qp01nNbY9zp62elp7YtVOWjLA4a1nd+\nDEu3+zR7h/VSsGWsunKu11NeswawDVI5fx3n/YCx17MumSce70sV91h8TPHjJMx7ygXDyy2/\nQs0aZ2/1mqUvGPV5/g0S9MGzeCbmNc07HHNI3GuYeJ3bniTK5iSXYa3zzlovYU3z3Ovx+mGW\nwd5Uns+YT9TD2sFYy26rOZHOvoZtGgZbrqvL1oH3Q/a02AQEyo1mgmpSdJUR4AWJ2QF+4PBy\n5CeHir+VvDDLjGxCHDSuk+x8lvcdd1kWNfJBhfuH8SGrH7qHqd0+3QY2XTZgzBvc8GrrJ5u+\nN3w2v1H5nqh775P4iWbTi5FDFS8rc1W00aifNiFvls7IyxdzOLzaepAfV7fztwk5JNEGGNF/\nv/wU7WS/otwfkA5oUWoP5aHPnnMU4WXGC4T50PdwT9vPL8rvo/h5Ei+hOkslbXHEeLYNR+S9\nvphCuJvq4LBwtdSnXzDaINlgxHrZX+Lw4IOGX5CsLQ4U75d+UWI+bpZuky6TGG+M+cc8R+UL\nnvcEzyQfhxnGqb4W4fpNCaN/bY21zQGkHPe2ZdvkYxzPkODDHMPWVRpcLPBBX9m3cGaa1vUC\nRSe+xX7BDxx4Lt8qLGSM581Sn7lEvfSTwxv99P7IuvE86luvqhhrPnCWfJl77D9YeYAcpsz/\ndDkY7SWxX5VGeczvFbhilKO/2FUSh2raQl9/LLleRTsZ/Lrum8xNDtGXVE8a9Z6pbk8U7KrS\n7AXm7spIw3BCkK+9R7blQV/YgzBC1zNI0Mc/Sa/xRS08UNecF8q9hb3kyFo+X85VEfrU1rzX\n/bUKHCt1YQ0D9k32BHNRdFGM+cwaxGByqMR+UBpsYYw8r8v7feLsl/Rvo+S9gHoc9/piXfEe\noA3MF+xSifHCniA9ZBDbyvjC6vqGKuQ9c4XEesHsQJbzb3hnvgPMOYv1bCfWIXlpP/shRry0\nPasL+sJ+iVEW1odIvCdY//U56zlCezHa7zSueX/RdnOgfu877CtwwtjXMO87PvMOU9t/ssYw\nP2N4lc/OBDjYxEKgTsAHxTndOEI6VVrogHqw7r9UanpRsXlvkthUd5RGmRe1Dyrl5rC+KlS+\nGEfVMyqd+nhR8lJhs2Lz8CZabmZK3mJsZN6c2fya2s8aol2nSfRzF6luPBcb56SyQfIcNk1v\nlooODI6Yw+HV1oOMx8zpk4QcEi6pKrhaIS+Ftkb7vi0dJr2pKnRAFY4KGHu/rA4tMpF2lcSh\nwy+14narKGOIA0y4jTQnbZA2Sk1jxXN4wbo9it7hYdLDiUzJOCTA9xrJh5wuVTOPfJigHPOY\n+c0avUCi/ZhfkNx7jMSzKMt4whSjHYw35vnHHCzXBO3dTiLfOgljLZT85nTNuNMWH4IUHWue\nG+PWxtiKRmRgPp4qwWS/Kg99YJxxOhYy+niddKXU1gFYqL4u945XZsbjTtK4Z9MXxp3++LCl\naGtjbdBPRJ8x5gjrBvP6x2n61UFKuw/a/oAxWakTc0ic8eFgjDGHmb+jrGTDPuz92vnZSzHm\n5c8lv2eYu+wBNh/eYfkjiZD2dzXPmWtUsO3aNnPWIlauvWHK9D5HvYu8Fng3won1jrF+sHJ8\nhinNn3NKdj+oZ/tatofp+u3SXrV0Lv0OO7i6h2PB+B4usXfXzWcS96l+v+maPYy5cLLE+M5J\nbc1zZin2A94/7jNjwLp7W62hsIUx8ryuZel86Xcu66icv457fXld0oYbq6dcqnA3ifbSHo8n\n8/lmifuY1yR1keY6XQ8h9ZbGHsAzbdRhx9ch47KzxNq9XPLcVXRgezqi0GVoF/PsUOkLElaf\n616PvBexGyT2ZhvlqYe1g7Gfuq3mRLr35k1cyHw9vGr/CQvMzxhe5bMzgTt2LpECa4GAD6O8\nYI6sOuyDalP//TK7f+0mGwGbAwueTc4vekVvZ97AWdTlpkHGw6rcHHD62m+p4D9JtMkbLnWx\nqZWbGWk28nKQwcjnjXCQUH2sU0gfL5LYgMsDmS4H5he0uTq9HlI/myuqb468fG+TCEvzZj2u\n7rLMuDgvrourTF0OchQ5RjpC+q7EAeMcaX+pbo8vEnav4syTQ4p0XmZXSVdLPoSz+X9Rcr8f\nq7gPCoreziiHc8Bex/zbR/qxtFFqGitemowlz7bNKQKThZ7jvG1C+suLH7bu10LlyFM+m/V2\nYVGAAx2sWR/1dLKxtp5NREY/6NtmLmQcVs0fPsxz5l85173uyOe5rOi8b2rM9TKluz7yjLMD\nqwy0azGM8YQ185l+cNCn//D0HFK00eBxnTRqXTcWmiDxQyrr+X+i4t+q6uJQWdpJuvhykcCB\nb0N1TbyruZ/0lT0PY86xDvjBgefoUxT/M+nOEvNtoXeCbg/m3NcVbsfFCGP/xMq1WM5v5rbf\nDYOM1cdzFT5GYgzZIzDGlzVVGuUxQhyF7bmQ8Tz2ABtzhHkLv7OlO0rlHqDLVga/ayXaYaeh\nqeALlfjH1Q0zpw1YufaGKdP79Pqtvy88RjfqUcjXrB/YleOjy5F2tO58o7p7k0LXQxJrj/H+\nqfSnUt3cJq8B5j3rFB771TPrmj0Ho0/ofRLjtpCxz1wiXSExH0qnSJcLGgzYC5g39fewC9LH\naRjcMdYfcdpZbytzmT6gkrMuextznvXE/PW8pDLmMvOAuYH9ROJdzHN5Psb83U3yOLKeMMbv\nOsnvnBtIlD1Neq/EesFcd1N/dtB95o2N599cXdiZ/aGuaT9r+JwqrmCLwc9rrCxLP/aX+jrA\njDlzfZOEHSa5rbSTtmMOmT+Yr4dX7T9pL+ZnDK/y2ZnAuM2ic4UpsCIJPFStXl+0nJcEGwgO\n8OFVetMLqLq15ae5bCKlHagLnLbzJTbAckPV5TzzIYdNloXtRU4m2vY9aV8uGoxDEM9ayB6o\nmwdItMEbLvnZjNmgm4xN33lpP226Uy3j/aprDotsbE0HhV2rPM5bXd4uuJtScEDYNInbWKds\n6hdL9RcvfefFMa5uZWltvLg4JGBXSz4ADxLGfLD5f0d6rfRy6XSpPi8Yz09LHjPmG/OEF9Ah\nku3eilwl0Qb6jzGGx0nHS8zJz0jM31HGGDL/MPrBoWmDxFjVWSppy8uTOcGLDZuTtpea8it5\npHEYaNpjzZd+0b6FjPl6lvTCIhMv8guKa78IYcM8tDl9RyU8TTpDgjUsN0sY40x7MPp8fSXi\nNphh9AcxJhwE95U+KL1dmpM2SJdK5GlrtBmjXYthO6tSDibnSMwX1ss2ErZuGGz55N5cdUUe\n1iDrfoNEXxfTGOfnSo+oHvIkhe+XGMM6zwcp7eGS9wjm9Y8ljHhXY37QT/Y65vz2EvOSOcIc\ndZ0HK87+x/w7UfpOda2g0chDfTi0owzmP5G8b25XxT2PuVe+C3Q5sNfo82USa3KDxHtjH+ka\nqTTKY9xHvGdoE/27UrKxDuBMX39UJbpN1eWWgLXBfIJD3cySdvCMUfYY3TihusnYY8zTG6Vy\n7ZE+TfNcqr8vYILdJNEGxoF2kQ4PxqmNPUSZvlFl/LlC5pKNZ7Mfvll6isQzSvMe4HfA7tVN\n3tFHlhkVZxxZvxukXSXWA3tkvV9Kmmc8g7HGLpQWmpuDTMUHc21jpaa5ASPWy+HSKKPd/0/y\n+2xUPt59GG0kzlyDB/xssIUx85r9qs5TSZ2N/fIqib2gnL/Ey7XFvrSDxDOZL9hlEmPsMfB4\nsiZ4r9xUhV6TZ+maseVZmOshLOcN99gDeKaNOm6pLhz+UNd7S3eWzpXMUNHBXGY+n8KFzGVu\nVvxQiTJfleDJvCrtbrqgTbQfo82k2Vgj1HOx9CXp0ZLbWuaFF3WYY9O+pttjzeUY99gEBMrF\nNEE1KbrCCfyR2s9LycYGxmbAZnJElbhfFTYFfoncv3bz4bpmU9osccBiIxxlLOpbJTYaFjYv\nCozDAAebj0tzUn3O7qk02voP0kLGS4kXGH3zhkv+coPiurRy0ycfVj+c8Hw2NDZ4Xo48A6Od\n75c4EOwqseFSX728krYY93gOmzsvFjZlbCfpThIvjHJT1+Vgs/6+wj24GGFsvM8dca/cyJ2F\nutjMMfpGuxcyDo1/J/HSeqD0beld0r9IP5L2l0o7oLrwfNld1xz+KHdIdY+Afl8lMX94BjY3\n+Bz+g2jHVPGDqrApoO3nVzfuq5C+4SxcKd1HqtvOSjinSiSOsQ4w5k5bYz4z909qKEA98OWw\n5H41ZBskvV6ftLvkwpzjYGTzyxaeTelPUDoc/kqi/3CFKXaJBH+MucD8Y62W83RO17SVOXmo\nxEHnPOkI6VnSGyTKwpX6OAS1NeYCz1to/ratqykf64U5dK7EHrZOwthrHB8k6OOt0j9VF/R/\nG4m2se5oJ9eLZV4L++gBzB3a+g3Jh0pFt9i+irG/PKBKYTxhj42bT8Nc8z/Zl+nntVUy19Rz\njcS4u07PQdbDgdIOkteGooP1/mtEZLTviYPY1jVbXc4LWIM/kJjjGGsDzp7HzG141A1eB0uU\nZy2zf8xJ7oOiA/tJFfJOQexRzAls4zAYfDJvmYP0lfV/m0TdTUbfGZ+HNNw0S9ix5kYZ4zxX\n3byHQp7HGKBy7elyanZn1UTfYVrfy7atnnKjQlRyOlPXo1hUxQYBdTM3mbcYzsR2g9jww8/8\nrC6ZH+XcIQf7EGPpecY+wnieKh0pleayX1PirpLfMYyLjXlUN+pk78WYY+yl4+z5yvBsiXc7\n7UNNPJiPrAn2w1H2GN04STp6VIYqnWcxFy6V4Eo7GT/ab2OMGCs4Y1z3sdeokNcf7zzeDXAv\n5y9x5rTN69JtIJ22MhZ7cSHzns58vn6QMqz7hirugH5iNw2DwfnnGYrTbxt7AM+0UcfN1cUt\nCuHAO8njf47i9MXmcWa+YGVZxmSDdLl0hWQWig6MNe32k8Czmb93kZhjd5Lc9ncrjrmtFyo+\nR4LsbhL7ke8xV/oYLHh/0efYBAQYxNjaJsAC5uVydIWBxcXG8VWJ+DESB0hvLIoONrbdiVTG\nhscL3C8hpx+ryH9WF2xybCQYG8Fp0qO4qIxncUDB2CC4xg6VaOMnJF6m3lQVHfx0+vMKefYR\nkg9qis4zNmBezBj52NxtbGyjDhxs+s7rTbqe937Kc1FVWflifJXSXiA9QeKlcKaEkX+U+UXh\nF4Q3SL8IzlJBXow2Xj608dvSQvWeoPsfasjDmF8usZGXBmMOhBgvvVFcBxn08XjpxdJjpQdK\ntMd2tiL1eXFAddNziudxKPmBdIjEeGP0m7l3tbSThO0zDAaHz4dV8QOrsB4wX+jbBdWNhypk\nz2MsGKuSpS4Hxtw/p4jzMvRcbGK8re6fLD2gKuPgiYrcQ3qME6pwXZUOF9gyfqOMNfZfJNiY\nFXMCLhdKNq+b+yuhTL9J1xwOniadIp0u3UeiDZsljHH2Wi7nXznPYU55jPFlznDYeIl0o/S/\nJdbgBulSqTyk6XKkmcXJysEcWAxjPDdJrJ2DJJ4JL9Ys8dLW64L+HS55r7pO8R9KzAH2ucUy\nxg5jnyLOGmCONPH0XHiQ7mOsDcaEfWPcWlWW2xl9pZ8IY94yL1l3yHUerDg2J7kNXsukHyO9\ngIjswRLri/XrNavoPKPdrJ8zJOYlxhq7VWJeYj+VYI+9TDpRYm4ydjybkLXMGG8vsaZK48CJ\nMeaI/cDP2qi4Dc7MD/YH0mm38yk6zzxWh85LHV7A7lqJdsBwlDHO9Iv2U4axo9+E9G8SO0WF\nH9pQAXsZ/fuuVN/Ltqvys2ewprn2/nim4pQdZw9Rhp9Lp1UZqYcxsfFM2J4rcQ8GpXH/cxLj\nwPzfXWIe0N4jpdLmdEEd35F2lZgLmOcl8X+Q3kikMPYZ6sQulOwYDRJGfPyq0n9LYj7Q/lHv\nDuYF/J4j1fumpIE9uQq9lqrLgXP7bl2wX2H3lpjTzEPa6LEo28tchjccMK67GnPtXdLzqoI8\nn2cyf5mXNvYA0mw/VYT5y/jSBuwy6c4SY3WztJvEOLK/XC9hvyn96yC29YP1grkfL1GcvfZb\nkp/BvOWZtlcr8oHq4haFV0ibJeYCdp5kllxTH+38NhcyymCE/DDl01zIqKc+12Hk9pPnUj5k\nzDn6i9Ff7KMS/NzWcxX3nOTd/ROJdyVt4Rp7i/S7g1i7D5i4/nYlkquRAJMqtrYJcDhho2OD\nYPPYXcL+cxgMNqBPKO5FTPKfSmyaNsqeJvlg4PRjFHE9bHI8Bzu8EvUeS4KMzftng9j8Q896\npV0gUf+t0r6S7ThF2LweIbGhEDYZBxU2YvIcIZUbORsbG1zdWBukO683wHpeXqgXVYV5MfKS\nJO0PJV5gB0lw/a7EJnk/aZTdTTc4ACGMa4yXIXaWtMsgNvzgWdi3JcZt1Ho+jEyyxw+DLZ8c\nWHhG/WVMXT4kXK04G/W20igz95coA/OJ9tjOVmRPqTwI7V/d9Fj6eWcoHb6ea7zArpJ4sd1L\nwqifzf+BEnPnRulAqclchnFg/GgnL7jLpY2S+Sm6xXZS7NzqiufPVXF40I+6PV8JtOP42o1n\n65q2MUdL46XJPD5HYm65jYrezqj7YunPJDNxGy4scnvdsIY8F32be7D6nERdrINDJbhi9Iv5\nSTrs4YTKeQ7zUyXWD3Vx0PmxxEHhU9LrpIdL10nUt7s0yl6oG4+tbjJusPiSxJqZtsGDwwJ9\nZe3AfjeJ8UfrJPrAHoLB5SbpRdKOEnattEFiLFnLkxptOll6cK2ick3QTtYdc/RSiTaXxrph\n7rgO5iz5EfE2BhcbfWXsEMY189J1EmefgBMHuDnJez1txXaR7i09VILpiRL7wHelOanJ4I99\nX/Ja5F3C/GIcMNa62/omxV8q+dmwPEq6UvJ8ZrxKozzGOmD+Uoa2Mu9cRtEBZ+Y5Rr9H7Q/c\n9/OZL3W7hxLgSDvuKbFuPU6KDmw7fXq+80zKuN3XK16uPV12MtYyY/DIhlKeR9/SvfsV93dW\nHC4Y8xxOMIcTca91RRsNHn8kPUpivD121LW9ZOOZF0mwP1/y/q/oIB/P+4xE/9nn2EcukU6T\neG+XBrcLJO7TZ89DeNseocjDfFGFcKcMdqHEc2zPU+T5vijCwxRnDKmbuTZqbsDhZAkGvy41\n2QlKhM/BtZs842XSM6p01tImiWe573Ar27udrhmfn0lYyXqYMv6TObyNdHyVlf2DdXGNxPy1\nMUdJs7EP+FzAOGPmCqszJNrHmN5N8t7yUcWZA6W5Xtdzqm4yhyn3Sslz02tZSYMvaNgbsVsk\n3uvwwm6TzpXgQR2Y5x5jjt08DLaEn66uL1fofalKGtRxvS8UMndPk54p3VnCPOcZi/8m/QeJ\nsrMl9k3ywQtu2A0Sa4y193rpqVJbg0fJom255KsRuGPtOpdrj8CR6jKbEwvzaImNgg3kLGmz\nxML+pMTmb+PQ8QhfKNxL+rx0L4kND+Pltpv0VS5kPGPHQWz4jwRsUPyD0vskNko2Ay9qNhFv\nemz+p0tsjhzgqdf2DEW+JF0mfU06TrK9ThE2F+xwiU3rHIl+XCvZ2Ii8STqNkLbyYnBeb4Du\nA3kwXkje0K9UnP6/ULpE+hPpIGlXibazYcN3lPHi5zneJNkwsftIpFPHvSWbN+pvK4EN1tfc\nJ/4WIjL6jz1+GGz5dPqhW1KGLw2ewbMwXiTYIcOg8ZO5wHxhPG6WvifZeAGwz5TzZ39d8zJ3\n2u6K8zyedZ70ZAnbSbpKYh4yt7B9pE9KsDpM+oQE4ya7R5V4jcKrpWMl5hLmsRpeDT+Zh8wF\n5hO8mT9z0ibpTKlp7P6r0unLeslGPfThndIBEuvAdqAiF0jMcdpUHjJ0Oc+O0dUXJBiaFW2A\nsV/+im5ZN8Qv5KOwnyrOPP6s5DG9r+IwxUjbVmKOwZR+IzjYYM64XCLtIXFI8Lz4F8VvkU6R\nMNpV9neQWH3cSeEfS6+prmEDC+pqYltlaxXcX7l+JLHWbLtUEcaP+cl6Okqi/Yg18nbp7yTK\nMd5/K72wiisY7Fv07xxp1DwjH+PzCCJj7BW6f6z067V8sIA7+xtxxhxjLsLzMdJfSrSRtcC8\nf5DE2HLNeDLPiY+y7Ysb31X8jdU16+Ra6brimnqoz3UerDjP+qK0twTv2yTaisGG66sl+L1I\nYm6cL81JTQZ/yrC2mH/Uv6fk/VTRwdqDCXsU9x4o7S/xHNYQ+xJrmX0Co72lkQcj5B0CA+Y/\n+Vm3tksUYX5isKRO2tRkPL++5plrtG9HCZa0A67/W/qoxP5s21uRO0o3SftI5KMMxhxgHfa1\n9VVBh2U98IbD96X7VTdgfob0S9U1bWKt0Bfaydq5QhrFQrcGjsDrFb5O+gYJlf1c4Xa+UMgz\nPbbnKs642pjjtOVkiXKMK++FS6VvS5Rl3Gy0bYPE+iD9QAnmrEOM8aB8nQNpjDV2gUQ/bbT/\nA9IbnKBwL+meEnOD9jIvEPXXjWefI71XenL9pq5pC/V9SGI9lfaQ6uJJVbizQthvlA6XbpF+\nIJXthS2sPMeZ213NfB6pgvDnuVdJsKTftnKOkvYT6a4Sz2RdYbSX+GGS5wHvi7tLzOtR5rnv\neshH/j+SGIt7S9hPh8HtPm9WCnOUdmO0nTHCXBZuF0qef/DEKIs+x4Xscon5VFpT+/9RGZ4l\neV1Th+3/KPLh6uIcheSZk+AFN4xwB+nXJBgyDvBvY9TjMW+TP3lGELjjiPQkrx0CR6qrp0nf\nko6W2LDYTHgRbpB+KP1AupvEC5SNn82E+P0lDs+7St5AOBxgD5fYhH7EhYzDFRsJi/xQ6Qzp\nv0qkeRPwomajY5FjD5G+MYgND8q8hDDqear0z1zIvigdR0RG+D+lp3EhY0P+nnSeRDlvuIqO\nPHCw4WNsphgb8m0S7S0NXt5U6S8HBTh+SYLbgRIvd17UbMD3kzAYvnIQ2/oB4xsqkco1xibO\ny4X6OZjyMsZ4Fi/A73Mhoy22VyjyVomXMv0/RXqsVK550rFDh8Hgk7ZiPiRcqviPJcazbrwg\nEfX8jgSfMyWPo6KDAwx98rwg7QCJ+eaxpN0XS9jHpacPYlv7zRjsVKVR5isS7eKl836JPt5Z\nsnEwoJ5DqgQOy2h36fQqbaNC5nJpvPyxzRIvU67npA3SRZLHTtGBPUmfB0rvlsySG4+Ttpf+\nu0RdzEcbffeaoF+Mcdl25yOE+VelcyU4014OUJdIt0o21ouNOVYa91h7X5eYK5skDB4YHDHm\nI2uOeY48z7dVnH4zB3guxlxmX6C+T0qlUR/7Aeusbo9XwjrpYdUN2MGCsb+XNCdR3w5SV3un\nCuwvPaYo6DnDWMLwRomxuLwSbTlaOkY6UrpFeptEuRMl5jNzF6O/tLfJ7qTEj0j/IvmZTfng\n+9vSF6WTpDIvc/gLVdqDFZ4tYTDfTXqu9CvSegn7sER7dpdY08wzBMcm206JZ0kvkeakA6Q3\nVuGOCpkjrKefSsw10q6WXOdBijPu35Yoy3xhDcMcI4259zGJvZc94E8k5s2c1GT3USL1M/6s\nAdrOXKMe24cUeYZE/6lzb4l3AnzoD3alxHrGyr2da48fZenbXST2U8qUxrzFWFfXSNynfU3G\nWJ0i0fdtqwzvUPheySyp407SCRJ9og+2fRS5STpNIu4yis5be1x3Nc8Ph2V55hFjyF62R3WD\nPZL0R0vMf/pPu7DHSpukKyTmD/OiNNIw5utHpQ9K/yjZfq7I9r5QCAfGGjtP2ncQG364PRfo\nkrV2mMTcvkQ6Q2L8jpJsc4pskOgPc2cX6bOS6zxCcWwv6R6D2DAfY+o2MM+Yx9tIO0iHS38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s+2iZ2DLclfFvkpzLJ8iDJBWT55DdSLaf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\ngf8DThV51Rv09h0AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x11(width=4.875,height=2.5,pointsize=8)\n",
    "plot(r.chef^2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From these 2 plots it's easy to see that the returns became more volatile towards the end of study period."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the squared and absolute returns for the CREF data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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t28ia9tAiZgAv1EwA5wP9WW82oCJmAC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/l/gKEWU4rhyLjz5wPpF3WBUukxCj/1zD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\ngAQkIAEJSEACEpCABCQgAQlIQAIdCfw/K9fikztcau0AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(TSA)\n",
    "data(usd.hkd)\n",
    "plot(ts(abs(usd.hkd$hkrate), freq=1), type='l', xlab='day', ylab='abs(return)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kAAp2SpPqRjEhJoR8AZ4HZkDJeABKaW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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(TSA)\n",
    "data(usd.hkd)\n",
    "plot(ts(usd.hkd$hkrate^2, freq=1), type='l', xlab='day', ylab='return^2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "From the above 2 plots we can see that the volatility clustering is evident particularly\n",
    "during the second half year of 2005."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since \n",
    "$$ \\eta_t = r^2_t - \\sigma_{t|t-1}^2 $$\n",
    "and\n",
    "$$ r_t = \\sigma_{t|t-1} \\epsilon_t $$\n",
    "where $\\{\\epsilon_t\\}$ is a sequence of i.i.d. random variables with zero mean and unit variance and $\\epsilon_t$\n",
    "is independent of $r_{t−j}$, $j = 1, 2, \\ldots$, we have\n",
    "$$ E(\\eta_t) = E(\\sigma^2_{t|t-1} (\\epsilon_t^2 - 1)) \\\\\n",
    " = E(E(\\sigma^2_{t|t-1} (\\epsilon_t^2 - 1) |  r_{t-1}, r_{t-2}, \\ldots)) \\\\\n",
    " = E(\\sigma^2_{t|t-1} E((\\epsilon_t^2 - 1) |  r_{t-1}, r_{t-2}, \\ldots)) \\\\\n",
    " = E(\\sigma^2_{t|t-1} \\times 0) = 0\n",
    " $$\n",
    "and for every k > 0,\n",
    "$$ E(\\eta_t \\eta_{t-k}) = E(\\sigma^2_{t|t-1} (\\epsilon_t^2 - 1) (r_{t-k}^2 - \\sigma_{t-k|t-k-1}^2) \\\\\n",
    " = E(E(\\sigma^2_{t|t-1} (\\epsilon_t^2 - 1) (r_{t-k}^2 - \\sigma_{t-k|t-k-1}^2 |  r_{t-1}, r_{t-2}, \\ldots)) \\\\\n",
    " = E(\\sigma^2_{t|t-1} (r_{t-k}^2 - \\sigma_{t-k|t-k-1}^2 E((\\epsilon_t^2 - 1) |  r_{t-1}, r_{t-2}, \\ldots)) \\\\\n",
    " = E(\\sigma^2_{t|t-1} (r_{t-k}^2 - \\sigma_{t-k|t-k-1}^2 \\times 0) = 0 $$\n",
    " \n",
    "Hence, \n",
    "$$ Cov (\\eta_t, \\eta_{t-k}) = E (\\eta_t \\eta_{t-k}) - E (\\eta_t) E(\\eta_{t-k}) = 0 $$\n",
    "which means that $\\{\\eta_t\\}$ is a serially uncorrelated sequence. Similarly, we obtain\n",
    "$$ E(\\eta_t r_{t-k}^2) = E(\\sigma^2_{t|t-1} (\\epsilon_t^2 - 1) r_{t-k}^2) \\\\\n",
    " = E(E(\\sigma^2_{t|t-1} (\\epsilon_t^2 - 1) r_{t-k}^2 |  r_{t-1}, r_{t-2}, \\ldots)) \\\\\n",
    " = E(\\sigma^2_{t|t-1} E((\\epsilon_t^2 - 1) r_{t-k}^2 |  r_{t-1}, r_{t-2}, \\ldots)) \\\\\n",
    " = E(\\sigma^2_{t|t-1} r_{t-k}^2 \\times 0) = 0\n",
    " $$\n",
    "So \n",
    "$$ Cov (\\eta_t, r_{t-k}^2) = E (\\eta_t r_{t-k}^2) - E (\\eta_t) E(r_{t-k}^2) = 0 $$\n",
    "which means that $\\eta_t$ is uncorrelated with past squared returns."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Substituting $ \\sigma_{t|t-1}^2 = r_t^2 - \\eta_t $  into Equation (12.2.2), we have\n",
    "$$ r_t^2 - \\eta_t = \\omega + \\alpha r^2_{t-1} \\\\\n",
    "\\implies r_t^2 = \\eta_t + \\omega + \\alpha r^2_{t-1} $$\n",
    "which is Equation (12.2.5)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Equation (12.2.2) tells us\n",
    "$$ \\sigma^2_{t|t-1} = \\omega + \\alpha r^2_{t-1} \\\\\n",
    "\\implies \\sigma^4_{t|t-1} = \\omega^2 + 2 \\omega \\alpha r_{t-1}^2 + \\alpha^2 r^4_{t-1} $$\n",
    "Let us take expectation on both sides of the last equation. Denoting $$\\tau = E (\\sigma_{t|t-1}^4)$$ and since $$E"
   ]
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