{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "The Floods of the Nile\n", "======================\n", "\n", "History\n", "-------\n", "\n", "The Nile river, in Egypt, played a crucial role in the development of the Egyptian civilization during antiquity. In particular\n", "its yearly summer floods would fertilize the arable land and allow the abundant production of food.\n", "\n", "The authority of the Pharaoh was based on the belief that he was causing the flood at will. As a consequence, predicting the\n", "time and amplitude of the floods was key to his political power. This led to the recording of the level of the flood every year.\n", "One of the first known example of time-series recorded in history.\n", "\n", "As we will see later in this notebook, modern study of the floods of the Nile led to the discovery of the so-called long range dependency effect. This effect occurs in many natural processes and reflect the fact that these processes have strong local correlation in time. This effect is also related to fractals and was also discovered by Mandelbrot when studying financial data.\n", "\n", "![](http://www.tufts.edu/alumni/magazine/spring2007/images/features/A4763_NS.jpg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Data\n", "--------\n", "\n", "The data we will play with is the monthly flow average at Dongola for years 1870 to 1984. Dongola is the station just upstream of Aswan. It is used instead of Aswan as after the [High Aswan dam](https://en.wikipedia.org/wiki/Aswan_Dam) was build, the flow became regulated and doesn't actually reflect the natural variability in the flow. \n", "\n", "\n", "\n", "The unit of the data is $m^3/s$.\n", "\n", "But, let us first start pylab." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now import our data from a text file and reshape it into a vector. We create a time-indexed vector where the unit is one year and months are spaced by $\\frac{1}{12}$. In the first few years, entries are missing, so we remove the data corresponding the these years." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Import data from a text file\n", "fp = open(\"FloodsOfTheNile_data.txt\", \"rb\")\n", "FN = loadtxt(fp ,delimiter=\",\",skiprows=2)\n", "fp.close()\n", "\n", "# Linearize the matrix\n", "amplitude = reshape(FN[:,1:-1], (-1,1))\n", "\n", "# create time index, slices of 1/12 are for months\n", "time = arange(FN[0,0],FN[-1,0]+1,1./12.)\n", "\n", "# identify unavailable values\n", "I = np.nonzero(amplitude >= 0)[0]\n", "\n", "# identify start of continuous values, start in january\n", "s = (ceil(max(nonzero(amplitude < 0)[0])/12)+1)*12\n", "\n", "# compact all this\n", "T = time[s:]\n", "A = array([float(amplitude[i]) for i in range(int(s),len(amplitude))])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's take a first look at the data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figure()\n", "plot(time[I], amplitude[I])\n", "title('Floods of the Nile')\n", "xlim(time[0], time[-1])\n", "xlabel('Year')\n", "ylabel('Flow [m$^3$/s]')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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SET2HXWXr6m5abdtCrnB1mgknEwDYsQM45ZTMCC+bxYssc5Q8wraV\nyfwU5dCi/J0Qhkx0vsCgHWRBkPlw06pu4RoVNv2Q6dMdocikrKwss7nnAGwd8KrVd9RBpUvbZqWh\n+lv3rFKjo+avyicdzeSBB4CXXkqQCX9PdaW4qTyquqkm5Jo1QGEh8PGPp/5mOseQrmYi0wvSTLq6\n/LJ+9rP+e7Y+Ew7TDjLduNbht7/1v+T4b/+m/j3KWNJBt/iIcs6EC0spOE0mNNVFmCYySdfMZZo/\nYdJTwURMmf6MsBU3nXvuuRmJk4uw3RqsW/1k0sxlMjuYoFsRcs3ERJqm+pjqoMrfdmuwzvQTBaq6\n0d88n0suAa69Vp+GCqbVu6mv03HAd3UBe/eqy5YJjSGsFnn55cDnP29OPyhtW6SrmejCw/hM+NUz\nPF2bdouCzk47bTEMbPoh02RipZm89tprmDhxojHO/v37M1Kg7obNKt20+snkbi45kGx3c+nC8/OD\nz4LYkKYqrsnvwmH6Qp4qXVOeJoEiy6Ujh1NOUYdH0Uw4Ojr8fyp/jyyfjkx0+UTRTHRIV+Bfdx3w\niU8An/lMcppAalvt2wd85CP+jcK2i6QgMnnvPWDEiGCtWM7ZMGaubGkmOnR0ROsLG42Gyvz228Cx\nT0HF0SNmrtdeey04oXQ/bt1D0H11MKpmYkKQNhJmxaPTDPhzfj7Q3m6OIx2yQQ54HjfsalcXLoW/\nTsiatAdZLl1c0/ZkXTivW2srsHIl8KUvJb9z6aX+HVr0vTaTmUln5lKNCVW8KNAtknTQtdPPfuZ/\nd4WTCc+D5/Pmm0DQ5s8gnwlPGwBGjvS/dU9f5rZdGEnBmQ6Z2GyhV0E3rrnDPYxMMREQL3dTE3Dx\nxcm7O4Ee0kyOR18JweSA1wkxE8nYrDBs1WdTuibhp7pNVCdEwvpMgggkKpnoyied1xR28KC+LEGa\njgqmPubPv/2tbyr70peS33nqKbtrzW00Ex4H0GsmLS3+guGkk8x52vSbhEmg6b4tIscSH4dRfD26\ncyb79gH08VTTODSRiY3PJMo85di50z8Me+zjsdr+5ppJFA1FBd5uR46od271iM/keIaJQII6OBOa\nSZRVvSpdnobqq222RBCkvus0Gh3xUhqmtjJpErqyHjqk7qugrcG2ZMLDbSe67lOuclzpyESVp6ls\nY8YAs2aZy8TLoCqLrr+jkInsq0xuaebtofOl2NbNlA+9K9PjY8pmngA+4ak2e/DyAr71IAqZmBZx\nPFzXF45MMgzbrcHZ8pmYfA9hzFz8mcjE5AMKyj8oT13athpBFDOXqc6muDYwaSY8zFRXU/upyMRG\nG5L5yDFhOrmvguy3KLZ/nQYm05bmGxuYzIM8Ttj5E4ZMuJmLpxfFZ7JnT2oaUpM0jX0TTHFl+6jI\nJNM+k1DJqU6/b9iwIVNl6RGYTD5BJKMS+DaDwaQZBK3wdfmoVoQ2aroMN00SHQnq0uZ/m+pjEp62\n5dZpJhK25SOE2RqsM0fZkKAsi24cyT4pLNSXm6dr01emfKRmEFRuz9N/CdBWyOvmg41mIsdyVDMX\nTy9Io1RB1u/IkQTB6BZBmfaZAOrxzTWT+nr/Trx0EIpMqqqqcMcdd8DzPBw6dAhf/epXccstt6RX\ngh4G10xMk043YWzJxCZtk+CMavLSreBsVnOmtE1aT0cH8H/+T/JvJrODFP5hBb6qzqZ+UP0tV266\nPrExj5jyNWmCtgsJ1TuqcgeFm/KJaubiYemauXTEK/1ouvxNZebQkYlpLkU9Z6KzcGQLJs2Ek8nT\nTwNvvJFeXqHIpL6+Hjt27MD555+PyspKnHzyyXjuuefSK0EPQ2omBDnpwgr5//1fvYCy0YaChFiY\nVbopfhifgKyDLo0dO4Cf/zz5vTCaiYwXJCBN7Zmuz0TXtqbyqNLQlU9XFlN7mBBEVDrhGwbd5YDX\nlVXnmLfx3dnko9JAZLgtmZjMdpnsE1X6PO0gMxft+kwHocgkPz8fgwYNQltbGw4fPozTTz+9139x\nUaeZmExeppUQ/f/RjwLr1qnztBlIQRqDTqiZVmqqiSbzDDJz6crHn1W/yUliq5nYTDQTmQYhSPja\nmrnCCCuZ3r59yX8HkauuDLo0TO1ps9tOwnQppo5MbIVkWJ+JqZ6mdE0IkgFR0zbNQRsyeeIJ4Mtf\nTi0nf87L87duE2w1k24nk8rKSgwcOBAvvvgi/vSnP+HXv/41rrjiivRL0YMwaSZBwtc0eFUIWpWY\nCMx2RSoFflB4JjQT3cqOw1QHKTxNAlL1jg3Z69ImpGvmClpTqcpH7TRihH9+hYfzNoxiUjH1cZj+\nVsFWM9GZucL4TAjSZ6LacRV1c0EQ2avCo2haPM2wG1gAYMkS4P77g+O+/XZqPkE+k0yQSaiThrW1\ntTjvvPMAACeffDLWrl2LX/ziF+mXogdhuoKeYCPwVR1rumhRRRSmgaybwKayRhG+UXwmkpBV5Btk\n5rLZ0WLTP0EkrCMqWwe8rt3z8vTC04bg+SreZOYypc3/thWQHJneGqxzwJtgo9HJ3VyyHDLcVGZT\nPqbnqGY7Xr6wBL9zp7kOBHk9CxCsmWTiBuFQmsldd92F+++/H//4xz/iYXPnzk2/FMewb98+fPaz\nn8UZZ5yBiooK1NfXY+/evZg+fTrGjx+PGTNmYB/ZBAAsXboU5eXlmDBhAtYxm9LGjRsxceJElJeX\nY9GiRcY85Ql4/hxmFaGys8or4G0IyVbIm4RiULnD7E7T5RlFM+Gw3c3F/7YlMxNB6NK21Ux0aZlO\nWPO4uvLptrvKtKKMA5uxLJHNQ4u2PgbduLIV+Lb10b1nakPbtFV5mcqdCciFCZCDPpOrr74aO3fu\nxFe/+lWcdtppuPzyy3HXXXelX4pjWLRoEWbNmoXXXnsNmzZtwoQJE7Bs2TJMnz4dW7ZswbRp07Bs\n2TIA/jbllStXoqGhAXV1dbj++uvhHeuRhQsXora2Fo2NjWhsbDRenW9rDgg7eAH1FdOqZx1RhSET\n3XtBdWtrS6xKgiaJLcHqNBPb3VyqOsl4UftE1262mokOpgNgNn3Mfwuzy8pEvJSOSbuKAtNJf56P\nbqHGEcbfwG9VDlpIyDlj69o19RV/TpccbUznprRMOHIktb9zjkwuvvhi/N//+39x++2349prr8UL\nL7yA++67L/1SwL8o8k9/+hOuvvpqAL6zf/jw4Vi7di3mzZsHAJg3bx5Wr14NAFizZg3mzJmDgoIC\nlJWVYdy4caivr0dLSwtaW1tRWVkJwNec6B0VTA54gu2OLxmu00xshLxp8Kp+162sgso6dar/FTxd\nPvxd2xWcSoiYVoo6AlLlqZuMqvYMo5mYdj/p3rUVVjZtZRL4YVa+unx4WWzGWCY0kyikpStrV1dw\nW9n2lfzbdmGiI6oou7lMdbDdFKFrX27monxU/WE6axMFoXwm06ZNw/vvv4/zzz8fH/3oR/Hiiy9i\ntLyKMiK2bt2Kk046CQsWLMArr7yCyZMn46677sLu3btRVFQEACgqKsLu3bsBADt37sSUKVPi75eW\nlqK5uRkFBQUopVvgAJSUlKC5uVmZJ3fkAXYCyjTA6H9+nYlqgIclliAHfJTJELRC0uVDMJnQsmXm\n4mnbbC4wTUwJk79DR4gcUR3wvD4Ek88kzEaMKOPXJh9bn0kU6Oag56k1E13fB/lMZPl1/RO2bk8/\n7TvA58yxz4enaUrblkzkzQM8T65BR9nYYUIoMjn77LPx4osv4u9//zsKCwsxYsQInH/++RjEv2YU\nEZ2dnXjppZfwk5/8BB/60Idwww03xE1ahFgshlgmah3HYhw+TGcipqKra2pk4cvDSWWM4tBXped5\nZgeiDFcNHt2k49CZosIKKBszlyyzidSC+sHWtm1KW6eZ2Jq5gm6l1bWVarVt8pmEqU+QIMwUmRBs\nidy2PvI5qK1kfFvzoM18lG2lq8P8+f4tvUQmYbaIy2cJ2+MBUjOh/jp6VG+ONfXJhg0brG46CUUm\nP/7xjwEAra2tePjhh7FgwQLs2rUL7RkwuJWWlqK0tBQf+tCHAACf/exnsXTpUhQXF2PXrl0oLi5G\nS0tLXBMqKSnBDrrvG0BTUxNKS0tRUlKCpqampPASumJUoH//xejq8m+BfeABfeeEXdlRc+iut4/i\nm4lyaNGmrDLNoBPeuhUcT0N1t1EYzURVLvo/yGeSKQe8qmwmgWtr5pJl1QlInQ8n6jmTKGNMh0xq\nJmHGdZBmEpUceXyTZsTj6IiKrBK6fG3y0cG2f+T5HtN8sEl76tSpmDp1avzv2267TRkvlM/k3nvv\nRVVVFc455xysWbMGV199NX73u9+FSUKL4uJijB07FluOXbq/fv16nHnmmfj0pz+N5cuXAwCWL1+O\nSy65BAAwe/ZsrFixAh0dHdi6dSsaGxtRWVmJ4uJiFBYWor6+Hp7n4ZFHHom/I5Gfb94arBtIBFW4\nbgVlWonYTPQwDkSCjTlA9y4QrJmo6sAFpGkgS3ttOpqJqT2jnoDXjQkdouzm4mNF57uTaYWpTxjB\nZSv8AXufSRQjgqk+QfNKZ7IGwmlDYQW+iUx0edn4l4IIUdd/UjMhyAVTRo08CKmZHD58GF/72tcw\nefLkrHwM695778UXv/hFdHR04F/+5V/w0EMP4ejRo6iqqkJtbS3KysqwatUqAEBFRQWqqqpQUVGB\n/Px81NTUxE1gNTU1mD9/Ptra2jBr1izMnDlTmV+/fuEduTaTkZ6lgAjKxzQxomgmNqYgmWbUrcE8\nju7WVdNuLlNb6vpEV2fTSkxHVBR30yaAf1TUVojY2uRl3XQ+Ex2y5TsLElwcYTWTIIJXpaV6j2sm\nOt+Zrj5RfCam+ujGMvdXyN9s2j5qW3HoPgNsuiut230m3/jGN/C3v/0N9913H2KxGC688EJMmjQp\n/VIcw6RJk/DCCy+khK9fv14Zv7q6GtXV1SnhkydPxubNmwPzozt+VBM67GpF5ycIM4lNwt92VRI2\nHw5duI3Q1k16VRxV+raaSZDD2iRQTHWjiTZpEvDkk+EFrrRFm+rK26S7fSYmx2/U3VwE2/EexSQo\n+14niPlzFLK3rYOufWzJxCYfCVvrBC8DzyfKxZthEMrMdffdd+PKK6/EO++8g927d+PKK6/EPffc\nk62yZR2xWPLJZZsJaFpRyN9NFz0GDaQgB7yETRpBA9ZmJaSrA48TdB4AiO4zCco/rGbC3yPwb1BE\nNXPZEryOTHSwXVTYOqkzQSY2wpeb86I64MMQpYn4TfmGtUjINMKYuYLSDlsHgmprsMxTots1kwce\neAD19fUYMmQIAOCWW27BlClT8B//8R/pl6SH0K+f3ixjQyCqjrJRwYMmhjSRhTm0qKsDL18YMtHV\nUVcfIhOZJ4ftORP+N49n6h9Tu+nqxom/tRUYPFidng5RzE8mP4BOsEc1c4WJE4SwZyekWSpdTcsk\n8AkmH50pzygOeJkO9wDYtpUuTxNMMkAnUzhsxtX+/b6mc+KJ5rIAEb60yG8J7u03BkfRTGxVbMDu\nK462JBPVZxJGcAQ5LYPIk+LoNBPbrcE2zvCwvi6ZlgSPe+CAOty0UoziGPe85BU7jxPmZDh/tun7\noPGrqo/Nb6Z8qB3DaiZhxrUtIYcpN8GUtoyvIxPbBZBuntpqpRy2Zi5d+/zbvwHs2J4RoTSTBQsW\n4MMf/jAuu+wyeJ6H1atXx0+s90bEYqmaiY2w5M8msrCd0KrBk45wCRIWUTUTW2EV5IMCUndz2a6y\nVFqfjR9LVw5VXP59eRsSBqJv3Q6qj0w7qgZkM/bCmjpiMeC3vwVOOSU4H65RRjVzEaKs6qOYb031\nMc0TG7IN8iHa1ME0HoNkii3eesv+qpVQZHLTTTfhoosuwp///GfEYjE89NBDOPfcc8OXMIcgNRNC\nlInJ3wWSO8/muymmgdwdmknYlZDNhLYRkFzYqMoRlJ6pzrbnMnQTzdYOH3SoVJWGyQEfhkB05Q5r\nEuSwJZaGBmDsWHPaYTSGsHPQ5Dvj6aieOaLMb/m3Km4650yi9omprXTQpW16RyL0/t7Jkydj8uTJ\nYV/LSUjNJKxjL0h70XWkrS+FpxfmCnrVsy5/maY8W2Kqj81E53narNhk3vxvW6Fomjwm4asqj63A\njbrbTjf2ePwoJ7mjCkKbfDjkVw9t+ifoYKyqPmHHnq7+qkWDnCe6dguqQxgyyTTBm0iSfotyzkSX\nrgpWZDJ06FDorjGJxWI4wI3MvQjSZ2IjAGwGLLcPh51ovONtJyDP37asqkFis6oPIg2bOEA0zUQ6\nclXxTZqEKe107+aKusJWacW27SbLZCN8o5pudNCZK6OSSdg5GMUXqcpT9buJtFQ+E64JEmy3BuvK\nzRHFzJWuzyTjmsmrr76KU0891T7VXoR0NBMVgfBwW3XcJjzMbi5bslO9a3o21TdIiJgGpY7cVPmH\nbVtbyLiqtE2IQvacRHWbNdLxl4V91pXXBBvNRIZHPWeiWlSY8olCJploK0kmNmPWJp90d3RGIROb\nsU+w2o516aWXxp8vv/xy+9RzHCrNJKzwVwl8VeeFFb46B7zNgFZNHF3dZBpBBBamfWT+tru5TAJF\np5noJqytz8REsKq2BaKtsGW7BR1aDNJMdHmGFVY2gkkFTiamtHXhtv1jM/Zk/VX5By2kMm3mMtVB\nl7aqPqYyq8JV+XR1AX/9K3Ds+sMkZEIzsSITj5X6zTfftE+9F6Bfv+StrATTxNTFkeFhTQ22cVTl\nsJkAOqGoq4NMM0pZgyaxqjxRBEqQMAhK2/ZSTh2iCkUbrTjMFuSwgstGAJoQxcxl2z+6+ZXOCl83\nf8KmbdoazNNTxTOVT5cOYK/RyTT4GH/6aeDFF1PL1m2ayfGKqA54mwkLJJsubHZzyY6X6fF8dJMh\nqEwynCNookv7qw2BBeVJ8Uw+E13aQfnrTBoq2LaJbgKGOQHPw4N8JrK8UXwmNm0VJCB1MGkmQYQc\n1D/ppGczT1VxbRaOYYiKm7nCyhSJKGYuOWfDHg0MQyZWPpNNmzZh2LBhAIC2trb4M3B8O+BtSYOe\naeDo7OBBg0c3CIImA3/XdgKqBonM32Ras524/Dnd3VzcVm67Uo2yNVjauVXvmohFFZc/6+qjqkM2\nD/nZjKsgM0e/fnbjWvcctd3C1CcsmajCbePIcvO/0/WZqMod9JscS2G/ZxLGzGVFJkezfUNYD4I0\nk1gsmp/EJHSkwJO/B6VnyifKpFPVhyNoIPPf+XemTYKdh3OYdnOp8g2qWxgBqYKMG3aiRzE/8Xqb\nFh6mfHR52q58gwRgkEDTrbxtx6GpDrIcNkKZv6d617RrL6jctnXj5TBpJrpypNv3pvpwzcRmY0fG\nfQlBd9EAACAASURBVCbHK7hmwtV1IJoqzcMBO83ExsylEtC2gyeorBy6Vb0qbd0116ZnnYotycQk\nFFSaia7fwgirKGTPEfWciY3gSlczMcXh4d21NdjUPyaNwoacgupP6et8GWHJSdfPhCjXqejSy4SZ\nK6xmEtT/HH2aTICEZkLfgw870Qkqs5BuAtgQVRgzV1iyM2kmqmdVmCQTVZ6yPt19aDGoDvxv2xue\nOZlFOUxoGhOETPtMbM0rUXwmOjOXrc9GQve7LWnYjkmbdouatq5O6Zq5MnGdim5B1227uY5XSM3E\nZlWSjmaie0/1HNYBH0Q8ujgcMg4NPNUEkGauIIESZMbSaQYy/zA+ExWB0W+LFwO//31yGrqyqcgk\nSMiGJcQwdTDlH1UQBqWnQ1gHvG3/hEmPkM5iLChtm7Ko2srWAa9qgyAyUdVDvifrE5ZMgvqfo8+T\nCddMoqxWCEE+k7C7ucL4TDhshEjQCoriqHYoURz5nWn+nq7cJjOXadCGmYw2AhIAbrsNWLZMTd78\nXVN9wuzmUpVPmiB0edpuQ7XpB9Oz6VS3DjY+ExOZSdi0FV9UhM3TRntQ5W879lSfb7Zph6A4lJaq\nzKq6qNKTZq4euU7leIZJM7EhDdVkDONUtRmw6fhMgoQih43PhGDjMwlj5rLRTEwT2tRWqrTkc1if\njRS+YRzwPIxrWkFjhf8dtMKWaeviBOUTJEyy7TNRpW2aS0FlsRkTNmnr4gf5t4LGry4fIFracsEi\n+ysobWfmsoRJM9Gpz7YkQ2GqQWwzMUyH6GTcsM+2Jh0+CGWY/JpbmLrJSSfJzUaY264gVXVU/S3j\n6ia6Kn/AfqLbCHMbARX0XhTbv67sJthsDdaNg7CCPUhY2s43VZ5h0tClp+or2+tUdPmYoBvLuvRy\nYmvw8QpJJqoOpnDdbbqmianTTGxX1WEEpM0kVj0TVGY+giST/v2TfSZhBYeKPGx9JkFtEmTD1qVt\ncwW9Seux3c0VdhwEkZ8uHxsC4X/bhktEMXOZiNJUDhtBzJ9V7+puDQ4zZ0zzzUQmUfLhiPJpaDne\nsrmbq0+TCZC6NVhFJjaDQEU4NOFVZ1iCnnUnzMP6THg4T0M1UHVllKe0CwrMu7mCTDcqLcA0aHk+\n6WomqnR1ZZJxeP4yPOpFj7r20QlcWS6dQLEhrSDBLtNXhZu2vurCTf1jGrP8OapQtvGZhEkvTBvq\n6q7LR8J2jJmsHbpzJraXiZrgzFzH7ubq10+9Og7a5cWfVRc9ep7/Gc8oWgpPW4aHXZXoJgNvC13d\npGaSn5/qgA8iDRke5Qp6m7qF0UwkYeqED4+jIzMTbPtHlWeYPuThJmFqk55J4JvyCVPPMP1j2/dB\n6QQRWFjTtI2ZS5UGX4zpIH+P4pcz+UxsYUs0fZpMgGAHfBjNhCBX5pKodP4QG4ESdBmBaTKq0ubt\noKunJJOCAv0JeNOuNZ6/qsy6Cc9/DxLmJtKScWWe8pkIVkU4chzYniy2Eb4mIcrraUo7irlGV15T\neLpmIVMdopBTmHmqyzNMWeSzrc+koyN6n+gQ1FZRzpkE/caRc2Ry9OhRfPCDH8SnP/1pAMDevXsx\nffp0jB8/HjNmzMC+ffvicZcuXYry8nJMmDAB69ati4dv3LgREydORHl5ORYtWqTNK8gBryICHoeE\nLA0YnWZCaaiEkm4ghXHA8791E0dHjgSdmQ9IaCGcTHS7uaRj3maSmCaPrYAIIzhU6OpKJSq5wOBx\nZD5BO7vCCL8wphaZXlDaprKEObSoMmXaCmKehmyrKJpBUPygMcHLZWuF4OU11YfH5+WQZKIrN0eU\nzynIuqt8JkEEZqvN5ByZ3H333aioqAB92XHZsmWYPn06tmzZgmnTpmHZsmUAgIaGBqxcuRINDQ2o\nq6vD9ddfD7oqf+HChaitrUVjYyMaGxtRV1enzCvo0KJK+KoGMr1LkL9LMtEJ3DDmLxshonpPlpUg\nw3ndwvhMTB950k3oTBGlzEdHTqr3pAlL1fe2Z0GCyMSGnIJIM8jcaUsgurYKIpMwBJIJU51pbgTV\nRyX8bdotitZl64A/ckRfbv789a8DVVWJtDhsZIBcxHIyCZpXYZFTZNLU1ISnnnoKX/rSl+LEsHbt\nWsybNw8AMG/ePKxevRoAsGbNGsyZMwcFBQUoKyvDuHHjUF9fj5aWFrS2tqKyshIAMHfu3Pg7KkjN\nRA5GSQRScAL6nVD8d+qkWMxeM1HlGTQZggSurWZCdSZ/D0+DyISXid7TaSw2Zi4bMgmzIs6EZmIr\n/IPS5/kECdZ0NJOwwjxIsOuEi64fwuQTJLhMpkxVP9jUOaxmErY9TT4TWzMXL9Mvfwk89lhqWqY6\nmGQKv9VCl+dLLwE1Neo6mJBTZHLjjTfizjvvRB7Tq3bv3o2ioiIAQFFREXbv3g0A2LlzJ0pLS+Px\nSktL0dzcnBJeUlKC5uZmZX5cM1GZs0j46lYrJPB124dVmol0xttMNNVksJ2sQeRI0J2z4d97IaKg\n7lEJf935k2xoJjbhthNQpXXIvldpL6r85TU0NkLJRviZ2jCoHVRxZBlV7aIjmbBEZSt8Zd427UYI\nMnPxsazKT1UfXXq6PG3rI7fW6/LJZ/ttw9zLpiqfzZdfu7p8begrX0mtRxByZmvwE088gdGjR+OD\nH/wgNmzYoIwTi8Xi5q9MYO/exYjFgNZWoL19KvLzp6Z0vMmXwMlENcBUu7nkTihbk0aQEOHPJpLh\nWpLqWQpXSSZA8i44mY/NrjVpW5Z1M7WJ1B5MdbbRTExpq8xcZCYwTUaTH8BGyNqaqFT1UZUpE4Jd\nl7ZtPwQJYiB1w4PtgsH2mS8YbbY0hzV5qfpeZ+bSaSa8DGHIRL4XRqbIOC0tyel2dW3A4sUbEISc\nIZPnnnsOa9euxVNPPYXDhw/jwIEDuOqqq1BUVIRdu3ahuLgYLS0tGD16NABf49ixY0f8/aamJpSW\nlqKkpARNTU1J4SUlJco8R41ajA98APiXfwH27FEPdJU/hAsXXRxKgw9iz/MP/Nl8pdDGAW8zeHga\npIlRHGl+U9WfkwlfTal8KYD5/InqWbaXbd1sJokN8fL6SjJTaaVc+zS1M09f18dRJnpQ3cKkZ9Mn\nOrKK2le6dgMSY0r1e1gtTlU3aX3gvwcRn23dgsiE0NFhl3Z+CAkdNGa4Zm2yjhw8KOswFYsXT43/\nfdtttynzzxkz1/e+9z3s2LEDW7duxYoVK3DxxRfjkUcewezZs7F8+XIAwPLly3HJJZcAAGbPno0V\nK1ago6MDW7duRWNjIyorK1FcXIzCwkLU19fD8zw88sgj8XckojrggeSBT3FUu7koLgkr004ok1AM\nEriEoBWU1EYIOmezikxMmont5gIO2V66uLaCwzS5JVQTjcIkwdqauVRkYtNXunBTOrq6c3I0tZuq\nrUwkI8OjaAm6tMNsXLAZH6axL/O2qY+q3DJ/084nnrbJzMWfucPcdAJe1oGHyTktn2W7RTmLAuSQ\nZiJB5qxbbrkFVVVVqK2tRVlZGVatWgUAqKioQFVVFSoqKpCfn4+ampr4OzU1NZg/fz7a2towa9Ys\nzJw5U5tP0K3BKgc8DweCNRPqnM5On0xsLoDkcaRZTEIKc1VcEnJSMyHoSJPahzvdOQnzctseztSR\nic1q10aY8zqbhC+Hqqwmf1kYMglrLrERokFkYhKEYfPUtZdtfWzaCjC3m016QfU0aSa8XunkH8XM\nxcvA4wBmM5euHrqySi2Fv2eqgy1ykkwuuugiXHTRRQCAkSNHYv369cp41dXVqK6uTgmfPHkyNm/e\nHJhPkGYCBAtZEjpcOFNH0e+xmD8ojhxRm7mCBK7Kqa2b8KbbfKk+vA4ESYhSM5EHFbnGQuUmf5BO\nsKueedm4gNLVU5W2rYDk/6vS5vlTm/A43GdiUy5Zv6A8bciHkAmhGKbddHmZBLiuzqryAsHmQVXd\nbMJVZGIqny05qeJEdcDrnqM44HXPJs2EkI5mkjNmrp5A0EWPRBCqcL5lVgpi2kNO7xGZdHSkbqvV\ndTbPM4hM+HPQoUGugQVpJpJMKG2VmQtIJRObScr/1pm5+HsmMjVpEkECwuaciU74yzhBZq6gZ9sV\nsak+Ns+mdFTPBLprzlRW23pymD7GFoZsVXfhAXY+k7DtKcsS5qJHno8uT5PPRNU3Mm3VAlE+yzyj\naiZ9mkyAVM2EIAUKDwfUmgnFIzLhqmR+PtDebjZzyc4mqK4uUU34fv2CbbFc4MorQHh8yp/qSROR\nm8tUd3bZfF0yHTOXKW3VzjtdnhIq7YK3lWpLt65utluDdULM1nSkQhAhRRGcMm0b4rOJI+sQxWei\nqoNuHHBtWgpiG6Ky6XsJ3TkTXdqyTGE+ZhXUD9n2mfRpMuErbCnkuYA2aSbU4TSQYjG1ZlJQ4Gsm\nJjOX3AdOaZu+HcLTMB0mVE00aeZSTViqJ9WB6sY1EyqT3FygM/8EkYyNZqKqm+yroJU8/ztIM6F2\n0JWR1021NVhX33SEsqyPDfFkgkBMaYchMB2ZBKVtMg9SOqp68nmqa5N0zFy6u69s+lL3HNXMpaqP\nXLjq3nVkEhG0wuaCEkg9kCgHLF/lSKHDNRMiE2nmUq3CVSsHFUHI9+j/oKvhqax85c3bgQtRqZlw\nv49JM9HlL9vQZK7ipBEkfKXZLqzwpTpKASXbRBVHJwBsd3PZkoaONHX1sUnD9lm3eAmjRdqkDdib\nB4PqFnSbhardbNImmExuUuDz8Rk0NlVxopwzMREI1T+KZlJaCrz8svo3oI+TCfeZyA8+8dPepgkt\nCYeTEtdMiEykZqIzc/HVPpVLp6bLvG2ELz0T+KDnJjyeJ2lXvN14WaJetc/rb4qrEkSSBINMKqoJ\nyLdu69oq6OaCIOEbtk0IKhK2+bphFEEsy617DiPYVXEI8jR60C44VZvIeQAE+z9leqb+UcXRtQ8t\numSdwqadLpno0jPtIuXPOnNaczPw/PPq3wBHJtrdSqQN6HZ5qTQTIFUzIXCfiUkzIUjNhBMYQZbJ\ndIaF/perbYI0f0kNjGsmFD9IM7EVBiqBr0tDxlGV2yTEVBNQR4KqtINMcWHMXDYEIgUXCRiVQDOV\nKSr56MjERkOzEW4cYcxcproFLQBlvWTdVHna1sf28wM2Cwl5MWMYnwlBt1iVZi4e32Tmku3G0afJ\nBEgIRdJMCEQsKge8FEDSUWvymdg44Pmgl5qJikx43qZzJrI+KjMXkKqZUJpUFrmbi94zmblshEGQ\ngFLF5Ss/kwPeJByDzFy8TYLMO5xM0hHgurRJM9GNAx6WCQGpI5N00iZI4SvrYWoHU/5BZ8Z09VKl\nbdMnNMdVCwnTbi5dm3B5oNrNRb/rNBWT5qYiFlku0+FIPsYk+jSZcM2EBho50aQ2IDtH5zPhZi6V\nz6R//4RmwvPh8XmeNpoJ5Se1Kz5IVJqWbmuwvP6FCITqQD4TeQI+zKFFKTDoNmVZbjkBTKYom63B\nElTfoLQ5wVIcnkYQmejiBmk6KiFmY+ayMWdxqMaVLtzzEuG2pj9VeNBGFBvNRIYDZmuCyswVtLhR\n1U22CdfgOWzIhKcjx7uJTGRYUD6Z2BqsGz9AHycTIKGZ8N1K3OkdtMuJCzHA7DNpbwcGDfL/7+oC\nBgxIFv6UHk+bl4Umg+xsOk2r2k1FkNuYKT0CH/ScKAcM8MvL6yZ9JtynYnNoUdWecqLbmLyof1TC\nXxdfNRlsHPD5+fZmLrmyi7raVcWRmomtkA2TPydnlcBLN22Cbqt10KIiSOCH3Roc1iSoisN3PUrY\nlFvVJl1dyWSielcFXXqZ2BrsNBMNuFDkZMLNNaoVqRR+pt1cBFrVDxkCHD7sx+VOf7mDSmXmIuFG\nnU1xTGTCBw+VVaWZyDpTHCIT1dZgedJfd2hRHiJTTUY50VUDXTUBpNmOE7hKiEky4e0qy2faGqwT\nkJS3zDNIKNoINyIz7jNJRygGCXwbMrHRTHREZaOZhCUwwG5rsK7dTP2qKwugX+jpbicO0q6oHUxk\nYpO2arFKz7q6mTQTRyYayC2u3K9BpigyS8kOkYcWaaKTtgEkCzZKe/Bgn0xkXNUOKkkQ0uRGWoIk\nEwIfJKrdaZxMBgxIpMNP93PNRLc1mPLUHVpUCWsplOVOGx0hSu2Bk4bJGS9JhOetOkMiyx3k3FcJ\nA1OYqZ5hNBOephR+KpNOEIHwcBOZUJq68WYSnIB+kQaotQf+rNNodBpqEJlw6MxfurLwtKOauSSR\n8mcVmejKrvqd3wHG553TTLIAOjWel5dMJkeOJAQ+nzAklLkjnQZvV1ciDUDvMwH89FUCXA56HZnQ\nu/37J9KQxCdXOUCqU5lA6VG4STORDnjKkzQTSQq6TQz8WZq5giaaSnDwcpNfQbaFSijodmqFObTI\nn20vLAy7qqcy6nwmmdZMVCv8MHXg78k4uq3WfJESpKGp6gmE85mYrnCx7RNOJlEPLRIkqYYxc6ny\n4WRiMnPxNJxmEgFcKKp8JkQOXEATyZDgBpIHL5muuGDjPpO8PGDgQOD995N9JioyIdKSu7l4PmTy\noDyJHIHEoCLnNhf4NHEJnNh0PhPd1mD6X2fm0t0iwJ85yZkEpBQiOnOjTqDwiUN/qxzwsl8l4QQJ\nF55OWDIJ0kykmSuMIJR14O0g05FXDMlyAOat6CbBKTUTPlaCzFxB7abbzaU6Z8LJRDdmgtqW5ITO\nzGUaG6a6ya3BvCyUNocqH9VBbFN9VJqJbAcd+jyZ0K4kqZnQJJGrfSKZgQPV/g7ud6GwWMyP39aW\nIJNDh9RkAqjNXDyc5xOL+WUkolJtTeZpSz8NgTQcyodrJocPJ7eP9DVxzURl5lKZiFSkwIWISmir\n0pZmLpNZitIj6MhOtpupbrKMKnONTVyTeUW2m8nMpUtbRQQ64c/bRZKvro426fFn3c4/05UnfA6q\nBD496zZiqMxcnExMpkxT39PRAtVqP6zPhLcn10xkG8o66343aSaqcnme280VGVwzIUHMzTVc+PLw\ngQMTwpcEMRfmcmAOHux/Hjgvz9/R1daWmnaQmYuIT5qc+vdPCHxOJpQ31xj4eZqCgkQ7qDSTrq5E\nWXna3GfCyU63AUCucHXmjSAhp3KAS21E9QyktokcA5LgKFySiUl7kn0eZK4JSk/VFiozF8G02uXh\n8m+ZDheEqnDeVjaaiYrAdGYuvqjQpR20wpYahvRF8rrotsfLPE23YavIJAzZyz7k5SbBrkub56HK\nR/pMVG0oyyU1E3lZpQ59mkxUmok0c3HNhPtSBg70tQES0ORX4ITEfSZDhvifwwzSTFTP8joVSRqc\nTFRbk7lmws1m5L8B9GYurlGpLnrkBKI7tCgnt+rKF53PJGh1qNvNpdqswMtE4CsxeW5G3gSg0qhU\n9SSErQ+VRSd0VG3F87fJh5OJSfhzQjblY+P3UWlgJpOoikxMixHZ3rINVbsk6TcyI3ESkvUNqict\nqkwam6yDjQmPLzZsL3uVaZh2c6n6ls8HVTvI+cPRp8kESPWZ6MxcQDLJSM2Em5k6OhLnEqhzuGZC\nAjrIAe95iQ0AFC7LaqOZ8BU214Y4mUgzF21KkGlzMxcnE8DuWhIgQcg8jmlrMEElLHXnTGSefBOF\nhO5Ev26HnSyLLk9KR5ou+LNKmOpWrZ7n/6bzmejKEYVMqF2CyMRWM5HPJs1E1W6yL236gaA69Eu/\nm8xcPD25a40/mzQTk4mTQ0e8vC3ku6rbA2S7hTVzqTQTFWGr0KfJ5Lzz1JoJCWSpmXBBTGRC4VKY\nS5+JrWYCJJuZeP6UNi8r95nI+7NMmgk9EzixcXIcMCBZM5G+Gb7C1H1pUa6kVZpJ0NZg3fZdvgqV\nu7mCNBM+ibjAkHny9NI1c6kWDLxcps0Kqh15tuXQkQlvC9kuupW6FHKq9gwiKh0587FqY+aSgs5E\npkG7uXR+NhXx8XS6utTXJPEyqd5T1UEuNlSkFLQY4O1GC0ReVlUbOjJJEw88kFiRqhzwJMxJ+Kk0\nEyl8+YWOfMBIzcRk5qI8ef5A8jZdGzMXDRKpaek0E9q1RQQSi6kd8P36JcL55NeZLuRJctXtzHLV\naGtj1+3gCmvmCtJMTFuDVWTG01EJdpMWZyKTvLzgr/ephCmvL9nigwS+jZkrym4uU/15P+jMMiaT\nE5XbROCyrehdHZGrFklcoKvMXNJkyuPq2kSGm+pvSoNrUTZmLtnHnEyCbirm6NNkAqQ6tU2HFrmQ\nJ58JkKoZyAsdSTMhAU1konPA83y4mUv6L4LMXFIoAslkw8mEHO2UD6XXv3+yA55vbz58ONVnYtqh\nI+sGJG8uCBLUqpUaF3j8bImNA56e5V1jqnKrVtI8HZUwUu3m0pGJrtycWEkrNR0mVBGSShCSqcxE\nBLp8eD/Y+ExUAl+2p7xxQpqWVDsqeV/xZ15u2m1IeUozF996q3PAqxZJkkzIzMX7SrYP1wxMC4ag\ndqbFL+8bHVHYkgkvIycTeTeY00wMkIcW29uTBbh0wNNAHjQo+eS59JnwlQr5TIDEbi7STLh2wzWG\njo5UzYgEeJjdXDqiomdCYaFvhpOkpTNzkWYStJuL6kzP8jJK1U4bnZlLtWqTPhMTgUnIG4eDNJMw\nZi4626MzOanIhPKU9edmH9JM5KTW+Y54npQPlUsl5HndbB3w8j2bZ1l/vrGjqytVgMvt8SpSV2lm\nujv0eL/T35KE+fjRmQqpf2QcuaCjtlItMHgby7ZVkQn1H39Xpe2r3rPpN66NSDLhZZVwZCKc2u3t\nyTf7Sgc810xI4JOWIs1c0mcCpDrgaRAMGuQLZyDVzEWDgwt2nZlLpZmotgZLMhk2zDfDAcmmLf5M\nGhWvQ9BuLincVN+N4YIYUK+apJlJdT2M3EZN4ZxMVJNBZeaSgijIzEV9K4mNkwNtpzalpzJz0Uqd\nb8tWtbHOxHf0aLLZhTQTXnYVsZh8JirBpSMQVVupNBPKk8rHBZ5O+1WtwqVZVbVgUZGJapcc+UNk\nPWV78sUjLShl+drbzQsmik8I0kzoXV533payf3R5yr5ymklESAf84cMJzYRrBlywcwKhZ7njSeUz\nofxUJ+DlVmMiKn6dCwl2024u1RX4Ng54IhNJWtzMReWWPhMuCOSqDUjVEriZQmXmUjnodStZrl3w\nunGBIv1IHFyo6MyDKgGtEpa8DvTMw7gw06WnCufjUGomkrB5P3ACo3xJQMkDiSoiUJEW1dfGzGVK\n26SZkHDmY0P6LVXCl8YhHxN8fEbxmVDb83y4tkjjnWsm/NYIuRBULUZUpmEZLkmGzJ3Ul0HaiCRv\nm36jtDl6BZns2LEDH//4x3HmmWfirLPOwj333AMA2Lt3L6ZPn47x48djxowZ2LdvX/ydpUuXory8\nHBMmTMC6devi4Rs3bsTEiRNRXl6ORYsWGfPVaSZ89X7kiP9v0CCzZkIrXNoaLH0mQMLM9f77yfmQ\nZkIDTzrgiXCkBmI6Aa/yx+jOmZCZC0gmE/5M5eY+E1lPCgfUQtZGM+E+FZ2Q5atQisPbSm6HVm0N\nJqHDNRNuTuN52tzNxU1HlL9uh5nuOhGV3Z6Elcpnomofam8yFxGZkMDjPhMuFKVAydbWYKlxA4mV\nvNRMeP+pSEiawmQb6g4Dc+Klv1VmLlVZqQ15O8tNLpJMyCep0kx0V54EaSa0qMjLS5jrZTtQGtIM\nZ/KZ8Dx7pZmroKAAP/7xj/Hqq6/i+eefx09/+lO89tprWLZsGaZPn44tW7Zg2rRpWLZsGQCgoaEB\nK1euRENDA+rq6nD99dfDO1bThQsXora2Fo2NjWhsbERdXZ02X6mZcJ9JV1fi+yOdnf4zd4Zz7SGM\nz4RuDlZpJkCqz0TngJdmLrnLi9+pxVdIJjOXzIdrPdzMRZoJX4XxLdBAYuCp/BfULnLgU/vpVrJc\no6H2VKUt6xlk5qJxIA8qSk1CEiWg1l7oWUVIKqGo0uKovJJMpM9ECkJp+iMzF41rTibcXMPT4+nw\ncCorFzjyPfmsWu1znyMtwKgfiASlr1JHJjQOuFaqIxOVz4Lqodv8oLqfTxLymWcC9fUJOcHJpKsL\nGDo0VTNRaeI2ZEJlpXHALRW8Tai+pOnJ9HjdVX3IfTOEXqGZFBcX45xzzgEADB06FGeccQaam5ux\ndu1azJs3DwAwb948rF69GgCwZs0azJkzBwUFBSgrK8O4ceNQX1+PlpYWtLa2orKyEgAwd+7c+Dsq\nyOtUpM9k2DBfOKo0E7KBDhmSELKq3Vx5eX46QIJMgOSbemlFz4UfERVNOumA15m5aPsuf4/KKjUq\nwtChvtZBeaoIRGom77/v14t2gQHJZKLyA/C6qfwtvL48DZVZRAo8rvUQyZnIROWA55qJShCReZJP\nKhLQ/funah4qM5eqPlyAy9WxikxUmomKvKmNjx5Vk4ncrMHbSKeZyH7QaTe656NHEwKXysjJRApL\nHbFQ28twaeLk/SPJRApOnWaiqjMnk0svBdav9+fC8OHJZNLZ6c+vw4eT/XL0LM26BN1VKCSvVBo/\n7x+plepMaNQPvM4UR/rWOPFI5AyZcGzbtg0vv/wyPvzhD2P37t0oKioCABQVFWH37t0AgJ07d6K0\ntDT+TmlpKZqbm1PCS0pK0NzcrM3LpJmQUMrP9wUkaSbSzEWrepVmQhODk8mgQf6zjc9k2DBfmEuN\nQZq5JJlwjYFMaFRuMtsRqQH+e0QW3LQ1eHDyYUsikwEDkskESNVMuF1aJfC5AKDySjJROay5s5wE\nnkqLkzvlAL1mIs1cQPJ2ZFocvP++LyzkSrGzU00mKs1ENblVpjAqL8Wn+9+kmYvaWEXeQWYuHZnw\ndHg/UFkpvKMjMc5syURqJlQ3TiZcy+b9p7P9c9LgNwRQ/M7OxJzkY5MgtVJKW2XCIjLhc/ykk4AD\nB/x68DnBx0b//v5c5u9R3jJP+k5RGM2EtGZKj0iYFmk6MxcnE6mZEJlIi4AK+fqfegYHDx7Evbpz\nMgAAIABJREFU5ZdfjrvvvhvDSAIfQywWQ8x0pWVILF68GBs3+s8tLVMxevTU+AWMRBqxmL+q2LcP\nKC1N3Rrc1eX7G1pbk8+ZSOFHVenfP2GnlWSi8pkMH566y4pvDQb854MH/bRJKHNyorRJMzlyxK8H\nJxMq4759yaTFT+4T2fTrlyCWIUOSBz2RD5AqlEjgc/MTF/601Zj7TKgOXNNSbaPu7PTLT23I688/\nQmbSTI4cST7pTsRy5EhCGzl40O8TuTqWZMKdo9QONCYobhifCWnFJjMXf1blOXBgQuCS+eLIEb/N\nebtIQgQS7cp/p/7hZMLLpIrPyUTebdevX7KlgJ51Zi5aCA4YkDxu+BkaTqZ8h6XUTDiZ8DBOwnzs\nUbmofwoLE3OHSIOPjfz8xPyRZEI3SVC5yNpBG3yAVLMU+Un4TlOeJ18AyTpQGjaaiT9ONmDx4g0A\ngOeegxY5pZkcOXIEl19+Oa666ipccsklAHxtZNeuXQCAlpYWjB49GoCvcezYsSP+blNTE0pLS1FS\nUoKmpqak8JKSEmV+ixcvxmc+sxjAYpSWTo0LUU4mJFD379c74KVmQluDX389IYiJTAoLE0JcOuBV\nPhMiExKKukOL8vwHF6ZcMyHBSrZdApWRtANOJkCCQLjP5P33/fryE/NcM+HOdRrUvA25kJBaF5n/\nyISmM1uReY4+iazS9IJ2c6k0E76aO3LET49rJrJufOXLNYxYLCH8eTuoyITaOchnwjUGEpqUj0kb\n4mYueiZikwQGJHxa+fmJcQ0kmyyJTFTnVmQZebjUxA8f9tPgGjetrFVmLqmJ8nCdmY+TCfXZzp2J\nv0kr4mRCc4YLbW7mIuFPc7qgIFWwU58QmfD3gFQHfGenmkx4uWjeU1vJPPn45XXnZCIXbLxvKY6P\nqbj55sUAFuPccxdDh5whE8/zcM0116CiogI33HBDPHz27NlYvnw5AGD58uVxkpk9ezZWrFiBjo4O\nbN26FY2NjaisrERxcTEKCwtRX18Pz/PwyCOPxN9RgVZodHUIv+aEyGTwYH/VIc1c5IcoLPRVXE4m\npEBt3eqHDx/u/z1kSEKIc7MD381FOz9I6+GHCbmjnSYxN3NJMunq8stP6dF24Pb2ZDLp1w8YMcJ/\n5j4T1S40bvKiFRcN5CFD/HDKg9Lr6EjWjEjQUXuSRlNQkEyO1CZ0g4AUIkOH+u+ZyMS0m4v+5xsA\nuJ+CJjdpJpJMpLbBNR2ajHKHEp/o3OzC81eRCQkRrplQXB6u0kykmYs0azIj6cxcBw/6fcP7mFav\ntAAiTVimQfF5+P79ajMX9TffCUU7lORNEZJAgGTSGDw4OQ1ef4rf2Qls25YYs9R/fJHASYsIhMbv\n0aP+fNm/P9HHVNf+/RNzgGsmAwcmxrgkE2ofSnvw4MScAVJ9NnxzDBELtbccYzqfCaUtzVwqAuM+\nIB1yxsz1v//7v/jlL3+Js88+Gx/84AcB+Ft/b7nlFlRVVaG2thZlZWVYtWoVAKCiogJVVVWoqKhA\nfn4+ampq4iawmpoazJ8/H21tbZg1axZmzpypzZfIhG+D5VcjcMGp00zIzDViRGL1Pn68ny6ZTmjn\nVHt78s4uGgQjRyY6ddiwxGCktIcPT94aXFDglzU/P/XQIh2IJDIZMiRh5uLvSs3kxBP9ZxLceXm+\nsKbfef40UGnFdehQQjM5cCAhFLhmJMmE+wH4RKN3OcHSJgdp5ho2zF9dUt7pOODJ3KDSTOj5/feB\nE05I9fvofCbcUWrSTI4e9dti4MBUX4pKMyFBwDUTykf6TFQOeCIClZmLt8nBg367dnUlCytO2Coy\nIZMgPXseMG6cr61T/vv3p2om/P451ZU9tOCTJi++MBk+PDUO93EACUFdXu4vFOkT2HIHIBFfa6tf\nrqFDE++OGQO8/XbC9Eh1JbP4gAHA7t1AS0uymYtIixMbtVtbW8IETf3D2xxIlgGHDvlpFxSkpi3J\nRPq9KH8iCt5XqjyprDrkDJl89KMfRZf0ih3D+vXrleHV1dWorq5OCZ88eTI2b95slS+tKEigAQnb\nLamQtLLWbQ0mgT9yZLJf4dxzEyt5wqBBiXxotd/a6v9PHU+r7cGDE5rJkCEJUiDNhCYgCV8q63vv\n+f8fPJi8UiPhT2QifSZEJrR1WXU+huJSHWiSkMORTIKkplOdSavgWh85DclURvZkFZmQvZ9WqjSo\niXgHDEjVTFQOeG57JnAzF5lI+GqOyKSz069HYWGqk5MLK2nmUmkmcqXY3p4gEymUqSxEvOScpd85\nmdCCgdLQbQ0eNizha6JFEtXJ8xKraRp7nZ3Jmkl7u98Ohw6pyaStLeFTo9VucTGwZ09CQL/zTqKv\naM7w1fawYf7ChB885IsEqZnQuBo6NHnhQfOU4lB6tNDjmjjNe242o3nX0eGnTdrD6NE+WfDts/n5\nfrn37vUXl7t2AV/5ClBR8f/bu9LgrKo0/WQl+UhCAoEQ1ghhEWJABBQVsWbsjgvFKMri0lSX2N1q\nYamDtjo0JTN222ijTrtV2zNit7HEUVGsnkZAQaQdFVBodjSNESSABEIgK/mSnPnx8uS89+Z+WQwQ\nCOepSuXm5n7nnvV93u2cz8oG1s/v5mLb9Zpl+yjYo6KsFacVSi1HOJYJCXJPE4suT5NJkGWiSa4l\nZHLGuLnaC343F+DN7KIWDlit2u/mCsrU0j5SvmPfPmDyZPuM/p4TCtTqahsHoFYP2IWpYyYUxH43\nlw7AU8hx4mmNRpOJtkK4eHR72H4+yz6JiZFytGVSVmYD881ZJtSsSH5xcVJeRYUlNS4i3tcapHZz\nhUJesvdbJlQSKBQBrxauyUQHyRkz2bXL6zaj5kshH7TPRJcdFL+gUKSwomVCQeN3tZBMgoLe2s0V\nKWZCi1tbJikp8n4KDGOsskEy0QoDrZS0tGDLhORAwWmMKDh9+8rc0K5XY8SSKC31zl+SyZEjVjGh\nZaLPxPO7vKiM0bLnfKTCoD0FVVVeawiw616TCeehdqXW1go5+smkc2fpz5ISqf+kScDQoVYeMIGj\noqLxetCJMkFkAngVR71+SGC0yoJiJlSMWB7ne1MxE0cmrYC2TDSZ+IPaQOTU4JQU+zktcHUqLQBk\nZgZvYCwrs9p+dbWdvBQeSUmyqJirrlMBI8VMuEBojWjtL8jNpV1xmrRY9+pq+7xuZ5Blwt9+y8S/\neOgSI5mUlUndmBmjTzJmv5WXe/fncB9QTY0s7l27ggO8fGd6umjHgNdFpAPwOk7BRaf35Gi/PWNX\nsbGN03O1m6uyUtrL8qhBarLVZMLUbbpU/G4ufzCc72EChRbsFFAksHDYumvCYZvKyvlOMmEyBclE\nWyZNkQldkuXlUnZ9vbiDsrNlvOvrxYovLbVkcuSI18oGpI4lJfJbu278ZAJ4hT/T6evqbNkcH7qA\n6dLWlgnXFdcGFccgMqmrAzIyxPLQZBIKWRKMjZXvTCov98ZM6G3geuBc4jzQbi7GyfxJD5RRbANl\nRGqqrPNIbi5NJpq0dDxGkwkVIq5vnSzgxzlPJkGWSZCABoJjJtSECL/AZfaTRhCZaMvEv7+Dlo8W\n8nRz0TLRE4waYRCZNBUzYXCeWqOud2VlZMtEx0zYNj1JgywTLvqjR+W9dI+RTI4elXcwCK8tE7oV\nKbgqKuSZkSNFWNHtFRQz6dZN3CuAXSh6B7w/BhIVZQUQof3z2kLUZOJ3c1VWypj4A+B1dV43CgP9\ndKkEkQktE00afA/HlfVISxOhrYVLdbXdWFdba91VVBh0yjmtzKbIhG1jXWgZcB+SMULgAwZYy6Rb\nNxF+fjLRgp1CWVurmkz8R64wRkg3Ujgs7yktlbI1mfjjNMxGpLZPIU83V1VVsJvr22/t+uQa1WQS\nClmFicpTSoq0ZfNmbxanXie0XvzJGvq0DZIJLROSCYkqEplQ0WHWGBVX//lhJJaYGGeZtAhBMRN/\npkSQZRIXZ7U45ohrAa2zn/xHEmg3V2KiTDBOamZI0X0TRCY68yyI+KhNajKhMGiJZRJEJv62+S0T\n1pWWiZ9MgiwTBiq1mR4XJwvp6FFpZ2qqPMO+YgD82DFb74QEeT4+3rZTx0z0RkkKLsBr0pNMGINh\nv2n/NwD867/a9FWeikDLRGuQeo9GdLQleL9lcvy41MlvmVBwcQwpRCNZIMzmYiYffd86ruGP+9Ay\nSUmxlolONtEB+MREb79VVso41NTIWJA0qqulr/xurqoq0eTLyqQ96eleMqHApzIUF9c8mWg3F+cs\nlbsgMklMlLHkXhB9/lyQZRLk5kpLs8I6I0OyNemZ4Bqlm4v1JplkZEgwPiUF2LsXePttq0xynezc\nKa6zrl3ld0mJVwngXiqdvKPnaWqqbXskMmGau05BDoe9iQtc8yRqWib6mxv9OOfJJFLMpDnLRGvy\nzOTQ6bZ+a0AjkmVCM5haDJ+h5UM3l3ahBZEJFx0Dtf49IlywJA/dZsCa8n4y0QkKfsuELiq/m4uL\nOyhmQsuE5MkFyPtRUbJ4Dx2yfUUyYSYQ+6WkpDGZ+FODjbFWD+B1EdHNRauHLi8u0hPbmzB5shVi\njNPoJAJqcH43Fy2qujortMNhayVoMjHG7qTWlgl9+doy8bu5KAiPHbMumC5drFCqrfVaJiQzkklV\nlfR3YqKUqclk924roGiNxMUBhw9L24wRd1ZWVmM3V3W13SUeyTLR8zcuzjsn9OZZvZeLVgJdW9rN\nFQ5bd1pMjLxz3z5rmUSKmdB60WRCy6RHD5k/tbVCDseO2bR/ABg40M4ZbY3ExIgbdt8+L/mUlMj/\n6W7csgVYv17m/UcfCVmR2KqrrRKgiY/r58gRmT/cxKyD7jqZRAfpNZlQ8WBMjXFbvbvekUkTCIqZ\naN9tJDJhRpUGhQHLa87NFRSA15YJy6FlkpTkTVcm8fi1LP9mQj+xsT26/rRYAC+REc1ZJtqUZxl0\no9AnH+Tm0pYJtVAGTaOjhTgOHpQ6s69omVCIUvvVZKJTo7Wbi0QFNHZzMU5B7T0mxqtl/upXwIgR\n1s3FDD9aJvq0AgY2acEyoSApybsBVgtzzh+mCfvdXBUV8n+6/rjJVLvTNOnfd5+UkZoqBBEXByxf\nLp9NT5e+LysTAVlVJfcrK22SSCgkBKLJJDPTWiahkPTzoUNeMjnvPK+biwkKaWleN1dpqVynplo3\nF1OGtWVCd1FFhff4IFogtbW2DzWxRCITbZnoWCXLZh/q7LBwWN7fo4e0sapKiAOw5FBUBLz0krx/\n1y5g3Tq7GTc2Vt7PY5mIhATg/feBRx+VfiO6drXXVMZoUfpd2toy0S5jfeJBfDywYYP0pw7SR7JM\n/BlxjkxagOYsE32fi5cB1iAyaY2bi9o2NZdIlol2HbGuumz+n3WlZkdXmN+SYXtIHnwP26PrR2gh\nFRQzISFGIhP/DnxO2CDLhFoo3VwHD8p4cPNo5852P4223EgmpaV20elgJsfQb5mwHSQFP8lRuD32\nmNUA//u/rWXCz6WkWFcQXVHx8fK/Y8ekbnoPAskkI8PudaBQDIe9WUzx8Vbb7NlTfPV0qRw+bMdf\nJ0oAIsBSU+UZCoLycuCyy4D/+z8r5EpLrVuOVtHkycDnn1syKSoSYUoy6dzZSyb19RKP6t9f+ozu\nuWPHZO7wpAjOAyZdaDdXWpqMt9/NpTfDUtEjefu16khkkpYmbiZaJnQRcS1pbd9/9Aw/2707sH27\njAFdn+zvXr1sAJ7gOikutve1PNCJHZpM9DXJhJYJvRB9+gDffNNYGeO6ohVTXm5jHQcP2iA943V+\nMvFbetridmTSBPSmxaCYiRacHFRaB02RSVNuLpanU3+bskxYL7/VQ+LRz9I8Z3lcMEGWiZ7UDFAC\n1t3VUsuEhBjk5qqttcdv+zfLcQcxFwMD4M2RSadO8n5ujuQ7SSbcuEY3DgWKdqEBXsskJUV81ImJ\nNpssJga45BJvnwDACy8Ae/bY8aabKyVF6pqYaPdoxMfLO4uLvWQSHy/lV1RIYLqoSOqqDwxkv9E6\nLS6Wtg8fDmzcKGUwoyjIMgEsmezbB0ybZgVa//7S3uRkeed331mBzySIYcPsWCY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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is quite dense. We also expect the curve to be very similar for every year. Let's try to overlap all the curves for every year in the dataset. We expect them to overlap quite tightly." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figure()\n", "plot(range(1,13), reshape(amplitude[s:], (-1,12)).T)\n", "title('Yearly curves overlapped')\n", "xlim((0.95, 12.05))\n", "xticks(arange(1,13), ('jan','feb','mar','apr','may','jun','jul','aug','sep','oct','nov','dec'), rotation='vertical')\n", "xlabel('Month')\n", "ylabel('Flow [m$^3$/s]')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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5bNu7t7w4detqnuQtWPBidR40SPN4rH17zWwy6a+99uAyaNAggoODH0tbtGgR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\nDi6Uww9LzjG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PtQhBIjnXkOYikUgkkrNOerqYSiQSiaRLIc1FIpFIJGcdaS4SiUQiOetI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\nIpFIJGcdaS4SiUQiOev8PwyLrQXnrOG3AAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get further intuition about the variability of the flow during every month, we visualize the previous curve with boxplots, showing median, 0.25 quantiles and 0.75 quantiles, as well as extrema." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figure()\n", "boxplot(reshape(amplitude[s:], (-1,12)),1)\n", "title('Yearly curves overlapped')\n", "xlim((0.95, 12.05))\n", "xticks(arange(1,13), ('jan','feb','mar','apr','may','jun','jul','aug','sep','oct','nov','dec'), rotation='vertical')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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f1+yrI4QQ0qwWdRbv2LEDPj4+AICsrCzIZDL+OZlMBrlc3mC7VCqFXC4HAMjlctjZ2QEA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\nTmDPnj2Cx42JicGKFStQUVGBtLQ0XLx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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "From this, we make the following observation.\n", "\n", "* During the dry months, the flow has a very low variablility.\n", "* During the months corresponding to the flood (August to October), the flow has a very high variability.\n", "\n", "From this simple observation, it would appear that the intensity of the flood is difficult to predict. As we will see, this is actually not the case." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Long term dependence\n", "--------------------\n", "\n", "A characteristic of many natural processes is a very long range dependence. The dependence here is how events are influencing each other with respect to their distance in time. In the case of the Nile, just like the Pharaoh of old time, we are interested in the amplitude of the yearly flood. From our previous study, we saw that the flood happens in September and we will limit our data to just this month." ] }, { "cell_type": "code", "collapsed": false, "input": [ "flood = A[8::12]\n", "flood = [float(flood[i]) for i in range(len(flood))]\n", "t = T[1::12]\n", "\n", "plot(t, flood)\n", "xlabel('Year')\n", "ylabel('Flow [m$^3$/s]')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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54sQVJ7JwPlKkzqezkwuPycR/12KhqRAfT5yPtOCguZlPHsHBfOIHbOMDHMWntNR/q+yF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\npE0+hfjExLjP+fhKdDSf+NSONySEb/H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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dependence of events of a time series can be quantified using the [autocorrelation function](https://en.wikipedia.org/wiki/Autocorrelation) (ACF). The value of the ACF is between 1, when two events are maximally correlated (they determine completely each other), and -1, when they are maximally anti-correlated (one is the opposite of the other). A value of 0 indicates that the two events are not correlated (the value of one has little or no relation with the other). The ACF measures this correlation as a function of how far apart in time events are.\n", "\n", "For example, for a time series where successive events are independent, we expect the ACF to be 1 at zero (correlation of an event with itself), and zero everywhere else. In practice, we can only compute an approximation of the ACF, so instead of zero, we see a function clustered around zero.\n", "\n", "For a process with long range dependence, the ACF follows a power law, i.e. the correlation between events decays as a power of their spacing in time:\n", "\n", "\\\\[\n", "ACF(t) = Ct^{-\\alpha}.\n", "\\\\]\n", "\n", "As an example, we plot the empirical autocorrelation of the Nile flood data, and a time series of random independent data. One notices that the flood data ACF only decays slowly, while the ACF of random data is close to zero everywhere, except at 0.\n", "\n", "A slow decaying ACF indicates a process that can be very well predicted. In other words, given the flood amplitude for several successive years, it is possible to fairly accurately guess what will be the next value of the process. In the case of the Nile, it means that several high floods are likely to be followed by a high flood, and vice versa. This was indeed the basis of the power of the Pharaoh." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def acf(x):\n", " R = zeros(size(x))\n", " mu = mean(x)\n", " sigma2 = std(x)**2\n", " n = len(x)\n", " for k in range(n):\n", " R[k] = sum((x[0:n-k]-mu)*(x[k:]-mu))/(sigma2*(n-k))\n", " \n", " return R\n", "\n", "t = arange(0,len(flood)/2)\n", "acf_flood = acf(flood)[:len(t)]\n", "acf_rand = acf(rand(size(flood)))[:len(t)]\n", "\n", "plot(t, acf_flood[:len(t)], 'b')\n", "plot(t, acf_rand[:len(t)], 'r')\n", "legend(('Flood data', 'Random'))\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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oUSj4RvDjj4bv1/fnAxysbt4c+Ptv68dR7GRmcl2NMWPyt4noO4a9e4FevfJf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\noE8fM+ny169TZuVaVL92Jv3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"text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Harold Edwin Hurst](https://en.wikipedia.org/wiki/Harold_Edwin_Hurst), a british hydrologist, is the father of modern Nile studies. He was in fact the first one to formalize the concept of long range dependency. He notably described the [Hurst exponent](http://en.wikipedia.org/wiki/Hurst_exponent), a characterization of the long range dependence of a process. The Hurst exponent is directly linked to the ACF in the following way. If the ACF is written as a power decay\n", "\n", "\\\\[\n", "ACF(t) = Ct^{-\\alpha},\n", "\\\\]\n", "\n", "then, the Hurst exponent is\n", "\n", "\\\\[\n", "H = 1-\\frac{\\alpha}{2}.\n", "\\\\]\n", "\n", "The Hurst exponent can be estimated using a quantity called the _rescaled range_ that we won't describe in further details here. For more information, one can consult [wikipedia](https://en.wikipedia.org/wiki/Hurst_exponent). We write a short routine to compute the rescaled range and the Hurst factor." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Compute the rescaled range for all partial time series of length n\n", "def rescaled_range(X,n): \n", " \n", " RS = 0\n", " \n", " for i in range(int(len(X)-n)):\n", " \n", " # compute the mean\n", " m = mean(X[i:i+n])\n", " # make zero mean\n", " Y = X[i:i+n] - m\n", " # partial cumulative sums\n", " Z = cumsum(Y)\n", " # difference max and min of this time-serie\n", " R = max(Z) - min(Z)\n", " # variance\n", " S = sqrt(mean(Y**2))\n", " \n", " RS += R/S\n", " \n", " return RS/(len(X)-n)\n", " \n", "# Routine to compute hurst factor\n", "def hurst_factor(data):\n", " \n", " # compute rescaled range for all size of partial sums\n", " logmax = int(floor(log2(len(data))))\n", " N = 2**arange(2,logmax+1)\n", " RS = zeros(size(N))\n", " for i in arange(logmax-1):\n", " RS[i] = rescaled_range(data, N[i])\n", " \n", " # compute the linear fit\n", " M = reshape(concatenate((log(N.T), ones(N.shape).T), axis=0), (2,-1)).T\n", " lf = dot(dot(inv(dot(M.T, M)), M.T), log(RS).T)\n", " \n", " # Hurst parameter is the slope of the linear fit\n", " return lf[0], lf, log(N), RS\n", " " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "While we expect the Hurst factor to be close to 0.5 for uncorrelated data, Hurst found a significant factor of 0.7 for the floods of the Nile. Let's see if we can find this from our data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Compute Hurst factor\n", "hf, lf, n, RS = hurst_factor(flood)\n", "\n", "# plot empirical rescaled range and linear fit\n", "plot(n, log(RS), 'b', n, lf[1]+n*lf[0], 'r--')\n", "xlim(n[0],n[-1])\n", "xlabel('log(n)')\n", "ylabel('log(R[n]/S[n])')\n", "show()\n", "\n", "print 'Hurst factor for the Floods of the Nile : %f' % lf[0]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "Hurst factor for the Floods of the Nile : 0.732528\n" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fantastic. We can now check that this indeed follows the decay of the ACF." ] }, { "cell_type": "code", "collapsed": false, "input": [ "alpha = 2*(1-hf)\n", "plot(t, acf_flood)\n", "acf_decay = arange(0,len(acf_flood))**(-alpha)\n", "plot(t, acf_decay,'r')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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g7RuGrdXW6mpaQu7aNdquXtV9Lb134QJ9L32m/VXaAAr+LVro3gy0X0vlld5r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\neTmdr/5T0ZgxQrz+OgV/f3/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"text": [ "" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "And finally, we check for random uncorrelated data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "hfr, lfr, nr, RSr = hurst_factor(randn(1000))\n", "\n", "# plot empirical rescaled range\n", "plot(nr, log(RSr),'b', nr, lfr[0]*nr+lfr[1], 'r--')\n", "xlim((nr[0],nr[-1]))\n", "ylabel('log(R/S)')\n", "show()\n", "\n", "\n", "print 'Hurst factor for random data : %f' % lfr[0]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "Hurst factor for random data : 0.558146\n" ] } ], "prompt_number": 382 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Study the discrete Fourier transform\n", "------------------------------------\n", "\n", "As an added bonus, the flow of the Nile is naturally a quasi periodic signal (but for the variable flood level). This gives us a chance to observe the Fourier transform of such signals. In particular, we know that for a perfectly periodic signal, the Fourier coefficients will be zero but at integer frequencies. Let's observe what happens here using the DFT. Since we have many periods, this should be a reasonnable approximation to compute the continuous Fourier series:\n", "\n", "$$\n", "X_k = \\sum_{n=0}^{N-1} x_n e^{j2\\pi \\frac{nk}{N}}.\n", "$$\n", "\n", "Rather than the dry linear index of the vector, we would like to know what the frequency corresponds to.\n", "Our time unit is in year, and our sampling period is one month or\n", "\n", "$$\n", "T_s = \\frac{1}{12}.\n", "$$\n", "\n", "Let in addition $N$ be the signal length and $T$ the signal duration (in years). We have the following relations:\n", "\n", "$$\n", "T = N\\,T_s,\n", "$$\n", "$$\n", "F_s = \\frac{1}{T_s}.\n", "$$\n", "\n", "Thus, our sampling period in the frequency domain is\n", "\n", "$$\n", "\\Delta F = \\frac{F_s}{N} = \\frac{1}{T}.\n", "$$\n", "\n", "Since our signal is real, the DFT is conjugate symmetric and we only need to keep $N/2+1$ first samples." ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = len(A)\n", "Ts = 1./12.\n", "Ttot = N*Ts\n", "\n", "# Compute the DFT\n", "F = fft.fft(A.T).T\n", "\n", "# since the signal is real, we can just keep one half of the spectrum\n", "F = F[:N/2+1]\n", "\n", "# construct the corresponding frequency vector\n", "freq = arange(0, N/2+1)/Ttot\n", "\n", "# display the magnitude of the spectrum\n", "figure()\n", "plot(freq, np.abs(F))\n", "xlabel('1/year')\n", "ylabel('|dft(A)|')\n", "xlim((-0.1,6.1))\n", "show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", 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RkfMYOA7gKTUiIucxcBzEHg4RkXMYOA5gD4eIyHkMHAexh0NE5BwGjgM4aICIyHkMHAfw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\n+WbPhIQEbNmyBZs2bWpx+/e///3vMBq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"text": [ "" ] } ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we see the expected behavior, i.e. integer frequencies are dominating since our signal is quasi-periodic. However, we observe that low frequencies (between 0 and 1) are not quite close to zero, as a close-up reveals. Here, we first zero the integer coefficient and then plot the residue signal." ] }, { "cell_type": "code", "collapsed": false, "input": [ "zero_range = range(0, len(F), int(Ttot))\n", "new_F = F\n", "new_F[zero_range] = 0\n", "figure()\n", "plot(freq, abs(new_F))\n", "xlabel('1/year')\n", "ylabel('|dft(A)|')\n", "xlim((-0.1,6.1))\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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IDw/H+vXrYbPZAADr16/HPffcg7q6OkydOhW33347AGDhwoWYO3cukpOTERsbi61btwIA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\ne02Iijj2Dz7Q0oevXAHWrOHvL1zgXuu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"text": [ "" ] } ], "prompt_number": 369 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We observe some relatively strong components in the very low frequency domain, which might be explained by the long range dependency of the data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Further reading\n", "---------------\n", "\n", "The study of long range dependency was later linked also to fractals and financial data and further studied in depth by [Mandelbrot](https://en.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot).\n", "\n", "Here are the different websites consulted in the making of this notebook.\n", "\n", "* Hurst exponent [wiki](https://en.wikipedia.org/wiki/Hurst_exponent) article.\n", "* A thorough [article](http://www.bearcave.com/misl/misl_tech/wavelets/hurst/) about the Hurst exponent and financial data.\n", "* The [history](http://www.safehaven.com/article/2729/the-riddle-of-the-nile) of the Hurst exponent." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Acknowledgement\n", "---------------\n", "\n", "The data was kindly provided by Prof. Mohamed Salah Siam. Thanks to Prof. Marc Parlange for the introduction." ] } ], "metadata": {} } ] }