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@chandinijain
Created August 6, 2017 04:25
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Integration, Cointegration, and Stationarity\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"import statsmodels\n",
"import statsmodels.api as sm\n",
"from statsmodels.tsa.stattools import coint, adfuller\n",
"\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Stationarity/Non-Stationarity\n",
"\n",
"A commonly untested assumption in time series analysis is the stationarity of the data. Data are stationary when the parameters of the data generating process do not change over time. \n",
"\n",
"*Mean of a time series $x_t$ is $E(x_t)=\\mu(t)$*\n",
"\n",
"*Variance of a time series $x_t$ is $\\sigma^2(t)=E[(x_t - \\mu(t))^2]$*\n",
"\n",
"**A time series is stationary in the mean if $\\mu(t)=\\mu$, i.e.mean is constant with time**\n",
"\n",
"**A time series is stationary in the variance if $\\sigma^2(t)=\\sigma^2$, i.e. variance is constant with time**\n",
"\n",
"As an example, let's consider two series, A and B. Series A is generated from a stationary process with fixed parameters, series B is generated with parameters that change over time."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def generate_datapoint(params):\n",
" mu = params[0]\n",
" sigma = params[1]\n",
" return np.random.normal(mu, sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Series A"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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BJ2fz+PCXnwjkpqTfqZpRczFzLQmlvYze6fk8SrpRd1F6LYf2j+ORM4tdt2bh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YPR87cA+dH792EpK+Nrl275+jnNoEtZL9fJNxzXmXa79M2Lq3nIioq79jaYrrgHj16nliazTZ9b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\n4Jn/DwEhiPKCrtPZAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xc9a4358>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Set the parameters and the number of datapoints\n",
"params = (0, 1)\n",
"T = 100\n",
"\n",
"A = pd.Series(index=range(T))\n",
"A.name = 'A'\n",
"\n",
"for t in range(T):\n",
" A[t] = generate_datapoint(params)\n",
"plt.figure(figsize=(15,7))\n",
"plt.plot(A)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Value')\n",
"plt.legend(['Series A'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Series B"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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w+iR++kptFFY2mcXhH3KuUIiQP7syKxkjHh/a+4YisLLoWuiA9yyAj47+/qMAnlng5xMR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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xd633c50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Set the number of datapoints\n",
"T = 100\n",
"\n",
"B = pd.Series(index=range(T))\n",
"B.name = 'B'\n",
"\n",
"for t in range(T):\n",
" # Now the parameters are dependent on time\n",
" # Specifically, the mean of the series changes over time\n",
" params = (t * 0.1, 1)\n",
" B[t] = generate_datapoint(params)\n",
"plt.figure(figsize=(15,7))\n",
"plt.plot(B)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Value')\n",
"plt.legend(['Series B'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This image from SEANABU.COM should help \n",
"\n",
"![Courtsey: SEANABU.COM ](download.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Why Non-Stationarity is Dangerous\n",
"\n",
"Many statistical tests, deep down in the fine print of their assumptions, require that the data being tested are stationary. A stationary time series (TS) is simple to predict as we can assume that future statistical properties are the same or proportional to current statistical properties.If you naively use certain statistics on a non-stationary data set, you will get garbage results. As an example, let's take an average through our non-stationary $B$."
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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JAH/AO9Hcg9dnwrWsqKaAJyIiIiIyD71c3kxNey/ffeZopJcypnanP+AF20UTYEVOCv0D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\nSZIkqSNs8CRJkiSpI/4B7S4s4OQCjQ8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xd33a278>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m = np.mean(B)\n",
"plt.figure(figsize=(15,7))\n",
"plt.plot(B)\n",
"plt.hlines(m, 0, len(B), linestyles='dashed', colors='r')\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Value')\n",
"plt.legend(['Series B', 'Mean'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The computed mean will show the mean of all data points till date, but won't be useful for any forecasting of future state. It's meaningless when compared with any specfic time, as it's a collection of different states at different times mashed together. This is just a simple and clear example of why non-stationarity can screw with analysis, much more subtle problems can arise in practice."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Testing for Stationarity\n",
"\n",
"Now we want to check for stationarity using a statistical test. We performthe standard [Augmented Dickey Fuller test](https://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test)"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def check_for_stationarity(X, cutoff=0.01):\n",
" # We must observe significant p-value to convince ourselves that the series is stationary\n",
" pvalue = adfuller(X)[1]\n",
" if pvalue < cutoff:\n",
" print('p-value = ' + str(pvalue) + ' The series ' + X.name +' is likely stationary.')\n",
" return True\n",
" else:\n",
" print('p-value = ' + str(pvalue) + ' The series ' + X.name +' is likely non-stationary.')\n",
" return False"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p-value = 7.34551801775e-20 The series A is likely stationary.\n",
"p-value = 0.982699395891 The series B is likely non-stationary.\n"
]
}
],
"source": [
"check_for_stationarity(A);\n",
"check_for_stationarity(B);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sure enough, the changing mean of the series makes it non-stationary. Let's try an example that might be a little more subtle."
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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JhKPXCGNhjx7xgPmWPWiGsRBCRpEdjl6jR4+HX26g0AsQIfTC5OiJa2k3ugnYgSymBTx3\nfcPPyyIkFBTqO3rpmIyxhIJcRYdhMoWW9BeRuAmEa7SfEEL8Qtvm6KlyBNGIxDAWl1DoBchKwXYD\nwiT0Kl0cvQcPjUOSwD09MpKIkZGkGsV4UgEA5Di+SfrM/HoZ2bg9plTRw/P+QAghfrHd0ZMkCUlV\nDtU98yBAoRcQ5arRGH8M04mtGN0UMbbbGUsouHs2Q6FHRhLxnLV39Gyht0GhR/rM/EYZd8ykAQCV\nEL0/EEKIX2zf0QPs916uDrmDQi8gxNgmEC5Hrzm6uftD43W3T+AHr63D5MgaGTFad/TGEyoAcE+P\n9J35jTLmJhKIKxFUdO7oEUJGj+2OHmAnXpdYmO4KCr2AWG4RemFKVRPuYnyX0U3A3tPLV3RcWS74\ndVmEhAKxBJ6K2T16AB090l9M08LCRgUHJxJIKDIL0wkhI0mlZiIiAYosNX4vFYs2duWJMyj0AkJU\nKwBAOUSnEyIBdLfRTQA4PJkEACzltF0/hpBhpKjpiEYkqHIE4wlb6G2yS4/0keWChqphYm48gbgi\nh2q0nxBC/ELTDcSiMiSpReipMusVXEKhFxBidFOSwjW6Wa7aY0K7hbEAzYhbzkmTUaOo6UjFopAk\nCeNJjm6S/nOjXq3QcPQ4ukkIGUEqNXPLfh5gmxCsV3AHhV5ArOTtm8PZTCxUJ7aNHr1d6hUAIBOz\nnQxG3JJRo6AZSNdLW0UqIkc3ST8R1QoHx5OI0dEjhIwowtFrJR2Tee/pEgq9gFguVDCRVJCNKyFz\n9OwnkBNHrxiikVNC/MB29OzHf1SOIBOPYoOjm6SPzLc4enEl0ggkIISQUULT2zh6DGNxDYVeQKzk\nq5hOx+xOkBAt25drBuSItGX5dTupuqORr/DJRkaLYlXfsr86nlSwSUeP9JH5jRLGEgrSsSgSdPQI\nISNKpdbO0WO9glso9AJipaBhOh1DQpXDFcZSNZFUti6/bicWjSAakWifk5GjqOmN0U0AGE+o3NEj\nfeXGehkHxxMA7PRjFqYTQkaRto6eKqNSM2Gw3ssxFHoBsVzQMJOJIalGw1WvUNMR77CfBwCSJCEV\ni1LokZGjqBmN0U3AdvS4o0f6yfx6GQcnbKFn1yswjIUQMnq0c/RS9Ykajm86h0IvIFbyTUcvXDt6\nBpJdhB4g7PPwXDchflCop24KxhIK6xVI37AsC/MbTUcvpkQ4ukkIGUk03URsm6Mn3n+LvP90DIVe\nAJSqOopVA9MZFcmQ7WCUqkbHIBZBmo4eGUFKVb1xogjQ0SP9ZaNUQ6lqYK7F0WMYCyFkFKnUzJ2O\nHsMAXUOhFwCiWiGUjl7NQNyB0EvFZC7EkpHDHt3cuqO3Wa7BsrgvQPaOqFYQQo+F6YSQUUXTjR07\neuKglUaDcyj0AmC5XpY+kxFhLOF5I6/UnI1upph8REaMqm6iaphIb9vRM0yLzwXSFxpl6eNJAGgU\npvMggRAyamhtHL2kcPQ4uukYCr0AWBFCLx1DUomiapjQjXAs3HN0k5D2iOXv1nqFbEIBAHbpkb7Q\nKEtvOHoRGKaFmkGhRwgZLTo5egxjcQ6FXgAIoSd69ACEpkuvXDOQcBjGQqHXP/7LP1zCR/72fNCX\nQTogXLut9Qq20GOXHukH8+tlJBQZE0n7cSXG6FmxQAgZNdrv6Nnvv5yicU60+4eQfrOct4XeVFpt\niKpK1UA2rgR5WQDs1E0njh5HN/vLty8vQ+epfagRoyJbdvSSKgA6eqQ/zG+UcHAi0egxbQi9kLw/\nEEKIX7R19Oqjm2HKtgg7FHoBsFLQMJFUoMiRpqMXkgetG0evoOmwLKtjuTpxxlKuAlWmwR5mxMHG\n9h49ANgoszSd7J3WagWgReixS48QMkKIkfXdHD1OlDmHd5YBsJKvYjodA4DwCb2qM6GXikVhWrwB\n6Qc1w8RKoYpchS9cYUbsBKTajG7S0SP9oLUsHUBjuoKjm6ONaVowTE58kNFB1Mpsd/SSCsNY3EKh\nFwDLBQ0zGVvoJeqLpeVa8Df5hmlB002HYSz2xwzS+GapquM/f/kClnKVoC9lC7fqo7wFTeebeYgR\nJ4ipNmEs3NEje6VU1bFeqm1z9Oy36DAlMxP/+fUvPIf/7f/5YdCXQYhvCBMhFt0qU6JyBLFohGEs\nLqDQC4CVgtZw9ISoCoOjV6kHwjgSevHBs8//8Nuv4I+/+yq+celW0JeyhVbhWaCrF1oK9RPE1jCW\nuCIjocjYKHF0k+yN+fWtHXpAi6MXkrAuEgxXlgu4uJAL+jII8Y2mo7fzfjTNjAhXUOgFwEpeC+Xo\nprgGRz166mAlHy1uVvCHT1wBgNA5ekubzevJVegMhZVimx09wN7T4+gm2Ss3RLVCi6MXq9/klCn0\nRpqCpmM5pwV9GYT4RsPRU3bKlGRMDsU986AQmNCTJOmQJEnflCTpgiRJ5yVJ+vdBXYuflKo6ilUD\n0xk7rU/sw4VhNEecGrc7QdlOesAibn/3qy/CNG0RuxSyN8xW4UmhF16KbXb0AGAsoWCDo5tkjwhH\nr+2OHnehR5qiZiCv6aG4TyDEDxqOXnTn/WhKpaPnhiAdPR3Ar1mWdS+ANwL4ZUmS7g3wenxhJW+P\neM1sc/TCcGIrrqG1EHo3Bin56NyNTfzND27g5996BEemUrgVMkdvsUV45jm6GVqKmg45Iu3YGRhP\nKtiko0f2yPxGGdGIhNlMvPF7YkePo5ujjbipFR28hAw7nRy9VCzKHT0XBCb0LMtasCzrB/Vf5wFc\nBHAwqOvxi2VRll4PY0kqtmAKgw0triGhdn9YDEpppWVZ+M9fuYDJlIpf/rG7sC8bw1I+XEJvi6PX\ngzNkWRZurJf6eUmkDUXNQEqVd9SJjCdU1iuQPTO/XsaB8TjkSPPxFeeO3shjWVZjmuBWyN67CPEK\nrba7o5dUZaZuuiAUO3qSJB0BcBrAM23+7AOSJD0rSdKzy8vLfl9a3xFl6cLRa45uBi+YxFiIm9HN\nsD/Z/vHCEp55dQ3/4R3HkI0r2D8WD+XoptjZ7MXR++aLt/D23/0WFjd5E+AlBU3fEsQi4I4e6Qfb\nO/SA5uhmGCY+SDCUqgasehizuH8gZNip6Ls7eulYdCCmycJC4EJPkqQ0gL8B8KuWZe2IlbIs61OW\nZT1sWdbDMzMz/l9gnxGjF6JeQY1GEI1IoXD0Ki5GNwchdbOqm/idv7+Eu2bTeO/rDwMAZjNxrBQ0\n6EZ4dl4WcxUcm00D6G1H78Z6GYZp8bTXY0pVHck2Qm8sae/oWRarMUjvzK+XMTeR3PJ7LEwnrVMz\nFHpkVBCO3vbCdMC+Rw3DPfOgEKjQkyRJgS3yPm9Z1v8b5LX4hRB6kym18XsJJRwJQo3RTQeOniit\nzIdY6P3509fw6koRH/7pE4jK9kN9XzYOy2qO0IaBWzkNdwmhV3b//RT7YWEfox10CpqxI4gFsEc3\nq7rJm3HSM1XdxFK+ssPRE/ugHN0cXVpf129R6JERQTh62wvTAbvHmfc7zgkydVMC8GkAFy3L+nhQ\n1+E3y3kNE0kFitz81idUORRpWs0wlu5CLxKRkFLl0Dp6G6Uqfv/rL+Ftx6bxyPGmE7wvazupYRnf\nLGg6CpqOgxMJJFUZ+R4cPVHWHfYx2kGnqOlIx3Y+N8aTdmk69/RIryxuVmBZWxM3Aft1NhaNUOiN\nMEU6emQE6ejoMYzFFUE6em8B8K8A/LgkSWfr//vpAK/HF1YKWmNsU5BUZZRC8EYu9gSd7OgBdiBL\nWIXef//6y8hXavjwu05sCc/Yl7UT7cLSpSeuY382jkw82tPoZlPohfNnMSwUNb3RH9nKeKIu9Lin\nR3rkxoYdpjS3zdED7INACr3RpVCh0COjR6cdvZQqo2ZYqOqconFC92Usj7As67sApK4fOGSsFKqN\n4A1BQo2GytFLOHD0AHshNoz2+SvLBXzuqat47EcO4Z792S1/Nlt39MJSsSDK0mezMWTjSk9hLELo\nhXmMdhgoVvW2o5tjdUdvk116pEfadegJ4lGZYSwjjHiPnU7HOLpJRgatQ69za72XGlV3/DnZSuBh\nLKPGSkHbIfSSqoxyLfib9HLVPh1xsqMH2IEsYXSRfufvLyEWjeA/PHr3jj+bSsUgR6TQjG4u0tEb\nGIqagVS70c2E/UZDR4/0yo31MiQJODDWRugpEe5/jjCiWuHodJKOHhkZNOHoRds5enWhx/FNR1Do\n+cxyvr3QC0UYS02HGo1s6XHqREoNn6P31JVV/OOFJfzbR+7cUjwskCMSZjOxEI1u2m/c+7JxZBO9\nOXq5+udQ6HlLQevm6HFHr1e+dmEJ//GLLwR9GYExv1HGbCYGtc1NTVyhozfKiNHNo9MprBQ0mCbT\nfcnwo9UMSBKgyu0L0wHmEjiFQs9HSlUdpaqxY0cvoYQjjKVSNRwFsQhSsSgKIXqiWZaF3/67i7ht\nLI5ffNsdu37cbDaOpZCcjC7lKsjEokjFosjElZ4K08XnhE10DxM1w0RVN7mj5xH/8MIiPvvUtZGt\nCJlf39mhJ4gr3NEbZcR77JHpFHTTwnqJB0pk+KnoJmLRyJaMBUGyPllDR88ZFHo+spK3X6Cn01tn\nihNhcfSqhuOxTcCOuA2Ti/TV80s4N7+JX3307o6BMvsyscZuXNAs5SrYN2Y7j9l4dE87eoUePpc4\no1S/2Wrn6CVVGYosYYM7ej0jbl6feWUt4CsJhvmNMg5u69ATJBQZGkc3R5aipiMiAYcn7cdHmKqB\nvGS1oOGDf3YG60UK21FEqxm73seJA9dSiIyGMEOh5yPLBVtcTLdL3QyB0CvX3Am9MKVumqaF3/va\nZdwxncK7Tx/s+LH7snEshcQ5WMxVGpUPmbiCXMVd8bZumA0nj6db3lGof2/b1StIkoSxhEpHbw+s\n1m/mnnl1NeAr8R/TtLCw2cnRi3B0c4QRI+NiFWFU9vS+fXkZ/3B+ES/c3Az6UkgAVGpm2/08AI1d\neU4xOYNCz0eW647ezPbUTSXaqDYIkkrNcJy4CdhhLGF5on3l3AJeXMrj37/jWKMcfTf2ZWPYKNVC\nMQ51K6c1Kh+yiShqhtVYQnZCrsXFC9MY7bAhDjTaOXqA3aXHHb3eEaf2T4+go3crr6FmWG0TNwHW\nK4w6BU1HOhZtrHzcCkmQmNdcWswDAIOIRhRNN9p26AEtjl4I7psHAQo9H1mpj1y069Er1wxXTo4X\nuB7dVKPQdBM1I9gXYt0w8Xv/dBnHZtP4n0/e1vXjZ7PhOBk1Tcse3RRCL27vernZ02v92LC4q8NI\nQ+i12dED7D09Onq9s1asQpUjePlWofE6OSrMd+jQA1ivMOoU60Jvtn7fMCqjmxcXcgDAQ44RpVIz\nEW/ToQdsrVcg3aHQ8xEhLCZTO3f0TAuunBwvKLt09MLyZPvi2Zt4ZbmIDz16t6PE0LCUpq8Wq9BN\nC/vr15OJ29/PnItdO7Gfp8oR7uh5SLHDjh5gO3oUer2h6QYKmo63HZsGMHp7ejc6dOgBQFyV6WqM\nMGJ0MxWLIqnKgR9Q+sXFBeHoUeiNIh0dvUYYCx8bTqDQ85GVgobJlApl22ihSLoMOnmz7DqMxb7p\nDXJ8s2aY+P2vv4R7D2TxP92339Hn7G8IvWDfMIXQFDt62Xp6o5suPSH0DozHQzNGO4wUGqOb7Z8f\nYwmVhek9IgTyj949g6Qqj9ye3vxGXeh1cPR4szu6iNFNwJ4GGgWht5zXGs5+JeADcBIMnRy9hCJD\nkoAS73kcQaHnI3ZZurrj94XQKwX8Zt67oxfcdf/NmRt4ba2EDz16NyIO+/+EsAra0WsKvWbqJuBu\ndFOIi9vGEgxj8RDhWqc7Onrc0euF1YL9fZvNxPDwkUk8/cqICb31MsaTyq5usV2YTqE3qhRbhN5s\nJjYSFSSXFnONX2shfOx//B9fxJ8/fS3oyxhqOjl6kiTVe5zD99gIIxR6PtKuLB1AI0I26ECWssse\nvXQ8WEdP0w184hsv49ShcfzEiVnHnzeWUKBGI4EnbwpHcf/Y1h09NxULDaE3nkBR0wPf8xxWxNJ3\nssOOXrFqoDrAp8+maeEHr637/veKaoXJlIo3HJ3E5aUCVkdkDwmwHb25XcY2Afv0WjetwHehSTAU\nNaNxCDCG/0s3AAAgAElEQVQqjt6l+tgmEPxKSzs+/8xr+LOnKPS8pJOjB4i0eh5uO4FCz0dWCtW2\nQi/ZSBAKfnSzU//cdtIBR9z+1T9fx/xGGR969O62pZq7IUkS9mWD79JbzFUgSWg8JjLx3kc3D04k\nXCd2EueIk8NOjh6AgR7f/PsXFvHuTz6JK8sFX/9eUa0wmVLxxjumAADff3V09vQ6laUDzYNAunqj\nSb5Sa7zXzqRHQ+hdXMhhXzYGSQrf4z5XqWG1WMXlW3nkXbxXE3d0cvQA+72Y6yrOoNDzkZWCtiNx\nE2gZ3Qxa6PXQowcEE8ZSqdlu3o8cmcCP1kMc3LAvEw98R+9WroLpdKyxs5lN2N9PN45erlKDGo1g\nqh7wE3QwzrAiSot3O2EcS9rf/0GuWBBunt8jqOstQu/k3BgSioxnRkToWZZll6WPty9LB+wwFoAx\n86OIZVkoVo3G9MxsNo5cRQ+d+Ok3FxfzOHEgG8r91GsrdkquZQHP32DHn1douolYJ0cvFo7+6UGA\nQs8nipqOUtVo6+iJvbggI7RrhgndtFyNboqo+SBOVf786Wu4ldfwoUePu3LzBGEoTW8tSwfsES05\nIrmuVxhLKKHYlxxmRPLdbo+18XqQziAnb56r37T4/ea5WqxCkoDxpB1U9fCRiZHZ09so1VCqGrsm\nbgJAvF4aHLYbXuI9mm7CMK3m6Gb9/mGYXb2qbuLlW3ncsz9b308N1wHH1dVi49c/DGDUfVSwC9N3\nvx9NqVEebDuEQs8nRIJUpzCWIFM3xc2du9HNYBy9UlXH49++gjffOYU33TnV09eYzcYCL55d3Kw0\nEkABe6Q0G4+63tHLxqOhSEAdZkpVfdcOPaA5ujmoQs8wLbxw0xZ6fr8OrRerGE8ojWqUNxydxKXF\nfMPpG2a6JW4CzYNACr3RQ7wXtKZuAsPdpffKSgE1w8KJAxnElRA6enWhd3A8gbPXNwK+muFF042O\nO3qpWJQBdA6h0POJ3crSASCpBL+jJ15MdwubaEdQo5ufffIaVgpV/No77+75a+zL2nUEQQqjW3mt\nUd4uyMQV1zt6YwmFQs9j7ECE3Q9BxhP2Ac7GgO7ovbpSaLz++D1ZsFasYqKlW1Ts6Y3C+Kbo0OsU\nxhKPBj/xQYJhe9qvuH8I+pDSS0RR+okDWVvohWzv/NWVEvZlY3jTnVP44WsbDEDzCK2Lo5dUZZQ4\nweQICj2fWM7bp9MdRzcDPJ0QN3kJ1flDQo1GoEYjyPsoLvKVGv7wiSt4+90zeOj2yZ6/jnDSbgVU\nsaDpBtaK1S2OHmDv6bl19OzRzXqBKIWeJ7R2WbVjbMDDWFp3Tfx29NaK1caOKQCcnBtHXImMRJ+e\nE0evGcYSrhte4j3N/s5mvQIw3I7epYU8VDmCO6ZTiEXDVy1ybbWII1MpnD48jtViFdfXykFf0tBh\nmhaqRufUTYaxOIdCzyeWOzh6iRCEsYibOzdhLID9ZPNTXPzVszewUarhQ4/27uYB9ugmEFxpujiR\n3S70MjHFdY8eHT3vKdZ39HYjE4siIgGbA9ql9/yNTYgaykAcvWRT6KnRCB66fQJPvzL8jt78ehlJ\nVW6M/rZDHL7R0Rs9CtscvcmUCkka7h29i4t5HNuXRlSOIBbC0c2rqyUcmUrhwUPjAIAfXueeXr8R\n6eGdHb0ow1gcQqHnEyt5DZJkv1BvR4irQIVeTTh6zkc3ASAVk30NAFnYsG+MTtVfZHtFlJQHVZou\n/t7Z7Fbh79bRy5V1W+jFg0tAHQWKVaPjWHMkImEsoQzs6Oa5+U3cf3AMgP+vQ2ulKqa27S6/4egU\nLi3msDmgO49Omd8o4eB4omOglLjZCdsNL/Ge7aObUTmCqVQMy0Ncmn5xIYd79mcB2EFEWoic7Hyl\nhpWChiPTKRzfl0FCkfHD17in1280XWRGdHL0ZBSr7A52AoWeT6wUNEzUU+W2I0ekwEcUenX0Uqq/\n9nlFd9f1txtBC73F+t8rytIFbnb0TNNCrrI1dZOOnjcUNb3RZbUbYwllIMNYdMPE+ZubeOj2CUR8\n7q2yLAvr2xw9wN7Tsyzg+1eH29Wb3yh3TNwEGMYyymwf3QSGuzR9paBhOa/hxIEMANR39MLzuL+2\nalcrHJlKIipHcHJuDD9kIEvfEWPqHR29WBSWxUkHJ1Do+cRyXmubuClIqsF2gpQbYSzuRFQm7u/o\nph25u/eHbToWRUqVAxvdFH/vvsy2Hb244tjRy2s6LAvIJpRAqy5GgW6jm4DdpTeIjt7LywVUaiZO\nzY0jofj7OpSr6NBNa8ekw6lDY4hFI0Nfs9CtLB1gYfoos310ExhuoXdpIQ/ADmIBUK9XCM/jXgi9\n26dSAIDThydw4eZmqK5xGHDi6KVUkUvA7303KPR8YqWgtQ1iEQQ9b1yqB8G4dctSPi/EarrZF0cP\nCLZLbylXgRqN7NjNySbs76dudB9XEbt82Xo0fUKRObrpEQUHQm88oQzkjp7oz7v/4BgSquzrCela\nS1l6K7GojNcdnhjqQJZSVcd6qdbd0WMYy8jSGN2Mtwi9dAy3hlXoLdqJm/fsbzp6WohSN0WH3pHp\nJADg9OFx1AwL52/mgrysocOJoxdU6vsgQqHnEyuFatsgFoF9gxXcA7bS2NELt9Cr1Iy+OHqA6NIL\nTujtz8Z37OZk4rbwc/I9FQmPY/Wy7nQ8igJPt/qObpjQdLNjjx5gd+kNoqN3bn4TKVXGHdMp+3XI\nxwMnIfQm2uwuv+GOSZy/mRvYJNNurBbsf/tMhwNAoHmqzRGl0UO8nidbDjdnszGsFDSY5vDtJl1c\nyGM2E8NU/TkRj4YrjOXqShGzmVhjX/u0CGRhcXpfceLoiZ8Bu/S6Q6HnE/boZidHL+DRzerONxQn\npFV/Rzc13USsT47e/mw8sNHNxc0K9mV3Ph6y9ZNbJ+Obue1Cj3HDnlCsPzc69egBtqM3iDt6z9+w\ng1gidVc4CKE31UboiT29Z4d0T0/s4mYTuyduAs0evTDd8BJ/KFR0pFQZkUjzQHAmHUPNsIbyAOTi\nQg731Mc2ATG6GS5H70h9bBMAZrNxHBxPcE+vzzhx9MQ4M5M3u0Oh5wNFTUe5ZnQUenGfd2O2U9qD\no+fnjHQ/Hb192TiWcpVAUptu5bVGIEwrwtFz8ia+3dGzE1Ap9PrN9uS73RhLqshVajAG6KS9Zpi4\nsJDDyTk7cTOhRn11jtaFo5fcKfQePDQOdYj39HJl+3GViXd+XEUiEtRohI7eCFLU9C1jm0BLafqQ\njW/WDBMv3yo0gliAehhLiB73V1dLjbFNwYOHx3GWyZt9xZGjVz945eF2dyj0fGClQ4eeIOnzyNR2\nKlUDkgTXIiodj6JY1X0bI9Fq/UndBOzTOE03fT8ZtSyr7ujtFHrZhHNHb4fQ8zkBdVQQ+6tJBzt6\nlmVHcA8Kl5fyqOomHpizR5ASSsTX16FV4ei1CaqKKzJOHxrHM68OuaMX7+zoAeGLmSf+UKju3A1u\nlKYPmdB7ZbmIqmHixP6moxer7+iFIUK/qOlYzmuNIBbB6UPjmN8oB7YGMow42tGrj26WuK7SFQo9\nHxAvyN1SN4M8sS1VDSQUuWOfUzvSMRmW1XQEvUbTTcT75ugFU5qeq9gO7/aydKB50+ekYmGzvHX0\nKxOPouCig484Q+zJdKtXEME6gzS+KYJYTtY79JJ+O3qlKmLRyK61Lm+4YwovzG86rhwZJMRhzliX\n0U0Avu9OknBQqOg7JgnEgfFyYbiEhQhiObFtdBNAKAJZGkEs24Xe4QkA4PhmH3GUuhkTqZu85+kG\nhZ4PCEev0+hmQokG+kZerhmuO/QA/5OPKjWjbzt6QXXp3dqlLB1oCj2njp4ckRoxw6lYlIvJHiAe\n207CWAAMVCDLuflNZOJR3D5ljyPZ9Qr+PYZWC1VMpdRdD5jeeMckTAs4c3X4wg4aqblOHL2Q9YkR\nfyhq+o7XncboZkD75V5xcSEPRZZwx0xTSMVCtJ/a6NDbNrp5321ZKLLE4vQ+4sbR4z1Pdyj0fGC5\nnq4222V0088brO2Ua4br/Tygubfk18hgXx29TDBCr1GW3nZHz/5+5hzu6I0llMZNsr0vyRe9ftOu\ntLgdYwnbsd8YoIqFc/ObeODgWOMxZO/E+Hd6vl6qtk3cFLzu8ARUeTj39IRLuX0Hqx2JkO0qEX8o\ntNnRS8eiSCjy0I1uXlzI4a7ZDBS5+f4uHJ0wBLIIR2/76GZckXHvgSyTN/uIM0ePYSxOodDzgeW8\nBkna2RXVShhSN3ty9NQgHL3+1SsA/i+1i1HR/WO7Cz1HqZsVfcvYF1M3vUEcwHTt0Us6D9IJA5pu\n4OJCDg/Ug1gA/0fIV4vVjq+LcUXGg4fG8fQQ7unlyvZYnhzpPi4fU2SUQ3CzS/ylWN05uilJkl2a\nXhguoXdpMbcliAUIV+Ls1ZUiptOxtqFcpw9P4Nz8pqP+W9IdJ46eGo1AkSXe8ziAQs8HVgoaJpIq\novLu3+6Eai8dB5XYV64ZSPbi6MWDcPT6M7oZV2SMJxXfHT3x97ULY4nKESRV2fGOXnab0KvUTL7Z\n9Bmxo+ekXgEYnB29y4sF1AwLJw+ON34v4fNkwXoXoQfYfXovzG8O3Rt6rlJr1Kl0I6FEQnGzS/yl\nUNHbvu7MZGJDNbq5VqxiKadtCWIB0AheC8PY8tXVEo5uG9sUnD48jlLVwOWlgs9XNZwIR6/boX5S\njaI0ZO8LXkCh5wMrea1jEAuAhpsWVCBLqdpbmmVjdNOHEBDLslDpY+omYI9vBiH0xhLKrv+ObFxx\nlNwoRjcFzX3J4N8UhwnH9QoDJvSen7d3Sk62OHqJ+uimXym6aw6E3hvvmIJhWkPXp5fbdlDTibDF\nzBN/KGoG0rGdj5HZIXP0Li3sDGIBQja6uVLcMbYpOH1IBLJwfLMfNB29zhLFnmLi62I3KPR8YKWg\ndaxWANBw04La06v0uKPXEBc+XHfNsGBa7isgOjGbjWHR55PR3crSBZl4tNGx1YlceasjIFIhC1xO\n7itFTYckoetoc1SOIBOLDszo5rkbmxhPKpibSDR+T7wG+HGCrukGCpqOyTYdeq287vAEFFnC068M\nl9DLV3RHQSxAuHb0aoaJ9//J9/GV5xeCvpShRtMNVA2zbdrvTCY2VDt6FxfzAIB7to9u1l9ztYAf\n+6Wqjlt5DUem2jt6hyYTmEypDGTpE5pu9yV3S4EPOttiUKDQ84HlgtYxcROwi4oBoFIN5uSqXO1t\ndDPVKK3058YQQH8dvWzc9/6bpVz7Dj1BNqEgr+3F0eMLXz8pagZSatRR9chYUsFGeTDCWLYHsQAt\nkwU+7AuvF+3H+GS3aQdVxr23jeHskJ2W5yq1Rm9mN+JKsPU7rfzVs9fxrReX8XfnKPS8pNgYGd/5\nGJlJx7BZroVG/O+Viws5TKdjO+6TGo5ewPUKzcTN9o6eJEk4fWicgSx9QquZjg707aTx4XgOeAmF\nng+s5KtdhV7D0asFc5O+19FNP8RFw87vUxgLYHfp3cprvo2qAXYYSyeh58TRsyxrh9ATPwsnQS7E\nOUWt/Z5MO8aTCjYHYHSzUjPw4mIeDxwc2/L7icZkgfdvnmv1svRujh4AnJobwwvzOV+fp15j7+g5\nHd2MhGJ8rVIz8N+//hIA++aceEenkXERJLYyJOOb7YJYgPDUK1xdad+h18rpw+O4slwcmImOMKPp\nzu5HUzGZB9sOoNDzmKJml2N3G9308warHZUee/QSioyI5I/Qazh6fQpjAWxHzzAtrBb9cWEM08Jy\nQWtbrSDIxpWuYSylqgHDtNoKPb7w9ZdCVe+auCkYT6iB9uh99Evn8b4/erqrILq0mIduWlv284Cm\no+fHjVVD6HXZ0QOABw6OoaDpeKV+wzUM5Mp6I2W3G3FFRiUEJ9efe+oqlnIa3nLXFF5dLXJsykMK\nHYReozR9CMY3dcPE5aXCjv08oCWMJWihV3f0bt9ldBNoFqc/x+L0PVOpmY4O9JMqK6WcQKHnMeKF\nuKuj5+PIVDt6Td2UJAmpWNQXF8kLR2/W5y691YIGw7Swr021giCb6P79FKeGHN30nqK2M+J8N8YS\nSqA9el+7sIQnr6zib5+72fHjzt2wb0YemBvf8vviNcCPMcG1knOhd+qQfZ3P3xiOmyjTtJCvuAxj\nCTh5MF+p4ZPfuoIfvXsG//pNR2BZwIv13SrSfzr1d86k7fcPv6uBvODVlSKqutnW0ROjm1rAbva1\n1SKm0yoyHRz4k3NjkCRwT68PaLrh6EA/HYuyMN0BFHoeI0YruqVuJtXgyh8ty7IL03vcfUv7VNTd\niNzto6Mnuuxu5f0ReqIsfV8HhzcTV5Ar12BZu7sy7YSe3+X1o0JJc34IMpZUAhvdWSlouLFeRkQC\n/s9/uNTx0Oj5G5uYSqm4bduBg3gN8GV0s/7a6ETo3TmTRlKV8fyNTa8vyxeKVR2mBVdhLDXDCrQ6\n5Y+/8yo2SjX8xjuP4966+3JxgULPKxqOXhvXd5gcvUYQy/4Ojl7AhxyvdkjcFGTiCo7Nppm82Qec\nO3oySkzd7AqFnscIodd9dNP+UQQxCqPpJiyrGQjjlpRPpyrC0Yv3eUcPaJaYe02nsnRBNq5AN62O\nOzlCTGzv0QMo9PpNwYWjN55QsFHqLNK94mz9JPnX3nkcC5sV/PF3Xtn1Y8/Nb+KBubEdATMJXx29\nGiQJGHewoydHJNx/29jQOHrCsXcexhJsKMVasYo//s4r+Kn79+OBuTHMTSSQiUW5p+chnXb0ptIq\nJGlIhN5CDoos4c6Z9I4/C8vo5rXVUsf9PMHpQxM4e30jkNf/YYKOXn+h0PMY8UI84zB1M4jRTXF6\nn+hRQKV86jIREcv9dPSm0zFIkl154AeLHcrSBWJvp9OeHkc3/aPoZkcvaYv0IJLAnruxATki4eff\ncgQ/df9+/MG3r7RNlC1XDbx0q7AjiAVoEXq+hLFoGE8okCPd00wB4IG5MZy/mQvU1eoX4rntxtED\ngrvh/YNvvYxyzcCHHr0bgD2yf8+BDC5Q6HmG6KZt99qjyBFMJtWh6NK7tJDDnTNpqG1SFkXyYpBB\nROWqgcVcZddqhVZOHx7HRqnW2OkjveFmR69SM4fiPcFLKPQ8ZrlQhSR1H09KBliYLv7OXnr0ACDj\n2+hm/x09RY5gKhXzbXRzabOCiNR5Z1O4dJ1K09sJPTUagSpHXIvu3/vaZZzlAvmuFDW9MVrdjfGE\n/TwPYk/v7PUN3L0vg6Qaxf/+U/egZpj4r//44o6Pu7CQg2Fa7YWez/UKEw7GNgUn58ag6XZww6Aj\nUnWd7ujFAtzhXtgs47NPXcP/cnoOx/Y196hOHMji0sJwJaGGiU5hLIA9JXTL5w5YL7i4kG8bxALY\n789yRArU0bu2ZgdA3b5LtUIrIpCFNQt7w6mjJ9KwS0NSM+IVFHoes1LQMJFUEZU7f6uDTN0UNw+9\nj276E3Fb8cDRA+zxTf9GNyuYycQ6uhjC0dvsULGQazO6Cbj/WVR1E7//9ZfwpS7hHaNMUTPalha3\nYyxp/zw2fK5YME0Lz13fwIP10JLbp1J4/5uP4AtnbuD8za17bSKI5eS2IBbA39HN1aKGKVdCz77e\nc/ODfyghnr9uUjeB5p6yn3ziGy/Dsiz86juObfn9EweyKFYNXF+ne+EFjR69XQ5gZzKxgXf01otV\nLOYqbYNYBPFosNUiV1fsx/dRB6Obd82mkY5FGciyR5w6epxickagQk+SpM9IknRLkqQXgrwOL1nO\na13HNgF7RCEiBXNi2xB6PYax+JW66YWjB9hjlH6lbi7mKh2rFYDmOFcnRy9XtvebMttOe9PxqKsd\nPVHuze6f9himHVTkvF7B/tn5/f18dbWIXEXH6UNN8fbvfvwYxhMKfusrF7fsjDw/v4mZTKyxn9qK\n746eg/08wZGpJDLxKJ4bgkCWXkc3y1V/b3ivrhTxV/98He99/WEcmtw6utYMZOH4phcUtBriSmTX\nQ+KZTAwrA76jd6lDEIsg6MTZq6u2o3fYweimHJFwcm6MgSx7xKmjJ0LSigxk6UjQjt6fAvjJgK/B\nU1YKGqYz3W9mJElCUo0G4+jVT+97qVcA/FuIFY5eL8XunfDT0bvVpSwdALKNHb3dv6ebZbtsObLN\nGUyp7oTeetG+4fTbgRoUxOPacRhLUoxu+vv9FN1Np1qE3lhCwa++4248eWUV/3TxVuP3z93YxMmD\nO4NYgBZB4YujV8VUlzTiViTJvok6NwRCrxnG4rwwHfA/ffC//dNlRGUJ/+7H7trxZ8f3ZxCRgAtD\nlLy5lKuEJkijoBlIx3Z/fMxkYljOa6G53l4QhwT3dHL0FDnQeoVrq0VMptQtaxKdOH14HBcX8oFV\nZQ0DTh09dgc7I1ChZ1nWEwDWgrwGr1kpaF079AQJVUa55v8DViR99iqgUj7t6DVHN/vv6K0WNdR8\nWOhdzFW6Cz2HO3rtEvvcVl2s13fJcnT02iK+l4539MToZtnfHb2z1zeQUmXcNbs1ue59bziMO2dS\n+O2/u4iqbqKo6biyXMD9bfbzACAq23ueXh84WZaF9VLVlaMH2OOblxZzgYww9hO3o5tBhLFcWszh\ni8/dxPvffBSzbV6z4oqMo9OpoXH0Pv3dV/GG3/46nnhpJehLASD6O3d/T57NxFE1zIGexri0mMN0\nWm302bYjpkSCdfRWSo6CWASnD03AMC28cHPwD6SCQqsZjlZ0xPsykzc7E7SjN9RYluV4dBOw38yD\ncPTEzcNeevRqhuX5zVdzdLPfjl4cltWswvCKSs3AZrnWsVoBaEnd7LCjt1mutT1hdCu6RWjIIN8s\neEljT8bpjl4imB29565v4IG5sR27n4ocwYffdQKvrhTx+Weu4cJCDqZlB5vsRlyJeC4ocmUdhmk5\n6tBr5eTBMdQMC5cG3EXKVWpIqjKULrvbgngAYSz/1z9eRlqN4oNvv2PXjzlxIDsUQu/T330V/+nL\nFwDAtzH+bhS0zmm/w9Cld3Eh33FsEwDiUbmRuB0EV1eLjqoVBCcP2a+tw9L5GQQV3emOXj3bgqOb\nHQm90JMk6QOSJD0rSdKzy8vLQV+OK9aKVVRqJqa7dOgJkmowQq8fo5uA93PSYiG7/46e/fPxumJB\n3EDMdutUVGREI1LHeoVcRW8r9NLxKPIuhN6aGN302YEaFDp1WbUjrsiIKxFfhXOlZuDCQg4PHppo\n++c/dnwWb71rGv/tn17Cdy7br6HtEjcFSTXquaBYqx8wuBZ69dHUQe/Ty5V1x/t5QGtxtD8jbD98\nbR1fu7CED/zoHR17Dk8cyOLGenmgD4qEyHvrXdMAgFJIxsC69XeKA+RbAyr0KjUDLy7lcd9tXYSe\nElwYS6VmYGGz0rUsvZWZdAxTKRUvLg7+AUgQWJaFqm46TN2ko+eE0As9y7I+ZVnWw5ZlPTwzMxP0\n5bjiL555DQDwyHFn151Q5UBihBs9ej0KPfFkK3gcyKLpBqIRqWuCqVvE2IjXe3pCSHZz9CRJQiYe\n7Tq62Vboqb2Nbg7yjZqXiO+l0zAWwK5Y8LNe4cJCDjXDwoOH2os3SZLw4XedQK5Swye/dQX7s/G2\no3iChCp7Hle9VrSfa26F3m1jcUyl1IE/Lc9Vao7HNoGWHT2fDgL/7OlrGEso+Pm3Hu34cSKQ5dKA\nunqfqYu8n7xvPx7/Vw8BQCAdmO0odhF6s9nBdvSevbqOqm7ijXdMdfy4uBLMfREAvLZmJ24emXY+\nuilJEo7vz+DFxcGeOggKMbnlyNFT/TEZBp3QC71BpVw18CdPXsWPHZ/pOpogCMzR26PQE3sEbkJA\neqFSM/s+tgk0y8u97tJbqr8hd9vRA+w9vd5HN50/hoQgqdTMQLuKwoq46Uu5qB4ZTyq+jm6KIJbd\nHD3Adl4ee/gQdNPCAx3GNgHbUfbc0as7yW6FnghkGQah5zSIBWjZ0fNpV2lho4K796W7Otn33ja4\nyZuf+e6r+Fhd5H3ifaeRUmXIEamxsx40xSEf3fzelRVEIxJef3Sy48cFmbr56oqduOlmdBOwg4ou\nLxWGqmPy2atrOPmRr3p+nySCd9z06DGMpTNB1yv8DwBPATguSdINSZJ+Icjr6SdfOHMda8Uq/u0j\nO9PKdiOhBJS62Yd6BcB7+1zTjb6PbQLAVEqFHJE8381Yqjt6joReXHEQxtLG0YvJKFZ1x28w6y2C\nhIEsO2k6es6fG2MJxVeH9Oz1DezLxro6xR96592YSCp4852dT9D9CIXq1dEDgAfmxvHSrXxobsh7\nIV/RG+m6TvB7R2+1qDn62cxmYphMqbg4YDuT20WeIkfqyddyaNyBbjt6mVgUsWjE8xtvr/jeyys4\nfXi867REkKOb11Z7E3r37M+gXDMajuAw8MTlZeQqOl5eKnj69whR78TRYxiLM4JO3XyvZVkHLMtS\nLMuasyzr00FeT7/QDROfeuIVPHT7BH7kyO6n7NtJqjLKATxgyzV7JNJpMMB2xKnvoDp6kYiE2Yz3\nFQtLuQoSiuzoBi8Tj+5ar1CpGajqZtsdn3Q8CsuC49G79WJzxJDjmzspuNzRA2xHz8/vZWtReidm\nM3E89X/8BN7/5iMdPy7Mjh4AnJobg2kB528OnoskyO1yULMbjR09n25414pVTDkIEZMkCScOZHBx\ngPaR/uR7O0WeIB2LhuYAoaDpHcd7JUlqVCwMGpulGs7Nb+LNd053/dhYNLjRzaurJUwkFYwlnT9X\nAeB4fYrr0hCNb4rX20WPD8TdOHpyREJc8T4letDh6KYHfOXcAm6sl/HBt9/ZtqtqN4IMY+l1bBPw\nr8uk4pGjB/hTmm5XK8QcPSY6OXpCROw2ugk4/1msl6oQQY0UejvpfUfPn+/lerGKq6ulLf15nYgr\nctfHX8KH16G1ooa4EnFcW9GKGD0d5PHNXMVdGIsckaDKEV/6DQ3TwlqximmHIvzE/ixeXMxD96Ge\nZpXhPDIAACAASURBVK/8+dPX8NEvtRd5gP0eHIYdPd0wUamZXUfGZzMxLHucFu0FT72yCssC3nqs\nu9AL0tG7ulJ0FcQiuHtfGpKEodrT803ouXD0APv+02uTYdCh0OszlmXhD751Bcdm0/iJe2ZdfW7c\nh5P0dpSrRs9jm4CPYSw1EzEPHD3ATt685bGj56QsXZCJR3fd0ct1EHpu3dWNUg1zE8nGr8lWij2M\nNY8nFd9STJ+7IfbznAk9JyR8CD9YK9Yw6bJDTzCbiePAWHxgkzcty6o7eu5EbsyH2gvA3ts1Ledu\n64kDWWi6iav1Mbcw839/42W8/uhkW5EH2O9lYUjddFrrMpPx/n3LC7738gqSqoxTc91ft2IB1itc\nWy3h6LR7oZdUozg8mcSLS4PjdHditaA1BJ7X6eQVF44eYH+vw/CcDTMUen3mW5eXcWkxj3/z9jsR\niTh384C6o1czYFn+LvCWa0bP1QpAi9Dz+Mnm1Y4eYDt6Xp9UOSlLF2QTPTp6qjtHb61UxZH6Gxkd\nvZ0UNR0pVXb1XB5LKr6F25y9vgFJsovE+0VSlT13jtaKGibTvQk9wK6HODegjl65ZkA3LWRcOHqA\nLcD9KIpfq49zOxndBGyhBwAXQr6nV9VNLOUreNMdU7uuKYTF0SvUx0e7JbPODKij970rK3j90Umo\nDt7P44rcSGL0k0rNwM3NMm53UZbeyvF9maEZ3Wwdk/da6Ll19FKxKAoh2asNKxR6feYPvnUFt43F\n8S9O3eb6c5OqDMO0UDN8FnpVY0+7bylVJB95XJheMxsx4/1mXzaOzXLNs5tzy7KwmKt0DcwQZOJR\nFKtG23GoTkIvHXfurhqmhc1yDUfqb2QUejvplnzXjtvGEgDs02Cvee76Bo7Ndk9HdENc8WF0s1TD\nRI+OHgCcOjSOV1aKA/mYFU69m9FNwL+Jj5WCEHrOfj53zaahyBIuhHxncmGzDMsCDk4kdv2YlMt6\nGq9wOjI+m4ljo1Tz5QCgXyxslvHKcrHRW9iNuBJB1TBh+JxgeX2tBMtyH8QiuGd/BldXikORZi2E\n3sm5Mc9XXJp9yc7uSVOqHJq92rBCoddHzlxbx/dfXcMvvO0ORydV20nU3Ri/xzf3uqMXlSNIKLLn\nyUcVfW+CtBOixNyrMZjNcg1V3XTu6NVvAtu5pB2Fngt3NVeuwbKAw5P10c0BvGn2mm6lxe2450AG\ngPeR85Zl4azDIBY3JH3o81wvVjHVQxCLQBS+vzA/eK6ecOrdjm7aI7XeOxur9UTUqZQzR0+NRnDX\nbCb0FQvz62UAwNz47kIvGQsm+Xo7+YozoScqFoQ4HwS+9/IqADgKYgGaQUR+i9mrq6JDrzehd3x/\nFqYFvHzL25RKPzh/cxMHxxM4vi/j246e00P9ZCwaChc+zFDo9ZHHv30F40kF//JHDvX0+WJ8suRx\ntPl2ytW9jW4Cwj73OnXT29FNAFjyKKpavDjuyzq7eRIjO+329ITQa5fa56bqQpSlT6dj9Z1ACr3t\nlKoGki6qFQDgzpk0VDnieRLha2slrJdqjoNYnJJQZNQMCzUPwzXWilVM7EHonRzgQJacEHquHT1/\nwliao5vOfz4nDoRf6N3YsIVeZ0dPDpWjl+km9NKD16X35MsrmEqpuGd/xtHHx+vv+X4HslxtdOj1\nOLpZ//cNw/jmhZs53HdbFvvH4ljOa54GL7l19NKxcDxnwwyFXp94aSmPr11Ywr9+0xHXo16ChtDz\n+XSitMcwFsB+snkexqJ7U68AtAg9j06rRHXDfhc7ekDzprCVhtBrs78hlved/CyE0BtPKr5XAgwK\nBU13VZYOAIocwV2zac+7xc5e738QC4CGu++VqNB0AwVN35OjN55UcXgyOZCBLI3RTRf1CkC9ONoH\nobdSqEKS4Gq09t4DWdzKa1gN8b7Y/HoZkgQcGOvg6KnhcPQcj25mB0voWZaF711ZwZvunHK899ys\nFvHb0StiLKFgvMcR8yNTSajRCF4coOqRdhQ1Ha+uFnHfbWPYl43DtODpXqhrR49hLF2h0OsTf/jE\nK4grka4dVZ1I+FyKK6jUjMbYaK+kYt7vNnjp6O1vCD1vXsCWcs7L0oEWR6+N0MuV7XHCaJtAgUxM\njHx2fwytt3SZjSUUbJQGZ/zHL4o9jG4CdkCF1w7H2esbiCsRHN/n7GTcKULoVTx6HRKPu704eoDt\n6g2yo9ctaGM7fgm91YKGiaQK2UUAkQhkCXNx+vxGGfsy8Y5rFamYvYLgdyDadvIO+zvF6OaglKZf\nWS5gKafhLQ7384DghN611VLPY5uAvdJybDY98I7exYUcLAu2o1e/f/EykMW9o8d6hW5Q6PWBmxtl\n/H8/nMe//JHDPRUACxIBOXrlmoHEHkNO/Bjd9NLRyyaiiEUjuOWRo7dZry4Yd1i8Ksa6dhvdbLef\nB9inYBHJWeqmcPQmkrbQo6O3k6KmI9mT0MtgOa9hxcOTz+eub+CBg2NtBf9eEAdOXr0ONUYD+yD0\n5jfKoXaR2pEr9z666cf42loP+5NNoRde92J+vdxxbBOw38csy/8xwe0UHQo9sUc5KI6e2M9zGsQC\nNJ0dv38mr64Uex7bFBzfnxn4Lj0RxHL/wbFGmJyXgSzuHT07PCzow5kwQ6HXBz793VdhAfjFtx3d\n09dpjm76ezrRj9HNTCzqfRhLzbswFkmSPK1YECLY6RiguAlsV7GwWa7tOvYlSZJj0b1ldDOhUui1\noVg1kHa5owd4f+Nb1U28cDPnqIfKLUmPRzeF0NtL6ibQrJR4fsACWXIVZ9H520ko3tdeAMBqoepq\nPw+wpwL2ZWPhFnobZRzsEMQCtCRIB5zi53R0U41GMJlSB0joreDQZAKHJp0LKNGdW/ExjEXTRbVC\n744eYCdv3sprWC8O7rTMC/ObmKo/v4XQC5Ojl4pFoZsWqh7uDQ46FHp7ZKNUxf/4/mv4F6duaxRP\n90pCsV/U/R5RKPdtdNO767YsC5pueja6CdhBKV6dVBVc9rGJRL5cm127XLmGsQ6JfU5HGdZLNUQj\nEtKxKLJ09NpS7GFHD/Be6L24mEdVN/Hg4f4LvbjXjl7JfdhHO+4/OAZJAp6/PmhCr4ZYNOL60Mq3\nHb2i5jhxs5UTB7K4EFKhZ5oWFja7O3rJ+nO9FHAvV17TocoRR+ndM+kYbg2A0NMNE0+9soq3OEzb\nFMQaYSz+/Uyur9lVHEen9+ro2e8Dgzy+ef5mDvfeloUkSZhMqlBkCYserbgALT16Du/1/Kr3GmQo\n9PbI5566hlLVwL95+x17/lpBhLEYpoWqbu7Z0UvFoo1IaC+oGiYsC545egAwm417Vq/gto9NjOzs\n6uh1GPtKO9yX3CjZyYeSJDVGNzn+0MQ0LZSqRk/hSk2Hw5s3+LPX1wH0P4gFaI5uenVjtVYftdyr\no5eORXHnTBrn5gcrkCVX1l0HsQB+7ui5d/QAO5Dl5VuFUHa63cprqBlWd0cvFh5HL+3Q8Z3JxAbC\n0XvhZg75iu5qPw9oqVfwcXRTJG7u1dE7UU/eHNRAlqpu4qVbedx3m51yHIlImM3EsbhZ9uzvrNRM\nqHLE8aG4WK1g8ubuUOjtkSevrODH75nFPfWTm70QhNATo0AJdW8PBa8jbpt2voeOXibumaOXd/HG\nDdiL3ClVbrujl6vsvqMHON+XXCtWMVHfGRxPKqgZVigS58KCuNlL9TC6CXgbyHL2+iam02rXG9de\naLganjl6NUgSek6za+XkwTE8d2NzoA4ocpVa28TcbsR96NGrGSY2y7WeHT3dtELZGza/YXeiOXX0\ngr5pLGqG49ed2QERet97eQUA8OY7p1x9XjzqfxjL1VVRrbA3oTeTiWEiqQyso3d5KY+aYeG+25r3\nt/vHvFtxAWxHL+YiMyLtolJqVKHQ2yN/8YtvxMffc6ovX6sRa+6n0KsKobf30c1yzYBhenPD1bDz\nPXX0YihWDU/e5AsV9+mN2YSyq6PXSeg5dfTWS7XGzbb4ehzfbCKETq91KSfqDkdV7//N+dnr63jw\n0DgkyXkyolPEoY93O3oaxhOKq1TH3Tg5N4blvOZZWq4X5Mo1ZFwGsQC201o1TM9eYwE0dokme3D0\nwpy8ecNBWTrQ6ugFPLpZcT4yLhy9sB92fO/lFdyzP4OptLtDBBHKoXnwOrobywUNqhxpHIT2iiRJ\nOL4/M7BC70I9iGW70PPy9bZSMx3v5wFNg4Sjm7tDobdHIhGpLyfTgPdpd+1oCL099+h5e6oixjbi\nHjp6IjF1zYPF6V5i+jPx6I56hZpholQ1ujh6siNHb6NUxWT9sTtOobeDgsPku93wyuHYLNdwZbno\nSRAL0Dz08bJeYS/pxK08UP8ePDdAfXq5Sq+jm97vKq0U7Ne+6R5+PkenU4grkVAGssw7KEsHWnf0\ngnb0dMdhPTOZGKqG2Xb6IyxUagaevbbuKm1TEES9Qr5if//7cZB2z/4sLi/lYXp4QOMV529uIqXK\nW5zN/dk4Fjcrnh0saLrhOHETaB7E+h1iOEhQ6IWIqByBKkdQqvn3gBWn9uJUpFfSHs9J++HoCdGz\n7kGfXKEHoZeNKzv2HoUQG+tw0piOKY5Ot9ZLNUyk7K8jhONGiUJPUHSZlLqdew/Y+xn9vvE9V++O\n8yKIBWg9cPLmubxa1Pom9O67LQs5IjW+J4NAvtz76Cbg7Q1vo/rCpesCAHJEwvF9mXAKvfUyJpJK\nQ8jthniuB+3oFavOd7pFl95yIbxdemeuraOqm67384BghF6h4lxod+P4/gxKVaPhKg8S52/mcOJA\ndsu+3P5sHOWa0TYorh9oNXehe6mQjFuHGQq9kJFQZV9HN8XNXD/CWAD7BdILKn44evVxpVUPHL1e\nhF47R68h9DqObnZ39CzLwnqx2nCjs3T0diC+h8ked/SOTKWgRvvvcIgglpNeOXqKqFfwZlSqn45e\nXJFx977MSDh6zZ+Ld+8Pq0V7JKvXn4/YSw3bGOH8RvfETaD5XA/aHSi4CO9qlqaHd3z5uy+vIBqR\n8Pqjk64/t+Fk+zi6WXC5U9+J4/VAlksDFshimhYuLuS2jG0CwD6PKxZsR8/5e25j3Jqjm7tCoRcy\nkj4LPXHTsNc0SyFivCpNF6d5vjh6Xgk9l28c9o5ee0evU+pmqr6j1+lmq6Dp0E1rSxgL0CxzJs2I\n9V5HN6NyxHY4+vwGf/b6Ju6YSXUU+3tB3FiVPXP0qn0TegBwam4M5+YHJ5DFDmNx/7OL+VAc3Rjd\n7LH64t7bslgv1TwNa+iF+fXuHXpA62RKsDeNhYqOjMPXndlM+EvTn3x5BacPj/e07xxEGEu+Uuv5\ndX87d+8TyZuDtad3dbWIYtVoJG4KDgih59FzvOLW0WMYS1co9EJGQpVR8vEFrdKn0c2Ux2+QYhHb\nS0dvwqMdPcuyXNcrAHVHb5vwEv/dyREQBaKdltfFiObEtjCWjfLgFrv2m2bqZu9v+CcOZHBxId83\nEWJZFs5e38CDHrl5gB0g4FU5t2VZWC/1V+g9MDeGjVIN19fCPxpVqRmo6majJ9MNXtdeAHZQTjQi\n9SREAe/7I3vBsqx6WXr3TrRYNIKIFLyj5+b9YiZt33iHVehtlmo4N7+JN7vszxNEIhJUOeJ54mwr\n+YqOdKw/B2npWBSHJhO4tDRYQu98PYjl3m2O3v6s/XhbCoujp4bjcCbMUOiFDL8dvVIjdXOvQs/+\n/EF29LLxKKIRqe87eppuomZYPe/otYoEJ6ObYreg089CiFkh9NKxKOSIxNHNFvYaxgLYN75rxWrf\nxqpublawUtA8288TJFVvhF6urMMwrT136LVyb11cXB6AGykxit1L6qYfu0qrBVuEO+2w2s49+8Ve\nanh+FhulGkpVw9HopiRJSKnRQG8aTdNC0UV/ZzYRhSpHsFwIp9B76pVVmBZ62s8TxJSIvzt6mt7T\nHu1uHN+XHThH7/zNHBRZajiSgtms7SCHxdGLK+E4nAkzFHohI6lEfX3A9it1M1M//fIujKXu6LlI\nY3KLJEmYSKl9d/SKPQqGTFyBblpbbrhzDoSek+VkIWZFGEtraTqxEaObe3G7++1wPHfd3kXzKnFT\nEFdkT9J/10oi7KN/Qk+Ixu37rGFEJCP2chMpDuO8Ht3ci9uaiSs4NJnAhRA5eiIEw2nnZDImB3rT\nKCYJ0g53gyVJwlRaxUo+nNMYT15ZQVKV8eCh3l+z4orcCGTzg37u6AH2AcirK0Vf/w175fzNTRyb\nzUDdJrpiURmTKdUzoefW0ROHM16ZDMMAhV7I8DuMpVIbLEcv7qJfpRcmk/0Xer06Q2K8qzU224mj\nl3KwL7l9dFN8TaZuNinsMXUTAE7s72+32OWlPCSpueDvFUlV9uQEfa0e9tFPR0842Nv3WcOIEKM9\n1StEvQ9jWStqmO4hcbOVE/uzoRrdFGXpcw4cPQCB3zQWG7vBzh8j0+kYVkLq6H3v5RW8/ujkDsHg\nhrji3+imZVn10c0+Onr7MzA8qNrxCsuycP7mziAWwb56xYIXuHX0AOC28UTjEJTshEIvZCQ8Oknf\njVKfHD0n4mIvCEcv5qGjB9gO13qxv2KnIRh6cPQAbClN3yzXkFDkjm+aaQcJqNtHNwH75pOOXpOi\npiOpyj2PsQF2DcbB8UTfbnyvLBcxN5HYc3hSNxKqR45e/bk1ldqbmGil3fMkrAgx2ssOnCiy93R0\ns1jds9t64kAWV1eKvh5YdqI3Ry+4a2++Xzh/jk+n1VAKvcXNCq4sF/GWHvfzBLGoNwdP7ajUTBim\n1dN49W6IkeZBGd9czFWwVqzi/oNjbf/8wJh3Qs+towcAP/vwHH7w2kaj4J1shUIvZCQ9usHaDXE6\nvFehF4tGEI1Ino1u+ubopdTGeFm/EILLbS+PGO/KbRN63YIcxMhJpxSqjVIVkrTVWRhPKEzdbMFN\nl1Un7tnfv26xV5YLuGM63Zev1Ym44s1kQcPRS/XvJkqNRhCLRgbD0Ws48u4fVzEfHL3VPY5uAnYA\nkWkhNO7F/EYZSVVuJAt3I6lGA+3k6mUCJKyO3vdeXgGwt/08QDh6/twX5TX7OdrP0c0j0ymocmRg\nhN75efv9qpOjtxSSHT0A+F8fmkMsGsGfP3PNk2sadLp+NyVJ2idJ0qclSfr7+n/fK0nSL3h/aaNJ\nwqORqd0oVw07aWwPrgVQn5OOefcGKcY2vHb0Jj3Y0et1dFOcKLYWk+bKetdY/XRjjHb3x9F6qYax\nhAK55ec+llCwQaHXoKgZSO1xpBn4/9l77yg5rvtM9KvcuXvyIJNIIphAkBRNUaJoSaTkqGBbXsmW\nZa+fJSfJsn3W+7T2efvW67zrnIPWu7YlS9bzSit6tbIkKlJZFAEwgQQIgARmBjOY0Lm7uqur7/uj\n+lYPZjpUuLeqetDfOTyWgcFMzUx31f39vmQxHBfWqr7f1+02wYXVKg7N8B/0eIWx8GD0AOu9wqvA\nlyVs6aaPMJYGp+eDbpioNFq+pZtznVS+qAwetFpBEJw945IBL1u3wounezqtYa3SRLsdrYqRb76w\ngVxCsRktr4jJ0sAUaZagCyOn9RZOoEgiDs2m8OyoDHpLJQhC12O+FfOZGNarTS6eQy+MXi6h4nuP\n78b/Ork4EsqOoOHk1Pw/AHwSwO7O/38WwM/zuqDrHWEwen6rFShSmjxwuPADekMJwqNXqDVhMnxg\nepVuZm2P3rWM3rBBr1t1MTiMZXKLT2ocxnItvFRi9MKxXRmYbYJzK/4YjislHXXDxKHZpO9rGoY4\nR0Yvpoi+PcFbkY6Nhhmf+m29yMLoz4wXo0cXXFM+Gb1JTjU1XuG0LJ0iocmhdnJ5eV5MpzSYbRK5\nRd1ioY4DU0nfi+SYEtwCnCpwWHr0AEvZMTKM3lIRN04l+74G57PWMuhqie0yhxDiidEDgB+59wBq\nTRMfPbnI9Jp2Apz8NKcJIR8G0AYAQkgLQDTE9zsQcVVG3TAD28zVm6Zv2SaFNejxedDoRhuq5J95\nHIaJpIo2YVscTh/cbqWbXe/RtWEsTge9QR69fK25TcqUS1jSzahthcNChdmgRyPn/ck3L6xag2IQ\n0s04R0aPNZsHWO+tUdjklnQDiiR4Sg+mHaK8QinWO2XpfqWbtI+UdU2NV1gdes4HvZQq24m7YcDL\noEEL7qPColKslHTMZ/y/34MMY/H6vB6Gl8ynsVzSURyBwLOnl0rb+vM2g7L2rJM3myZVbrk/kx7f\nl8Nte7J4/9deZNZbu1Pg5GlTFQRhCgABAEEQ7gVQ5HpV1zEou6YHFMNbM0zEGG3Xk5rEsTDd9LTl\ncQt7G83wkFL1yOhlbOnmVo/ekEFPHR6Mk68a25IPs3EFbQKUR4AZCQLVJpvktQNTScQVyXfk/PmO\n52nUGT2W/jwKa9CL/uu2VDeQiSmOZYSbIUsiFEngxmysdfyTUz6lm2nN6iPlxei58f5VGy0UaoZL\nRk8KldGz6xVcDBoznd/ZWsRK01dKDXso8ANNkQI7E9H7CEuPHtANZHl2OdqBIYVaE4uFOm7Z3TuI\nBQB2Za33E+tAFtui4/Gs97Z79+PsSgXffCHP8rJGHk5+mr8I4GEAhwRB+DKAvwfwbq5XdR2DDnpB\nyTf1JjvpZlLjJ5/SjTbXsnQKHrKjit6CIAAJl9cfU6yDXfkaj95wRk8SBSRUaaB0s1Br2pt3CjpA\njgNZLNQabN4bkijgJfNp3w/486tVpGOyfajjibjCidGrGZjkwehpykgwemW95alagSIm8/m9AMBG\nh9Gb9pm6SftIeTB6Z66U8ODvfwFfOrfm6OMXC+4SNwFrUVZrmqGxAp7CWNLWeypKpem6YaJYN5gM\nejFZQiMgRo/eR9Iu6i2c4KZO1U7UfXo0ubJfEAtgefQAMA9ksS06Hs96rz++B+mYjH/42jiUZTOG\nDnqEkMcBPADgPgA/CeAWQsgTvC/segV9gQcVTV1jLN3kVphuBMPoUZaL6aDXMJFUZdeyU0EQrJCJ\nzuBltgnKjeFhLIA1dA/aSm/UmpjYKt3sfN6xT89CpcGuS+nYrgzOXCn7OjxeWKvg0EzKExvkFjSM\nhfVhd6PawKTD9EM3GBlGTzc8laVTxFSJn3Szw+j5lW4CfPpIge7B8hsX1x19/GKnWsFphx5gMXpm\nmwQW/rEVFb0FSRRcPe9ogM5aJRpyWaD7u2Iy6AWYuslLujmX0ZCNK5Ef9J52MOhl4jJiisic0Wv4\nZPTiqoQfuGsv/vWpK1iNGLsdJpykbr4dwA8BuAvAnQDe2vmzMTggwdlwvxV1w0TcRyH0ZnAd9Fpt\nT74Wt6CHnDzTQc/wPDBkNh1gyy4S+1Ja/4OvbpjQjTZyPaSbAMal6R2wCmMBgJt3pVGsG7ji48F4\n/moVB2f4yzYBa6AgBMwPu/kqJ0YvpozGoFc3fPVz8TzwrleaUGWRyXKDRx8p0C0TP7XgzD2yYDN6\nCcdfg0rfw6pYqHYWTG4WOrlOgnKUPHornaCOOSYeveDDWFjd+ykEwVJ2PBdx6ebTS0XMZ2IDJdyC\nIGA+E8OViDF6APC2ew/AMAk+/NhlVpc18nBycn7ppv/uB/CfALye4zVd1whcummYiDMaoJKazM3f\npRvuI3e9gI9Hz3RVfrsZVmy8dWAq2h1czga9fgcVKqnaurmng9+Y0bOqDKpNNvUKAHBTJ6baayBL\npdHCckkPpFoB6MqMWSoLGi0rvn+Sk0ev0mgxTcvlgZLeGtqDOQhxjgfe9WoT00mVCWPMo48UgB32\ndfpywRHbvJivQ5EEzKadDxtBP4O3otIwXQ/boihgKqlGyqNHgzrmWTF6ATGslUYLmixC5aAgumk+\njbMrlUiHhTy1VBrI5lHMZWJYiZhHDwAOzaRw36Ep/OPXL0X+eRAUnEg3373pv3fAYvWCOW1ch4gr\n1g2+FpAZnId0k8dNrNHyFrnrFjFFQkKVbL8KC5QbLaQ8bvEz8S4z52bQGxSMQzftW6WbWQ7Szb/6\nwnl84ewqs88XFCijzmqrS434Xgc9mrgZ1KBHo/xrDIcK+rrjw+gNDyCKAmgYi1fEOHknAWC90sCk\nT38exURCZaqKoKD1PcW6gRfWa0M/frFQx65s3JVs3q6nCSmQxVISuH8mR600/Wpn0Jtl5NEz2wSG\nyX/YK+kt5rJNipfMp1FptLDQkRRHDfWmiQurFUeD3q5sjHnqJgtGD7BYvcVCHZ9/7iqLyxp5eDk5\nVwHcyPpCxrBgSzcD2iaylG4mNRltwif+OyhGD7AOKaxTN1NeGT2t69GzBz0HHqfUgGAcyuj1lW7W\n2XzvjZaJ//LJ5/CT//AYnlocraBer0mp/ZCOKdg3GceZK978GRdWqwCAQwFJN+k9geV9qOsB48Po\nASMw6OnDU3MHISbzZfRYVV9MdsJYWFe1bFYpnL5cGPrxi/maK38e0H0G80qQHgav3mBamh4VLBd1\nxBXJlyeVQlNotQj/30ml0fIlrx4EuvCLap/emeUS2gS4eUDiJsVcNoarpQbTxT4LRg8AHrp5DrNp\nDe8fh7IAcObR+xdBEB7u/Pe/ATwH4KP8L+36RNCyEbY9etbn4XHYCorRAzqHFMapm549enHZk3Rz\nUAIqHfS21ivEFEuuworRu7hW7WxhCd7x94/hapnt9o8nvCTfDcOx+YxnRu/8agWSKGD/lHOvkR/E\nOUg3+TJ6tHMyurLjZqsN3WhHN4yl0sQUQ0avTa6thmGBSqMFVRaRUCWccjLouezQA7rLnaBUNVvh\ntb9zOqVGitFbKTcwl9GYSIHpkjeILr2K7t1TPwxH5zqD3ko0Bz0nQSwU85kYmmabaegSK0ZPkUS8\n5Z79+PzZVVzeGM7873Q4OTn/LoDf6/z3WwBeSQh5L9eruo4RD5DRI4R0GD02AxTtneFhYg+U0Uuq\n2GAYSGJtaL1tCDeHTJTq1v91nLrZd9DrSDe3MCuCICAbV5jVK5xdseSGv/P9t6NQM/BT//Atqh6W\nMwAAIABJREFU+0YeddBtPqvqEcBK3ry4XvX03j6/WsH+yQQ0OZj3gD3oMdygB8HoRTmQxQ5T8sXo\n8QljIYRgvdrAFIPETYBPTQ1g3UszMRm37skOHfSarTaulhuuOvSAzWEs4dyrqh4ZvZmUhvVKMzL+\nr5WizkS2CVhMNoBAnh9lH4vZYUjHFOzJxSObvPnMUhHZuOKIBafeSz8BY1thM3oMciPees8+iIKA\nD3z9ku/PNepw4tH7wqb/vkwIWQjiwq5XJNTgtomGSWC2if01/cJJUbdX6AEVpgPAVFLFRpXdZrTi\nQ7qZiSmoNU0YZttm2px4fNKDGL3O4SsX336oy8YVZqmb51bKkEQB33P7Lvz+Dx7H45cK+OWPPBWZ\ng8gg2KXFLBm9XRkQ4m2be2G1GphsE9i0cGLq0aMhQNcno1fS/ce2x1U+0s1a00ri9VuWTkE7Oll3\n6dEh6MS+HJ5ZKg08+F8p1kGIuw49ALY/LkxGz5N0M6WhabbthWDYWCnrTIJYgM3SzQAYvQY/jx5g\nyTejmrz5dCeIxQkLO59l36VnM3oMFpq7snE8eGwWH37s8sgsmHmh78lZEISyIAilHv+VBUGI5qt0\nB6C7Sed/Q6PMAiumjD6cuEg3jXagHj1W0eCEEOvB7fHBYXuP9BaKdQOqJDqqmUhqMhqtdk/zer7W\nREqTe6aK5eIKM+nm2ZUyDkwlEFMkfOdtu/DzDx7B/3x8Ae979CKTz88TrD16AHCzx+RNs01wYa2K\ngwEFsQCbpZvs3ssb1SYEwRkj7RajwOiVXCxq+oFXYTpl3pgxenYfKWPppm7JGo/vy6FptvHsAM8r\n7dBzy+jRxWc1tNRNj9LNtPUzj0JpOiEEKyWdSbUCsFm6GRCjx3HQe8l8GhdWq2iG1NMIWEuMpxaL\nePj0Ev7wkbP4uQ+exHf/8aN4arHoSLYJdAc9loEsDYaMHmCFsmxUm/jEk8tMPt+oou+rmRCSDvJC\nxrAQU0QIAtsDVj/QAwMreZqdVjbi0s3JpIJKo4VGy/QtlWu02jDbxPPAQGVeJd1AsW4FOTjZtm3+\nXWwNXSnUjG2yTYpsXGEmxTi3UrE9CQDwc68+grMrZfzmJ87g8GwKr7pplsnX4YEKh0Fv70QcKU12\nPegt5utottqBMno8+jw3ak1MJFRILhIQnYIOeqUoD3oMpJtxTh496u2aZsboWd8j6+RNOgQd35cD\nAJxeKNj/eytoh95eFx16wCZGL4RgH0KID+mmdfBeqzRweDbcYPRSvQXdaDMpSwe6g14QzEyl0UKa\nk3QTAPZNJtBqE6xWGq7ZZr/4i8+fxz989QUsbXrGC4LFeh+cSeFH77sBP3rfDY4+10xKgyiAacUC\nHeRZMHoA8PJD07hhKoH3f+1FvPHEHiafcxTh+NUsCMIsAPtdSwgZC185QBAExBUpkDAWKk1hFcaS\n5MnoBRjGQmVHhZqBuYy/nw1lGLw+ODYzFaW6gazDDq7NwThbB72NanNbEAtFNq4w8Q/ohokX1qv4\nntt32X8migJ+983H8cJaDT/3wZP46M/eh8Oz0dwnUX+O1/7DXhBFqzDX7aB3PuBqBWBTvQLD+5D1\nuuOTZpcZBelmR1Lnh9HTFJELo7de6d2t6RU8+kgBS1I9l45hdzaGmbSGU5cKePvLen/sYr4OQegy\nD04RkyUIQjiF6XXDRJvAE6NEGb0oBLKsdIK3mA16cjDSTb8KHCegy5S1crCD3mfOrOB3/vVZvOzg\nFN56z34cnEnh0GwSN0wlPS3RZUnEdEpjy+i12DJ6oijgbfcewK9//AzOrZRxZC6a5w3ecJK6+XpB\nEM4BuAjgCwBeAPAJztd1XSOhSkz7q/qBHhhYMWVpO4yF7bUTQqxBLyBGj8qX1hlEVfuVANJDYalu\nMXpOZW80/KXX76JQa24b/iiyCTZhLBdWq2gTbLuxJlQZf/Ojd0NTRPxff/cYChxKlVmALkFYMnoA\ncGxXGs9eKbvyKdJBL0jpZoxD6uYGw/j+rdBkEYokRFq62Q1j8ZG6KUtottrMawtoUA6r1M24IkGT\nReaMXrVhIqnJEAQBx/fmcGqhfyDLYqGOuXTMdfG1KApIKFIo0k0/SoLNA0TYWO6wPG6H7H4ISrpZ\nN0yYbcKtXgEAZtKd31OAA/lyUce/+/9O4+ZdGfz3f/tSvPs1R/Ddt+/CTfMZX+e/+WyMTxgLw9Cx\nlx+eBgCcu1ph9jlHDU7ugL8G4F4AZwkhNwJ4DYCvcb2q6xxxVQokdVPnJN2sNNhu1e0tT1CMXoJd\nkIDfmP7NkrSS7nzQS9qM3vbfRb5m9GVWsnEF5UYLLZ/FtOeuWqzg0R4btD25OP7qR+7ClYKOn37/\n4/jk08v40rk1fOvFPJ5dLuHyRg3rlQZ0wwwtuMU+cDEKKqI4tiuDssvC3POrVUwkFGZsixPw6PPc\nqDb7Sob9QhAEpGMKKh4GvYdPL+HRc6scrupa2NJNH4dIyrTqjCVs67ZHj80gLggCJpMq89TNst71\nr53Yn8OF1SqKfcKjFvN11/48ioQmhxLGQhdzXsK7JhIqRAGR6NKjAR1zadaDHl9Gj94/eKVuAlYN\nBhDcoGe2Cd7zoZNotNr4kx86wdQCM5+JMQ9jUSSBqbyfnudYhcyNIpy8mg1CyLogCKIgCCIh5HOC\nIPwh9yu7jpFQgnnIUFlWnNGgl1DocMH2EEINusF59NhFg/sd9LJbPHo3TjvzaXWDcbb/LvK1wdJN\n6+u1fA0Wzy2XIYtC3+u968AkfvP7bsMv/fNpfPXCet/Pc+ueDP73u+/3fB1eUW20EFck5n6yY51A\nlmeulLBv0pl36PxqJVDZJmD1EMmiwNajVzVw1wE+jB5gvea9SDd/71PPodY08ei/fxXXe0yp3oIk\nCr4Wa5slbH3ewp6wXmkioUrMngVAJ9SKS+qmdY3H91revCcWC7j/yMy2j10s1HFHH//eMCRVKZR6\nBTpoeFkwSaKAyaQWDelm5/A/yyyMJZjCdBbJuMNAmdfVgJjXP/vc8/j6xQ387puPM3+OzGdj+NqA\n57db6EabmT+PItdZarO+F40SnLyaC4IgpAA8CuADgiBcBVBl8cUFQfgOAH8EQALwPkLIb7P4vKOO\nuBqMR49u61l59ERR6Dwg2Q6pul2iGaxHjwmjRzeEHh8cXe9Ry5V0s18wjmG2UdZbfQc9elMs1g1f\ng97ZlQpumE4OlE39wF178YrD01irNFBrmqg1W6g1TVQb1v/91DPL+Or5dRBCmJTuukG1aTL151Hc\nNJ+GIADPXinjdbfMO/o3F1areE0IwTVxlV3CY7tNkK81uXToUaRjsifpZqFmLVE+/NhlvP1lN7C/\nsA5KuoF0TPb1WrYZPcYH3vVKg5lsk4I1o2e2rd5XKku/bW8WAHD68vZBr90muFKs47s3eYTdIKGG\nw+jZi0GPz4uolKavlBrIJRRmixOb0eMcxuJ3MesEMUVCOiYHwrx+4+IG/vCRs3jTiT34/jvZh5HM\nZWIo6S3UmyaTJVGjZTLz51HEOjJyVmnio4i+r2ZBEP4MwAcBvAFAHcDPA/hhAFkA/9nvFxYEQQLw\nZwAeArAA4JuCIDxMCHnG7+cedcQVPl1JW0EPcSy3uIOKur2iwUG3PQi5zjDFxKPns4+NPvCLdaMT\nxuLUo9c7GKfQpyydgn5+yzvnPeXx3NUybt2dHfpx89lYXx9HtdnCl59fR6MVXLWG/bU9RpwPQ0KV\nccNUEs9cKTr6+GLNwFqlgYMBJm5SxBV2EvKy3oLZJlw69Ci8DHpmm9iSyr/8/Hm85aX7XXu6nKJU\nN3zJNoFN3knWgx4H/+REUsViwblEeRi6/jXrZ5CNKzg0k+xZnH613IBhEs9hFylNDoXRq/ocNGbS\nGlYjIt1kJdsEuraNoKSbPD16gJVYybsGo1Br4j0fOon9kwn82htv5bIspT2JyyXdsdpoEHSjzeWc\nZ1Vmhf++CAuDnmhnAfxXAE8D+G0AtxFC/o4Q8seEEBZc7T0AnieEXCCENAF8CNZQed0jMaKMHmAN\nJqxTN4Nm9GRJRC6hMGH0yj41/5IoIKXJuFKoo02cd5DZg56+ddCzvqdh0k0/269608SljRqOzPmT\niVD5Uhjpd9VGi7k/j+LE/hy+dmHDkQ/y/FrwiZsULBk9GvbBl9FT7KHNKcq6AUKAB47OYKmo4yOP\nL3C6OksW5ieIBeAXSrFeaTLr0KOYTChMGb1eQ9DxfTmculzc5uVdLNQAuO/Qo0hoUqiMntcl03RK\ni0QYy0pJxxyjIBYguDAW6mnnyegB1u+Jp3STEIJf+ucnsFZp4E/eeie374cuaa8U2Sx0eDB6gKVU\nKlzHjF7fnygh5I8IIS8D8ACAdQB/KwjCs4Ig/EdBEI4y+Np7AFze9P8vdP7sukdQYSyse/QA6wbJ\netALmtEDrMJfph49H5r/dEzG5bx1cHHawdVPukm/p/6DnvXnfga986sVENI7iMUNeET8O0XFY5eV\nEzx0bA7FuoHHXswP/dgLq5ZK/lAIvVgsa17o0iRqjB5luF9/fDdu35vFn3/+vO8gon4o6+wYPeaD\nXpW9dHMiqaJYN5j9PKs97qUn9uWwVmlsYw5p2NFej4xeUpVDTd30WsdDpZthhVhRrJQamEuze69T\nRq/BuWQ8CI8eYDGvPCW2f//VF/HpZ1bw3u88ZkuceYAOeqwCWXh49ABr0OsX2nQ9YOjoTAh5kRDy\nO4SQEwDeCuBNAM5wv7IOBEF4pyAIjwmC8NjqKv9ktCggKEaPfg2WsrikOly6+fEnrrjqEgua0QOs\nQwoLRq/aaEEU/LGmmZhiH1ycMnqqLEKVRFS2bKXznZtdbkDqJuBv0Du7QhM32TB6YQ16CQ4ePQC4\n/+gMVEnEZ86sDP3Y86sVKJKAfR6ZCT+wyrnZ/OyXi9ahZoZRIXcvZGKK6zAWuuWdSCp416sO49JG\nDf/yxBKPy0Op3vI96MU5pA8SQqzqC8a/G+rxZbVJL/dgu+zi9MvXSqHp4OeZ0VOlUArT/dbxTKc0\nNFptLl22TmF2ysBZVSsAVoqrJoto8Gb0Ahr0plMqN+b16aUifuPjZ/Dqm2bx4y+/gcvXoLClm0U2\n3ws3Ri/OPhhqlOCkR08WBOF7BUH4AKz+vOcAfB+Dr70IYN+m/39v58+uASHkrwkhdxNC7p6Z2Z6s\ntRMRlBFcN0yIAtvagqQmD0zdzFct3fh/+9JFx5+THjaDZPQmEioTjx6NA/ejj0/HZLurxs1BMRXb\nPnTb0s0+Mi170POx/Tq7Yg0nB6b8afbpoFUNQUK1mK9jN6cy25Qm495DU3jkzNWhH3v+agUHppKQ\npeCWHBQJhsqCJZ8HbydId2TjbtgM+n7IxlU8eGwON82n8aeffZ55Tx3QDWPxA7rsYqn4KOktGCZh\nLt20a2oYyTd7STdvms9AlUWc3tKnt5ivYyKhIOFRfp3koExxgkqjBUHwrrKxu/RC9OmtVxow2wSz\njMrSKWIBZBf4lc46xXRKQ0lvocE4XKbWbOHdHzyJiaSC//oDt3MPMUtqMtKazIzRa3Bi9CaSY+lm\nTwiC8JAgCH8LS1L5DgAfB3CIEPIWQsjHGHztbwI4IgjCjYIgqADeAuBhBp935MHSGzMI9aaJuCIx\nvRmktMGpmx9/8gpabeKq76pbrxDcYXeKIaPnVwKYiSswOwdPp4weYIUWbP05b1AJXR/ppiqLSKiS\nL0bv3EoZB6dTUHwOJzajF3AoQr7aRL5m4CADc3k/PHhsFhfXqnYZej9Y1QrBB7EAbKWbi4U6UpqM\nDMdNeTomo03gSnJHX+e5hAJRFPCzrzqM86tV/OvTy8yvr1Q3HEuv+4FH+uB6hW1ZOgXLmhqg96Cn\nyiJu2Z3BqUtbBr2C9w49oKuqCVoCWWm0kFK9LwanQyjj3oplu0OPLUMcU0T+YSyNFmKK6PvZNQzd\n0nS2A/nDp5ZwYbWK33vzHcwZ+n6Yy8awzKg0nRejl42rKNSaoUuaw8Kgn+h/APAVAMcIIa8nhPwj\nIYRJrQIAEEJaAN4F4JOwpKAfJoQ8zerzjzISigTDJDA4eUUoagabSNzN6MUibcbDpyxZlBuWpivd\nDJDRS6rIVw3fNwYWXq/NLEC2j+SyF5Lqdna1UDOgyeLA33s27m/79dxK2XcQC9DdagfN6F1ct25z\nLFLE+uE1x+YAAI8801++aZhtXNqohRLEAgBxVWa2QV8q1LEnF+e6Yaax+26WSNSjR5N2v+u2XTg4\nncSffPZ5poeCltlGtWkyk26yLrIH2JWlU9iMHiPJVL9gq+N7c3hysXiNF3AhX/ecuAlYTEWrTdDk\n/AzeCr9pv3YZd4iBLCsl62uzlG4CHUaPc71CWTfs+whP2Mwr49/TC+s1KJKA+w5NMf28gzCfieFK\nxD16EwkFhklCsYFEAYPCWF5NCHkfIWR4YoBHEEL+DyHkKCHkECHkN3h9nVEDPYTzZvV0Rt0nm5HU\nZNtLsRWLhTq+8cIGgO2x/4PQDWMJjtGbTCpodg5nflBhENO/+XDohtFL9ai6yFf7l6Vv/hpeGb1q\no4WFfB0v8RnEAnTlM0Gn311c5T/o7cnFcfOuDB4Z4NO7vFGDYRIcDGvQU0SmjN7uHNuD31bQhYgb\nnx4d9Oj7ShIF/MyrDuPMlRI+++xwaa1T0CHFb+om3XbrDEMpKKvgpzezF7qMHhvJVD//2on9OdQN\nE2dXLHacEILFfB17cgnPX4sumYJWE1Qb/vo7Z1IRYvRYSzdl/tLNst7iqjqg4MW8LuRr2J2LQxSD\n652dz8awEnFG73ovTQ/e+DHGUNiDHuftQ60j3WSJlCqj2Wr3ZCMpm3fL7oyrrXsojF5nGNrwKa2o\nNFq+fTn030udQnqnSMXkbWxYvmb09edR+Bn0nr9qHbaOsBj0KKMX8GHr4loVkihg36T3g6ITPHhs\nFt96Md9X2naeJm6GKN1ktWxaKvDzPFLQ90nJDaNXbyKlydd4IN9wx27sm4zjjxmyevagx4jRYxlK\nQasvphlLvVgfrujSbesgdHxvJ5Cl49PL1wzUDdOXdNOudgl4yVRutJDy8RqZTKoQBITapXe1pEMU\n2L+egpJu+knIdgrKvLKuWFgs1LE34OCu+UwMqx1fpl9YPXp8pJtAd7F3vWE86EUQiYBi5euGiTjj\nrrB+sf4A8LFTi7hzfw43zWdcdaOFwehRv8qGz0MKiz426uvJxhVX0rekJm8bqPO1JiaGyD+zce9R\nxKwSNwEgERajt1bF/skEd5/GgzfPoU2Az/Vhji50/HuhMXqqzGTZVGu2kK8ZAQx61uvaDaNXrBnb\nWHJFEvHTDxzG6csFfOn5NSbXRvv9WHn0WC4B1zkxejFFQlKVmHn0ynoLqiRuC+U6MJVALqHgdKc4\nfbGTUOxXugkEn/hrebq9LzRlScREQg2V0Vsp6ZhJa5AYs0paAGEsZZ1frc5mTHNiXhfydez1wWR7\nwVw2BrNNmHwvjZbJZaFPzzzjQW+MyCCuBHPArRsm4oxpcruoe8sg99xyGc8ul/GGO/YgpUmupJth\nMnp+E+Mquv8NIWUq3EpKUur25Dhr0Bt8oMslvDN6565WoMqi78RNoMteBH3YurBW5SrbpLh1dxaz\naQ2feba3fPP8agXTKc2VXJcl4oqEptn23YO2VLBkPbw3zRlbuumG0TN6Vo18/117MJ+J4U8++zyT\nayt13k9+2X1FEiGLAlOv0ka1iXRMhsphkWZ5ndmFsfSSNQqCgON7czhFB71OWbqf15ud+Btw8iaL\nxSDP6H4nWC417Nh9lrA8epwZPd2/AscJYoqEdExmGsaiGyZWyw2uyca90K1Y8C/f5MXo5RK06mUs\n3RwjIkgEJN2s85Buxiijd+21f+zUIiRRwHffvgsplzHoeigePTaJcSzCWKjcy+2BP9nDo1eoGZhI\nOmD0PA56Z1fKODSTYrLNlUQBMYY+MSdotwleWKtyTdykEEUBrzk2hy88t9ozZvv8ajU02SbQvQ/5\nPVzRTrPgGD03YSzNnoOeJkv4yQcO4hsXN/D1C+u+r81m9HxKNwHrkFhvsvToNZjL7Cgmk6pvVQTF\noKCS4/tyOLtStj3CgE9GL6QOzzKDxeB0im8Z9zBcLenMqxUAIBZEj16jFUgYC2D5KVcZ/p5ohU3Q\n0s1dndCdKz4HPUIId0YvP2b0xogKgpRueu0Z6oekzeh131CEEHzs1BJecXga0ykNSc2KQXeqt2+0\nTKiyyL0TZjMmGAx6hBCmqZtuZV+WR8+0O8HabYKCA0YvG1dQN0xPHT/nVipMZJsUSXVwiitrLJd0\n1A0TNwY0YD108yyqTRNfu7Cx7e/Or1ZwaDYc2SYAxOz7kL+f/1Jgg56HMJa6gVy89/vhLS/dj+mU\nij/9nH9Wr1RnE8YCsE8fXK80mXfoUUwk2DF6g+6lJ/bl0CbAk4tFLBbqSKhSzwHeKezE36AZvab/\n54U16IXHXCyXdMxl2C8ONEVCgzOjV2bQdekU02mNqUePLjj2TgQs3ewM9X679AyToE34LPRpWnlx\nHMYyRlQQD2rQa7LfnlB/weZY/8cv5bFYqOMNd+zufExveWc/WCWawb5U05oMRRJ8baPrhok2ge8N\n7WaPnhukthSOl3QDbdKVMfRDtvP3blm9sm5gsVDHUQZBLBQJjV2XmxNcXOOfuLkZ9x2aRkwR8Zkt\n6Zsb1SYKNSO0agWgK53VfbJHS4U6JFFg3qu1FQlVgii4Y/SKNaNvZUlclfAT9x/Eo+fW8MSWQm63\nYOXRAzqhFIzrFVj78yhYMnqDBr3b92YBAKcvFzqJm/6qPGyveYD+YEKI73oFIFxGTzdMFGoGH+mm\nLHL16LFazDrFDOPfE1VOBC3dnEqqUCTBTlv1igZHi44mS0io0tijN0Z0YB+wOMsUrDAWti+BXmEs\n/+vkEmKKiNfeMg/Aw6DXMqEF6M8DLN+H3210pU8cuFv4kW4CXRktlS04CWMBur4ipzjXSdxkOegF\nzehd6Ax6B6eDGbBiioT7j8zgkWdWrpEyn7eDWMKXbtYMfz//xUId85nYNcmWPCAIAlLadl9qPxBC\nOoxe//fDD33bfsiigE885a9AvaS3IAiWb9YvmDN61Qa3cmXrHsquXqHfvXQqpWH/ZAKnFwq+y9KB\ncBJ/G602DJP4Z/TSKmpNM/AQKwC42unQ4yLd5BzGUmtai9nAGD3GXsqFfA1yAAu1rRBFAbNp/xUL\nvC06ubgylm6OER0kAvIH1JscpJvqtUOcYbbx8Sev4MFjc/YDbFAyZy/oRhsxDt0qwzCZVH1JN2ni\nZdr3oGf9e/eM3rW/Cxpz7qReAXCfUHWOYeImRUINmNFbrSKuSFykR/3w0LE5LBV1nLlStv/sfGdo\nPhwBRs+vV3gxz79DjyIdU2z2bBgqjRbMNhko8cvEFNx5YAJfPLvq67pKdQMpTWbSbxVXJGYx8+02\nwUa1ace9s8ZkUkGl0fIkA9+KYdH3x/flcOpSZ9DzKRMOI/GXPg9ZSDcBYK0cvExtpWwd9vmEsfCt\nV6DPySDqFQBgJq2hpLeYDa8L+Trms/wXar0wl9GYMXq8lvq5hIriOIxljKggzsgbMwjtNkHdYC/d\nTMeuHeK+9PwaNqpNvOGOPfbHuGX0dMNETA6W0QOsbbSfQY9ug/0yetmEgkxMxg0ukyxTWwZqyk4O\nTd3sDHpupZtnVyqIKSL2MfQIJLXtXYA8cXGtghunk4H6QV910ywEAdeUp19Yq0KTRe6+tkGw+zx9\nHkSWivw79CjSMdmxdJMuMvp59CgeODqDp5dKvmRWJd1gEsQCWAdeVkFdhbol5+bm0Uuy66+qNFoD\nGdHje7NYKuoo1AzfjB5dcgTJ6LF6XtDSdJZBH05BkxdZl6UDXSabVbflVlBvb1DSTTqQrzPysC7m\ng+/Qo9iVjftO3eTO6CXGjN4YEUIQqZvU1JxwUcDtBHYYS+ew9fCpJWTjCh44OmN/TGrLxwxDo9WG\nFgajl/LnLyk32Dw4NFnCo//3q/H9d+119e+S2xg9d9JN94NeGYdnU0xYC4qEKqEW4GHr4lo1sCAW\nipm0hjv25a7x6Z2/ag2crLuo3IAFo2e2CZaLemCDXiamOA5joa/vfh49ivuPTAMAvnTOe6deqd5i\n4s8D2Eo31zvDwCSv1M0Em/RiwBqEBg1BJ/bn7P/tN5BCEgXEFSlQRo/V84JXR5sT0EAOHoqImCKB\nEKDps+6lH+iCiNVCZhi6zCub39NCvh54EAvFXCaG5ZLuawjn6dEDrEGvMA5jGSMqUCQRiiSgxlGP\nTrf0rOsVFEmEKouoNFuoNVv45NPL+K7bdl3T0eTW6B4Wozfp06NHN7QsNoTZuOL60L+VOS1wl25W\ncHSWnT8PsGTMfj1iTtFstXE5Xw+kWmErHjw2h9MLRfugdH61EmoQC8CG0VurNGCYxLeUzincMHp0\n0Bvk0QOsvsPJpOpLvmkxemyYAqtegc2zgaYzTnNm9Pwmb7bbxEqkHPAzvGV3FnLnHsni9WapCYJn\n9Fh49IBwBr2r5QY0WeTS/UmZHl7yzaClm9NpdgN5s9XGSlkP7D67FfNZDbWmibIPPz1/Rk8dh7GM\nES3EGT7Me4FuKlkPeoD1oKo2WnjkzFXUmqadtrn57wE3YSzhMHoTSRWFugGz7W1LRSsmgnpwbMVW\nL+RGtQlZFIZ6BjMeGL1i3cBySccRhkEsQLCM3uV8DWabBJa4uRkPHpsDAHzmzFU0WiYu5+uhdugB\nbArrWXSauYEn6eYQKbMoCnjF4Wl88dya5411WWfH6MUZxsxTpo1XGIvdR+pzk14zTBDSTRLuhZgi\n4aZd1v2HhYQtqUmoBRgEVbXDu/w9k6eS4Xn0los65jIxLtJ3yvTw6tKjCqPAUjc7gx6LioUrxToI\nCb5Dj8KuWPAh3+TO6MUVFOoGN+lvlDEe9CKKhCpzlY1QA3CcsXQTsB5U1YaJh08tYle2OeDGAAAg\nAElEQVQ2hntumLzm71NbfHzDEB6jp4AQeKb7K7bnIvhrB3p49GoGcgll6ENYEgWkY7KrQe/5q+yD\nWIBgPXoXV4OtVtiMo3Mp7JuM4zNnVnBp3Ro4w+zQA7r3Bj9hAUF16FGkXUg3Cx1jvpO+tfuPTGOt\n0rgmMMcNSvVoevTWqx3pJscePcA/o1d1mGB85/4JxBXJ9qn5QUINltGjbIjf1Ee1w6iFJd3kEcQC\ndAcAXoxeOeBBj/piWfye7IVaSIMe/Z37CWRpcGb0JhIqzDbxxTqOKsaDXkQRVyXUOSZM0S09H0ZP\nwUK+hs8/t4rXH9+9zbOV6HzN6Hv0rMNC3uugZ6duBqP53wr6wCpvkm4OYy8osnHF1aB3doV9tQJg\nMXq60fbMqrpB0B16myEIAl5z0xy+9PwanloqAgiu4qEfWHiFu4NeUKmbFqPnZGtLGT0nMrNXdjzG\nXzznTb5ZYljEzNKjt1ZpQhCG+3a9gg7RGz4rFioOEyl//sGj+OA772XiE06qwXr0nA6zTjCdUkMb\n9GY5JRbT5G2W1SKbQZ+TQXn0YoqEdExmUm6/2Bn0WAahucGurDVgXokwo9ctTb/+5JvjQS+isKSb\n/B4y9PDGOowFsOQ133whj1ab4PVbZJuAJYVKqtI1peqDEKZHD/B+SKk2WpBEIZRqCMB6MIrCtdLN\nSYeDXi7hdtArI6FKzCV6SbtqhP+B68JaFZNJ1fEwzBoP3TyHRquNv/vKiwDC7dADYL/n/Eg3lwp1\nZGIy0gEdntIxBa02cSRtLNYNxBTR0cFiLhPDTfNpPOph0Gu3rSJmltJNZoxepYGJhMotkl2RRGRi\nsudlGYVTWd1kUsUd+3IDP8YpEprs+BnFAmwHveBL0wkhWCk1+DF6Mt9+YfoaC1KBM5PWmEg3F/I1\niAIwnw1mobYVdLj3I93k7dGj6oLr0ac3HvQiCt79YTRgIcZFumk9qA7PpnDzrkzfj3HToxd0YToA\nTCTpNtqrdLOFpCoFGtW/GYIgdH7O1u+60JFuOkE27i6h6uxKGUcYJ24CQELzP2w4Ba1WCAsvvWES\naU3GqcsF7MrGmBz4/EDsLCn8HKwWC8FVKwBdWbiTLr1CrTm0WmEz7j8yjW9ezLteOpQbLRACZmEs\nWsejx8JrslFtcpNtUvjtIwXYDkFOkVSD9ehR6WCSQbftdFpzzBSVdYNJKmpJb6FumFyqFQDYqh5W\n/tStqDQMxBUp0B666ZTGpAZjIV/HfCYGJYQOPcBi4SYSij/pZgCpm4B3hdYoYzzoRRRx3oMeR+km\nfRi/8Y7dfYecVEx2EcZictvyDIIdJODxIVjWW4ExGf2Q1uRrCtOHdehR5OKqa+km6yAWoHvocboU\n8IOLa9VQBz1VFvHASyyJYNhsHoUVMe9n0As2CY4OU04CWdwsPgBLvtk02/j6hQ1X11TqvI9YMnoA\nmwPveqXJrUOPYiKp+mf0GJWJu4Hlkw+W0UuoEpNKlZmU5ji2/70feRJv/9uv+/6aVzuHfH7STb6M\nnvW8Dna5NsOIeV0ohFetQDGXidmp0V7An9HrpIm7rI3aCRgPehFFQuWbukkZPS7Szc7h/PXH9/T/\nGM3FoGe0uW15BsEOEvB4SKk2WqEFsVAkNRmVjmepUDOGVitQZOIKinWn6YVNrJYbzINYgO7rk/eB\nq9poYaXUCHXQAyz5JoDQqxUo4orkq15hKWBGL+1m0KsbrmLgX3rDJDRZdO3TY93PRaXgLJ4Pa9WG\n3efFC5MJ/4xeGINeUpMCC4ICrLohVozldEpFudEaOhQRQvC18+t4arHkujd1K1ZK1sDCX7rJKYyl\nMbi+gwdYSTfDLEunmM/GcHGt6tlPz92jF6fSzTGjN0ZEwLs/jGcYyxvu2I1fePAo9k/13zAlVWfS\nzXaboGm2Q2H0YoqEpCr5km4GeTDpBZpaWW2aaJptx6ELVhhL05E8jAax8GD0ErZHj++gR4NYwujQ\n24xvPzqLXELBXQcmQr0OiriPhVOl0UKxbgSaBEcZdCfJm0WXjF5MkfBtB6dc9+lRGWkmzuZeQO/Z\nLEIpgpBuToyodDOhyoFVuwBWSjOr54XT0vSFfB3rnd/NqcsFX19z2S5L55W6SXv0+Hn0hlUPscZ0\nSkVZHz6QD0LLbGO5pIeWuEnxHbfM4/xqFb/y0Sc9ycp5M3pe+4F3AsaDXkTh54DlBDzrFe47PI33\nPHhk4Mc4lW5SeVIYjB7QkR358eiFPOhR5pR+D46lmwkFhkkcsTlnV2i1AodBr8OI8t6s24mbIUsm\nswkFj/3Kg3j98e0hRmHASv/1dh8KuloBcMvoufPoAcArj0zj/GoVi53vzQls6SYzRs9/GioAGGYb\nhZqBqVQwHj0/nsIKozJxN0hpEppmG01OnrCtqOgGh0Fv8LPr8Ut5+3+f3PS/vWCF+6DHW7ppBM7o\n0d/Tuo9FyJWiDrNNQmf03nLPfrz71YfxoW9exq9//Izr93ujZUIWBW4eSVUWkdL8B0ONIsaDXkTB\nuzCdfu6wBiin0k16Uw8ruXIyqXq+CVcawWv+tyLVkW52y6GdM3qAs9L0cytlpDQZuzkkftmpm5w3\n63TQu2EqfG+cLImhBfhsRUKRPd+H6DC0J6BqBcAdo+fWowcAD3RqFh51weqVmEs32UjY8pzL0ikm\nEioarbYvCXClYQSeYEzVBDyfw5tRbZjMpP7TaVqaPpjRO3W5gJgi4vBsCo9f8sforZR0ZGIyl+Ux\n0A1j0bmFsbQCr0KyB3If8k27Qy8XrkcPAH7xoaP4sftuwH/70kX80WfOufq3usFfuZWNK+N6hTGi\ng4QqoWaYTJLVeqFmmFAkIbSUJqtU3Tmjp4VQrwBYg54vjx6DBDU/oOmmG53vwalMy43MwQpiSXEZ\nTqhHLwhGb08uHtriI6qIde5DXhBlRk83TDRabbtbySkOz6Ywn4m58ul1w1hY9eh1PHo+mQ26wOId\nxjLpM70Y6AxBAScYJwNSE1CwlPpPp5yVcZ+6XMDte3J46Q2TOHkpj7aPvtKVks413p/emxscpZth\nePQA+PLp0YVa2IweYCV9/8fvuRk/cNde/OEj5/C+Ry84/reNlsn9+TuRVMaM3hjRQVyVQAi/KOF6\n0+Tiz3OKlKaMBqPnI0ggjAfHVqQ0CZVGyzYgO+2Iy7lh9K6WcXSWvWwT6HpyeMecXwg5cTOqiCsi\ndK+MXr4OWRQwmw6O0aNBUMMGPZvhdindFAQBrzw6jS+dW3McOkA9eqwO8awOvOuVYAY9O9TKR2l6\nGH7nRIAdngDrQW+4R6/RMvH0Ygl37M/hzv05lPUWLqxVPH/N5VKDm2wT4N+jVw7hNWYzrz6SNxfy\nNQgCsCtA5cQgiKKA3/6+2/Cdt87j1z9+Bv/0zUuO/l0jAEYvF1fHqZtjRAcJhW/aYL1pcpNYOEFK\nk2CYxE5a6oewGT2vHj1CCCrN4M3dW2GFsZj2sOo0jCXjcNBbrzSwVmniCIfETWAzo8dPPkUIwcXV\ncDv0ogo/oVBLhTrmszEmcfFOIYoCUpo8fNCr08WHe6nWK4/OoKS3cHrBmdStrFsHSFbeE7qg88/o\nWYdL3tJNu6bGxya9GkIiImX0gipNrzL0dMcUCWlNHujRO3OljKbZxol9OZzYb4U/Pf6id/nm1ZLO\ndamjSAJEgU/qZrtNQrFa0CWLv0Gvjtm0FtoZqRdkScQfvuUOPHB0Bu/9yJP4l9NLQ/+N3uKfrp5L\nKOMwljGiA97bxEozXFkhfaBVhzxEQ2f0kiqqTdP1FrHWNEFIsClxvZCKyTDbBMtFHYIAx3Hytkdv\nyE2RJm7yCGIBrAQuSRS4btU3qk2U9NZ40OuBmCKh3vR2sFoq6IHKNinSMXmoR6/L6Lkf9F5+aBqC\nAMfpm6W6wawsHWDn0QuM0UtSRs/7oBdGsJX9DA6oNJ01azmdHlzGfaoTvnLH/hwOTieRjSvXhLO4\ngdkmuFpuYD7Lb2kgCAJiisSF0bNsMgh80IspEjIx2Z90Mx9+h14vaLKEv3zbXXjpgUn8wj+dwmef\nXRn48Q3DhMqb0Uso43qFMaIDyrbxMoKvVxrc09YGIWUPeoMfomEzenQb7VbXTb+v8KWb1tdfyNeR\niSmOWQXKdAxj9M5d5Ze4CVgP94Tqr7R7GKKSuBlFJFTvB6vFQj3QsnQKa9BzJt1069EDrMHl9r05\nPHpuzdHHl3TDDolhgTij9MH1agOSKLjqEvSCyY50049HLwzpJl2E8lQTUBhmG41Wm+2gl1IHhnyc\nvFzAXEbDrmwcoijgxP4cTnoMZFmvNmC2CVfpJmANRixqRbaiotOexmDDWABrIB+WjjoIC4VaKPdZ\nJ4irEt73Y3fj2K4Mfur9j+OxFzb6fmwQjN5EQkWxbvjyoo4ixoNeRMG7KHqt0uRelDsI9IHmJDQB\nCI/Rm/B4SCmHUPDbC/SwspCvOZZtAtZ1S6IwdNA7c6WETEzGXIbfaymhSlxTNy9EpEMviogrEmrN\nlutQKLvbKZRBT0G5Mfh1W6y786xuxQNHpnHqcsGRh7VUbzELYgEYhrFUrA49kbO0NhNXIArul2Wb\nUQ3Do6fRZzB/Ro9HT+B0ShsoCTx1uYAT+7p9nSf2TeDs1bLtKXWDq52ydN6DniaLaHCQblIFQBiL\n2enUYOZ1EMw2wZWCHokgln7IxBT83Y/fg5mUhl8bULvQMMxAUjfbxFn9zk7CeNCLKFj5MPohbEbP\nlm4OeYh2B72QGT2XQQLdDWH4Hj0AuJyv2xIqJxAEAZmYbHuZeoEQgs89u4qXHZrimoaXVGWuyXcX\n16pQJCGS8pewEVcltAnQNN0drq6WrQ1/eNJNp2Es3jb49x+dgdkm+Mrzw1m9km4wq1YArCRUgAWj\n1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yfxa2+8FV84u4qHTy1xeX1Z9QreDrtPLBQwn4lhNqDETQov6cWAxeSzLBJ3A7pkqg65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\nR0REREREFDH/H3tK5IOU43UbAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xd43c860>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Set the number of datapoints\n",
"T = 100\n",
"\n",
"C = pd.Series(index=range(T))\n",
"C.name = 'C'\n",
"\n",
"for t in range(T):\n",
" # Now the parameters are dependent on time\n",
" # Specifically, the mean of the series changes over time\n",
" params = (np.sin(t), 1)\n",
" C[t] = generate_datapoint(params)\n",
"plt.figure(figsize=(15,7))\n",
"plt.plot(C)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Value')\n",
"plt.legend(['Series C'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A cyclic movement of the mean will be very difficult to tell apart from random noise. In practice on noisy data and limited sample size it can be hard to determine if a series is stationary and whether any drift is random noise or part of a trend. In each individual case the test may or may not pick up subtle effects like this."
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p-value = 9.96108840867e-15 The series C is likely stationary.\n"
]
}
],
"source": [
"check_for_stationarity(C);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's try this out on some real pricing data."
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reading SPX\n",
"Reading AAPL\n"
]
}
],
"source": [
"import auquanToolbox.dataloader as dl\n",
"\n",
"end = '2015-01-01'\n",
"start = '2007-01-01'\n",
"symbols = ['SPX','AAPL']\n",
"data = dl.load_data_nologs('nasdaq', symbols , start, end)['ADJ CLOSE']\n",
"\n",
"X = data['AAPL']"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p-value = 0.989212880403 The series AAPL is likely non-stationary.\n"
]
}
],
"source": [
"check_for_stationarity(X);"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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LRjuzCgFsfSRCCP/jk5nUSqlQjOTwltb6Q7P4rFIqSWt9WimVBPi+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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xca33550>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X.index, X.values)\n",
"plt.ylabel('Price')\n",
"plt.legend([X.name])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's take the delta of the series, giving us the additive returns. We'll check if this is stationary."
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p-value = 4.49727767774e-27 The series AAPL Additive Returns is likely stationary.\n"
]
},
{
"data": {
"image/png": 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u5fwLNu2nf+v6PD5lNeNuOt9t+jhdWBRy7n7fz+LZye49msfCLQe5ptNZIbVl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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xbae2d30>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X1 = X.diff()[1:]\n",
"X1.name = X.name + ' Additive Returns'\n",
"check_for_stationarity(X1)\n",
"plt.plot(X1.index, X1.values)\n",
"plt.ylabel('Additive Returns')\n",
"plt.legend([X1.name])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Seems like the additive returns are stationary. That means we will probably be able to model the returns much better than the price. It also means that the price was $I(1)$.\n",
"\n",
"Let's also check the multiplicative returns."
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p-value = 0.0 The series AAPL Multiplicative Returns is likely stationary.\n"
]
},
{
"data": {
"image/png": 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IvggJyrAV7awVW+LuaPy6fmeYEghlv9VD37zrAGu372XkRz+HRfTt3l/C+S9M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\nqlAURVEUT/h/2POBvkTNi9gAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xcd872e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X1 = X.pct_change()[1:]\n",
"X1.name = X.name + ' Multiplicative Returns'\n",
"check_for_stationarity(X1)\n",
"plt.plot(X1.index, X1.values)\n",
"plt.ylabel('Multiplicative Returns')\n",
"plt.legend([X1.name])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Seems like the multiplicative returns are also stationary. Both the multiplicative and additive deltas on a series get at similar pieces of information, so it's not surprising both are stationary. In practice this might not always be the case.\n",
"\n",
"### IMPORTANT NOTE\n",
"\n",
"As always, you should not naively assume that because a time series is stationary in the past it will continue to be stationary in the future. Tests for consistency of stationarity such as cross validation and out of sample testing are necessary. This is true of any statistical property, we just reiterate it here. Returns may also go in and out of stationarity, and may be stationary or non-stationary depending on the timeframe and sampling frequency.\n",
"\n",
"\n",
"\n",
"### Note: Returns Analysis\n",
"\n",
"The reason returns are usually used for modeling in quantitive finance is that they are far more stationary than prices. This makes them easier to model and returns forecasting more feasible. Forecasting prices is more difficult, as there are many trends induced by their $I(1)$ integration. Even using a returns forecasting model to forecast price can be tricky, as any error in the returns forecast will be magnified over time."
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"## Order of Integration\n",
"\n",
"### Moving Average Representation\n",
"\n",
"An important concept in time series analysis is moving average representation. We will discuss this briefly here, but a more complete explanation is available in the [AR, MA](https://github.com/Auquan/Tutorials/blob/master/Time%20Series%20Analysis%20-%202.ipynb) and [ARMA Models](https://github.com/Auquan/Tutorials/blob/master/Time%20Series%20Analysis%20-%203.ipynb) sheets. Also check Wikipedia as listed below.\n",
"\n",
"This representation expresses any time series $Y_t$ as \n",
"\n",
"$$Y_t = \\sum_{j=0}^\\infty b_j \\epsilon_{t-j} + \\eta_t$$\n",
"\n",
"* $\\epsilon$ is the residuals or errors - a stochastic white noise process\n",
"* $b_j$ are the moving average weights of residuals\n",
"* $\\eta$ is a deterministic series\n",
"\n",
"$\\eta$ is deterministic (such as a sine wave),something we could perfectly model it. The difference between predictions from this model ($\\eta$) and actual observations leads to residuals($\\epsilon$). The residuals are stochastic and there to simulate new information occuring over time. \n",
"\n",
"Specifically, $\\epsilon_t = \\hat Y_t - Y_t$ where $\\hat Y_t$ is the in the optimal forecast of $Y_t$(actual observed value) using only information from time before $t$. In other words, the best prediction you can make at time $t-1$ cannot account for the randomness in $\\epsilon$.\n",
"\n",
"Each $b_j$ just says how much previous values of $\\epsilon$ influence $Y_t$.\n",
"\n",
"\n",
"### Back to Order of Integration\n",
"\n",
"We will note integration order-i as $I(i)$.\n",
"\n",
"A time series is said to be $I(0)$ if the following condition holds in a moving average representation. In simpler terms, the autocorrelation of the series decays to 0 sufficiently quickly.\n",
"\n",
"$$\\sum_{k=0}^\\infty |b_k|^2 < \\infty$$\n",
"\n",
"This property turns out to be true of all stationary series since autocorrelation is 0, but by itself is not enough for stationarity to hold. This means that stationarity implies $I(0)$, but $I(0)$ does not imply stationarity. For more on orders of integration, please see the following links.\n",
"\n",
"https://en.wikipedia.org/wiki/Order_of_integration\n",
"\n",
"https://en.wikipedia.org/wiki/Wold%27s_theorem\n",
"\n",
"### Testing for $I(0)$\n",
"\n",
"In practice testing whether the sum of the autocorrelations is finite may not be possible. It is possible in a mathematical derivation, but when we have a finite set of data and a finite number of estimated autocorrelations, the sum will always be finite. Given this difficulty, tests for $I(0)$ rely on stationarity implying the property. If we find that a series is stationary, then it must also be $I(0)$.\n",
"\n",
"Let's take our original stationary series A. Because A is stationary, we know it's also $I(0)$."
]
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AE/LDAgKvMNo0UAAAzNabO57y51lJ40+ToO58f3nfRoZw/PUPXsLr/t8fYrbL3XOzgNBh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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xe7f94e0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(A)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Value')\n",
"plt.legend(['Series A'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Building Up Orders of Integration\n",
"\n",
"If one takes an $I(0)$ series and cumulatively sums it (discrete integration), the new series will be $I(1)$. Notice how this is related to the calculus concept of integration. The same relation applies in general, to get $I(n)$ take an $I(0)$ series and iteratively take the cumulative sum $n$ times.\n",
"\n",
"Now let's make an $I(1)$ series by taking the cumulative sum of A."
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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0Gf7rHwfZ8EkhNy+bwo/Xzu5+bW5iKDNig8mrbCQqyLe7i01NTrE99j//4nL7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\nkzXN/OnWpXhZziyVHhPsR4ifN/lV9h3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"text/plain": [
"<matplotlib.figure.Figure at 0xe7f9470>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"A1 = np.cumsum(A)\n",
"\n",
"plt.plot(A1)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Value')\n",
"plt.legend(['Series A1'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Once all the math has settled, remember that any stationary series is $I(0)$**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Cointegration\n",
"\n",
"Finally, now that we've discussed stationarity and order of integration, we can discuss cointegration.\n",
"\n",
"A linear combination of the time series ($X_1$, $X_2$, $\\dots$, $X_k$) is a new time series $Y$ constructed as follows for any set of real numbers $b_1 \\dots b_k$\n",
"\n",
"$$Y = b_1X_1 + b_2X_2 + \\dots + b_kX_k$$\n",
"\n",
"For some set of time series ($X_1$, $X_2$, $\\dots$, $X_k$), if all series are $I(1)$, and some linear combination of them is $I(0)$, we say the set of time series is cointegrated.\n",
"\n",
"For example, $X_1$, $X_2$, and $X_3$ are all $I(1)$, and $2X_1 + X_2 + 0X_3 = 2X_1 + X_2$ is $I(0)$. In this case the time series are cointegrated.\n",
"\n",
"#### Intuition\n",
"\n",
"The intuition here is that for some linear combination of the series, the result lacks much auto-covariance and is mostly noise. This is useful for cases such as pairs trading, in which we find two assets whose prices are cointegrated. Since the linear combination of their prices $b_1A_1 + b_2A_2$ is noise, we can bet on the relationship $b_1A_1 + b_2A_2$ mean reverting and place trades accordingly. See the Pairs Trading notebook for more information."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's make some data to demonstrate this."
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Length of series\n",
"N = 100\n",
"\n",
"# Generate a stationary random X1\n",
"X1 = np.random.normal(0, 1, N)\n",
"# Integrate it to make it I(1)\n",
"X1 = np.cumsum(X1)\n",
"X1 = pd.Series(X1)\n",
"X1.name = 'X1'\n",
"\n",
"# Make an X2 that is X1 plus some noise\n",
"X2 = X1 + np.random.normal(0, 1, N)\n",
"X2.name = 'X2'"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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fFmKInNzEg7llY3/DG1aVs6WxmC9uP8agP5zy2mM9Pi4v0nbdRfXKSihqAGRG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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xd1e44a8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X1)\n",
"plt.plot(X2)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Series Value')\n",
"plt.legend([X1.name, X2.name])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Because $X_2$ is just an $I(1)$ series plus some stationary noise, it should still be $I(1)$. Let's check this."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p-value = 1.03652371022e-20 The series Z is likely stationary.\n"
]
}
],
"source": [
"Z = X2.diff()[1:]\n",
"Z.name = 'Z'\n",
"\n",
"check_for_stationarity(Z);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looks good. Now to show cointegration we'll need to find some linear combination of $X_1$ and $X_2$ that is stationary. We can take $X_2-X_1$. All that's left over should be stationary noise by design. Let's check this."
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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157Sxpfxzybb21QgCcgwt22rVAHLsm2Z1Y/RBKzM9jVvPGBP1/l3N9+eRn2SZ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\ntu+vJzsjjb4F3pt0eprwzePKAHj8qiO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"text/plain": [
"<matplotlib.figure.Figure at 0xd4bd0f0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"p-value = 0.771138236834 The series Z is likely non-stationary.\n"
]
}
],
"source": [
"Z = X2 - X1\n",
"Z.name = 'Z'\n",
"\n",
"plt.plot(Z)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Series Value')\n",
"plt.legend(['Z'])\n",
"plt.show()\n",
"\n",
"check_for_stationarity(Z);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Testing for Cointegration\n",
"\n",
"There are a bunch of ways to test for cointegration. This [wikipedia article](https://en.wikipedia.org/wiki/Cointegration) describes some. In general we're just trying to solve for the coefficients $b_1, \\dots b_k$ that will produce an $I(0)$ linear combination. If our best guess for these coefficients does not pass a stationarity check, then we reject the hypothesis that the set is cointegrated. This will lead to risk of Type II errors (false negatives), as we will not exhaustively test for stationarity on all coefficent combinations. However Type II errors are generally okay here, as they are safe and do not lead to us making any wrong forecasts.\n",
"\n",
"In practice a common way to do this for pairs of time series is to use linear regression to estimate $\\beta$ in the following model.\n",
"\n",
"$$X_2 = \\alpha + \\beta X_1 + \\epsilon$$\n",
"\n",
"The idea is that if the two are cointegrated we can remove $X_2$'s depedency on $X_1$, leaving behind stationary noise. The combination $X_2 - \\beta X_1 = \\alpha + \\epsilon$ should be stationary."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's try on some real data. We'll get prices and plot them first."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reading MSFT\n",
"Reading ADBE\n"
]
}
],
"source": [
"end = '2017-01-01'\n",
"start = '2011-01-01'\n",
"symbols = ['MSFT','ADBE']\n",
"data = dl.load_data_nologs('nasdaq', symbols , start, end)['ADJ CLOSE']"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"X1 = data['MSFT']\n",
"X2 = data['ADBE']"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Weh0mcF+JUUrVUUrNUEptUUptVkqdoZSKVkrNV0ptt5Vl9LokCOVETqYRBs7Y\nj7UVMo4U30HNvg3U/erSK6ft2LesZAVR6Tmans1ZLy6ixURjjrwzJR2AYZ0a0qu5/0Ok+CIgwrXW\n/7q1eQlGXyz+B8zVWrcHugGbgYnAAq11G2CB7VgQqg7zHofPx0Dyekebs1Pcif1Qp1nJrp1XhhYr\n9i2mXuPK7ppCmZCVk8ddX69i5R5jmNDv+QXsTcvI7+/fuoxWkT7ii5I6VSnVCtAASqlLgYMlvaFS\nqjZwFjAOQGudDWQrpcYAg2zDPgMWAw+X9D6CUO7YM7Md22t8FYLCjM9BTgbUjYdThwu3HLrwPfjh\ndhOpNe80rPjY0eecEa60BIXBE2ne05YKFcqG/ceZve4gianpjOzSiNO5roYE/VvHlOt8fBEQdwFT\ngPZKqf3AbuCaUtwzHkgBPlFKdQNWAvdidBx2wZMMeM14opS6FbgVoFmzEr6NCYI/sAfQ2zATvrkK\nYto5fBhyMk2ob/cwG850v9J8wHhPx7aHOQ+Z42FlrPIL8JKyVKhwdqeaLaSNB06w8cAJwKwa/txx\nBICGUaHlOp8iXyG01ru01kOBWKC91nqA1jqxFPcMBHoC72qte2DyTLhsJ2mtNbYVi5f5TNFaJ2it\nE2JjJU22UImwWxltmGnK1K2OvlO2XA6+KqkDLA6z1rYjJCR3DWHPkQyPth5NHerYi3vGled0Cl5B\nKKWu0Vp/qZS6360dAK11ScNt7AP2aa3/sR3PwAiIQ0qpRlrrgzbHvMMlvL4gVAzOZqgJN8GKjzzH\nBBRjqygj1ZR2qyOh2nM8M4daIYGcOu1Q89YOC+LOQa1oFl2KKL4lpLAVhN1gO7KAT4nQWicDSUqp\ndramIcAm4Cfgelvb9cCPJb2HIFQIzg5w7Uc66i0HO+oniuH9Gn+WKXteW7p5CVWG7FwrESGu239R\nYYE8NLw9Y/uU/5Z6gSsIrfX7SikLcEJr/VoZ3/ce4CulVDCwC7gBI6ymK6VuAvZgQnsIQuVFa7Dm\nOhTI2mlXtHFPUw55Es4cb6Kzpu2CRsUIhtygE0wqID+EUKXQWpOdZyUpLYPJc7bw5OhONLWtCA4c\nyyRAKQ4ez+Tk6RyCAwP47MY+XP+xMR49mVVao9GSU6iSWmudp5S6EihTAaG1XgN4y74+pCzvIwh+\nZcaNsPE7mJhkfBTsPgsx7YzO4D8HjcWQUjB+NZw8BLXqV+ychXJHa038I7+4tP22+TDf3NqPxNR0\nJn633qVTSH9pAAAgAElEQVQvJDCAs9vGMnfCQIa/voSz21acrtUXK6Y/lVJvAdMwCmUAtNar/DYr\nQagKbPzOlJObGt+CjmPM8S0LTemukI70apgnVHP+2nnEa/vYKcu8tttNW9s3jCJx8vl+m5cv+CIg\nutvKp53aNHBO2U9HEKoQHS+ETT+Y+smD8M97pl6WPgtClcceVO+dq3sSUyuEhlGhPPDtGpYnHvU6\nvneLyhNEwpdgfYOLGiMINZIjOx31oAjj5wDigCYAZmvplXnbeGvRDgBGdG6YbwXawMmfoVVsBB9c\nl8Dhk6c5lpHD8M4NvV6vIvAlo1wDpdRHSqk5tuOONkWyINRcDm+BQ057x427O+oiIKodVqtmx+Hi\nxa7aeOBEvnBoUicsXzgADLB5RNePDGHBA4NoGVuLfi3rVSrhAL7FYvoUkw/Cboy9DZjgrwkJQqUn\nOx3e6Wvqgx+FB7dDklO4MhEQlZI56w/yx7aUEp372d+JDH31D9YmHfP5nGnLk/Lrv9w70KXvit5N\n2fz0cP59tHIn5/Tlf3KM1no6YAXQWucC5ZMQVRAqI6+0d9Qb9zSWSWO/crQ5vSkKFYfWmu2HTrJo\n62HeXbyTO75axXUfu8cdLZw9R9LZdugkn/+9B4Bvlu/1+dxsm7J541PnUTvMVS+llCIsuPKHO/FF\nSZ2ulKqHI1hfP0CMs4WaydE9cPqE49juHNf2vIqZj1Agq/Ye45J3/yrVNcZ9sjw/PhLAku2pPp8b\nExmMJUAREeLLz2zlxJcVxP0YL+dWSqk/gc8xjm6CUPNY6hZhxnm10FkSLVYm3rbt/7tjD6W9/1gm\nP67Z73XM+n3H2Zp80kU4AAzv5LuOIDdPE2Sp2qtJX6yYVimlzgbaAQrYqrUuw+D0glCFsOdlCAg0\nXtTO3tMXTYHRb1TMvAQA/tqRSp/4aAItASzc4hrOrVHtUA4ez+KSd/8mcfL5vDh3Cz+uOUBc3TCP\n5Duj31rq9fq5Vq8xRD3QWvP+H7tK9hCViAJXEEqp3kqphpCvd+gFPAu8opSS0JJC9UdrSNvtOD66\nx+SIBrj8C1AWqN/B0W8JhJBC8j0IfmXlnjSu+vAfnvp5E//5fr1H//ldTKKk6AiTqjPcpgNYvddV\n8Zyb55qDoWtcbUZ0bkhYkIU8HwXE3A3JxZ5/ZaSwFcT7wFAApdRZwGTM1lJ3TH6IS/0+O0GoSFZ+\nArPuM8l+wurAgdWmffBjJhjfk2kVOz8hn4dnrGPaCmM19MWyPV7HXNW3GYlH0tl/LAuA0CAjIJwj\np4LZenLmiVEdSWgRTZ9nf/NYQew4fIpv/t3LwyPaE2RxvG+v3Vc91LSFCQiL1tr+F3AFMEVrPROY\nqZRa4/+pCUIFs32+KY/uBmen11YSRKCyYRcOzrRvGMmPd/cnK8eab0UUEmQh9dRpktIy8ncH020C\nIjM7j7cX7cj3Xbj97FZ0bBxFr+bGszkwQJFndV1dTJi2mg37TzC0YwP6tXSkA92abAwZXr+iO1WZ\nwpTUFqWUXYAMARY69VVdtbwg+EprL7EjIxtBo27lPxehQLT2vu0zd8JZhARaXExMQwMtpJw8zcAX\nF5Ft20o6dTqP/87aRIcn5uYLB4CJI9pzQbfG+Q5uFosiN89xr9RTp9mw3wiCsVOWcTo3j7VJx0g+\nnsWirSnc0L8FF/ZoUubPW54U9kM/FfhdKZUKZAJLAJRSrREzV6EmEBjm2Xbhu0bXIFQajmZ42sx0\nb1rH69jkE47to6//MT4N6adzmfpv0f4NSWmZJKXt59mLupBjtfLi3C0u/f+dtZkvlu3hmn4mb8PA\nNuWbP9ofFJYP4lml1AKgETBPO8R0AGLmKtQEtM0f9Lof4XNbpFbnpEBCpSAj26FD+PKmvuxNy+Di\nnt7f3FvH1srP72zngJvOAeCsQkJs70lLZ/jrS/KP7zmnNW8u3JGv+/hymRE2sbXKN3+0PyjUD0Jr\nvUxr/b3W2jnM9zYJ9S3UCKy2H56Ydo7VhAiISoddLfDyZd0Y0CaGq/o2y1dAu/PYqI4ebYdPnvZo\n6x5X26Pto+tNCpsl21yd5a47owUxtYJd2lrGRtC5SZRP86/MSNAYQSgIq20FERDocIgLKv+8wELh\n5Nk2NwIDinZKC7IEcMvAeJe2vWkZLsfBlgCu6tvc49yOjc0P/rO/bHZpjwwN9Aib8dH1vV2C81VV\nREAIQkHkCwgLnP2QqUdUXHYvwTt2y6IAHwQEwPDOjfLrl/WKy6///cg5rJs0jK3/HU7D2p7bQ/Uj\nvW8ZhQZZcDNuok5Y9cgJIto2oWZitZoUoYUpnLWTgBhwH5xxjyioKyF2vzZfVhAAvZrXZVC7WHLz\nNPVqhQBQOyyIRrW9GCU4YXG7/pZnhnMiyyjIX7ikK+O/WU1aejYAUSIgBKEKM+1q2PoLhNcz+aJD\n3facM9Lg1/+YeoDtz0SEQ6Uk1/b67v4DXhif3tAHgF/WHwTgeKZv0YN+nXAW8zclc/PAloQGWfJ1\nHQPaxLDq8XNpMXF2sedSmZH/8ULNZKstiXzGEXjnDOhzC5w53qwWABY95xgbWPWtUaoz9u0dSwn2\n/O2mqE3qFL56sNOuYSTtGkYW+z5VFREQQvXDaoWAQtRrOVmuxyf2w2+TzOfJY0Yhbd9eOv9Vh9AQ\nKiX5K4gSRE6NDA3i1wln0ahO2bwEfHpDb1JPZZfJtSoDoqQWqhf/TIGn68LpUwWPeau3KdsO94y+\nemCVCcq34mOTZ7p3zciuu37fcTYdOFH0wBLw/C+bCwy9XRZYbVZMJVlBgFkVRIWWjc5gULv6XOqk\n+K7qyApCqF6sn27KbXOhi5d4knm5cNzmNTvsvxDTBnpcC7sWwZcXw5GdcHCd6T/jzvKZcyXgsvf/\nIivHysIHzmb/sUxa169VpNLWV+xhr3PyrPy+LYXv7+xfJte1k5FtVnvVZd+/MiECQqhexLSFfctN\ngD139q+CDwabevxZRjiA2Y5q0svUf7gTrDaFZY9r/D/fSsC05XvJyjHbNOe88nt++6rHz+XdxTt4\nYFi7Ah3PisLqFP309d+2A7Byz1FaxkRQNyK4oNMAOHwyi5iIEA6fPO3V7DQ3z8q7i3fyyvxtACWe\no1AwIiCEqo81z7z5R8RArs0rNsNLKG67cACTz8EZuxWT1cmaJbIRNYGXft3mtf2thTv4+M/dNKkT\nxrj+8V7HFIV70h4gPw3o2ieHeeRqzrNqPl66m57N63DJu3/nt8+84wyPpD4LtxzOFw4AUaHyc1bW\nyDcqVH3mPQ7L3nZtW/YORLc01kngmvmtfkeT38EZ5/1rZYH/2wGBIf6ZbwWgteZ0rtXjLdtq1WRk\n53LTgHj+2JbC9sMO3c3nfycC8M3yJL5fc4BHRrSnb3x0sTyEU095hrGw8/wvm7mhfzyBFkWrWJNo\n6d3FO3h5nqfA2nc0k15uzs27nNKBThjahjYNao51UXkhSmqh6rN2qvf2Xx40OocDq+G0kwK2+1Xe\nx494yXhKP7QLwqtP0kStNe8s3kn7x+dy6ISrBde/iWlkZOfRpUltPr2xD31aRPPiJV0Bk14zPNjC\nluSTrE06xnUf/Uuf5xbwzKxNPt/bPcHOa1c4QqV/szyJ817/gyGv/J6fqe2NBd6V2XY9gzOr9hwl\nKjSQZy7szL1D2vg8J8F3REAIVZu/3oRMp+2kdue7xkta8yVMGQSTmznawup6v1bfW+HB7Z6riyrO\nxJnreenXrQD0fW4Bv6w/yNokk2bz3cU7CVAwrFMDmtQJY/rtZzCsU4P8c+1v9gDZeVZSTp7mo6Ve\n9DsF4J6i86Iecfx0d39GdXXdvpu5cl/+PewM7dAg30/B7qFsR2vN6qRjDOnQgGv7Na8WcY8qIyIg\nhKpL+hGY95ip97gGJh2HK792zfi2Y4HnedkZnm12qtkPTVZOnke2tTu/WsWYt//kaHo2v29Lwaoh\nPNix21wnPJh7zmkNUOqIpPYVxBtX9uCdq3sC0DWuDhOGtnUZ9+lfiWxNPunSltCiLl/c1JfAAJWf\n9c3OiaxcUk6epkMj2VbyJyIghKqJ1jDvUcdx+1GO+oXvQuuhpr75J89zO13o37lVIhZs9lQS27n1\nixUF9tnfyGNrhTCic8MS398eSO+c9vUZ2cWxamhdvxbf3XkmF/dsQqvYCJKOZvDb5kMA+bkczmpj\nAiMGWQLIyXONhpdiC9FdUAA9oWwQJbVQNdn4vUP3cNW30HaYoy80Cq6ZCW/0gLRdruc9tLta6RcK\nYvqKJL5atoe1+0zyxx3PjuDg8Sxu+HQ5O2yKaHsmtp/vHuBxvn0dFR0RzNNjOtMgKpTP/k6ka1wd\nNuz3PaFkYYH0ejarS89mdfnm371M/M5sgzWpE8arl3fn1csduZyDAwNIS88hO9fKkfTTDH55MbGR\nxoDAXgr+QQSEUDWZcYOj7iwcnKnVwAiIsGho2AXqd6i2wkFrjdaOkNcPzVjn0h9oCaBpdDi/3X82\n7R+fQ0RwIDsOn6JlTARdvCTHueWsluTkWbmybzNCAi1MuqATky7oxOu/bWNt0jHyrBpLgGJXyimS\njmZydgEZ2PJ8CKTXzSk96NntPK9jCVDMXLWPmav25bclpZkscCIg/IsICKHqkeOUIvL/dhU87pKP\njMNcC8835OrE4ZNZXPjWnxw4nsXu50eybJdDaR8ebOEFm1WSnfM6NWT2OhPF1NlU1JlaIYE8NLy9\nR3uQxexK5+RZ2Z2aydBXjWPdtf2a88yFnT3G23UQhYXBaN8wkjeu7EHj2qG0b+Sp88h1215ypr4I\nCL9SYQJCKWUBVgD7tdajlFLRwDSgBZAIXK61PlpR8xMqKR8Ng6R/TD0oHCLqFTy2dhPzqeb8tukw\nB44b89VfNyazO9Uo4ddPGkaklxhD4cGW/B/uS3oWL25QsE1ApJ46nS8cAL78Z49XAZFn1ShVeDIf\npRQXdGtcaL87H12fwOaDJ6gTXrg3tlA6KlJJfS/gnLtvIrBAa90GWGA7FgRX7MIBIKcQa6QaxNEM\nhwnoj2sOsDX5BI1qh3oVDoDLdtAToz1zNBdGkC1i6p4j5rs/v0sjru3XHK3hqZ83cs2H//D6bw5H\ntzcX7nDxUSwJ7vme//3PEIZ0aMDd54jvg7+pEAGhlIoDzgc+dGoeA3xmq38G1BxTE8F3GnWH1udC\n3RbGI1rgRGYOwYEBXN23GXM2JPPDmgN09LJVY8c55aZ7qIuiCAo0Pxnf2kxnx/VvweD2RuB88mci\nS3ek5sdc2njAd2V2YTSIclgqvXp5N+pHieVSeVFRW0yvAw8BzkbMDbTWB231ZKCBx1lCzSY7HQ5v\nht5nwlXTQImVNsCJrBxqhwXRvJ7DQfBiH7aOIksQu8iug/hhzQHAmMG2d0ugUyskkOxcK+e/sRSA\nZ8Z0KvZ9nImp5dAzDC+Fya1QfMr9L0wpNQo4rLVeWdAYrbUGvC5MlVK3KqVWKKVWpKSk+GuaQmVk\n0XOQdxpaDTFJfKqZU1txOHAskyGvLGbD/uMs2HyYOmFBXNuvBee0r8+EoW04v2vhgQY3PHUeyx4Z\nUuz7rtrjUAue16kBLWIiiAwN4q7BrfLbFXDOK4vzjzs18bSSKg52ofTCJV1cHPoE/1MR33Z/4AKl\n1EggFIhSSn0JHFJKNdJaH1RKNQK8evhoracAUwASEhJKubspVHqy0+HT86FpP/jnXdMW07pi51SB\nHMvIJj07j/6TFwIw6k3zlj6gdQxhwRY+Htfbp+vUCinZn75d9wDwv7E98uunsoync1zdMPYdzeSk\nzfP57at60rNZAaFNfMS+0gmowS8EFUW5ryC01o9oreO01i2AscBCrfU1wE/A9bZh1wM/lvfchEpA\nylb44mI4vh9Sd8C340ywPbtwAKN/qGbk5Fn5YfV+snI8g9LZOZ6RQ/en5+cLBzt1w4OYVMptHF+Z\nMNShGHaODHvfuW15cFhbZt5xZn7bZzf2KXIl4wsPDGvLHYNaMaZ79bdIq2xUpvXaZGC6UuomYA9w\neQXPRygvck/D329B7Wbw3c2m7bWapYD+fWsKE6atYXxKa+4f1o5Tp3NJSsugg03ZnJWTR7en5+WP\nv6RnHK9c3q2gy/mNzrbtoviYCJf2OuHB+VZFNw2I56Olu+layq0lO5GhQTzsxSdD8D9Kl9YGrQJJ\nSEjQK1YUHE9GqCLMuh9WfFT4mAnrYfp10Oli6D++fOZVTmzYfzx/q8gSoHj/ml58sWwPv29L4e2r\nenLX16s8zplx+xkktKgYr/DZ6w7Sr2U09Wp5d1LTWpOVYyUsWDK8VVaUUiu11glFjhMBIVQ4k9ze\nNG+aD/9Ogd63wJHt0HUsWCrTYrdsaTFxts9jOzaK4vOb+rhY9ghCcfFVQFTfvzqhalG/IxzeBHWa\nQ9M+5gPQrG/FzsvPnM4tWOfgztc39+XM1jF+nI0guCKG5ELFYl/BdhgNl38O43x/m64OLNmWml/v\n7hS07sb+8YTbtmgu7N6YxMnni3AQyh1ZQZSW9TPAmgfdrqjomVRN9toS06fthsH/qdi5lILvVu3j\nxzUHeO2K7kRHFB0fKDfPyso9Rwm2eSa/eElXLujemKXbU9mRcorbzmrJxT2b8Or8bTx/cdciriYI\n/kEEhDtZx41D1tkPwz/vQ4dRJlR0Qcy8yZQ56ZBwY/nMsbqQeQw+GWHqu/+o2LmUgjyr5v7pawF4\n9Pv1vHtNr0LHbzt0kmGvuT5vx8ZRhAZZGNqxAUNtQQQ6N6nts1+DIPgDERDu/P0O/PMebJ4FJ/bB\n75NNKsuimHUf9BwHAVVg185qhaxjFZ8bYeN3jvodf1XcPErAmqRj/O+3bfSOjybMyR9gZ8opr+M3\nHjjOloMnGdGlYb7FkjNN6oT5ba6CUFJEQNj3wO1emnkmlSEnHMlJOLYXajeFX/8Dy96BdufD2K9A\nu8Wpf7qu2UfvOMb/8y4J+1fCD3dCyhZz/GgyBPnhh2nFxybv85l3u7bvWABrvoIx70BQKKz52rQ/\nsK3wsN2VkAvf/hOARVtdw71k51qZve4gT8/ayLMXdmFoR7MaGP3mUqwavl+9n+xc8/+mQ6MozmhZ\nj74to6nrw7aUIJQ3IiBm329+0PreDiNegIw0zzEbf4DoeCMcALbOht9fNPGA3Jl+nW8rjvJmz9/w\nyXDXtiM7ICAIYtqWfEWRl2O+l1ZDoKEtH8Cs+0zpLCA2zIQZti24VudA96sheT10uRwiq15cxmBL\nANlOiWxuHhBPQIBiyh+78v0Wbv58BR+PS+Cf3WnY0i+wdEcqY7o35pXLuhFoqQKrTaFGU7MFROJS\nIxzAbCv9855rf7uRsH+VscXPPe3at/g5R/26HyHpX1j0LER4T71YYRzbCx+PcF0R2XnPnmlNARrG\nr4bolsW7/l9vwoKnYP4TRjDmOnITkHUcQmub/NEznPQzuVlGOZ2b5TBnrWKM7NKQH9YcICzIQnxM\nBI+N6siPa/bn99eLCOZIejY3furppzPuzBYiHIQqQc3+X/r7i97bO4w25aWfmB+44/vg5EGTwWzS\ncYhu5Tq+eX84+yFoOxzSUyDrhH/n7SvZ6WZF4y4cul3lNtD2epu63fs1vK2q7Bza6Ho8/wlHfft8\ns8L4dpw57nwJoODEQYdyuk7zIh7CP2itWbz1MHnWkjmKHs/MoXOTKNZPGsZPd/cHYHTXxvn6iG9v\nP6PAc3uUMnidIJQXNVtA2PUOfe9wagswuYz/b6fZJw+rAzsXmlAQkbZY9Hf8Bb1uMPWwaLDYkq7Y\nE9gseaV85l8YKz+F5xqbQHd2mp0JfW6DkS+ZbR53vh1nftCdeas3vBhv8jBsnuXat+t32DDD1INr\nma0l56B6M2+C318w9cjGcMGbZqtuycuOMfEDS/qEPpOVk8cxp6xrAC/P28q4T5bz89oDxbrW8cwc\nrpyyjEVbU2hUO4xAS0D+aiAgQLHp6fPY9dxIWsbWcjmvZ7M6dG4SxQPnti3dwwhCOVJzBUTKNti1\nGFoOhr63mbZRr8OTRyEwBCJsTkkWJ+Vh+1GmDAqF0a/Do4fg/k2O/oEPmPLfKUYhrDXs+QtOeY1c\n7j+yM+Dnez3b67aAkS9CSC0Y8qTn23tOBjwTY6KpJv0LR3bCCdu2yTv9YNrVkH7EHOdmw8ybne55\nyrFd58wfL5lyzFsQHGHua+eBbf5Rkjux4/Ap2j8+l+5Pz2ffUUeo6k//TARcw1f7wvTlSfy9y3wH\nV/dt5tGvlMrPvzz5YmMePbBNDN/d2Z9Z9wzkniGSJlOoOtRcHYT9zTf+LPNW+8g+CIn0HJfn9OZ5\nzuOufUFuqQ9DbG+NORnwwTlw1kPwx4sQ2wHuWlZ2cy+KX50czi56HwICzdu886qhcXeYsM7oVpLX\nmx/4z23WVzsXmI83Fj8Pyz9wbet+tbFOsjP2a4g/G/b9C19cZNqa9TNl+1HQ7y7ofZNfldOr9h7l\n5s9WkJbu+Pcb8MIivr39DHo2q0t6tgl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rXw/8WN5zEwRBEBxUxBZTf+BaYL1Syh6p7T/A\nZGC6UuomYA9weQXMTRAEQbBR7gJCa70UKMgxYEh5zkUQBEEoGMnPKAiCIHhFBIQgCILgFREQgiAI\ngldEQAiCIAheqfBQG6VBKZWCsXgqKTFAahlNp6KpLs9SXZ4D5FkqI9XlOaB0z9Jca12kI1mVFhCl\nRSm1whd386pAdXmW6vIcIM9SGakuzwHl8yyyxSQIgiB4RQSEIAiC4JWaLiCmVPQEypDq8izV5TlA\nnqUyUl2eA8rhWWq0DkIQBEEomJq+ghAEQRAKoFoJiOLmu1ZK1bONP6WUesvtWs8qpZKUUqeq8rMo\npcKVUrOVUlts15lcFZ/D1jdXKbXWdp33lFKWqvosTtf8SSm1oTyfw3bfsvx3WayU2qqUWmP71K+i\nzxGslJqilNpm+3u5pLyeoyyfRSkV6fRvsUYplaqUer1Ek9JaV5sP0AjoaatHAtuAjsCLwERb+0Tg\nBVs9AhgA3A685XatfrbrnarKzwKEA4Nt9WBgCTDi/9u7mxc5qiiMw783dnCRIYpGRkV0IDBoXERD\nDH6gjF8IfiDowpEguNCl4j8gRJKFiCLRhSBu3CgSRYIrg4EoougQkUmMxuAQUFEQ3USCLpzj4t4h\nxVCTnum+1TXVvA80Xd3VXX1O3646U1V36nYtjzxvc74XaTyR2S62SWV5jwDvAMe7+vvK844AO0ed\nQwN5vADsy9MbgC1dzWXZco8CdwwUUxuNOsIv/CBwL3ASuKLSCCeXve7Jlb5gWioQTeSS5+8Hnu5y\nHsBG4CPgsa62CTABfJ43ACMvEIVzaa1AFM7jZ2BT2zmUyKUybzrnpUFiGKtDTFVK413fCHwFTEbE\nb3nW78BkS2ENpFQuki4GHgIOFw5xtZ8/xZB5SPqYNNrgGeD98lGuToFc9gKvAGebiG8tCv2+3s6H\nM56XtNLl/Bs1TB553QDYK+kbSQcktbadKLj9mgXei1wt1mosC4SWjXddnZe/qM503SqVi6Qe8C7w\nWkQsFA+0/+cXySMi7iP9FXUhcFfpOFdj2Fwk3QBsjYgPm4tydQq1y+6IuB64Pd+eKB5oHwXy6AFX\nAV9ExA7gS+DlJmLtp/D2a5a03g9k7AqEhhjver0pnMubwKmIGOxk1RBKt0lE/EPa/X64dKz9FMrl\nFmCnpNOkw0zTko40E/HKSrVLRPya78+QzqnsaibieoXy+JO0N7f0/gPAjgbCPa+S64qk7UAvIo4O\nGs9YFYi8azsW412XzEXSPuAi4LnSca7is4vkIWmispL0gAeAH8pHfN4YiuQSEW9ExJURMUU6yfhj\nRMyUj3hlBdulJ2lLnt4IPAiMrFdWwTYJ0nmtmfzU3cCJosH20cD263GG2HsAxuskNWllC2Ae+Dbf\n7gcuJR13PwV8AlxSec9p4C/gb+AXYFt+/qX8eDHf7+liLqTd5gC+ryznqQ7mMQnM5eUcB14n/XXU\nuTZZtswp2unFVKpdNpF6ycwD35E6QVzQtTzy89cAn+VlHQau7mKbVOYtANcOE5P/k9rMzGqN1SEm\nMzMrxwXCzMxquUCYmVktFwgzM6vlAmFmZrV6bQdg1gWSlroaAlwO/Af8kR+fjYhbWwnMrEHu5mq2\nRpL2kC7i2MqlGMxGxYeYzIakPGaIpBlJn0o6KGlB0ouSdkv6WtIxSVvz6y6T9IGkuXy7rd0MzOq5\nQJiVtZ10ff7rSBetm46IXcBbwDP5NfuBVyPiJuDRPM9s3fE5CLOy5iJfmlnST8Ch/Pwx4M48fQ+w\nrXJV7M2SJiKildELzVbiAmFW1r+V6cXK40XOrW8bgJsjXZXWbN3yISaz0TvEucNNS+NDmK07LhBm\no/csaTyIeUknSOcszNYdd3M1M7Na3oMwM7NaLhBmZlbLBcLMzGq5QJiZWS0XCDMzq+UCYWZmtVwg\nzMyslguEmZnV+h8taZ5f0AiuMwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xcd870b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X1)\n",
"plt.plot(X2)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Series Value')\n",
"plt.legend([X1.name, X2.name])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now use linear regression to compute $\\beta$."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"const -17.414721\n",
"MSFT 2.114956\n",
"dtype: float64"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X1 = sm.add_constant(X1)\n",
"results = sm.OLS(X2, X1).fit()\n",
"\n",
"# Get rid of the constant column\n",
"X1 = X1['MSFT']\n",
"\n",
"results.params"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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f37F3Tk8b2WAQVID/gsKsUQxvqDL0P586PJyabTEEFR57ARHtAHA8gGeI6J8AwBhbBeAh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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xd249ac8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"p-value = 0.00484736194367 The series Z is likely stationary.\n"
]
}
],
"source": [
"b = results.params['MSFT']\n",
"Z = X2 - b * X1\n",
"Z.name = 'Z'\n",
"\n",
"plt.plot(Z.index, Z.values)\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Series Value')\n",
"plt.legend([Z.name])\n",
"plt.show()\n",
"\n",
"check_for_stationarity(Z);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see here that the resulting $Z$ was likely stationary over the time frame we looked at. This causes us to accept the hypothesis that our two assets were cointegrated over the same timeframe."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**This is only a forecast!**\n",
"\n",
"Remember as with anything else, you should not assume that because some set of assets have passed a cointegration test historically, they will continue to remain cointegrated. You need to verify that consistent behavior occurs, and use various model validation techniques as you would with any model.\n",
"\n",
"One of the most important things done in finance is to make many independent bets. Here a quant would find many pairs of assets they hypothesize are cointegrated, and evenly distribute their dollars between them in bets. This only requires more than half of the asset pairs to remain cointegrated for the strategy to work. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Luckily there are some pre-built tests for cointegration. Here's one. Read up on the [documentation](http://statsmodels.sourceforge.net/devel/_modules/statsmodels/tsa/stattools.html) on your own time."
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(-3.7855667724973134,\n",
" 0.014168263039705158,\n",
" array([-3.9037028 , -3.34017673, -3.04725807]))"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from statsmodels.tsa.stattools import coint\n",
"\n",
"coint(X1, X2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.13"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
@SeanLXP
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SeanLXP commented Oct 12, 2018

When I run the sample code, Why is the code reporting this error?

Traceback (most recent call last):
File "D:\Python\pytest.py", line 107, in
data = dl.load_data_nologs('nasdaq', symbols , start, end)['ADJ CLOSE']
File "C:\Python27\lib\site-packages\auquanToolbox\dataloader.py", line 166, in load_data_nologs
raise ValueError("%s or %s is not valid date. Please check settings!"%(start, end))
ValueError: 2007-01-01 or 2015-01-01 is not valid date. Please check settings!

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