Detecting Local as well as global anomalies in time series data using AnomalyDetection package by Twitter INC.

Anomaly_Detection_IN_R.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Anomaly Detection \n",
    "\n",
    "##### Using R programming\n",
    "### PSL AI LAB\n",
    "\n",
    "###### By Twitter Inc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The underlying algorithm – referred to as Seasonal Hybrid ESD (S-H-ESD) builds upon the Generalized ESD test for detecting anomalies. Note that S-H-ESD can be used to detect both global as well as local anomalies. This is achieved by employing time series decomposition and using robust statistical metrics, viz., median together with ESD. In addition, for long time series (say, 6 months of minutely data), the algorithm employs piecewise approximation - this is rooted to the fact that trend extraction in the presence of anomalies in non-trivial - for anomaly detection."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the Anomaly Detection Library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "library(AnomalyDetection)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function AnomalyDetectionTs is called to detect one or more statistically significant anomalies in the input time series. The documentation of the function AnomalyDetectionTs, which can be seen by using the following command, details the input arguments and the output of the function AnomalyDetectionTs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BQJKoBMgEiITBQJKoBMgEiITBQJKoBM\ngEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBM\ngEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBM\ngEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBM\ngEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBM\ngEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBM\ngEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBM\ngEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBM\ngEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBM\ngEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITBQJKoBMgEiITNFI+32mhinSXAFkAkRC\nZIpD2u/3PCItEUAmQCREpiikfflvpsYp0lwBZAJEQmSiSFABZAJEQmSiSFABZAJEQmSKQao8\nokgLBJAJEAmRKV4kkakJFGmuADIBIiEyxZ/aUaQFAsgEiITIRJGgAsgEiITIRJGgAsgEiITI\nFP9AliItEEAmQCREJr4iBBVAJkAkRKZ4JB6RFgggEyASIhNFggogEyASIhNFggogEyASIhNF\nggogEyASIhNFggogEyASIhNFggogEyASIhNFggogEyASIhNFggogEyASIhNFggogEyASIhNF\nggogEyASItOcIp1Ph/zw/NGMvubV1OfL1NO5ne0y18Ortlgmlwng3kBkAkRCZJpRpPMhL3Ko\nTfrIK5EeqqlqtmquU7tcJpcJ4N5AZAJEQmSaUaRT/nyW52P+VI0+VCK95se/8u9D/lvN9XQu\n/v2rlsvkMgHcG4hMgEiITDOKdCjFOdcHoqdDNfBcKvSqDkGH/FzO9ayWy+QyAdwbiEyASIhM\n899sqPz5kb9WA8dSnI/8aHws8we1QCaXCeDeQGQCREJkml2k3+Wxp/i3UqYRJ68/b45I5XhW\nZkD1KQHcG4hMgEiITLOLdDyci/sOR+kR6VSIdrmSytUSmV1ipgDuDUQmQCREprlFOuav5b8f\nPpGqe3sUqQogEyASItPMIlUenfKf0ieS/HjODydJkcoAMgEiITLNKtLH8VDe5c5VmpsNZ3Wz\nocrf5ia5pEhgAURCZJpTpNfDsXoYq4t0qm9/N7e7q5sNP7QnspldZ6YA7g1EJkAkRKYZRfpr\nHXX0B7LVKV+RU6HU7wc+kC0DyASIhMg0o0jP7WGoTD1QvRL00Ew58xUhLYBMgEiITDOKlLtF\n+iheWn0+qykfF+GOfGm1CiATIBIiE3+MAiqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqA\nTIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqA\nTIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqA\nTIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqA\nTIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqA\nTIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqA\nTIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqA\nTIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqA\nTIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqA\nTIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqA\nTIBIiEwUCSqATIBIiEwUCSqATIBIiEwUCSqATIBIiEyxSPs9RVoggEyASIhMUUj7/f7yT6bG\nKdJcAWQCREJkikHal//yiLRAAJkAkRCZKBJUAJkAkRCZKBJUAJkAkRCZIpAqjyjSEgFkAkRC\nZIoWSVCkBQLIBIiEyBR9akeRlgggEyASIhNFggogEyASIhNFggogEyASIlP0A1nBB7ILBJAJ\nEAmRia8IQQWQCRAJkSkaiad2SwSQCRAJkYkiQQWQCRAJkYkiQQWFab9XgyhIegCZKBJUIJiq\nl/0blyCQrAAyUSSoIDCVApUulaMISHYAmSgSVBCY9uYhCQHJDiATRYIKApO6PqoGEJDsADJR\nJKgAMO3lvh2UEEidADJRJKjE747ZECqRRDUoN95My4UiQQVApPrVStkotelmWi4UCSooIu33\ngiINCkWCyoDdMRvDvs0gpAUDyESRoIIikhQUaVgo0uIJKYAhUnNqN0qkGU86VShSTLLeOdJk\n0N5I2D3gRSqOSUKMfSBLkcKhSKkCLtK+fUVozBFpRsPbUKSYZL1zpAlFcqb2SMhxz5EoUk8o\nUqqgizTtZgNF6glFShVwkfTnSEUoUlQoUlxuSSR1RBqGVIUi9YQipQpFmhyKFJOsd440oUjO\naC828BopPhQpLqm6h9iASHLKA1mK1BOKlCQbEamsT5EGhCLFhSJFhiL1hCIl6SH4IvH296hQ\npLjckkgT79otYBJFiknWO0eaUCR3ph6RKFIwFOlmROIRaUQoUlzWE0n77cF6nVRAjhVKHpGG\nhyLFZSWRzN8erNeZTaS9qj/y7W+KFAxFWkGkfWdA1aFIWKFIccETScx5alc9R3Ih9YUi9YQi\nUaSYiCVMokgxyXrnSBN8kfbOwarOvCJNutlAkUK5aZHEmiKJdlCrM59Isrn97ULqDUXqCUVa\n69ROXfYbdXhEwgpFisnNicRrpKGhSDEBFWnG+98UaWAoUkzWEsm6XNHrzCbS9OdIFCkUigT2\nitDNinRpEIoUk6x3jjRZSaRgP3MxOefHPLUTs4vkfWdq7Vy3SMFduo5I4X5GkcJRt+ThTKJI\ncXUoUkwoUn8WFCnZjgjvUorkWYP+y7goUmQoUlQhRJHS9ViPSCOOSGJekRp9/nM8EFg5FCmq\nUN9NgvhK+CKVDgn1I7J4IgmKJL/n1f/n0yE/nM7l8O9jnj9/tPNQJHvlnjqziSTH/n2kuUVq\nnlDf/Knda16J9HHIixw+qmnF4FnNhChSsiuSTYgEe0SiSFV+5rVIz/np8u8pf74cm/LDX3l+\nKidUoUjWIr46qXqsWafyp3ogu/cgBSpRpJ4kEOliSy2S9t/PUqGLTmo2imQt4qtzgyL535la\nO0uKlH9vDDrUIh0Ku/5as2XpTlkoUhyTMapE2gOKJPmKUJlapO/1qd330qnTIX+qbjZkZVKK\nFChFkVQtY7S6z4ArUnXXDi3riCR/FHcbDj/KKcfOzQaKZCziqzObSMYfSKJIUVlJpKfyVt1z\nOeX4URyc9JsNFMlYxFdnTpHG/TFmitSfpCKd6lO7UzGlOBaZNxsokrGIr878RyQfUqASRepJ\nUpHy9mbD0ZhSBFakFFibEEmOeSArJEWKySwi5cVhqbhrd84f1Dx4IgmRrIfgi3TRZ9QRiSLF\nJalIT/mPc+HQk5R/8+O5voFX55pF6uv+CCJJijQi64ikvyJ0KgfbAxJFspfxFkpyrul4IFu5\nNP7UbmaTKFJ7KaS/tPrz4TKozUORrGW8heYSqawvxx+RKFIgS/4YBUUylvEWokg4oUhRdW5L\nJHWJNOSBLEWKC0W6DZG0e3YUaUAoUn+VmxRp8M8jJROpd2mKFJcs5X3dZCKl6bh9ZdYSSauk\n/VwfRYoPRYqocmsiVa9yUKQhoUgRVfBESsXjOyKNO7UTFKk/FOmWRBLDf4yCIsWFIl2pSNWd\nlHZC/V6DGPqDfRQpLhQJUaRURJ4jkg/JWYgiRYUiTccSWxBp7M8jUaS4UKQbEWlPkcaEIkVU\nuUWReNduWK5XJCF7XkagSFqlttD4I5KgSBGhSDco0rC7dhQpJhTpRkQa+3vtKFJcKNLtiKTe\ntRsjkqRIwVCk2xFp0hGJIoVDkaabtAmRxr/9TZFiQpEARUr2rkX3ZsOI298UKSYU6bZEGn5E\nao6RFCkYinQzIo38vXbqdJMihUKREojUWwVApPJmgxjxK4spUlS2J1Lfr1mgSG6mSad2iUQK\nVqBIcaFI1lIhpmlATiaKNCYUKaIQmkjpfx2L5/b3oOdIFCkqFOl2RKoeyFKkIblmkUZ02kCh\nmxKpmECRhoQiRdZJ0G8jqqwv0l6JNPQVIV2kKVwUKVEokrWYY8qcIslWJB9SsBBFCiYk0q6d\nsMvl1FAkazHHlPlEGv+KUDKRBEWS77vpR6vrF8lfBkWk9qbdKJEmcd2oSHc7M3eTkbIkHeSq\nRUoEpNdSE6pXhMr7316kYCGKFIxPpDfTo/v3yUhZ0h7in2GISP3V4ongRVJHJC9SsBBFCiby\nGilBKJK1WKDQPEek6jetDhFJUKTYGTcmkuj2EDvriBR+Sry+SNWhqDyxG3CNlFik8PLXK1La\nUCRrMXeh2USqpw76sy4UiSL1VhLVuQaYSHImkSqT2gNSpEiCIkUmKNLb5/Z2w2QkSJFkIpFk\nApH0Y+QkIFXMFMl4jLSSSKEC1yuSceduMlIKkcStiDTZpO6p3Zi/2NccaSlSb0Iifd7dvyXi\nkRSps5irznwiyTEPZNOLFKhwvSLtdgk9SiSSsHtIJyuJFOwl0SI1QMlFqi+P9msfkQIlrlmk\nRDRlQEXq+ZqMrwQvkqxP7WT8298UKYlI97t/iXCKUCRrMR9RCpG6zUSRRiWJSL92j4lwilAk\nazEf0TwiyVEPZClS7IzB298vu6/T37FrAiWSuG6RXM1UKSQG/TySLtLUhrphkXaAt78pUiyS\nfbu5vP1NkQaGIvUU0rpFApH66iwsUtNEZp19feNu+ANZitSfBV8Rmv7dDymSfmgbwrS4SLL5\ndQ1epHAhihTKDYskb08k7YfFKVJUrlukYN+nSBQpXQb8/GOmRma+RqJIFoKnEEUCCkXqL5RG\npLZzXK1IkiL1JihSk/evu5epQMlF8paiSEb/NypRpKFJKpKUX3e/pvFIitRZ0Mkk6zuKE4gM\nJSnStCQW6d/ufhqPTClS+EubIlGkdEksUooXwfFEaoenIvXVoUgUqcwbRQoi9dXZvkiSIgUT\nJ9Lb/e7zRCCK1FnQxwQokqRI4YigSPrd7wS/aRVIJGN5DJEERboBkT4n+JlzimQtaI+2TBQJ\nJklESpts8q6gSAOY6gFjNdXPI/mRnIUoUkQokkwhUm+dgSLJVCLphyD1E7J+JGchJVKKb5xb\nFenfl/viT1F8SfG7G7KEIoUqbVmktugEIrdI+2Z070dyFqJIEekR6SWvr5HyJK8IpRGp7zSD\nIjmZRoskr12k4EYlEek9330qXg369WmX4PcJZRTJXNAepUjXKtKjenr0OcHvE8pSiWQMdEOR\nXEz7ZiXN4Hoi+Ypcr0i5Og79S/HHmK9dpED3X14ke4gieTO/SPpfNU/xihBFMha0R2cVacKp\nXbWgnLr7dJGcZeJFmtY6g6rxiNRbR2hj05AcgxFM5rxiGZGK3yPkR3IVEr6xEVDqKunGRLqR\nayQckdIQWSK153bGkySK1BRb4K7drr1rl+JdO4pkLGiVMUXqVoqHFC6RNI32PqRQpc7Y0Nyw\nSKDPkYyBbiiSWySp/hwzRTKKLSAS5JsN5kA3FMknUn3XbvQRadptmZsWKWUyMJH0sWlIjsEI\nJlsk67u/Z/4eJOepnWxO7fYepFAlH1YsE0VKlWyySHG/+X64SJN2zIZEav/4pQcpVMmHFct0\n2yJ9vSv/yz8n+OsumZx4bhD5kwbrieTfJzAiVad2FEkvtoBI9/Vz2EQ/IXsDInkqTRep+Ouv\nA5DCd+0okl5sfpG+Nn/V/N99mudIFMm70qBIdfffxyN1Rar/zNigP30pbkSkQL0kIt2pv2r+\nll3m40oAACAASURBVObNhqkiiRiR/kRW0kenMekj7rmmibRv5o80yS3Svr39XZgU0UNsj5BE\nSufSAiIlf9eOInlXuoRI5V07sZcUySg2v0jtu3ZAIrXDnrkWF8kzomdRkYRLpL3+QDby1I4i\nJRLp8+5LPfQ1ye+1SyySp9QYkcZTLSDSvp0/yiS/SOURSVIks9j8Ir3Vv4fr7XG3m/77uDI5\nUSTh7CGdRIpkjk6A8pdtk0AkMU0kdbNBxN9soEjJ3rVTv9guzbt2CUXyl7o6keqfgIg9tfN8\n39TndkPetZtLJOFu8CsWKfW7dglE0sfcs1Ekn0iyfWWVIrXFlhApZTIZOiGLCEWaItKI32vX\n2ZwpIgmKlCiZvEKRRBqRhN0yZiHLgV4kp0iyut3QjFIkRbZBkSad292uSHLIK0JGM9llKZKD\njCI5M0qksVSLiRQvO0UaSkaRnFlSpE73p0ghKoqUIlm9wgBNuEAykTp/gGhtkcRGRJp2DkyR\n0iSrVxigCRdIKpJduXchL1JMnSiRzMLdVQ1gokhDyG5RJGPMPRtFSiSSSC2SpEgpktUrDNCE\nC2xCJHehXpHsJa9TJEVHkSYkq1cYoAkXoEjRTLcgkqiHpsa708pQpFChlCJZo8lEGt2Hb0Qk\nQZH8NOEC6USyl00lkrcQRbpukcQaIvmpKVKg0CCR3CMIIkmKNDVZs0Y/TrgARfItbzN4m4ki\nBcic2aBIwZsn3WVjRXLMRZE8SKFCbojoYIvkL3P9Inl3apRIPRNisxGR2kumgSJ1J/Uu1UdF\nkaYma1bpg0klktW3O6sBFamnEEXS56RIy4lk/qetxinSuD0CKpI9RpF6yCaKJCiSs3J8lhPJ\nYVYUU1qRxndcQyR3Mw0QSVCk8SLZG0yRYpjM73+K1FknRaJIMUwgIrVbiCaSF6fKTYjknn85\nkTrvbE8RqUPUM4EiiQk87TpvUyRr3DnfCJFG3rbbiEgCRCQdiCKNT9as008TXD6ZSI6G6xXJ\n+TFFio4mkveihCLFJWvW6acJLp9CJJFSJDFKJNEZmFUks6NQJAcXRUIQqVvHNStFSixSU4Mi\nOWmCy1Mkk8eD7GimMSI5LyU3KVJwFoo0XiRXwyGKFDxp3JZIAlqk4N6/SpGk3bec821PJAeR\nSyR9wjIiOSePyAZE8s1FkW5AJCfzCJHcvTpSpL6Wa1ZLkVIla9bppwkt3t1aBJH6p5Wj4CK5\njaFIMl4kSZEi1u2TprvUFkVyFkovkj5MkSYkU+v00wQyUiTHNfrVi9RZcHWRLASK1OR7Xv1/\nfs7z4297qns8U+v00wTi6v3OGTWROr1hUyJ1Dixm1QkiCbm8SBaRa65ZROrtVWuK9JrXihzy\nIq/WVHuuKplap5+mB9ae4pzxjzoUiTVE6ihR/LOUSI6HZPOK5PkZPXsuiuTMz7xW5JQ/S/kj\nfzCn2nPVydQ6/TQ9sPYU54xjRepZ+1ZF6pxXyUiRfH51ZuvO1VmKIrnylJ9qRQ75+fJvNdJO\nteeqk6l1+mn8qMNEEolFcn6+WZHEtYjU+0PVElqk/LvUFfmenxxTO+NziORcIL1InqbepEjq\nnI0iKbK1RJJSU+Qprzwyp7rGM7VOP403iUVyrTsgklO+sSIJ/YO2vmOVgcI+kXpKUSQXGYRI\nP54OyiSvSFkZtU4/jR+VIlEks8KViXTJc/7DMbUznql1+mm8mV+kwNqvRSThEslrTLRIMZ2Z\nIrljKHLOD46pnfFMrdNP482KIolFRHIWsnpfB6rLGimSuBqRelceK5JntiVFUmOJRHI38hWI\nJKo59A/ChbYiUl9vxhfJu/uXEam6/f1RP0iaWyTvAmYMkQSoSIIiOWoPEEmmFMndmGWWEal8\nIHt+SnyNdM0iNZ+vLpL4T6qJTmPcLXJVIgnVzGuLVL8idLSmuk/1MrVOP0014PrwykXqrvV6\nRfJ1W0ukQNHEInmJ5HLXSKdD/vDDngoikvCK5Fr3QJE8lbrzIYskpHfTvZ3dHKNILU+mxkF+\njGKASK5ZdZHsWbYjkt1B1YKiBU4oUmzjjhKpsxemiVR/PSKJJDFEUnu0Ge0mmUiBDujh9ojk\nPiaMEcl7SPCJpLbOvR0jRIpu3EEiNZPnE8m/17SV+T9Sne4qRXI3cvy+/tM2crRIoV0SEslZ\nyJ5PJhNJWCI5m4QimXP3iBQiklG/I6Y5NmZq6nWKpM+zikhirEj6ZIqkr1X4m6AzN0UyZhki\nUnO/bjaR1BqchYwugC6So5ECUOlEcm0xRYpKtZ7UInVn/mNYRJGuSCS1GYlEUlfek0WSWxfJ\nMXNKkYTQRdK6PrJI3mmaSIIiXblInjuafpE6k9OJJPpEcoMGRFJrt0TybDFFchWsF791kRwN\nlFwkM+aakonk7f/bEOmPNC4loxrEIZLZMO6ZU4lUN129tI/cuZDvI4ok40XSu2NQAAeX3tna\n3r+6SK4viWYZNJEEsEiqZW5JJNe0wSJ5m97ZmcaJZB4Dy8X+qHpdkUKFhDFaiyTmEMm1lIvK\nGuuIJDozU6TEyeo1ryaS8PQ0VczBpV9uTRKp2baRItX+xIjkIxIziNQ2jGuGLYhkD9m5XZFE\nQKRA03d2dsOiiySUSN5CFMkepkiJk9Vrdn7zS10ktzSuaWuIJIL7MChSu9QWRHI2k4PRmHWb\nIvk29zZEcp+ouUQSaosHi2SUiRVJ71g9Inm21yOSddU2SiRBkTSOdtA9T9QfNqRIZi2TyS2S\noEg2Y4xI/ZgUKTZZveagSGJLIvnqOEUyFxsokrb2ZUTybp6DsSnfmYEizZKsXvNaIom1RdL3\n/CiRdJ3iuz9F8n9EkZqJaUWyTlEskZp+PFWkutv5uplRSdv81CINryTHidSp5Wm9ASLpK3dh\nmisLfHR1IgmK5Kykbf5YkdSejhfJe5gcK5Jjy65JpKpCpqauLJK2mzsLX59IYqxIQlAkfeUu\nTHNlgY+uWCRPIyOJFNqFGxBJXJlIYZVuSCTRiuTtoilFctKNEMlbp08kITcrktlr9RZeXCTZ\nrjuUwIboH1Ek6zsymUgilUgivUh6pc5GuDdNralZ0v6xLasVA/3P3liRViS1zY4NMeppezeQ\nwIboH920SLI7b9VDOt0/TiTrSDJKJJupGnOKJJr2oEj17IuKZLb8aJEaHAiRmr4VEslVsjuv\nQBRJdERqCyQUydf966lNM9cJihRop+58Yg6RXH6MFcnTd65YJOderWdxlezOK3pF8rS7td4O\nkVbMB+lkqkZvVyQXlKd8lEhaPW3vBuLbEorUXdKc4hcp1O7WeoUwL8X1Yj5IrZKNmEykDo2+\ngK/TCIrknk6RzCXNKVclklDDmxBJbFgkdxmKpPeRWUTybWezNTriH+mq0bRH/0micLOYi04T\nSZgL+KgGi+Qo5SlPkeKSqTXbME3Xc+7UehZnye68wi2SWEmk5somhUi9hyQvlvCINLxSGpEc\n+62afZhIUq07FN+WOHa4KxTJ7Ld999rsWm1vdxTrL7SGSH4qMatIVVstJJJAE0kVARWpczLg\nLGm1hfSLJOJEEtrYTCJppbub4Ns6gSaSdnLV/FtvrzWvs5S7vCmSa4YJIjm+m+3mcy4eEkno\nW4IpkqXHRJG0/b2OSGKLIvmgqg6kzVf/W2+vPq+Pyl0/TiR9WbVm384QPSJZG+ZIK5IL+BZF\ncvSXbi2/SLI7ECiUWKS6pL0h5qJ+KkGR0ohknydtTSTHMsaSaswWyfUl7sMzP7UWlo5SoULD\nRAoR6SXt9ZvL+qnEtYokmzUnEclZBFwkg6jZw4lE+k8rYncWf68197i9sGqzyEJNs/eKFKqk\n76RpIkltVc3iPSL5+uZCIrlnSC2SNe6qoInUvXK/WpFESpHMPptOJN2p8SJpfcS1AWahHpHM\nSiK9SP4tMzEpUkyyeuVLiuQwyYenPm2/R81lhhRq+1vda5cSyV1ooEhNfTeUJZLSqV1TWwlG\nJDeDNe6q4BNJtNWvXyRpFw302nQi1RwekfRCS4kkZxDJrqj6v7lWd1O5USlSXLIawC2SfT2v\nE4dF0lu1VyRvkw8Wyb+hwiGSwaTBhCqZq3aIVO180ZndUar9vCmQUCSp5jcJRovkaZfUIgXH\n6zQiCa9I6uicqQ+vTCR9nt7ev5BIVqFkInWOT1aptlxToE8kL1QykezJ84nk6kD2CjzbDCxS\nZ8NVz3D2UxiR7GNbqFISkZRJWm/XlpQJRdIXDm+eQyStO5kLjhfJjUCRymQNQGqRtB4wQaS2\n29oLWV2st1Sz4+YUqV0TjkhimkgCWCRRi6TaCFgk4RapOXdwluz0c10ku3ywz8p270WJ5L/W\nSi2S6gsbEMlaME6kuh/OKpKbITheR/+jpZZIwvjmoEjmfC6RHJUWF8m5IYp3kkjNqqy1+ph8\nInWbeKxIvp0FJZK4JpHM/SSSiNTps65K/l2nOJYWKbh90SL5DweKaYBIvmavt102J0hykEjS\n3COLiCTMFaOIZDIbvaoZaD9cXaQuabCOJpLYrEgBJrdIrqbxtla97U6Ruocdfd3tLlKFblgk\ni9noVc1A+2F3AXvRdgRJJP0Qa4ikH9l6Om3bLM4NETOI1LOBQrR3FYylHU3jba16u5RIzbfO\nUiLVzdHZMEccIrXfkfru24BIgT1rtFG95H/lMlKY8/T0D2k2lnAvFFVnHZHCXCGR1KqqGXs2\nUBgiNV3L3cTe1qq3awGRnKectyKSsVGxIrUlKJKjUjNLr0h9GyjmEUksLVJnBZ6NtkUS7dJm\nYWyRbO3ttJvSlkggkvAsE1XHL1Kzw7XafZ1WNYu1WLumhCJ5ToS6G5dYJLERkdqVtftFQ8nU\nQkgi1fs3ViRtT/5XH1Ts8sH+0daKECl0y04uL5L2mbdSM0tKkZrWSi1SYDHtq8PE9tJGiyTd\nG02RRopkdLbuMqo1w4VWEslfSaFTJDlNpLZLmnXxRQrtWPWhticXECkctSntvz6RwuX0ZjEW\nmyySnCZSI9FmRXKtwC+S9o1of0MiiaRDaju7nrtnx3Y7WSFSvSKrfsSRRO9szv0Z7mVqHk0k\nqYtkE4WL6c3i3pC6/ECRypHlRPJsmDpLQhfJFGdTIqn2ghOp6Yg9dRYUSSf2V5KqqZpaf4z1\nN1V7qdqeNI9IoZZpRLJxvCKp1rMWc67AjXpbIhlbZv9KP60tU4jk+eYy6xgiyZBI/UALiuTu\ndo6NSyOSGCxSZ6qgSCo6YdNJxECR9HR/N2Zv77BnC+1NMJH0eVYTydNggSZsylCk4anWcwUi\n9W2otilC77XdLe5hMprl2kUSpUjBpnFMFRRJbb1O2HQSQZHUfK1I3Q0xm44iOWHtNhsmki2O\nNa4tnqlhBJHkDCL1FTHn6hOpN4pIF0mKbvfvq2/NFxCpr9gaIgX2XbvHTZH+hJvGMbXBCcF2\nuChSN6Ibr0h9gCZIX48K1llHpEAlqbphi1QhtoW0HtK3cUgiaVvhhu1wJRRJXzxTwxgi1dOS\ni9QLaIL0dqlQIZdIbug4Il0kX6VBIsnlRAo2kCGS9WuU3c3haqFRItkLuVmdIrkYIUQy+51M\nLpKnkXy15hYpur49X6cDmFseKKQWTidSs4hvg+YRydlCFKkicIsUtWdFN+uLJPU6kiI5iqwq\nknshN+t/doegSL2AzqYato1mJb9IMq6+zdHpAOaWBwpJt0gyvUhq2bBIstkUijQ01XpWE6kf\n0FFrnEeziaR6nxs5UEjaIknrjnxccy8mknOPOao1c0fAdrhGiuRp8dVFakFNkUTUnnVsXEKR\n+p8ZBSu1Iv1nFroekZqdKLsUUSKZ651PJNnP5ZootiWSOmcxOoxw7Z1OuhuHI1JD3mEaL5L1\n9NG7W+1CUnWUZr6uSHGV4kXyl1pPJJFUJHPxTA0vJFLTSLcsktQ+jqrTLLiISL1IWxBJuEXq\nnOoZpTo1/qjNtb9srLlXE0kMEclf1d62rYgkPbvTV0dbdA6ROsxhpAiRQrXWFckD5ppoixRo\ncCyROg9p+7tIJ6NF6taaSyRtptg6ahKYSE39zsKhWhEiuXaZo1xgP7UGVQYY53We6psXqW6j\nlUUasNr4OrI80/bOFFtHTTJEiu7+UnWUZr4/VqPEVnI2UHsnbLsiSUelkEjSLIEpkt2l/VWF\nHU+njULs1BoZq8bWRIrdtEQiCVOkpi+MFUlYH4mab7JI0hLJnBdMpBbLucO6EXYokqtQM+uG\nRXJeNzWrtbZV/yihSNpWOZTO1PCKIjXTWqzIHi06czo7bRxit9i4dGr45E4pUrBQMyuWSE0f\ndYnUaZupIolJIrW9VStrLp2p4RVEam+n2GeckT1adOZ0ddrIRK81uo7sESm+UC9xsE4z622I\nJPSPTJECG9mp5BBJw+4snanhpUVS/zbTdKzYHi3sWSmSYzapOmIz3x/pa/FIInPWerSdFioW\nKZLdqR3ljFZW2+oWSVurE6xTqZj0py1ibBaESJpCLRGeSCnq1BMARfrP1+KxROa8bUc1Z/QU\nWVAktWxSkTq7jiKNWmtsnXqCk2l1kdyVYonMeduOas7oKdIjUl3A2gbHbe6miLmtSiQ5n0jd\npTM1jCpSsKy5ZzFE6vRKimQVmVUktby2iL42rwoRIkn/0pkaXlAkASnSgNVG1qnHx4rU370j\nG0nqTV0jwYok3SL5Ov8YkVwtT5G2K9LgQv45wmWkQ6QxhTYuUrA5r12kng43m0gTymxYpD4q\nX3esF00jkqqo0ywiUkfejkgeEIrkLTahTDqRgv3RWFW4ity8SO5ia4gkoUQSFCmlSH1V5BIi\nyTQi6RXXFUlsSiQnXXyHpkjAInmqzSlS1bHqkoNEktEiuRfO1DBFSi1SMz63SL1VZL9Iwa5v\n83SpporUnke1BVQbieEiqeoO7uEimfO5F87U8PIiCZ9IsmebXTOmFMl9+B5cpxkfz9TfCDGs\nlUgyRqQ4npBIQqs2XCR9TU13GSySthtnEMmzcKaG1xBJhEUa8KQlrUhxx4u+Os34LYhk1gju\nviEiCYpkpVrPZkSaFIoUK5Lq8GGRxEiRpNa/Bosk4EWSFGlgpdAcVyCSGCtS9wySIo0VSVoN\ndGsidZrONYdcSaQAcLRIrRo+noEi+TqVRyR5gyIVE6aI1DFgdBlzr9yOSPWuHSxSOXlOkaS5\nLu+2WeMbFMnmihRJIookKVK4x9qVlhQpvG3W+DZE0slt1rp9KNKiIsXyXKVIdgtclUgRoUhp\nRJJDReqsYrpIkiL1plqPdk2aSiTr7PcKReprCByR5NIidS7GKFKXbMMiyS2KFHMi3bRPj0g9\nrRgvkhguklG1I1JoG7cnkn06Jl0iRV0gacVkMpFiVxyspI9cj0iqhWYSyV5Rv0gWylSRrFJ/\n6sNibyiSo1YKkYxMFWlqYkWKBdLevdFX0X4OKFJEU966SO3OLUZSiJQ6ICLpmV+kwO5zn+B7\nRQqJOZtI4lpE8kxzJbFIkwo4M+03G01ff0KRmmP24iLJdUSS2CJ1v2amdBeK1FdEJhfJrtfZ\nsaFdOptIIiiSp4S1aUapWxNJtt+AFMlRRFIkGUZqN80oRZFGl6JIPbXmE+m/sEieUmplol+k\nuE3TCt+gSDKJSGk6rp3rE6lTL4lInfWkFCniKUG9Pq3wdkRSIBNKG8d9iuQoIhcTSWqdOMgj\nDZPK0fEiCZdIVRUHYnjTblwkNUKRHEVkUpFc9eYXyVcqWqSYTaNIamSiSMOaPjIUyVdK7wXW\n39EWZnw1UoukFhS3J5JMKdI0Encokq9UOpHqVdoiDdy0mxepzZWJlIRnGyLZTMNFMuYf0W7a\nohSJIrlLLCxSdw5nqVQitTb1zB8DZIsUU4siBYslCkXylaJIg1OthyINDkWiSHqq9ThOpRMk\nqUgz5JpEaq4ZKJK1aKaGKdJcWZtpAZHaT69IJCk3I1Ka2hQpnDlE8n46QCTr6zQgkt/beUX6\nT25CJLjrkZmyNlNakcKKDBCpvuCaJJK8BpHyJsXI72OeP3+oz86nQ37QxinSikktUnBdGCJN\ngV9NpMNl+LUaOtcfnQ/VeGtStZ6WiSItlyVFkqojR4rUvryBIpKqtOyp3Wv++yJOfvgrz0/5\nqZ54yp/P8nzMn9Rs1Xoo0hrBFkn2iNTTk+cQSRVZUKSP/Pny789SoXN5cCpyKE/3ztVZX5lq\nPRRpjWxdpIj1bV+kY+nOU/7X9SFFKrM206IiNZcXUTvXeLXUZropkX7kP4r/Lkeg0yF/+jA/\n/K1O9Rwi9d1HHZm1O60razMtL1Kz1v55tTlTidRedQ3NiiIdqpO5PD8aNxuqHKvxrEy1vnbN\nFGmxLCySjBdJhkRqzxKDFWyR5BZF+pl/L/+/iPRR3GI46R8e89d2pFqPIVJkWw/L2p3WlbWZ\nlhVJDhapjluk/pVdg0gPeXUMysv/25sNRQyPKNKKWVqkATs3vUhyiyJ95Mdq4FjdVdBuLnwc\nD7/1Wav1UKQ1srhIaq2DZpoqkmhFiqcMFVtOpObM7nJSV9y1O+cPzSevh6N556FaD0VaI+uI\nFJUekSJ68VWI9JzXR52/+fFc6FR7VYxbs1brmcEcKyg9RM/aTLckUr3cWJyVRHrIm8POqXwl\nqDwgFed3z/preGWq9VCkNQIskp6xInVeVt2eSJooPx/yw0lNzCmSlrWZKFJs1hJpQKr1UKQ1\nsmWRepeaTyRJkcCyNtNWRZIxHcb1c0gUaXq20kOWDEWKDUVS2UoPWTJXLZKcS6QGiSLBZG2m\nDYsUkQRvfbe1KFKTK+ohyUKRomtRpCZX1EOShSJF16JITa6ohyQLRYovRpHqXFEPSRaKFF+M\nItW5oh6SLLciUoLuZSlJkaCyNhNFGlCNIlW5oh6SLBRpSDm9FEWCytpMFGlIOYpU5op6SLLc\nhkiJfpkORapyRT0kWSjSkHL63T+KBJW1ma5fJEmRUueKekiy3IxIKUKRqlxRD0kWijSknP5c\nlyJBZW0mijSkHEUqc0U9JFmuW6Ry29KJJPVfFEGRoLI20w2IFPf7HSKrUSR5ZT0kUW5CpGSd\niyKVuaoekigUaVg1iiSvrIckyo2IlCgUqcxV9ZBEuXaR0kY/tlEkqKzNRJEGhiIh7Y02azNR\npIGhSEh7o83aTBRpYCgS0t5oszYTRRobigSVtZko0thQJKiszUSRxoYiQWVtJoo0NhQJKmsz\nUaSxoUhQWZuJIo0NRYLK2kwUaWwuSPs9RULJ2kwUaWz2+70UxT99oUhLZG0mijQy++bUrtck\nirRE1maiSCNDkbCyNhNFGpl9c41EkSCyNhNFGpd9e43UZxJFWiJrM1Gkcdm3p3YUCSFrM1Gk\nkeE1ElbWZqJII0ORsLIyU3leQpGGh6d2YFmTqblcpkjDw5sNYFmRqewAQnZOTthMMeHtb6xQ\npKjgMe2bIxJFgghFigoeE282YGU9pqoDlHftzL7AZorJXqVvToq0RChSVPCYKBJWeGoXFTgm\n3v4Gy8oilb2AIg0PRQLLmiJ57juxmWLCmw1YoUhRgWPiEQksPLWLChzTvn0gS5EQwpsNUcFj\n4l07rPD2d1TwmCgSVihSVPCYqvfmeWqHEp7aRQWPqb1VQ5EQQpGiAsdU+sObDTgBEElQpOFp\nb3/3mkSRlgh/sC8qcEz6cySKBBCAHzW3fxM8mykmvNmAlbWZBEUaF14jYWVtJoo0Mrxrh5W1\nmSjSyPCBLFbWZqJII7P/jyIhZW0mijQyvNmAlbWZRLfh10ZyBY6p/HV21ZMDioSQtZko0rjw\nF0SCZW0mijQy2k/I8oEsQNZmokgjQ5GwsjYTRRqZffMDxrzZAJG1mYoTfWvS2kiuwDGV10h7\nPpCFyapM5Qur/OUnYxJ/1+7SvpkaoUhzZdW3v2V9asefkB2efdSrDdVhK1PjFGmuUKSo4DFF\niVQ/tc3UBIo0VyhSVPCYtJsNfpMo0mJB+AlZ6zSfzRSTfXuzgSIBZHWRBEUaF3Uw6vGIIi2S\n1U/tBE/tRmUfcZFEkZYLRYoKHlOMSM3D2kxNoEhzhSJFBY9pH/MjshRpsaz+QFbwgeyoqLt2\noXeEKNJiWZuJrwiNTNQRqfrNDnwgu0BW/3VcgiKNSpxIkq8ILRSEXxBpTWYzxSTq1K5OpoYo\n0lxBeI7Ea6QRiT4iSYq0RChSVPCYeETCCkWKCh4Tj0hYWY+p2v18jjQ28b8hkiItEIoUFUAm\nigSVtU/tHD2BzRSV9hqpd9ZMDVGkubKqSO4vVTZTVP7b9/00kkqmhijSXFlTpOL3DpQ3G8zf\nKMVmikqBFGORpEhLZO0HstU7LBRpeAYgZWqIIs2VlUWqf8iTIg0PRYLKqqd27VWSbhKbKSoU\nCSrriuT84TQ2U1QoElRWP7Xr3rZjM0WFIkFl7bt2snwgS5GGhyJBZeVTO+0fBCRvAJkoElR4\njRQVQCaKBBWKFBVAJooEFZ7aRQWQiSJBhXftogLIRJGgwlO7qAAyUSSoUKSoADJRJKignNpR\npKGhSFDhzYaoADJRJKjw1C4qgEwUCSoUKSqATBQJKhQpKoBMFAkqFCkqgEwUCSood+20yWym\nqFAkqKAckbTpbKaoUCSoUKSoADJRJKignNrxGmloKBJU1hVJ8oHs6FAkqKx+ROr+QQU2U1QW\nEul8OuSH54967HtuffyqTyjXE/lLK6cEcG+sLxKvkUZmGZHOh7zIoTLpNbdE+shNkZpvxqGr\nGRbAvbEuE0WakGVEOuXPZ3k+5k/FyM/cFunBFKn6k1cy5hf7Twng3kARSZ/KZorKMiIdSlHO\npS9P+ckS6elAkepQpKgAMi16s6H0Jf8uTZF+5K8Uqc66TC6P2ExxWVKk3/mpGjC8KabmnZsN\n1V27WU0C3BvrM3UvTFdHcgSQaUmRjodzNaB7cz4c2wlZmXKQIoEEEAmRaUGRjvlrPaSLdMw/\nrENUpvThqR1AAJEQmZYTqfVI9+aU/5QUSQWQCRAJkWkpkT6Oh99qRPMmV2nXQ5GQAoiEYALE\nqQAABbxJREFUyLSQSK+H40c71iNS9ecQ+EAWI4BIiEzLiPQ3P+qj9gNZx107viKEEkAkRKZl\nRHo2Dzv2/67b3/MHcG8gMgEiITItI1JOkeICyASIhMgE+2MU8wdwbyAyASIhMlEkqAAyASIh\nMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIh\nMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIh\nMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIh\nMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMlEkqAAyASIhMiGKxDBXnYVE\nWirZ2gCOZGsDdJOtDeBItjZAN9mYhSjSXMnWBugmWxvAkWxtgG6yMQtRpLmSrQ3QTbY2gCPZ\n2gDdZGMWokhzJVsboJtsbQBHsrUBusnGLHQdIjHMyqFIDJMgFIlhEoQiMUyCUCSGSZDtiHQ+\nPeT58Uf/bIf88PwhO3/tFoJJysvgw+t8RHVen/PLGn/bk/92Zvw+Y+tYiWM6X+Y6dmZaFSmq\nG21GpI9DtTmHc3C2czXb4aMV6QDEJKvB02xIVZo/Pf9sTn7qdIbXOb9mRjFVDTT/V0080t/r\nEukpL77SP449nfCUP5/l+Zg/NRNe8/m+3oYznfKnc/Fv99CQMs/54fWymtcHq4t0OsPPWY/X\nY5hOxcc/8gcgpL9tZwpkMyLVW3fu2fOH3Jzrw/66WZfpkJ/LwRmhij1/qE4j5YNprM35lJ+W\nEimWqWqgRahikX7kvefuckMiPeQf2tiPh/xQbt5loy+d4WSfW6m2OM53YjeGqeaa9xv3lP+s\nh36Wx8riEu3hd32uaxB9X6bLDmEq8n32c98hSFcm0mt++K6+N47lxh5lsdXfHddBv5s9EdcI\nyzE1R6RZu2/r90dpbHPZ4eq0S4k0gOlp/mvIQUhPeXFP4jl8HbwdkeTvh8v2PZVfIj/yY3nR\n8Vp0hMNf+fdo+XJsLv8Pcx6QRjCdij5ymWvW7qtVLwa/F2Snoq84VruUSAOYfjwdFjEpFukp\n6o7SdkS6fHH8fD6UX/nH+nv9qdjo4l7CX/Nc6djc9fl5OXmBYqpu4C0rUvvNiyNSkKm4DTDn\nicRApLw8BTz1yL0lkYr8KK7TtSdEzUWHvu3Ko0vj9ByQF2f6eM4Pp5m7b7vVZ/MLdkWRhjAV\n88x7JjECSfYgbUUktXFVTw102o/jobnh/VEeK7CYisTdUB2dk/o+/1F8jUKINITJOxUZaSsi\nPdVbfa6OwupAk5d3Ln+3xrwejupW2sxndiOYqpsNP+a9BlD3dT8OBQnEqV0sU9VAH0s8SBqG\ndO5B2opIv/P8x2V7fpcPPy8X9h/Fv+X1yNG4sP+rH4SeZ3wYO46pfN74+2HmB7Kn/FCcSL4e\nyudVJ+0qunOmu9gD2UimsoHOT0tcI8UjnaR+/HJnKyIVT2bU/eX6VnP1HtBRTS3y3J5h2c95\nEJjOy7wi1IBVz33VWzeXAftrdblXhCKZDrnRdgBI5yikzYgk/z4f2hdEi5dF6zdTL2dYh/bL\nQrtUWaCXDGf6KN7JnP9Nst/Ph/ZtTPUe6OtD54p5OZFimYrHokscj+KRzjFI2xHJnQU7QnQQ\nmZiZQ5HSB5GJmTkUKX0QmZiZQ5HSB5GJmTlbF4lhIEKRGCZBKBLDJAhFYpgEoUgMkyAUiWES\nhCIxTIJQJIZJEIrEMAlCkRgmQSgSwyQIRWKYBKFIDJMgFIlhEoQiMUyCUCSGSRCKxDAJQpEY\nJkEoEsMkCEVimAShSAyTIBSJYRKEIjFMglAkhkkQisQwCUKRGCZBKBLDJAhFYpgEoUgMkyAU\niWEShCIxTIJQJIZJkP8BNewMw1d1Z/4AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data(raw_data)\n",
    "res = AnomalyDetectionTs(raw_data, max_anoms=0.02, direction='both', plot=TRUE)\n",
    "res$plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot, we observe that the input time series experiences both positive and negative anomalies. Furthermore, many of the anomalies in the time series are local anomalies within the bounds of the time series’ seasonality (hence, cannot be detected using the traditional approaches). The anomalies detected using the proposed technique are annotated on the plot. In case the timestamps for the plot above were not available, anomaly detection could then carried out using the AnomalyDetectionVec function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Often, anomaly detection is carried out on a periodic basis. For instance, at times, one may be interested in determining whether there was any anomaly yesterday. To this end, we support a flag only_last whereby one can subset the anomalies that occurred during the last day or last hour. Execute the following command:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PxAREqCSLxI/EBESoJIvEj8QERKgki8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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res = AnomalyDetectionTs(raw_data, max_anoms=0.02, direction='both', only_last=\"day\", plot=TRUE)\n",
    "res$plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "From the plot, we observe that only the anomalies that occurred during the last day have been annotated. Further, the prior six days are included to expose the seasonal nature of the time series but are put in the background as the window of prime interest is the last day.\n",
    "\n",
    "Anomaly detection for long duration time series can be carried out by setting the longterm argument to T."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.3.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}