analysis/basic_stats.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "from datetime import datetime,timedelta\n",
    "DATES=[\"20141001\",\"20141002\",\"20141003\",\"20141006\",\"20141007\",\"20141008\",\"20141009\",\"20141010\",\"20141013\",\"20141014\",\"20141015\"]\n",
    "\n",
    "import pandas as pd\n",
    "pd.options.display.float_format = '{:20,.2f}'.format\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import ScalarFormatter\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "import math\n",
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Control Period 1\n",
    "The first point of comparison is to compare [09:30-09:33) on Oct 15 to the same time interval of every proceeding weekday in our dataset (1 Oct-14 Oct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date</th>\n",
       "      <th>mfcs</th>\n",
       "      <th>equities</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>20141001</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20141002</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20141003</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>20141006</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20141007</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>20141008</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>20141009</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>20141010</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>20141013</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>20141014</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>20141015</td>\n",
       "      <td>13</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        date  mfcs  equities\n",
       "0   20141001     1         1\n",
       "1   20141002     3         3\n",
       "2   20141003     0         0\n",
       "3   20141006     2         2\n",
       "4   20141007     2         2\n",
       "5   20141008     5         5\n",
       "6   20141009     1         1\n",
       "7   20141010     3         3\n",
       "8   20141013     3         3\n",
       "9   20141014     5         4\n",
       "10  20141015    13        11"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "#Number of MFCs between 09:30:00 and 09:33:00\n",
    "START_TIME=datetime.strptime(\"09:30:00.0\",\"%H:%M:%S.%f\").time() #Greater than or equal to this\n",
    "END_TIME=datetime.strptime(\"09:33:00.0\",\"%H:%M:%S.%f\").time() #Strictly less than this\n",
    "\n",
    "def get_time(str):\n",
    "    format=\"%Y-%m-%d %H:%M:%S.%f\" if \".\" in str else \"%Y-%m-%d %H:%M:%S\"\n",
    "    return datetime.strptime(str,format).time()\n",
    "\n",
    "results=[]\n",
    "#print(\"Date\\tMFCs\\tEquities\")\n",
    "for date in DATES:\n",
    "    with open(\"../data/{}_miniflash_crashes.csv\".format(date),\"r\") as fh:\n",
    "        count=0\n",
    "        equities=[]\n",
    "        header=None\n",
    "        for line in fh:\n",
    "            fields=line.split(\",\")\n",
    "            if header==None:\n",
    "                header=fields\n",
    "                continue\n",
    "            start=get_time(fields[header.index(\"start_time\")])\n",
    "            end=get_time(fields[header.index(\"end_time\")])\n",
    "            if start>=START_TIME and end<END_TIME:\n",
    "                count+=1\n",
    "                equities.append(fields[header.index(\"symbol\")])\n",
    "    #print(\"{}\\t{}\\t{}\".format(date,count,len(set(equities))))\n",
    "    results.append([date,count,len(set(equities))])\n",
    "df_mfcs=pd.DataFrame(results, columns=[\"date\",\"mfcs\",\"equities\"])    \n",
    "df_mfcs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date</th>\n",
       "      <th>trades_09:30-09:33</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>20141001</td>\n",
       "      <td>354394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20141002</td>\n",
       "      <td>357221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20141003</td>\n",
       "      <td>364482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>20141006</td>\n",
       "      <td>377942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20141007</td>\n",
       "      <td>368060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>20141008</td>\n",
       "      <td>320907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>20141009</td>\n",
       "      <td>354617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>20141010</td>\n",
       "      <td>593973</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>20141013</td>\n",
       "      <td>376676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>20141014</td>\n",
       "      <td>444223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>20141015</td>\n",
       "      <td>730379</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        date  trades_09:30-09:33\n",
       "0   20141001              354394\n",
       "1   20141002              357221\n",
       "2   20141003              364482\n",
       "3   20141006              377942\n",
       "4   20141007              368060\n",
       "5   20141008              320907\n",
       "6   20141009              354617\n",
       "7   20141010              593973\n",
       "8   20141013              376676\n",
       "9   20141014              444223\n",
       "10  20141015              730379"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_volume=pd.read_csv(\"../data/trade_volume.csv\",sep=\"\\t\",dtype={\"date\":\"str\"})\n",
    "df_volume"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date</th>\n",
       "      <th>mfcs</th>\n",
       "      <th>equities</th>\n",
       "      <th>trades_09:30-09:33</th>\n",
       "      <th>mfcs_per_trade</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>20141001</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>354394</td>\n",
       "      <td>354,394.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20141002</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>357221</td>\n",
       "      <td>119,073.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20141003</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>364482</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>20141006</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>377942</td>\n",
       "      <td>188,971.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20141007</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>368060</td>\n",
       "      <td>184,030.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>20141008</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>320907</td>\n",
       "      <td>64,181.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>20141009</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>354617</td>\n",
       "      <td>354,617.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>20141010</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>593973</td>\n",
       "      <td>197,991.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>20141013</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>376676</td>\n",
       "      <td>125,558.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>20141014</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>444223</td>\n",
       "      <td>88,844.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>20141015</td>\n",
       "      <td>13</td>\n",
       "      <td>11</td>\n",
       "      <td>730379</td>\n",
       "      <td>56,183.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        date  mfcs  equities  trades_09:30-09:33       mfcs_per_trade\n",
       "0   20141001     1         1              354394           354,394.00\n",
       "1   20141002     3         3              357221           119,073.67\n",
       "2   20141003     0         0              364482                  inf\n",
       "3   20141006     2         2              377942           188,971.00\n",
       "4   20141007     2         2              368060           184,030.00\n",
       "5   20141008     5         5              320907            64,181.40\n",
       "6   20141009     1         1              354617           354,617.00\n",
       "7   20141010     3         3              593973           197,991.00\n",
       "8   20141013     3         3              376676           125,558.67\n",
       "9   20141014     5         4              444223            88,844.60\n",
       "10  20141015    13        11              730379            56,183.00"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#This is Table 1 in the article.\n",
    "df = df_mfcs.merge(df_volume,on=\"date\")\n",
    "df[\"mfcs_per_trade\"]=df[\"trades_09:30-09:33\"]/df[\"mfcs\"]\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mfcs</th>\n",
       "      <th>equities</th>\n",
       "      <th>trades_09:30-09:33</th>\n",
       "      <th>mfcs_per_trade</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>10.00</td>\n",
       "      <td>10.00</td>\n",
       "      <td>10.00</td>\n",
       "      <td>10.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.50</td>\n",
       "      <td>2.40</td>\n",
       "      <td>391,249.50</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.65</td>\n",
       "      <td>1.51</td>\n",
       "      <td>77,712.44</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>320,907.00</td>\n",
       "      <td>64,181.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.25</td>\n",
       "      <td>1.25</td>\n",
       "      <td>355,268.00</td>\n",
       "      <td>120,694.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.50</td>\n",
       "      <td>2.50</td>\n",
       "      <td>366,271.00</td>\n",
       "      <td>186,500.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.00</td>\n",
       "      <td>3.00</td>\n",
       "      <td>377,625.50</td>\n",
       "      <td>315,293.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>5.00</td>\n",
       "      <td>5.00</td>\n",
       "      <td>593,973.00</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      mfcs             equities   trades_09:30-09:33  \\\n",
       "count                10.00                10.00                10.00   \n",
       "mean                  2.50                 2.40           391,249.50   \n",
       "std                   1.65                 1.51            77,712.44   \n",
       "min                   0.00                 0.00           320,907.00   \n",
       "25%                   1.25                 1.25           355,268.00   \n",
       "50%                   2.50                 2.50           366,271.00   \n",
       "75%                   3.00                 3.00           377,625.50   \n",
       "max                   5.00                 5.00           593,973.00   \n",
       "\n",
       "            mfcs_per_trade  \n",
       "count                10.00  \n",
       "mean                   inf  \n",
       "std                    nan  \n",
       "min              64,181.40  \n",
       "25%             120,694.92  \n",
       "50%             186,500.50  \n",
       "75%             315,293.25  \n",
       "max                    inf  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=df.copy()\n",
    "x=x[x.date!=\"20141015\"]\n",
    "x=x.describe()\n",
    "mfcs_mean=x[\"mfcs\"][\"mean\"]\n",
    "mfcs_3sd=mfcs_mean+3*x[\"mfcs\"][\"std\"]\n",
    "equities_mean=x[\"equities\"][\"mean\"]\n",
    "equities_3sd=equities_mean+3*x[\"equities\"][\"std\"]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f53e1334c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Figure 1\n",
    "matplotlib.rcParams.update({'font.size': 9})\n",
    "dates=df.date.apply(lambda x: \"Oct. {}\".format(int(x[-2:])))\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7.5,4))\n",
    "rects=ax.bar(df.index, df.mfcs, color='black')\n",
    "plt.xlabel(\"Date (2014)\")\n",
    "plt.ylabel(\"Number of mini flash crashes\")\n",
    "plt.xticks(df.index,dates )\n",
    "plt.axhline(y=mfcs_mean, color='black', linestyle=':')\n",
    "plt.axhline(y=mfcs_3sd, color='black', linestyle=':')\n",
    "\n",
    "for rect in rects:\n",
    "    height = rect.get_height()\n",
    "    ax.text(rect.get_x() + rect.get_width()/2, height,'%d' % int(height),ha='center', va='bottom')\n",
    "#plt.show()\n",
    "plt.savefig(\"mfcs.svg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f53e1334080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Figure 2\n",
    "matplotlib.rcParams.update({'font.size': 9})\n",
    "dates=df.date.apply(lambda x: \"Oct. {}\".format(int(x[-2:])))\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7.5,4))\n",
    "rects=ax.bar(df.index, df.equities, color='black')\n",
    "plt.xlabel(\"Date (2014)\")\n",
    "plt.ylabel(\"Number of unique equities\\nwith at least one mini flash crash\")\n",
    "plt.xticks(df.index,dates )\n",
    "plt.axhline(y=equities_mean, color='black', linestyle=':')\n",
    "plt.axhline(y=equities_3sd, color='black', linestyle=':')\n",
    "\n",
    "for rect in rects:\n",
    "    height = rect.get_height()\n",
    "    ax.text(rect.get_x() + rect.get_width()/2, height,'%d' % int(height),ha='center', va='bottom')\n",
    "#plt.show()\n",
    "plt.savefig(\"equities.svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Control Period 2\n",
    "Now we compare [09:30-09:33) on Oct. 15 to all three minute windows [09:30-16:00) on the proceeding weekdays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20141001 Counter({0: 325, 1: 41, 2: 19, 3: 3})\n",
      "20141002 Counter({0: 310, 1: 62, 2: 14, 3: 1, 4: 1})\n",
      "20141003 Counter({0: 358, 1: 27, 3: 3})\n",
      "20141006 Counter({0: 343, 1: 42, 2: 3})\n",
      "20141007 Counter({0: 332, 1: 48, 2: 7, 3: 1})\n",
      "20141008 Counter({0: 310, 1: 64, 2: 10, 3: 3, 5: 1})\n",
      "20141009 Counter({0: 301, 1: 75, 2: 7, 3: 5})\n",
      "20141010 Counter({0: 278, 1: 84, 2: 20, 3: 6})\n",
      "20141013 Counter({0: 312, 1: 60, 2: 8, 3: 4, 4: 4})\n",
      "20141014 Counter({0: 293, 1: 68, 2: 23, 3: 3, 5: 1})\n",
      "3881\n",
      "[3162  571  111   29    5    2    0    0    0    0    0    0    0    1]\n"
     ]
    }
   ],
   "source": [
    "START_TIME=datetime.strptime(\"09:30:00.0\",\"%H:%M:%S.%f\") #Greater than or equal to this\n",
    "END_TIME=datetime.strptime(\"16:00:00.0\",\"%H:%M:%S.%f\")#Strictly less than this\n",
    "\n",
    "def get_time(str):\n",
    "    str=str[11:] #Chop off year\n",
    "    format=\"%H:%M:%S.%f\" if \".\" in str else \"%H:%M:%S\"\n",
    "    return datetime.strptime(str,format)\n",
    "\n",
    "#three_minute_windows={}\n",
    "#x=START_TIME\n",
    "#while x<END_TIME-timedelta(minutes=2):\n",
    "#    three_minute_windows[x]=0\n",
    "#    x+=timedelta(minutes=1)\n",
    "\n",
    "WINDOWS_PER_DAY=388\n",
    "        \n",
    "results=[]\n",
    "for date in DATES:\n",
    "    if date==\"20141015\": continue\n",
    "    three_minute_windows=[0 for x in range(1,WINDOWS_PER_DAY+1)]\n",
    "    assert len(three_minute_windows)==WINDOWS_PER_DAY\n",
    "\n",
    "    with open(\"../data/{}_miniflash_crashes.csv\".format(date),\"r\") as fh:\n",
    "        count=0\n",
    "        equities=[]\n",
    "        header=None\n",
    "        for line in fh:\n",
    "            fields=line.split(\",\")\n",
    "            if header==None:\n",
    "                header=fields\n",
    "                continue\n",
    "            start=get_time(fields[header.index(\"start_time\")])\n",
    "            end=get_time(fields[header.index(\"end_time\")])\n",
    "            if start<START_TIME or end>END_TIME:\n",
    "                continue\n",
    "            \n",
    "            x=(start-START_TIME).total_seconds()/60\n",
    "            x=math.floor(x) if x>math.floor(x) else math.floor(x)-1\n",
    "            #Each MFC is part of up to three, three-minute windows\n",
    "            if x<WINDOWS_PER_DAY:\n",
    "                three_minute_windows[x]+=1\n",
    "            if x-1>=0 and x-1<WINDOWS_PER_DAY:\n",
    "                three_minute_windows[x-1]+=1\n",
    "            if x-2>=0 and x-2<WINDOWS_PER_DAY:\n",
    "                three_minute_windows[x-2]+=1\n",
    "    print(date,Counter(three_minute_windows))\n",
    "    results.append(three_minute_windows)\n",
    "\n",
    "big_list=[]\n",
    "for l in results:\n",
    "    big_list+=l\n",
    "big_list.append(df[df.date==\"20141015\"][\"mfcs\"]) #Append the count for the 09:30-09:33 window on Oct 15\n",
    "\n",
    "\n",
    "hist=np.bincount(np.array(big_list))\n",
    "print(sum(hist))\n",
    "assert sum(hist)==WINDOWS_PER_DAY*(len(DATES)-1)+1\n",
    "\n",
    "print(hist)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rDQsW2Yg4V9I3gEcBt0bE1vxjmZmZdb9merJExO+B3+ecxczMrKd47GIzM7OcNCyykvok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\nmpmZ5eT/A7WHAruXPPAuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f53df135828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Figure 3\n",
    "matplotlib.rcParams.update({'font.size': 9})\n",
    "\n",
    "vals=np.array(hist,dtype=np.double)\n",
    "vals[vals==0 ] = np.nan\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7.4,4))\n",
    "ax.scatter(range(0,len(vals)), vals, color='black')\n",
    "plt.xlabel(\"Number of mini flash crashes experienced\")\n",
    "plt.ylabel(\"Number of windows (N=3,881)\")\n",
    "ax.set_yscale(\"log\", nonposx='clip')\n",
    "ax.yaxis.set_major_formatter(ScalarFormatter())\n",
    "#plt.show()\n",
    "plt.savefig(\"control_period2.svg\")"
   ]
  }
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