SOME_COMPANY_1_test_problems.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm, normaltest, t, chisquare\n",
    "from math import sqrt\n",
    "from statsmodels.tsa.stattools import adfuller"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Теоритическая часть"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Три стрелка, попадающих в мишень с вероятностями 0.3, 0.8 и 0.9 независимо друг от друга, делают по одному выстрелу по мишени. Найти вероятность того, что в мишень попадут ровно две пули."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вероятность того, что независимые события произойдут одновременно равна произведению вероятностей этих событий. У нас есть три варианта, какие два стрелка могут попасть: 1 и 2, 1 и 3, 2 и 3, соответствнно в каждом из этих вариантов оставшийся стрелок должен промахнуться. Тогда вероятность попадания ровно двух пуль равна $0.3 \\cdot 0.8 \\cdot (1 - 0.9) + 0.3 \\cdot (1 - 0.8) \\cdot 0.9 + (1 - 0.3) \\cdot 0.8 \\cdot 0.9 = 0.582$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.582"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eval('0.3 \\cdot 0.8 \\cdot (1 - 0.9) + 0.3 \\cdot (1 - 0.8) \\cdot 0.9 + (1 - 0.3) \\cdot 0.8 \\cdot 0.9'.replace('\\cdot', '*'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Точка наудачу бросается в круг с радиусом R. Найти функцию распределения расстояния от этой точки до центра круга."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Хотим найти $F(t) = P(x \\leq t)$, где х - расстояние от случайной точки до круга. Считаем, что случайная величина равномерно распределена внутри круга. Если расстояние $\\leq t$ значит точка попала в круг с радиусом $t$. Для $t \\in [0, R]$ Вероятность этого в силу равномерности равна отношению площади круга ко всему, то есть $F(t) = \\frac{t^2}{R^2}$. Для $t<0$ $F(t) = 0$, для $t > R$ $F(t) = 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Найти доверительный интервал для оценки математического ожидания a нормального распределения с надежностью $0.95$, зная выборочную среднюю $=75.12$, объем выборки $n=121$ и среднее квадратическое отклонение $\\sigma=11$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "По ЦПТ знаем, что: \n",
    "$$\\sqrt{n}\\frac{\\overline{X_n} - \\mu}{\\sigma} \\sim N(0, 1)$$\n",
    "Возьмем квантили $N(0, 1)$: $z_{0.025} = -1.96$ и $z_{0.975} = 1.96$. Тогда с вероятностью 0.95:\n",
    "$$ \\overline{X_n} - 1.96 \\frac{\\sigma}{\\sqrt{n}} \\leq \\mu  \\leq \\overline{X_n} + 1.96 \\frac{\\sigma}{\\sqrt{n}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Доверительный интервал для среднего: (73.16000000000001, 77.08)\n"
     ]
    }
   ],
   "source": [
    "X_n = 75.12\n",
    "z = 1.96\n",
    "sigma = 11\n",
    "n = 121\n",
    "print(f'Доверительный интервал для среднего: ({X_n - z * sigma / (n ** (1/2))}, {X_n + z * sigma / (n ** (1/2))})')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Практическая часть"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В качестве акций гугла я взял GOOGL."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_apple = pd.read_csv('SOME_COMPANY_1_data/daily_AAPL.csv', sep=',')\n",
    "df_google = pd.read_csv('SOME_COMPANY_1_data/daily_GOOGL.csv', sep=',')\n",
    "df_fb = pd.read_csv('SOME_COMPANY_1_data/daily_FB.csv', sep=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_returns_from_df(df):\n",
    "    return df.sort_values(by='timestamp')['close'].diff().dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_apple_returns, df_google_returns, df_fb_returns = list(map(get_returns_from_df, (df_apple, df_google, df_fb)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В функции ниже я строю гистограмму исходного распределения, отсекая выброы, после чего высчитываю выборочные средние и дисперсию. Заменяю выборочную дисперсию на несмещённую и строю различные распределения такого же размера выборки с такими же средними и дисперсией. Для t-распределения я сначала высчитываю количество степеней свободы по дипсперсии. Также провожу тест на нормальность и хи-квадрат тест на соответствие t-распределению. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\text{Var} = \\frac{\\nu}{\\nu - 2}\\implies \\nu = \\frac{2}{1 - \\frac{1}{\\text{Var}}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для того, чтобы высчитать частоту в t-распределении я беру для данного интервала разность CDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_returns_hist(df):\n",
    "    fig, axes = plt.subplots(3, 1, figsize = (8, 6))\n",
    "    df_foo = df[df.between(df.quantile(q=0.001), df.quantile(q=0.999))]\n",
    "    axes[0].hist(x=df_foo.values, bins=500)\n",
    "#     plt.xlim(df.quantile(q=0.001), df.quantile(q=0.999))\n",
    "    \n",
    "    distr_mean = np.mean(df_foo)\n",
    "    distr_std = sqrt(np.var(df_foo) / (df_foo.shape[0] - 1) * df_foo.shape[0])\n",
    "    \n",
    "    x = np.linspace(df_foo.min(), df_foo.max(), 1000)\n",
    "    axes[1].hist(\n",
    "        x=np.random.normal(size=df_foo.shape[0], loc=distr_mean, scale=distr_std), \n",
    "        bins=500, range=(df_foo.min(), df_foo.max()))\n",
    "    \n",
    "    nu = 2 / (1 - (1 / distr_std ** 2))\n",
    "    \n",
    "    axes[2].hist(x=t.rvs(loc=distr_mean, df=nu, size=df_foo.shape[0]), bins=500, range=(df_foo.min(), df_foo.max()))\n",
    "    \n",
    "    df_freq = (pd.qcut(df_foo, q=[(1/4) * i for i in range(5)]).value_counts() / df_foo.shape[0]).reset_index().rename(\n",
    "        columns={'index': 'interval', 'close': 'count'})\n",
    "    \n",
    "    df_freq['expected'] = df_freq['interval'].apply(\n",
    "        lambda x: t.cdf(x=x.right, df=nu, loc=distr_mean) - t.cdf(x=x.left, df=nu, loc=distr_mean))\n",
    "    \n",
    "    normal_pvalue = normaltest(df_foo).pvalue.round(4)\n",
    "    t_pvalue = chisquare(df_freq['count'], df_freq['expected']).pvalue.round(4)\n",
    "    \n",
    "    axes[0].title.set_text(f'Original Data, Normal pvalue = {normal_pvalue},' + f'T pvalue = {t_pvalue}')\n",
    "    axes[1].title.set_text('Normal Distribution Simulation')\n",
    "    axes[2].title.set_text('T-Test Distribution Simulation')\n",
    "    \n",
    "    fig.tight_layout()\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DI0mSOscAR5IkdY4BjqRpOZ9G0kpmgCNpyRk8SRo2AxxJI2GQI2mYDHAk9WUQImmlMsCRNHQGSpKWmgGOJEnqHAMcSZLUOQY4kiSpcxb1Uw1JrgJuA+4B7q6qNUm2Az4KrAauAl5aVT9cXDEljcqg5884H0fSUhhED84zq2qvqlrTPj8aOKeq9gDOaZ9LWkEMQiStdMMYojoQOKF9fAJw0BD2IUmS1NdiA5wCPp9kXZLD27Qdq2o9QPt/h0XuQ5IkaV4WNQcHeGpVXZ9kB+DsJN+b64ZtQHQ4wG677bbIYkiSJG2yqB6cqrq+/X8DcDrwJGBDkp0A2v839Nn2uKpaU1VrVq1atZhiSBoQ595I6ooFBzhJHpRkq4nHwLOB7wBnAIe1qx0GfHqxhZQ0XMshsFkOZZDUHYsZotoROD3JRD4nV9Vnk5wHnJbklcA1wEsWX0xJw2JgIamLFhzgVNX3gSdMk34TsM9iCiVJkrQYfpOxJGC0PTn2IkkaNAMcSSNjYCNpWAxwpDEzW1Cx1EGHQY6kYTDAkSRJnWOAI42JldZTstLKK2l5McCRJEmdY4AjadlYffRZ9txIGggDHEnLjkGOpMUywJG0bBnoSFooAxxJktQ5i/ktKkkrlD0jkrrOHhxJktQ5BjiSJKlzDHCkMbDSh6RWevklLT0DHEmS1DkGOJJWFHtzJM3FggOcJLsm+VKSS5JcnOR1bfoxSa5LckH7d8DgiitprsYpEBinY5U0N4u5Tfxu4PVVdX6SrYB1Sc5ul/11Vb178cWTJEmavwX34FTV+qo6v318G3AJsMugCiZp8ab2bHSlp6P3OLpyTJIGayBzcJKsBvYGvtkmHZHkwiTHJ9m2zzaHJ1mbZO3GjRsHUQxJkiRgAAFOki2BTwBHVtWtwAeARwJ7AeuB90y3XVUdV1VrqmrNqlWrFlsMaWyNSw/GuBynpMFYVICT5H40wc1JVfVJgKraUFX3VNXPgQ8CT1p8MSXNVVeHpRbLepDGy2LuogrwYeCSqnpvT/pOPau9EPjOwosnSZsYpEiaq8XcRfVU4FDgoiQXtGlvAg5JshdQwFXAqxdVQkljzaBG0kIsOMCpqq8BmWbRZxZeHEkanNVHn8VVxz531MWQNAKL6cGRpJGxZ0fSTPypBqlDJi76XvwljTsDHGmF8MvtZjddHVlX0ngywJHUCXMJZAx6pPFhgCN1gBfsmdn7JY0fAxxpGZlvD4MX68GxLqVuMcCRlrGZAh6/sbg/60KSt4lLK4gXbkmaG3twpGXOoGZ+rC9JYIAjLTteoJfWTEN983ktfN2k5cUAR1oCM138vDCOjnUvdZcBjjQHXggFtgNpJTHAkXoM+wI20/CHF8+lZX1L3WaAI02xmAvfXIai5nLL92LLocHzu4mklcUAR503n6/wn8+yuW4zU/DixXB5mO21nK23baGv43R5SxqMoQU4SfZLcmmSy5McPaz9SL0GfbFYyB01/izAyrfQwGO2bUbRHoa5T9u3lrOhBDhJNgP+Htgf2BM4JMmew9iXRmPQPRCDuB13LoHF1AtX7/OF/FjjTBdCT/4rz6B+sHOiXUzXTvq1mYUEVQtpu4tlu9ZKMawenCcBl1fV96vqp8CpwIFD2tesFnrSGEYZ5vIJb7HDG3PtQeg9CU934e63z+mWLeQEO9t2/QKRueYxl7qcad/zCVwcahhfw+i1mS4g6vdenWlf8ynbXM41cw3u5rvvuaTPNZ/ZzmELMcye4eViWMPmozzWVNXgM01eDOxXVa9qnx8KPLmqjuhZ53Dg8Pbpo4FLB16QxdseuHHUhVgmrIvJrI9NrIvJrI9NrIvJrI9NBlkXD6+qVVMTh/VbVJkmbVIkVVXHAccNaf8DkWRtVa0ZdTmWA+tiMutjE+tiMutjE+tiMutjk6Woi2ENUV0L7Nrz/GHA9UPalyRJ0iTDCnDOA/ZIsnuS+wMHA2cMaV+SJEmTDGWIqqruTnIE8DlgM+D4qrp4GPsasmU9hLbErIvJrI9NrIvJrI9NrIvJrI9Nhl4XQ5lkLEmSNEp+k7EkSeocAxxJktQ5BjhTJPlokgvav6uSXNCmr05yZ8+yfxh1WZdCkmOSXNdz3Af0LHtj+1MclyZ5zijLuRSSvCvJ95JcmOT0JNu06WPZNmC8f5Ilya5JvpTkkiQXJ3ldm973PdN17Tnzova417Zp2yU5O8ll7f9tR13OYUvy6J7X/4IktyY5cpzaRpLjk9yQ5Ds9aX3bwjCuJ87BmUGS9wA/qqq3JlkNnFlVjxttqZZWkmOA26vq3VPS9wROofnW6p2BLwCPqqp7lryQSyTJs4EvtpPo3wFQVUeNcdvYDPgv4Fk0Xw1xHnBIVX13pAVbIkl2AnaqqvOTbAWsAw4CXso075lxkOQqYE1V3diT9k7g5qo6tg2Ct62qo0ZVxqXWvk+uA54MvIIxaRtJng7cDvzLxLmxX1sY1vXEHpw+koTmRHXKqMuyTB0InFpVd1XVlcDlNI2zs6rq81V1d/v0XJrvdxpny+onWZZaVa2vqvPbx7cBlwC7jLZUy9KBwAnt4xNogsBxsg9wRVVdPeqCLKWq+ipw85Tkfm1hKNcTA5z+ngZsqKrLetJ2T/KfSb6S5GmjKtgIHNEOyxzf06W4C/CDnnWuZbxO7r8P/FvP83FsG+PeBu7V9uLtDXyzTZruPTMOCvh8knXtz/EA7FhV66EJCoEdRla60TiYyR+Ux7VtQP+2MJRzyVgGOEm+kOQ70/z1fvo8hMmNcj2wW1XtDfwxcHKSrZey3MMyS318AHgksBdNHbxnYrNpslrx451zaRtJ/hS4GzipTeps25hFJ9vAfCXZEvgEcGRV3Ur/98w4eGpVPRHYH3htO0wxttJ80e0LgI+1SePcNmYylHPJsH6Lalmrqn1nWp5kc+BFwC/3bHMXcFf7eF2SK4BHAWuHWNQlMVt9TEjyQeDM9mknf45jDm3jMOB5wD7VTmDrctuYRSfbwHwkuR9NcHNSVX0SoKo29Czvfc90XlVd3/6/IcnpNMMMG5LsVFXr23lLN4y0kEtrf+D8iTYxzm2j1a8tDOVcMpY9OHOwL/C9qrp2IiHJqnayGEkeAewBfH9E5VsybSOc8EJgYkb8GcDBSbZIsjtNfXxrqcu3lJLsBxwFvKCq7uhJH8u2wZj/JEs7T+/DwCVV9d6e9H7vmU5L8qB2sjVJHgQ8m+bYzwAOa1c7DPj0aEo4EpNGAsa1bfTo1xaGcj0Zyx6cOZg6ZgrwdOCtSe4G7gFeU1VTJ1B10TuT7EXTXXgV8GqAqro4yWnAd2mGa17b5TuoWu8DtgDObq5tnFtVr2FM20aHfpJloZ4KHApclPbrJIA3AYdM954ZAzsCp7fvjc2Bk6vqs0nOA05L8krgGuAlIyzjkknyQJo7DHtf/2nPp12U5BTgGcD2Sa4F3gwcyzRtYVjXE28TlyRJneMQlSRJ6hwDHEmS1DkGOJIkqXMMcCRJUucY4EiSpM4xwJEkSZ1jgCNJkjrHAEeSJHWOAY4kSeocAxxJktQ5BjiSJKlzDHAkSVLnGOBIHZPkmCQnLjKP25M8YkDleVOSD7WPVyepJJsPKO/d2rJuNoj85rHfe49pCHl/OcmrFrjtSOpDWo4McKR5SnJVkg1JHtST9qokXx5hseYkyTOS/Ly9CN6e5NokpyX5ld71qmrLqvr+HPK6drZ9VtVfVdWCLtjT7POqJPv25H1NW9Z7BpH/lH0dmOSCJLcmuTHJOUlWt/sd2DEtxlLWh7TSGOBIC7M58LrFZpLGUr8Pr6+qLYGtgF8Fvgf8e5J9Br2jQfXULLUk/wP4F+D1wIOB3YH3Az8fZbkkzZ0BjrQw7wLekGSb6RYmeUqS85L8qP3/lJ5lX07ytiT/AdwBPKJN+8skX297Vv41yUOSnNT2IJw30XvQ5vG3SX7QLluX5GnzPYBqXFtVfw58CHhHT/7VXuRJckCS7ya5Lcl1Sd7Q9l79G7BzT2/Qzu3w2MeTnJjkVuD3+gyZ/X6S65OsT/L6nv3+c5K/7Hl+by9Rko8AuwH/2u7vT6YOebVlOCPJzUkuT/IHPXkd0/ZW/Ut7LBcnWdOnevYCrqyqc9p6uq2qPlFV1/TkdWL7eKIMr2hfkx8meU2SX0lyYZJbkrxvSjlO7Hned9guySOTfDHJTW0v0kkTbW6J60NacQxwpIVZC3wZeMPUBUm2A84C/g54CPBe4KwkD+lZ7VDgcJpelKvbtIPb9F2ARwLfAP4J2A64BHhzz/bn0VyEtwNOBj6W5AGLOJ5PAk9Mz7Bbjw8Dr66qrYDHAV+sqh8D+9P2BrV/17frHwh8HNgGOKnP/p4J7AE8Gzi6d5iln6o6FLgGeH67v3dOs9opwLXAzsCLgb+a0jP1AuDUtmxnAO+7Tw6N84HHJPnrJM9MsuVs5QOe3B7TbwN/A/wpsC/wWOClSX5jDnlMFeDt7fH8ErArcAwseX1IK44BjrRwfw78YZJVU9KfC1xWVR+pqrur6hSaYaDn96zzz1V1cbv8Z23aP1XVFVX1I5rekSuq6gtVdTfwMWDviY2r6sSquqnd/j3AFsCjF3Es19NcTKfrkfoZsGeSravqh1V1/ix5faOqPlVVP6+qO/us85aq+nFVXUQTxB2y8KI3kuwK/DpwVFX9pKouoOmZOrRnta9V1WfaOSofAZ4wXV7t/KNn0ASbpwE3tr1LMwU6f9Hu9/PAj4FTquqGqroO+Hd6Xr+5qqrLq+rsqrqrqjbSBMtzCpQGWR/SSmSAIy1QVX0HOBM4esqindnUKzPhapqL5YQfTJPlhp7Hd07z/N6La5LXJ7mkHQK7hWaeyPbzO4JJdgEKuGWaZb8FHABcneQrSX5tlrymO7aZ1rmaps4Wa2fg5qq6bUrevfX+3z2P7wAeMN3QEEBVnVtVL62qVcDTgKfT9Mr0M+fXb66S7JDk1HZo8FbgROb+Og+0PqSVxgBHWpw3A3/A5IvG9cDDp6y3G3Bdz/Na6A7b+TZHAS8Ftq2qbYAf0fTALNQLgfPboadJquq8qjoQ2AH4FE2PBvQ/hrkc2649j3ejqTNoej4e2LPsofPI+3pguyRbTcn7uj7rz1lVnUczjPe4xebF7MfY6+00x/z4qtoaeDmTX+eR1Ie0EhjgSItQVZcDHwX+qCf5M8CjkvxOks2T/DawJ01vzyBsBdwNbAQ2T/LnwNbzzSSNXZK8GXgV8KZp1rl/kpcleXA7lHYrMHEL8gbgIUkevIBj+LMkD0zyWOAVNHUIcAFwQJLtkjwUOHLKdhuAab+fp6p+AHwdeHuSByR5PPBK+s8D6ivJryf5gyQ7tM8fQzNf5dz55jWNC4Cnp/nOmgcDb5xh3a2A24FbkuwC/N8py5ekPqSVyABHWry3AvdOzq2qm4Dn0dxifBPwJ8DzqurGAe3vczRzdP6LZsjhJ8xtWGjCzklup7lwngf8T+AZ7dyR6RwKXNUOkbyGpheBqvoezSTW77d3Cs1nmOkrwOXAOcC7e/b9EeDbwFXA59kU+Ex4O/D/2v3dZ4I3zVye1TS9F6cDb66qs+dRrgm30AQ0F7V19dk2v+km8s5LW56PAhcC65g58H0L8ESaHrqzaHqRei1VfUgrTqoW3FMuSZK0LNmDI0mSOscAR5IkdY4BjiRJ6hwDHEmS1DnL4gudtt9++1q9evWoiyFJklaYdevW3dh+IeckyyLAWb16NWvXrh11MSRJ0gqTZOo3xwMOUUmSpA4ywJEkSZ1jgCNp6FYffdaoiyBpzBjgSJKkzjHAkSRJnWOAI0mSOscAR5IkdY4BjiRJ6hwDHEmS1DkGOJKWLW8vl7RQBjiSJKlzDHAkSVLnGOBIY2o+wz8zrdtvmcNLkkbJAEeSJHWOAY6kebN3RtJyZ4AjaUkYFElaSgY4kiSpcwxwpDFnz4qkLjLAkSRJnWOAI2law+jZsbdI0lIxwJEkSZ1jgCNJkjrHAEcaQwsdKhrUENPqo8+aNq+55u9Ql6TZGOBIY2a+P7swkTZ1mUGGpOXMAEeSJHWOAY40RgbR6zKXPHrXsedH0igY4EiSpM5ZdICTZLMk/5nkzPb5dknOTnJZ+3/bxRdT0lLpNwG437q9//stn0se873q13QAABrXSURBVN1OkmYyiB6c1wGX9Dw/GjinqvYAzmmfSxqxhQQNS7WNJA3aogKcJA8Dngt8qCf5QOCE9vEJwEGL2YckSdJ8LbYH52+APwF+3pO2Y1WtB2j/7zDdhkkOT7I2ydqNGzcushiSeo2iF2WQ35EjSYu14AAnyfOAG6pq3UK2r6rjqmpNVa1ZtWrVQoshaRlZTHBiYCNpkDZfxLZPBV6Q5ADgAcDWSU4ENiTZqarWJ9kJuGEQBZUkSZqrBffgVNUbq+phVbUaOBj4YlW9HDgDOKxd7TDg04supaSh6EKvSReOQdLgDeN7cI4FnpXkMuBZ7XNJkqQlM5AAp6q+XFXPax/fVFX7VNUe7f+bB7EPScMz6l6QUe9fUvf4TcZSxxgsSJIBjiRJ6iADHKnjutCj04VjkLS0DHAkSVLnGOBIWtbsvZG0EAY4UgfMFgQs9Fe9l5Op5Vvu5ZU0WgY4kiSpcwxwJK0o/Xpu7NGR1MsAR1phxvkCPw7HKGkwDHAkSVLnGOBIK1QXejNGcQxdqDdJszPAkSRJnWOAI3XYuPVWjNvxSurPAEfqKC/2ksaZAY4kSeocAxxJy9Jie6Dmur09XVI3GeBIkqTOMcCRJEmdY4Ajdci4DbfM53jHrW6kcWeAI0mSOscAR1qGVh99lj0OA2AdSuPLAEdaxuZygfYiLkn3ZYAjSZI6Z8EBTpJdk3wpySVJLk7yujZ9uyRnJ7ms/b/t4Iorja/enhp7bfqbrm4m0qw3aXwspgfnbuD1VfVLwK8Cr02yJ3A0cE5V7QGc0z6XJElaMgsOcKpqfVWd3z6+DbgE2AU4EDihXe0E4KDFFlLqMufZLL3penSsY6lbBjIHJ8lqYG/gm8COVbUemiAI2KHPNocnWZtk7caNGwdRDKnzvAhPb5D1Yh1L3bDoACfJlsAngCOr6ta5bldVx1XVmqpas2rVqsUWQ5Ik6V6LCnCS3I8muDmpqj7ZJm9IslO7fCfghsUVUeqWmXoIZpogO9+81OhXRw5PSd22mLuoAnwYuKSq3tuz6AzgsPbxYcCnF148SZKk+dt8Eds+FTgUuCjJBW3am4BjgdOSvBK4BnjJ4oooSZI0PwsOcKrqa0D6LN5noflK0mI55CTJbzKWJEmdY4AjDZE9CSuTr5u08hngSAM0iAujF1dJWjwDHEmS1DkGOJIkqXMMcKQh85esVz5fO2nlMcCRJEmdY4AjzWIYn95XH32WPxWwDPk6SN1hgCNJkjrHAEeS+rBHR1q5DHCkEXKYSpKGwwBHkiR1jgGOtAhz7XWxd2Y8+DpLy4cBjjQk013svAB2n6+xtDwY4EiSpM4xwJEWwE/p3TfdN1D3fn/RTG3A9iGNngGOJEnqHAMcaY76fSp3rs14mO319zWXlhcDHGnAvNB131yHqWwL0ugY4EiSpM4xwJHmoN+E0+nW0fixJ0dafgxwJElS5xjgaKzNZ+LwQvKRJnhbubS0hhbgJNkvyaVJLk9y9LD2I8H0wwBzveul3/9+eXgx0mJMbavzvQvL9ifNzVACnCSbAX8P7A/sCRySZM9h7EuSJGmqYfXgPAm4vKq+X1U/BU4FDhzSvtQBc52IOd9vkp3rp2U/FWsp9PtW5KlpMy2bmtdsPY4zlWE+20krTapq8JkmLwb2q6pXtc8PBZ5cVUf0rHM4cHj79NHApQMvyOJtD9w46kIsE9bFZNbHJtbFZNbHJtbFZNbHJoOsi4dX1aqpiZsPKPOpMk3apEiqqo4DjhvS/gciydqqWjPqciwH1sVk1scm1sVk1scm1sVk1scmS1EXwxqiuhbYtef5w4Drh7QvSZKkSYYV4JwH7JFk9yT3Bw4GzhjSviRJkiYZyhBVVd2d5Ajgc8BmwPFVdfEw9jVky3oIbYlZF5NZH5tYF5NZH5tYF5NZH5sMvS6GMslYkiRplPwmY0mS1DkGOJIkqXMMcKZI8tEkF7R/VyW5oE1fneTOnmX/MOqyLoUkxyS5rue4D+hZ9sb2pzguTfKcUZZzKSR5V5LvJbkwyelJtmnTx7JtwHj/JEuSXZN8KcklSS5O8ro2ve97puvac+ZF7XGvbdO2S3J2ksva/9uOupzDluTRPa//BUluTXLkOLWNJMcnuSHJd3rS+raFYVxPnIMzgyTvAX5UVW9Nsho4s6oeN9pSLa0kxwC3V9W7p6TvCZxC863VOwNfAB5VVfcseSGXSJJnA19sJ9G/A6CqjhrjtrEZ8F/As2i+GuI84JCq+u5IC7ZEkuwE7FRV5yfZClgHHAS8lGneM+MgyVXAmqq6sSftncDNVXVsGwRvW1VHjaqMS619n1wHPBl4BWPSNpI8Hbgd+JeJc2O/tjCs64k9OH0kCc2J6pRRl2WZOhA4taruqqorgctpGmdnVdXnq+ru9um5NN/vNM7G+idZqmp9VZ3fPr4NuATYZbSlWpYOBE5oH59AEwSOk32AK6rq6lEXZClV1VeBm6ck92sLQ7meGOD09zRgQ1Vd1pO2e5L/TPKVJE8bVcFG4Ih2WOb4ni7FXYAf9KxzLeN1cv994N96no9j2xj3NnCvthdvb+CbbdJ075lxUMDnk6xrf44HYMeqWg9NUAjsMLLSjcbBTP6gPK5tA/q3haGcS8YywEnyhSTfmeav99PnIUxulOuB3apqb+CPgZOTbL2U5R6WWerjA8Ajgb1o6uA9E5tNk9WKH++cS9tI8qfA3cBJbVJn28YsOtkG5ivJlsAngCOr6lb6v2fGwVOr6onA/sBr22GKsZXmi25fAHysTRrntjGToZxLhvVbVMtaVe070/IkmwMvAn65Z5u7gLvax+uSXAE8Clg7xKIuidnqY0KSDwJntk87+XMcc2gbhwHPA/apdgJbl9vGLDrZBuYjyf1ogpuTquqTAFW1oWd573um86rq+vb/DUlOpxlm2JBkp6pa385bumGkhVxa+wPnT7SJcW4brX5tYSjnkrHswZmDfYHvVdW1EwlJVrWTxUjyCGAP4PsjKt+SaRvhhBcCEzPizwAOTrJFkt1p6uNbS12+pZRkP+Ao4AVVdUdP+li2Dcb8J1naeXofBi6pqvf2pPd7z3Rakge1k61J8iDg2TTHfgZwWLvaYcCnR1PCkZg0EjCubaNHv7YwlOvJWPbgzMHUMVOApwNvTXI3cA/wmqqaOoGqi96ZZC+a7sKrgFcDVNXFSU4DvkszXPPaLt9B1XofsAVwdnNt49yqeg1j2jY69JMsC/VU4FDgorRfJwG8CThkuvfMGNgROL19b2wOnFxVn01yHnBaklcC1wAvGWEZl0ySB9LcYdj7+k97Pu2iJKcAzwC2T3It8GbgWKZpC8O6nnibuCRJ6hyHqCRJUucY4EiSpM4xwJEkSZ1jgCNJkjrHAEeSJHWOAY4kSeocAxxJktQ5BjiSJKlzDHAkSVLnGOBIkqTOMcCRJEmdY4AjSZI6xwBHEgBJ/meS/x5gfqck+aP28UFJvjPAvJ+X5FuDym8e+733mIaQ9y1J1ixw25HUh7ScGeBIi5Dk9p6/nye5s+f5y6asu2/Psh8nqSnb77DAMmzT5rX9DOscmeTunn1dkeS4JKsn1qmqi6rqoXPY35FJzpxtvao6pKr+bq7HMcP+7nN8VXVmVT1psXn32d/rklze1tP6JJ9Osnm734Ec0yLLt6T1Ia1UBjjSIlTVlhN/wDXA83vSTpqy7hd61v1l4J7e7avqhiEX97PtvrcBDgC2ANYlecQgd5LGZoPMc6kkORD4Y+AFbV09Hpg1mJO0/BjgSMtIku2TnJxkQ5JrkrwpSdpl/zPJN5L8KMkNST7UbvbV9v9Vba/DfjPto6rurqpLq+ow4LvAm9r890pye09ZXtuW4ba2R+PAJL8GvAPYr93XVe26n0ry3iRfBH4M7N2mvWHK8b09yQ/bHqQDe9IvSPLinue9vUT3Ob6pQ15J9k7y9bZuLkiyb8+yTyV5V5Jz2mP5apJd+lTPrwBfqqrvtnW1sao+WFV39+T1hvbxQUm+k+StSW5K8oMkz0rykiRXJrkxyRFTyvGGnud9h+2SPDPJee3xXNeWf+J8vZT1Ia1YBjjS8vIx4Hrg4cBTgJcBL22XvRM4iaYHZjVwfJv+9Pb/6rYn6LPz2N/pwNOmJiZ5KPAW4OlVtRXwDOB7VfUN4Cja3qCqWt2z2cuB/wtsBVw4zb4eA9wF7Aj8IXBykofNoYwzHl+SBwGfoamb7YH/B5w+Je+XAf8HeAjwI+DP+uzrXOC3kvxpkicnud8sZXsMcHN7TH8HnEDTO/ZY4LnAu7Kwoce7gFcD2wG/SdMGfrddtpT1Ia1YBjjSMpHk0cDewFFV9ZOquhZ4H3Bwu8rPgN2BHavqjqr6+gB2ez3NRXSqnwObAY9NskVVXVtVl86S16lVta6q7qmqn06z/A7gbVX106r6DPAfwAsXVfrGbwK3VdXfV9XPqupM4GvAi3vWObmqLmzLdQqw13QZtdseRhP0fQG4MclfTPSiTeNm4G/bHp5TgZ2AY9vX55s09bvnfA+oqr5eVee3dXkp8E/Ab8xx84HVh7SSGeBIQ5Jks0yeRLzzLJs8nKb346Y0d9TcQjMctGO7/AiaT+TfbocdfnsAxdyF5iI9STsf6BXAG4ANSU5Psvssef1gluUbqupnPc+vBmark7nYuc2r19U0xzah9+6wO4At+2VWVZ+sqv1oesp+h2ZOzkv7rH5DVVX7+M72/4ae5XfOtK9+kjw+yefaocof0fSa9Z1EPsVA60NaqQxwpCFpP333TiK+fpZNfgDcVFXb9PxtXVVPafO7pp0381CaoaATk+wI1Ax5zuYg4N/7lP9TVfVMmgvjRpohGGbY32zl2HHKkM9uND0c0MzbeWDPst67uWbLd2JIr9duwHWzbDej9vU7C/gG8LjF5NWa6Rin+ifg68AjqurBNIHuRC/SSOpDWmkMcKTl43vAd5P8ZZIHJfmFJI9O8hSAJAcneWjbY/Cjdpu7gVuBnwBzuhuq7VnaI8nxNHNF3j7NOg9vJ6/+Is18kB8D97SLNwC7pb11eh4eCLwxyf3aidBPAz7VLrsAeEmSLZI8jmY+z4TZju+LwNZJ/leSzZMc0Ob9iXmWb6KOX5TkwWn8BvAkmrk5i3UB8IIkWyfZDfjfM6y7FXBLVf04yeOB3+9ZtmT1Ia1kBjjSMtEGLi+m6TG5jGboaGKiKDSTSy9Ic6fTR4DDquqmdrs/B85sh7ae02cX+7Xb3gp8jmaezZqqumKadTdv89xA03vzWJpJqdDcNr0R2Jhkum37+R5NkHMD8H7gZVU1Maz1V8CDgZtoeopOnNhotuOrqh/TTOj93Xb7twO/1ZP3fNwCvA64kqae/gF4Y9uTs1j/SNO7ci3wSeDkGdZ9HfCH7ev1Xpr5PcCS14e0YmXT8LEkSVI32IMjSZI6xwBHkiR1jgGOJEnqHAMcSZLUOfO9zXMott9++1q9evWoiyFJklaYdevW3VhVq6amL4sAZ/Xq1axdu3bUxZAkSStMkqnf3A04RCVJkjrIAEeSJHWOAY4kSeocAxxJi7b66EH8koEkDY4BjiRJ6hwDHEmS1DkGOJIkqXMMcCRJUucY4EiSpM4xwJEkSZ1jgCNpUbxFXNJyZIAjSZI6xwBH0kDYkyNpOTHAkSRJnTPnACfJZkn+M8mZ7fPtkpyd5LL2/7Y9674xyeVJLk3ynGEUXJIkqZ/59OC8Drik5/nRwDlVtQdwTvucJHsCBwOPBfYD3p9ks8EUV5IkaXZzCnCSPAx4LvChnuQDgRPaxycAB/Wkn1pVd1XVlcDlwJMGU1xJkqTZzbUH52+APwF+3pO2Y1WtB2j/79Cm7wL8oGe9a9u0SZIcnmRtkrUbN26cd8ElSZL6mTXASfI84IaqWjfHPDNNWt0noeq4qlpTVWtWrVo1x6wlSZJmt/kc1nkq8IIkBwAPALZOciKwIclOVbU+yU7ADe361wK79mz/MOD6QRZakiRpJrP24FTVG6vqYVW1mmby8Ber6uXAGcBh7WqHAZ9uH58BHJxkiyS7A3sA3xp4ySWNnN99I2m5mksPTj/HAqcleSVwDfASgKq6OMlpwHeBu4HXVtU9iy6pJEnSHM0rwKmqLwNfbh/fBOzTZ723AW9bZNkkSZIWxG8yliRJnWOAI0mSOscAR5IkdY4BjiRJ6hwDHEmS1DkGOJIkqXMMcCRJUucY4EiSpM4xwJEkSZ1jgCNJkjrHAEeSJHWOAY4kSeocAxxJA7P66LNGXQRJAgxwJElSBxngSJKkzjHAkSRJnWOAI0mSOscAR5IkdY4BjiRJ6hwDHEmS1DkGOJIkqXMMcCRJUucY4EiSpM4xwJEkSZ1jgCNJkjrHAEeSJHWOAY4kSeocAxxJA7X66LNGXQRJMsCRJEndY4AjSZI6Z9YAJ8muSb6U5JIkFyd5XZu+XZKzk1zW/t+2Z5s3Jrk8yaVJnjPMA5AkSZpqLj04dwOvr6pfAn4VeG2SPYGjgXOqag/gnPY57bKDgccC+wHvT7LZMAovSZI0nVkDnKpaX1Xnt49vAy4BdgEOBE5oVzsBOKh9fCBwalXdVVVXApcDTxp0wSVJkvqZ1xycJKuBvYFvAjtW1XpogiBgh3a1XYAf9Gx2bZs2Na/Dk6xNsnbjxo3zL7kkSVIfcw5wkmwJfAI4sqpunWnVadLqPglVx1XVmqpas2rVqrkWQ5IkaVZzCnCS3I8muDmpqj7ZJm9IslO7fCfghjb9WmDXns0fBlw/mOJKkiTNbi53UQX4MHBJVb23Z9EZwGHt48OAT/ekH5xkiyS7A3sA3xpckSUtB36hn6TlbPM5rPNU4FDgoiQXtGlvAo4FTkvySuAa4CUAVXVxktOA79LcgfXaqrpn4CWXJEnqY9YAp6q+xvTzagD26bPN24C3LaJckiRJC+Y3GUuSpM4xwJEkSZ1jgCNp4JyALGnUDHAkzZsBjKTlzgBHkiR1jgGOJEnqHAMcSZLUOQY4kiSpcwxwJElS5xjgSJKkzjHAkSRJnWOAI2le/A4cSSuBAY4kSeocAxxJQ2FPj6RRMsCRJEmdY4AjSZI6xwBHkiR1jgGOpKFxHo6kUTHAkSRJnWOAI2nO7JGRtFIY4EiSpM4xwJE0VPb6SBoFAxxJktQ5BjiSJKlzDHAkzclihpocppK01AxwJElS5xjgSJrVIHpg7MWRtJQMcCTNyMBE0kpkgCNJkjrHAEfStFYffdbQem/sFZI0bEMLcJLsl+TSJJcnOXpY+5E0WMMMPnqDpmEGUJI0lAAnyWbA3wP7A3sChyTZcxj7kjQ3vcHEdIHFbMuHaZT7ltRNqarBZ5r8GnBMVT2nff5GgKp6+3Trr1mzptauXTvwckjDtvros7jq2OeOdP/AfcrQxSDhqmOfO+PxTiwf5eshaeklWVdVa+6TPqQA58XAflX1qvb5ocCTq+qInnUOBw5vnz4auHTgBVm87YEbR12IZcK6mMz62MS6mMz62MS6mMz62GSQdfHwqlo1NXHzAWU+VaZJmxRJVdVxwHFD2v9AJFk7XVQ4jqyLyayPTayLyayPTayLyayPTZaiLoY1yfhaYNee5w8Drh/SviRJkiYZVoBzHrBHkt2T3B84GDhjSPuSJEmaZChDVFV1d5IjgM8BmwHHV9XFw9jXkC3rIbQlZl1MZn1sYl1MZn1sYl1MZn1sMvS6GMokY0mSpFHym4wlSVLnGOBIkqTOMcCZIslHk1zQ/l2V5II2fXWSO3uW/cOoy7oUkhyT5Lqe4z6gZ9kb25/iuDTJc0ZZzqWQ5F1JvpfkwiSnJ9mmTR/LtgHj/ZMsSXZN8qUklyS5OMnr2vS+75mua8+ZF7XHvbZN2y7J2Ukua/9vO+pyDluSR/e8/hckuTXJkePUNpIcn+SGJN/pSevbFoZxPXEOzgySvAf4UVW9Nclq4MyqetxoS7W0khwD3F5V756SvidwCvAkYGfgC8CjquqeJS/kEknybOCL7ST6dwBU1VFj3DY2A/4LeBbNV0OcBxxSVd8dacGWSJKdgJ2q6vwkWwHrgIOAlzLNe2YcJLkKWFNVN/akvRO4uaqObYPgbavqqFGVcam175PrgCcDr2BM2kaSpwO3A/8ycW7s1xaGdT2xB6ePJKE5UZ0y6rIsUwcCp1bVXVV1JXA5TePsrKr6fFXd3T49l+b7ncbZk4DLq+r7VfVT4FSadjEWqmp9VZ3fPr4NuATYZbSlWpYOBE5oH59AEwSOk32AK6rq6lEXZClV1VeBm6ck92sLQ7meGOD09zRgQ1Vd1pO2e5L/TPKVJE8bVcFG4Ih2WOb4ni7FXYAf9KxzLeN1cv994N96no9j2xj3NnCvthdvb+CbbdJ075lxUMDnk6xrf44HYMeqWg9NUAjsMLLSjcbBTP6gPK5tA/q3haGcS8YywEnyhSTfmeav99PnIUxulOuB3apqb+CPgZOTbL2U5R6WWerjA8Ajgb1o6uA9E5tNk9WKH++cS9tI8qfA3cBJbVJn28YsOtkG5ivJlsAngCOr6lb6v2fGwVOr6onA/sBr22GKsZXmi25fAHysTRrntjGToZxLhvVbVMtaVe070/IkmwMvAn65Z5u7gLvax+uSXAE8CljxP4M+W31MSPJB4Mz2aSd/jmMObeMw4HnAPtVOYOty25hFJ9vAfCS5H01wc1JVfRKgqjb0LO99z3ReVV3f/r8hyek0wwwbkuxUVevbeUs3jLSQS2t/4PyJNjHObaPVry0M5Vwylj04c7Av8L2qunYiIcmqdrIYSR4B7AF8f0TlWzJtI5zwQmBiRvwZwMFJtkiyO019fGupy7eUkuwHHAW8oKru6Ekfy7bBmP8kSztP78PAJVX13p70fu+ZTkvyoHayNUkeBDyb5tjPAA5rVzsM+PRoSjgSk0YCxrVt9OjXFoZyPRnLHpw5mDpmCvB04K1J7gbuAV5TVVMnUHXRO5PsRdNdeBXwaoCqujjJacB3aYZrXtvlO6ha7wO2AM5urm2cW1WvYUzbRod+kmWhngocClyU9uskgDcBh0z3nhkDOwKnt++NzYGTq+qzSc4DTkvySuAa4CUjLOOSSfJAmjsMe1//ac+nXZTkFOAZwPZJrgXeDBzLNG1hWNcTbxOXJEmd4xCVJEnqHAMcSZLUOQY4kiSpcwxwJElS5xjgSJKkzjHAkSRJnWOAI0mSOuf/B1/oREXSY4ugAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[None, None, None]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(map(show_returns_hist, (df_apple_returns, df_google_returns, df_fb_returns)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Получаем, что ни в одном случае нормальным распределением исходное не приближается ни по картинке, ни по p-value. Для 1 и 3 картинки, однако, хорошо подходит t-распределение: и по картинке, и по p-value. Для второй картинки распределение плохо приближается t-распределением. Возможно, это связано с тем, что у гугла две разных акции, GOOGL и GOOG, и из-за этого распределение ведёт себя не так, как остальные два."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pvalue теста стационарности: 0.0\n",
      "pvalue теста стационарности: 0.0\n",
      "pvalue теста стационарности: 3.579357849918425e-18\n"
     ]
    }
   ],
   "source": [
    "for df in (df_apple_returns, df_google_returns, df_fb_returns):\n",
    "    print(f'pvalue теста стационарности: {adfuller(df)[1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Значит, на разумном уровне значимости можно заключить, что все три временных ряда не стационарны."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}