04_Introduction_to_pandas.ipynb

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    "# pandas 入门"
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    "Pandas 是一个提供了一系列强大的用来管理数据的数据结构的 Python 库。本章节，你将学到如何使用 Series 与 DataFrame 对象来处理数据。"
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    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import os\n",
    "from tiingo import TiingoClient\n",
    "\n",
    "config = {}\n",
    "config['session'] = True\n",
    "config['api_key'] = os.environ['TIINGO_API_KEY']\n",
    "\n",
    "client = TiingoClient(config)\n",
    "\n",
    "def get_df_from_tiingo(symbol, start, end):\n",
    "    df = pd.DataFrame(client.get_ticker_price(symbol,\n",
    "                      startDate=start,\n",
    "                      endDate=end,\n",
    "                      frequency='daily'\n",
    "                     ))\n",
    "    df.set_index('date', inplace=True)\n",
    "    df.index = pd.to_datetime(df.index)\n",
    "    del df.index.name\n",
    "    return df"
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    "使用 Pandas 可以方便的储存、可视化、计算数据。仅仅几行代码便可以修改呈现数据成更便于理解的形式。现在我们使用 NumPy 模拟一些回报数据，将他们放入 pandas 的 DataFrame 中，计算得到价格，并绘制出来。"
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       "      <use xlink:href=\"#DejaVuSans-57\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p71a87f8e78\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"50.14375\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "returns = pd.DataFrame(np.random.normal(1.0, 0.03, (100, 10)))\n",
    "prices = returns.cumprod()\n",
    "prices.plot()\n",
    "plt.title('Randomly-generated Prices')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Price')\n",
    "plt.legend(loc=0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "39820805-efaf-489e-83a6-a13b9e55b294"
    }
   },
   "source": [
    "## pandas 数据结构"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "a1e0e7ef-cc81-4806-b24e-43745261297a"
    }
   },
   "source": [
    "### Series"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "78632999-3a32-4c54-95a6-55be5c750e31"
    }
   },
   "source": [
    "pandas 的 Series 是一个带标签的一维数组。我们主要用它来处理时序数据。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "nbpresent": {
     "id": "ecbde831-5b6a-4e0f-8903-a7be452d44b6"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0    1.0\n",
      "1    2.0\n",
      "2    NaN\n",
      "3    4.0\n",
      "4    5.0\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "s = pd.Series([1, 2, np.nan, 4, 5])\n",
    "print(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "d3e40ca9-1669-4348-8806-7f94ee3fbbd7"
    }
   },
   "source": [
    "每一个 Series 都有 name。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "nbpresent": {
     "id": "8e3dd79d-c7e9-4f22-9fd5-c0204bf03831"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None\n"
     ]
    }
   ],
   "source": [
    "print(s.name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "b8db3f1c-7919-4264-9d1d-56cebb69aace"
    }
   },
   "source": [
    "name 可以直接修改"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "nbpresent": {
     "id": "c638a844-2833-4cc9-8f9c-160d81d9e698"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Toy Series\n"
     ]
    }
   ],
   "source": [
    "s.name = 'Toy Series'\n",
    "print(s.name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "edeb41c0-7b23-44bc-a126-f0d31373afde"
    }
   },
   "source": [
    "一个 Series 的轴标签是它的 index。index 可以被作为参数传入 Series 或者之后再添加。没有 index 的时候，Series 会使用从 0 开始的整数做 index。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "nbpresent": {
     "id": "7c84f9c5-3416-4e66-a0a6-e02d7f595636"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RangeIndex(start=0, stop=5, step=1)\n"
     ]
    }
   ],
   "source": [
    "print(s.index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "9e6a8e35-f7d9-42c8-88a9-464ca813b084"
    }
   },
   "source": [
    "pandas 有用来创建日期 index 的内置函数 `date_range()`。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "nbpresent": {
     "id": "57081bf1-9399-4962-8d39-71252cf0e5cd"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DatetimeIndex(['2016-01-01', '2016-01-02', '2016-01-03', '2016-01-04',\n",
      "               '2016-01-05'],\n",
      "              dtype='datetime64[ns]', freq='D')\n"
     ]
    }
   ],
   "source": [
    "new_index = pd.date_range(\"2016-01-01\", periods=len(s), freq=\"D\")\n",
    "print(new_index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "1c2662a8-1ebb-4668-87b6-d2a67ec585ba"
    }
   },
   "source": [
    "index 的长度必须要与 Series 的长度相同。它们之间一一对应。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "nbpresent": {
     "id": "13495775-b101-4138-a30f-7b36d8be6ccd"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DatetimeIndex(['2016-01-01', '2016-01-02', '2016-01-03', '2016-01-04',\n",
      "               '2016-01-05'],\n",
      "              dtype='datetime64[ns]', freq='D')\n"
     ]
    }
   ],
   "source": [
    "s.index = new_index\n",
    "print(s.index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "8f0a80e0-383b-4112-8b1b-2a8126493545"
    }
   },
   "source": [
    "#### 访问 Series 中的元素"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "e09a79a0-0f64-4d53-b3de-981f5f4cb79b"
    }
   },
   "source": [
    "Series 可以通过 `iloc[]` 与 `loc[]` 访问。`iloc` 通过整数 index 访问元素，`loc` 通过 Series 的 index 访问元素。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "nbpresent": {
     "id": "9663f4d5-0476-439b-a2b2-5f7afec86069"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First element of the series:  1.0\n",
      "Last element of the series:  5.0\n"
     ]
    }
   ],
   "source": [
    "print('First element of the series: ', s.iloc[0])\n",
    "print('Last element of the series: ', s.iloc[len(s) - 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "nbpresent": {
     "id": "45722d52-c7b6-466d-8c91-c3fe222f6b27"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2016-01-01    1.0\n",
       "2016-01-02    2.0\n",
       "Freq: D, Name: Toy Series, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.iloc[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "nbpresent": {
     "id": "98c8fb40-6b30-4538-9199-d7dd5313b48f"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2016-01-01    1.0\n",
       "2016-01-02    2.0\n",
       "2016-01-03    NaN\n",
       "2016-01-04    4.0\n",
       "Freq: D, Name: Toy Series, dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "start = 0\n",
    "end = len(s) - 1\n",
    "step = 1\n",
    "s.iloc[start:end:step]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "nbpresent": {
     "id": "fb2698ad-bbef-499a-9409-5a1c840134de"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2016-01-05    5.0\n",
       "2016-01-04    4.0\n",
       "2016-01-03    NaN\n",
       "2016-01-02    2.0\n",
       "2016-01-01    1.0\n",
       "Freq: -1D, Name: Toy Series, dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.iloc[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "nbpresent": {
     "id": "185eccc7-c424-405c-97a9-f43dad6b4919"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.loc['2016-01-01']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "nbpresent": {
     "id": "0d8092f2-b76a-4c0d-8239-adfd3e27b059"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2016-01-02    2.0\n",
       "2016-01-03    NaN\n",
       "2016-01-04    4.0\n",
       "Freq: D, Name: Toy Series, dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.loc['2016-01-02':'2016-01-04']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "1f4e517a-123a-49ac-9b72-4a7d481a28a4"
    }
   },
   "source": [
    "对于 Series 也可以用括号（[]）来访问元素，但这不是最佳实践。因为括号既可以使用 index 也可以使用整数值访问 Series（与 DataFrame），结果会随着上下文而改变。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "3a7daee5-25fe-4e9b-852e-c9911fb695bc"
    }
   },
   "source": [
    "#### 布尔值检索"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "64f86edb-e1db-46ec-bcc6-c877143fde79"
    }
   },
   "source": [
    "除了上述的访问方法，你还可以使用布尔数组筛选 Series。Series 兼容标准的比较运算符。使用比较条件，我们可以得到一个填充着布尔值的 Series。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "nbpresent": {
     "id": "2a849921-8edb-40b2-b492-985ed054d9ff"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2016-01-01     True\n",
      "2016-01-02     True\n",
      "2016-01-03    False\n",
      "2016-01-04    False\n",
      "2016-01-05    False\n",
      "Freq: D, Name: Toy Series, dtype: bool\n"
     ]
    }
   ],
   "source": [
    "print(s < 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "3052bdd1-2fd6-4750-b1f6-44f509eb19ee"
    }
   },
   "source": [
    "我们可以回传这个 Series 到原 Series 来筛选得到条件为 True 的值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "nbpresent": {
     "id": "355fc134-2f3e-4fd3-bfc9-08f185fbb66c"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2016-01-01    1.0\n",
      "2016-01-02    2.0\n",
      "Freq: D, Name: Toy Series, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(s.loc[ s < 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "3e7c7537-0863-4b05-a870-0ffcd9914c63"
    }
   },
   "source": [
    "我们能够使用逻辑运算符 `&`、`|`、`~` 来组合多个条件。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "nbpresent": {
     "id": "2790174b-c989-4270-b26e-10314cddd463"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2016-01-02    2.0\n",
      "Freq: D, Name: Toy Series, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(s.loc[(s < 3) & (s > 1)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "5979b0d3-a9b4-4db4-96ac-9256939485e1"
    }
   },
   "source": [
    "这样我们能够非常方便的从 Series 中取得符合条件的元素。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "272dd30c-6f82-4bd4-a6c7-c702c5d5db05"
    }
   },
   "source": [
    "#### 检索与时间序列"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "ef1f5a28-b39f-4753-8cb8-f539552c125c"
    }
   },
   "source": [
    "由于我们使用 Series 来处理时序数据，所以有必要讲解下如何来处理时间组件。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "nbpresent": {
     "id": "bfb22e5e-a554-4404-b2e8-415d3439a1d4"
    }
   },
   "outputs": [],
   "source": [
    "symbol = 'CMG'\n",
    "start = '2012-01-01'\n",
    "end = '2016-01-01'\n",
    "prices = get_df_from_tiingo(symbol, start, end).loc[:,'close']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "bb94721f-f8dc-479b-88eb-a89216581ef9"
    }
   },
   "source": [
    "我们可以使用 `head()` 方法查看 series 的前几条元素。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "nbpresent": {
     "id": "0165802a-4116-4b31-8ab7-5e7c323172cd"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.series.Series'>\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2012-01-03 00:00:00+00:00    341.27\n",
       "2012-01-04 00:00:00+00:00    348.75\n",
       "2012-01-05 00:00:00+00:00    350.48\n",
       "2012-01-06 00:00:00+00:00    348.95\n",
       "2012-01-09 00:00:00+00:00    339.74\n",
       "Name: close, dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(type(prices))\n",
    "prices.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "c1a593dc-ebb2-4591-adcc-9840945935fe"
    }
   },
   "source": [
    "我们可以为时间序列指定 name。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "nbpresent": {
     "id": "28ac6725-8cd8-4604-9a47-5e60a14a3e84"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Old name:  close\n",
      "New name:  CMG\n"
     ]
    }
   ],
   "source": [
    "print('Old name: ', prices.name)\n",
    "prices.name = symbol\n",
    "print('New name: ', prices.name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "3901b10f-785c-4fac-b435-00baa3c20ef7"
    }
   },
   "source": [
    "现在查看一下时间序列的 `DatetimeIndex`。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "nbpresent": {
     "id": "772ee4ae-ea86-47de-bd35-4f4974ddd92b"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DatetimeIndex(['2012-01-03 00:00:00+00:00', '2012-01-04 00:00:00+00:00',\n",
      "               '2012-01-05 00:00:00+00:00', '2012-01-06 00:00:00+00:00',\n",
      "               '2012-01-09 00:00:00+00:00', '2012-01-10 00:00:00+00:00',\n",
      "               '2012-01-11 00:00:00+00:00', '2012-01-12 00:00:00+00:00',\n",
      "               '2012-01-13 00:00:00+00:00', '2012-01-17 00:00:00+00:00',\n",
      "               ...\n",
      "               '2015-12-17 00:00:00+00:00', '2015-12-18 00:00:00+00:00',\n",
      "               '2015-12-21 00:00:00+00:00', '2015-12-22 00:00:00+00:00',\n",
      "               '2015-12-23 00:00:00+00:00', '2015-12-24 00:00:00+00:00',\n",
      "               '2015-12-28 00:00:00+00:00', '2015-12-29 00:00:00+00:00',\n",
      "               '2015-12-30 00:00:00+00:00', '2015-12-31 00:00:00+00:00'],\n",
      "              dtype='datetime64[ns, UTC]', length=1006, freq=None)\n"
     ]
    }
   ],
   "source": [
    "print(prices.index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "81c681e6-3956-490d-839e-014d2f2411bf"
    }
   },
   "source": [
    "可以看出 `DatetimeIndex` 有一个关联信息的集合。包括频率（freq）与时区（tz）。频率是指数据是每日的、每月的或是其他周期的；时区是指 index 所用的时区。我们可以修改这些信息。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "062b303d-be72-487e-bc73-663e905013ac"
    }
   },
   "source": [
    "如果我们从 Series 中重新取样，我们可以修改频率。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "nbpresent": {
     "id": "c0fb29fc-b67f-463b-aa15-f2b415834d86"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-31 00:00:00+00:00    354.829000\n",
       "2012-02-29 00:00:00+00:00    379.535500\n",
       "2012-03-31 00:00:00+00:00    407.002273\n",
       "2012-04-30 00:00:00+00:00    422.799000\n",
       "2012-05-31 00:00:00+00:00    405.805455\n",
       "2012-06-30 00:00:00+00:00    403.033333\n",
       "2012-07-31 00:00:00+00:00    353.880476\n",
       "2012-08-31 00:00:00+00:00    294.535217\n",
       "2012-09-30 00:00:00+00:00    326.513158\n",
       "2012-10-31 00:00:00+00:00    276.573333\n",
       "Freq: M, Name: CMG, dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monthly_prices = prices.resample('M').mean()\n",
    "monthly_prices.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "d4cce6b6-56ee-48af-bba2-a8bb186316ea"
    }
   },
   "source": [
    "`resample()` 方法默认使用低级的数据创建高级的数据。<del>我们可以通过指定 `how` 参数来指定如何取样。</del>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "nbpresent": {
     "id": "d765810b-06b6-4e97-8cab-25a3e519adb2"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-31 00:00:00+00:00    355.505\n",
       "2012-02-29 00:00:00+00:00    378.195\n",
       "2012-03-31 00:00:00+00:00    408.995\n",
       "2012-04-30 00:00:00+00:00    420.835\n",
       "2012-05-31 00:00:00+00:00    405.240\n",
       "2012-06-30 00:00:00+00:00    402.450\n",
       "2012-07-31 00:00:00+00:00    380.470\n",
       "2012-08-31 00:00:00+00:00    295.390\n",
       "2012-09-30 00:00:00+00:00    332.810\n",
       "2012-10-31 00:00:00+00:00    286.560\n",
       "Freq: M, Name: CMG, dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monthly_prices_med = prices.resample('M').median()\n",
    "monthly_prices_med.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "4e27a68a-d7d8-4941-be7c-f32874795f56"
    }
   },
   "source": [
    "时间序列已被本地化为 UTC，我们可以修改时间为 'Asia/Shanghai'。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "nbpresent": {
     "id": "70f9e9a1-2423-4845-b7ce-53002facd137"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-03 08:00:00+08:00    341.27\n",
       "2012-01-04 08:00:00+08:00    348.75\n",
       "2012-01-05 08:00:00+08:00    350.48\n",
       "2012-01-06 08:00:00+08:00    348.95\n",
       "2012-01-09 08:00:00+08:00    339.74\n",
       "2012-01-10 08:00:00+08:00    341.12\n",
       "2012-01-11 08:00:00+08:00    347.60\n",
       "2012-01-12 08:00:00+08:00    347.62\n",
       "2012-01-13 08:00:00+08:00    354.62\n",
       "2012-01-17 08:00:00+08:00    353.38\n",
       "Name: CMG, dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eastern_prices = prices.tz_convert('Asia/Shanghai')\n",
    "eastern_prices.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "c764fe2d-b94a-4ddf-9337-709e8761ce52"
    }
   },
   "source": [
    "我们得到的数据只包含交易日。如果我们想获得日历中每一天的价格呢？首先让我们创建一个新的 DatetimeIndex。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "nbpresent": {
     "id": "8c654952-302c-41bb-9d51-7eeef8359f13"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DatetimeIndex(['2012-01-01 00:00:00+00:00', '2012-01-02 00:00:00+00:00',\n",
      "               '2012-01-03 00:00:00+00:00', '2012-01-04 00:00:00+00:00',\n",
      "               '2012-01-05 00:00:00+00:00', '2012-01-06 00:00:00+00:00',\n",
      "               '2012-01-07 00:00:00+00:00', '2012-01-08 00:00:00+00:00',\n",
      "               '2012-01-09 00:00:00+00:00', '2012-01-10 00:00:00+00:00',\n",
      "               ...\n",
      "               '2015-12-23 00:00:00+00:00', '2015-12-24 00:00:00+00:00',\n",
      "               '2015-12-25 00:00:00+00:00', '2015-12-26 00:00:00+00:00',\n",
      "               '2015-12-27 00:00:00+00:00', '2015-12-28 00:00:00+00:00',\n",
      "               '2015-12-29 00:00:00+00:00', '2015-12-30 00:00:00+00:00',\n",
      "               '2015-12-31 00:00:00+00:00', '2016-01-01 00:00:00+00:00'],\n",
      "              dtype='datetime64[ns, UTC]', length=1462, freq='D')\n"
     ]
    }
   ],
   "source": [
    "calendar_dates = pd.date_range(start=start, end=end, freq='D', tz='UTC')\n",
    "print(calendar_dates)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "f39f8350-fc51-4c32-b92f-2c7f01d939c1"
    }
   },
   "source": [
    "现在可以使用新的日期序列来 reindex 我们的时间 series。这里要用的的填充方法是 `ffill`，意即 \"forward fill\"。任何 NaN 值都会被填充为上一条值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "nbpresent": {
     "id": "04a83de3-d707-4a81-8f06-1f782ece4c0c"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-01 00:00:00+00:00       NaN\n",
       "2012-01-02 00:00:00+00:00       NaN\n",
       "2012-01-03 00:00:00+00:00    341.27\n",
       "2012-01-04 00:00:00+00:00    348.75\n",
       "2012-01-05 00:00:00+00:00    350.48\n",
       "2012-01-06 00:00:00+00:00    348.95\n",
       "2012-01-07 00:00:00+00:00    348.95\n",
       "2012-01-08 00:00:00+00:00    348.95\n",
       "2012-01-09 00:00:00+00:00    339.74\n",
       "2012-01-10 00:00:00+00:00    341.12\n",
       "2012-01-11 00:00:00+00:00    347.60\n",
       "2012-01-12 00:00:00+00:00    347.62\n",
       "2012-01-13 00:00:00+00:00    354.62\n",
       "2012-01-14 00:00:00+00:00    354.62\n",
       "2012-01-15 00:00:00+00:00    354.62\n",
       "Freq: D, Name: CMG, dtype: float64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calendar_prices = prices.reindex(calendar_dates, method='ffill')\n",
    "calendar_prices.head(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "525bf2e6-d88f-4733-bd6a-bd31ad43de27"
    }
   },
   "source": [
    "由于前两条一天周日、一天休市，所以值是 `NaN`。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "56001bcc-467a-4522-ad84-e8e9c2765ace"
    }
   },
   "source": [
    "#### 缺失的数据"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "7baf2da9-3dfe-4271-a104-caab4fbc75f6"
    }
   },
   "source": [
    "当我们处理真实数据的时候，很有可能遇到缺失的值。有两种方法解决这些缺失的数据。第一种是用 `fillna()` 填充缺失的数据。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "nbpresent": {
     "id": "c6d964be-2318-4fd9-8c0b-2f6b7ec7d7f7"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-01 00:00:00+00:00    501.068188\n",
       "2012-01-02 00:00:00+00:00    501.068188\n",
       "2012-01-03 00:00:00+00:00    341.270000\n",
       "2012-01-04 00:00:00+00:00    348.750000\n",
       "2012-01-05 00:00:00+00:00    350.480000\n",
       "2012-01-06 00:00:00+00:00    348.950000\n",
       "2012-01-07 00:00:00+00:00    348.950000\n",
       "2012-01-08 00:00:00+00:00    348.950000\n",
       "2012-01-09 00:00:00+00:00    339.740000\n",
       "2012-01-10 00:00:00+00:00    341.120000\n",
       "Freq: D, Name: CMG, dtype: float64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meanfilled_prices = calendar_prices.fillna(calendar_prices.mean())\n",
    "meanfilled_prices.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "ea8f4a47-9af8-4966-91a5-cfc4e61352fe"
    }
   },
   "source": [
    "除了使用特定值填充数据，还可以使用参数 `method`。我们能够用 'backward fill' 来用后一个数据填充："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "nbpresent": {
     "id": "1f176847-2bf9-4b56-a577-3bdab2a1e434"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-01 00:00:00+00:00    341.27\n",
       "2012-01-02 00:00:00+00:00    341.27\n",
       "2012-01-03 00:00:00+00:00    341.27\n",
       "2012-01-04 00:00:00+00:00    348.75\n",
       "2012-01-05 00:00:00+00:00    350.48\n",
       "2012-01-06 00:00:00+00:00    348.95\n",
       "2012-01-07 00:00:00+00:00    348.95\n",
       "2012-01-08 00:00:00+00:00    348.95\n",
       "2012-01-09 00:00:00+00:00    339.74\n",
       "2012-01-10 00:00:00+00:00    341.12\n",
       "Freq: D, Name: CMG, dtype: float64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bfilled_prices = calendar_prices.fillna(method='bfill')\n",
    "bfilled_prices.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "319a09b0-501d-4367-bdf5-12baf1847da6"
    }
   },
   "source": [
    "现在时序数据已被清理，所有的 NaN 值都被合适的处理了。是时候讨论如何使用 pandas 数据结构做分析了。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "cee924df-7522-4761-9867-f1aa7ebe6a86"
    }
   },
   "source": [
    "#### 使用 pandas 分析时间 series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "nbpresent": {
     "id": "4f2f9d44-58c6-44ac-a889-2010eb01298b"
    }
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   ],
   "source": [
    "prices.plot();\n",
    "plt.title(symbol + ' Prices')\n",
    "plt.ylabel('Price')\n",
    "plt.xlabel('Date');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "nbpresent": {
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean:  501.6366540755467\n",
      "Standard deviation:  146.68873568766415\n"
     ]
    }
   ],
   "source": [
    "print('Mean: ', prices.mean())\n",
    "print('Standard deviation: ', prices.std())"
   ]
  },
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   "execution_count": 31,
   "metadata": {
    "nbpresent": {
     "id": "74b003d8-94c9-432e-86ac-8daba1411664"
    }
   },
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Summary Statistics\n",
      "count    1006.000000\n",
      "mean      501.636654\n",
      "std       146.688736\n",
      "min       236.240000\n",
      "25%       371.555000\n",
      "50%       521.270000\n",
      "75%       646.835000\n",
      "max       757.770000\n",
      "Name: CMG, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print('Summary Statistics')\n",
    "print(prices.describe())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "3462b8db-7fbd-4933-ac0b-5c1c860df950"
    }
   },
   "source": [
    "我们能够轻易的使用基础数学运算符与标量修改 Series。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "nbpresent": {
     "id": "db8ad46b-895c-4906-89ff-dc844d019cec"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-03 00:00:00+00:00    672.54\n",
       "2012-01-04 00:00:00+00:00    687.50\n",
       "2012-01-05 00:00:00+00:00    690.96\n",
       "2012-01-06 00:00:00+00:00    687.90\n",
       "2012-01-09 00:00:00+00:00    669.48\n",
       "Name: CMG, dtype: float64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "modified_prices = prices * 2 - 10\n",
    "modified_prices.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "nbpresent": {
     "id": "e71580bd-81b8-42a6-ab76-5b81820c21e3"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-03 00:00:00+00:00    361.501422\n",
       "2012-01-04 00:00:00+00:00    397.655743\n",
       "2012-01-05 00:00:00+00:00    388.307735\n",
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       "2012-01-09 00:00:00+00:00    438.567435\n",
       "dtype: float64"
      ]
     },
     "execution_count": 33,
     "metadata": {},
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   ],
   "source": [
    "noisy_prices = prices + 5 * pd.Series(np.random.normal(0, 5, len(prices)), index=prices.index) + 20\n",
    "noisy_prices.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "622048bc-2921-47a5-9365-761e9197bb43"
    }
   },
   "source": [
    "如果没有匹配的索引，会返回空的 Series。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "nbpresent": {
     "id": "80cccef7-de84-462f-b6d1-fdd1cdd3904b"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-03 00:00:00+00:00   NaN\n",
       "2012-01-04 00:00:00+00:00   NaN\n",
       "2012-01-05 00:00:00+00:00   NaN\n",
       "2012-01-06 00:00:00+00:00   NaN\n",
       "2012-01-09 00:00:00+00:00   NaN\n",
       "dtype: float64"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "empty_series = prices + pd.Series(np.random.normal(0, 1, len(prices)))\n",
    "empty_series.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "d495ea80-c13c-4bf3-a8e9-1fffd11a1ed3"
    }
   },
   "source": [
    "除了观察时间 series 本身，我们还希望看到它的一阶导数或是变动的百分比。这两个都有内置方法。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "nbpresent": {
     "id": "946d0a54-bfb8-42c5-920e-ef78303a142d"
    }
   },
   "outputs": [],
   "source": [
    "add_returns = prices.diff()[1:]\n",
    "mult_returns = prices.pct_change()[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "nbpresent": {
     "id": "f3adaa6b-e1b9-4a90-82ca-75f85b56557b"
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   "source": [
    "plt.title('Multiplicative returns of ' + symbol)\n",
    "plt.xlabel('Date')\n",
    "plt.ylabel('Percent Returns')\n",
    "mult_returns.plot();"
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   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "6f30cc87-f6b1-4171-bede-ff36fd14dc6d"
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   },
   "source": [
    "pandas 有用来计算移动平均值与标准差的函数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
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   "outputs": [],
   "source": [
    "rolling_mean = prices.rolling(window=30).mean()\n",
    "rolling_mean.name = '30-day rolling mean'"
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   "cell_type": "code",
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   "metadata": {
    "nbpresent": {
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    "prices.plot()\n",
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    "plt.title(symbol + 'Price')\n",
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    "plt.ylabel('Price')\n",
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    "rolling_std.name = '30-day rolling volatility'"
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   "source": [
    "rolling_std.plot()\n",
    "plt.title(rolling_std.name);\n",
    "plt.xlabel('Date')\n",
    "plt.ylabel('Standard Deviation');"
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  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "id": "a71dc8bd-601b-49f6-8c4f-ef207f0865a0"
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   },
   "source": [
    "许多 NumPy 的函数也可以在 Series 上和对一维 NumPy 的数组效果相同。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "nbpresent": {
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     "text": [
      "0.00023598024508242332\n"
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   ],
   "source": [
    "print(np.median(mult_returns))"
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   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "6eeb6407-5e0d-4986-b1f5-41f0a2277b23"
    }
   },
   "source": [
    "大多数这些函数已经被实现为 Series 和 DataFrame 方法。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "nbpresent": {
     "id": "14b26a05-3e43-44db-9488-77742b409833"
    }
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00023598024508242332\n"
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    }
   ],
   "source": [
    "print(mult_returns.median())"
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  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "06d11ae3-c82c-4e33-86a8-779a53db4ff5"
    }
   },
   "source": [
    "### DataFrames"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "13a83942-6dc3-4e7b-a84a-fde4225509b7"
    }
   },
   "source": [
    "许多与 Series 相关的工作都包含在 DataFrame 中。pandas 的 DataFrame 允许我们用它直观的结构轻松管理我们的数据。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "c6d357b6-3e7c-40d9-a85c-19527bec4e44"
    }
   },
   "source": [
    "和 Series 相似，DataFrame 能够保持多种类型的数据，但 DataFrame 是二维对象。每一个 DataFrame 有一个 index 和一个 columns 属性。index 属性和 Series 的 index 类似。columns 属性为 DataFrames 提供第二个维度，允许我们合并命名的列到一个索引一直的内聚对象。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "7383476f-9e62-4f26-9374-a684fbaf3db8"
    }
   },
   "source": [
    "我们可以通过对字典或 NumPy ndarray 调用 `pandas.DataFrame` 来创建 DataFrame。也可以使用 `pandas.concat()` 来合并一组 pandas Series 到一个 DataFrame。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "nbpresent": {
     "id": "c85862e5-3100-482b-a76e-3cc3928f9966"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': [1, 2, 3, 4, 5], 'b': ['L', 'K', 'J', 'M', 'Z'], 'c': array([-1.27158305, -0.05931433,  0.12999317, -0.25936177, -0.17653564])}\n"
     ]
    }
   ],
   "source": [
    "dict_data = {\n",
    "    'a': [1, 2, 3, 4, 5],\n",
    "    'b': ['L', 'K', 'J', 'M', 'Z'],\n",
    "    'c': np.random.normal(0, 1, 5)\n",
    "}\n",
    "print(dict_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "029b106c-a36d-4696-957f-d0ae8f586298"
    }
   },
   "source": [
    "每一个 DataFrame 有一部分我们要留意的属性。第一个便是 index 属性。我们可以像 Series 那样加入一个 Timestamp 对象的 index。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "nbpresent": {
     "id": "43e251a4-0e71-46f7-a8da-12070b2fdc5c"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            a  b         c\n",
      "2016-01-01  1  L -1.271583\n",
      "2016-01-02  2  K -0.059314\n",
      "2016-01-03  3  J  0.129993\n",
      "2016-01-04  4  M -0.259362\n",
      "2016-01-05  5  Z -0.176536\n"
     ]
    }
   ],
   "source": [
    "frame_data = pd.DataFrame(dict_data, index=pd.date_range('2016-01-01', periods=5))\n",
    "print(frame_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "c0d71a61-1ab5-4e40-ad31-82c0436c5680"
    }
   },
   "source": [
    "我们可以合并 Series 到 DataFrame。合并 Series 是基于对应的 index 的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "nbpresent": {
     "id": "cb43df93-6d35-4f38-8343-5b232d9e7a44"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Events  Odds\n",
      "0       2     1\n",
      "1       4     3\n",
      "2       6     5\n",
      "3       0     7\n",
      "4      10     9\n"
     ]
    }
   ],
   "source": [
    "s_1 = pd.Series([2, 4, 6, 0, 10], name='Events')\n",
    "s_2 = pd.Series([1, 3, 5, 7, 9], name='Odds')\n",
    "numbers = pd.concat([s_1, s_2], axis=1)\n",
    "print(numbers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "8cd163dc-de0f-4a74-86e1-d8b7d043ce6b"
    }
   },
   "source": [
    "我们稍后会用 `pandas.concat()` 来合并多个 DataFrame 到一个。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "e43eaf37-0635-4341-b5e6-f60c47d0f3f8"
    }
   },
   "source": [
    "每一个 DataFrame 还有一个 columns 属性。当我们合并两个 Series 时，列名就是 Series 的 name。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "nbpresent": {
     "id": "6c8f66d8-027d-4947-bfa1-f528d0dfb964"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['Events', 'Odds'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "print(numbers.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "3b88d19c-c4fb-4659-9813-20f80acaf482"
    }
   },
   "source": [
    "同样的道理，DataFrame 的 index 可以在事后改变。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "nbpresent": {
     "id": "ce8bff30-86d5-48cc-bf2a-3bc3c5f101bf"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RangeIndex(start=0, stop=5, step=1)\n"
     ]
    }
   ],
   "source": [
    "print(numbers.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "nbpresent": {
     "id": "d7ad89a3-54ff-4193-8235-a370ac6094a8"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            Events  Odds\n",
      "2016-01-01       2     1\n",
      "2016-01-02       4     3\n",
      "2016-01-03       6     5\n",
      "2016-01-04       0     7\n",
      "2016-01-05      10     9\n"
     ]
    }
   ],
   "source": [
    "numbers.index = pd.date_range('2016-01-01', periods=len(numbers))\n",
    "print(numbers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "1a291a38-5337-4423-bf7d-c2f0a55e7a79"
    }
   },
   "source": [
    "除了 index 和 columns，我们还可以通过 values 属性之间访问它包含的值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "nbpresent": {
     "id": "818953a6-df55-4891-810d-f2096c667bf2"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  1],\n",
       "       [ 4,  3],\n",
       "       [ 6,  5],\n",
       "       [ 0,  7],\n",
       "       [10,  9]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numbers.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "d9da4996-947d-4edb-97fc-c69b14958bff"
    }
   },
   "source": [
    "这返回一个 NumPy 数组。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "nbpresent": {
     "id": "a55d0ea7-4bf7-401f-9972-5c10060874f1"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(numbers.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "983bdab7-2b01-40f3-be17-56f93ad6c210"
    }
   },
   "source": [
    "#### 访问 `DataFrame` 元素"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "nbpresent": {
     "id": "4295fc12-d5e8-4e78-a76c-29f4e1948c24"
    }
   },
   "outputs": [],
   "source": [
    "symbol = ['CMG', 'MCD', 'SHAK', 'WFM']\n",
    "start = '2012-01-01'\n",
    "end = '2016-01-01'\n",
    "\n",
    "prices = pd.concat(\n",
    "    [\n",
    "        get_df_from_tiingo(\n",
    "            ticker,\n",
    "            start=start,\n",
    "            end=end\n",
    "        ).loc[:, 'close'] for ticker in symbol\n",
    "    ],\n",
    "    axis=1,\n",
    "    keys=symbol\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-03 00:00:00+00:00    341.27\n",
       "2012-01-04 00:00:00+00:00    348.75\n",
       "2012-01-05 00:00:00+00:00    350.48\n",
       "2012-01-06 00:00:00+00:00    348.95\n",
       "2012-01-09 00:00:00+00:00    339.74\n",
       "Name: CMG, dtype: float64"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.CMG.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在我们可以直接访问 CMG 列。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "nbpresent": {
     "id": "25277401-4d61-4f09-9354-47732c665939"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-03 00:00:00+00:00    341.27\n",
       "2012-01-04 00:00:00+00:00    348.75\n",
       "2012-01-05 00:00:00+00:00    350.48\n",
       "2012-01-06 00:00:00+00:00    348.95\n",
       "2012-01-09 00:00:00+00:00    339.74\n",
       "Name: CMG, dtype: float64"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.CMG.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们还能够使用 `loc[]` 来访问单个列。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-03 00:00:00+00:00    341.27\n",
       "2012-01-04 00:00:00+00:00    348.75\n",
       "2012-01-05 00:00:00+00:00    350.48\n",
       "2012-01-06 00:00:00+00:00    348.95\n",
       "2012-01-09 00:00:00+00:00    339.74\n",
       "Name: CMG, dtype: float64"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.loc[:, 'CMG'].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "访问单个列会返回一个 Series。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.series.Series'>\n",
      "<class 'pandas.core.series.Series'>\n"
     ]
    }
   ],
   "source": [
    "print(type(prices.CMG))\n",
    "print(type(prices.loc[:,'CMG']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当你传入一个二维 tuple 到 DateFrame 时，tuple 的第一个元素对应行，第二个元素对应列。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CMG</th>\n",
       "      <th>MCD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-01-03 00:00:00+00:00</th>\n",
       "      <td>341.27</td>\n",
       "      <td>98.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-04 00:00:00+00:00</th>\n",
       "      <td>348.75</td>\n",
       "      <td>99.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-05 00:00:00+00:00</th>\n",
       "      <td>350.48</td>\n",
       "      <td>99.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-06 00:00:00+00:00</th>\n",
       "      <td>348.95</td>\n",
       "      <td>100.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-09 00:00:00+00:00</th>\n",
       "      <td>339.74</td>\n",
       "      <td>99.64</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              CMG     MCD\n",
       "2012-01-03 00:00:00+00:00  341.27   98.84\n",
       "2012-01-04 00:00:00+00:00  348.75   99.39\n",
       "2012-01-05 00:00:00+00:00  350.48   99.83\n",
       "2012-01-06 00:00:00+00:00  348.95  100.60\n",
       "2012-01-09 00:00:00+00:00  339.74   99.64"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.loc[:, ['CMG', 'MCD']].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们还可以使用 `loc[]` 通过 index 值访问 `DataFrame`。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
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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>CMG</th>\n",
       "      <th>MCD</th>\n",
       "      <th>SHAK</th>\n",
       "      <th>WFM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-12-15 00:00:00+00:00</th>\n",
       "      <td>554.86</td>\n",
       "      <td>116.93</td>\n",
       "      <td>41.58</td>\n",
       "      <td>32.970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-16 00:00:00+00:00</th>\n",
       "      <td>567.83</td>\n",
       "      <td>117.84</td>\n",
       "      <td>40.17</td>\n",
       "      <td>33.650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-17 00:00:00+00:00</th>\n",
       "      <td>554.89</td>\n",
       "      <td>117.50</td>\n",
       "      <td>38.54</td>\n",
       "      <td>33.380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-18 00:00:00+00:00</th>\n",
       "      <td>541.08</td>\n",
       "      <td>116.66</td>\n",
       "      <td>39.75</td>\n",
       "      <td>32.750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-21 00:00:00+00:00</th>\n",
       "      <td>522.01</td>\n",
       "      <td>117.69</td>\n",
       "      <td>38.19</td>\n",
       "      <td>32.980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-22 00:00:00+00:00</th>\n",
       "      <td>494.61</td>\n",
       "      <td>117.72</td>\n",
       "      <td>39.75</td>\n",
       "      <td>34.785</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              CMG     MCD   SHAK     WFM\n",
       "2015-12-15 00:00:00+00:00  554.86  116.93  41.58  32.970\n",
       "2015-12-16 00:00:00+00:00  567.83  117.84  40.17  33.650\n",
       "2015-12-17 00:00:00+00:00  554.89  117.50  38.54  33.380\n",
       "2015-12-18 00:00:00+00:00  541.08  116.66  39.75  32.750\n",
       "2015-12-21 00:00:00+00:00  522.01  117.69  38.19  32.980\n",
       "2015-12-22 00:00:00+00:00  494.61  117.72  39.75  34.785"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.loc['2015-12-15': '2015-12-22']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CMG</th>\n",
       "      <th>MCD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-12-15 00:00:00+00:00</th>\n",
       "      <td>554.86</td>\n",
       "      <td>116.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-16 00:00:00+00:00</th>\n",
       "      <td>567.83</td>\n",
       "      <td>117.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-17 00:00:00+00:00</th>\n",
       "      <td>554.89</td>\n",
       "      <td>117.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-18 00:00:00+00:00</th>\n",
       "      <td>541.08</td>\n",
       "      <td>116.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-21 00:00:00+00:00</th>\n",
       "      <td>522.01</td>\n",
       "      <td>117.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-22 00:00:00+00:00</th>\n",
       "      <td>494.61</td>\n",
       "      <td>117.72</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              CMG     MCD\n",
       "2015-12-15 00:00:00+00:00  554.86  116.93\n",
       "2015-12-16 00:00:00+00:00  567.83  117.84\n",
       "2015-12-17 00:00:00+00:00  554.89  117.50\n",
       "2015-12-18 00:00:00+00:00  541.08  116.66\n",
       "2015-12-21 00:00:00+00:00  522.01  117.69\n",
       "2015-12-22 00:00:00+00:00  494.61  117.72"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.loc['2015-12-15': '2015-12-22', ['CMG', 'MCD']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用 `iloc` 可以通过整数 index 访问 DataFrame。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-01-03 00:00:00+00:00    98.84\n",
       "2012-01-04 00:00:00+00:00    99.39\n",
       "Name: MCD, dtype: float64"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.iloc[0:2, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CMG</th>\n",
       "      <th>WFM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-01-04 00:00:00+00:00</th>\n",
       "      <td>348.75</td>\n",
       "      <td>71.49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-06 00:00:00+00:00</th>\n",
       "      <td>348.95</td>\n",
       "      <td>72.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-10 00:00:00+00:00</th>\n",
       "      <td>341.12</td>\n",
       "      <td>72.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-12 00:00:00+00:00</th>\n",
       "      <td>347.62</td>\n",
       "      <td>71.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-17 00:00:00+00:00</th>\n",
       "      <td>353.38</td>\n",
       "      <td>76.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-19 00:00:00+00:00</th>\n",
       "      <td>358.09</td>\n",
       "      <td>77.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-23 00:00:00+00:00</th>\n",
       "      <td>360.46</td>\n",
       "      <td>76.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-25 00:00:00+00:00</th>\n",
       "      <td>363.14</td>\n",
       "      <td>77.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-27 00:00:00+00:00</th>\n",
       "      <td>366.76</td>\n",
       "      <td>74.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-31 00:00:00+00:00</th>\n",
       "      <td>367.29</td>\n",
       "      <td>74.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-02-02 00:00:00+00:00</th>\n",
       "      <td>362.82</td>\n",
       "      <td>75.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-02-06 00:00:00+00:00</th>\n",
       "      <td>371.63</td>\n",
       "      <td>76.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-02-08 00:00:00+00:00</th>\n",
       "      <td>374.02</td>\n",
       "      <td>77.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-02-10 00:00:00+00:00</th>\n",
       "      <td>376.45</td>\n",
       "      <td>81.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-02-14 00:00:00+00:00</th>\n",
       "      <td>378.94</td>\n",
       "      <td>80.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-02-16 00:00:00+00:00</th>\n",
       "      <td>382.04</td>\n",
       "      <td>80.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-02-21 00:00:00+00:00</th>\n",
       "      <td>383.58</td>\n",
       "      <td>80.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-02-23 00:00:00+00:00</th>\n",
       "      <td>386.80</td>\n",
       "      <td>81.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-02-27 00:00:00+00:00</th>\n",
       "      <td>388.89</td>\n",
       "      <td>81.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-02-29 00:00:00+00:00</th>\n",
       "      <td>390.22</td>\n",
       "      <td>80.74</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              CMG    WFM\n",
       "2012-01-04 00:00:00+00:00  348.75  71.49\n",
       "2012-01-06 00:00:00+00:00  348.95  72.88\n",
       "2012-01-10 00:00:00+00:00  341.12  72.68\n",
       "2012-01-12 00:00:00+00:00  347.62  71.93\n",
       "2012-01-17 00:00:00+00:00  353.38  76.73\n",
       "2012-01-19 00:00:00+00:00  358.09  77.33\n",
       "2012-01-23 00:00:00+00:00  360.46  76.12\n",
       "2012-01-25 00:00:00+00:00  363.14  77.15\n",
       "2012-01-27 00:00:00+00:00  366.76  74.89\n",
       "2012-01-31 00:00:00+00:00  367.29  74.03\n",
       "2012-02-02 00:00:00+00:00  362.82  75.60\n",
       "2012-02-06 00:00:00+00:00  371.63  76.41\n",
       "2012-02-08 00:00:00+00:00  374.02  77.93\n",
       "2012-02-10 00:00:00+00:00  376.45  81.62\n",
       "2012-02-14 00:00:00+00:00  378.94  80.99\n",
       "2012-02-16 00:00:00+00:00  382.04  80.60\n",
       "2012-02-21 00:00:00+00:00  383.58  80.58\n",
       "2012-02-23 00:00:00+00:00  386.80  81.02\n",
       "2012-02-27 00:00:00+00:00  388.89  81.65\n",
       "2012-02-29 00:00:00+00:00  390.22  80.74"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 使用整数 index 访问价格数据在\n",
    "# [1, 3, 5, 7, 9, 11, 13, ..., 99] 行\n",
    "# 0 或者第 3 列\n",
    "prices.iloc[[1, 3, 5] + [i for i in range(7, 100, 2)], [0, 3]].head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Boolean 索引"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CMG</th>\n",
       "      <th>MCD</th>\n",
       "      <th>SHAK</th>\n",
       "      <th>WFM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-01-03 00:00:00+00:00</th>\n",
       "      <td>341.27</td>\n",
       "      <td>98.84</td>\n",
       "      <td>NaN</td>\n",
       "      <td>69.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-04 00:00:00+00:00</th>\n",
       "      <td>348.75</td>\n",
       "      <td>99.39</td>\n",
       "      <td>NaN</td>\n",
       "      <td>71.49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-05 00:00:00+00:00</th>\n",
       "      <td>350.48</td>\n",
       "      <td>99.83</td>\n",
       "      <td>NaN</td>\n",
       "      <td>72.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-06 00:00:00+00:00</th>\n",
       "      <td>348.95</td>\n",
       "      <td>100.60</td>\n",
       "      <td>NaN</td>\n",
       "      <td>72.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-09 00:00:00+00:00</th>\n",
       "      <td>339.74</td>\n",
       "      <td>99.64</td>\n",
       "      <td>NaN</td>\n",
       "      <td>72.89</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              CMG     MCD  SHAK    WFM\n",
       "2012-01-03 00:00:00+00:00  341.27   98.84   NaN  69.64\n",
       "2012-01-04 00:00:00+00:00  348.75   99.39   NaN  71.49\n",
       "2012-01-05 00:00:00+00:00  350.48   99.83   NaN  72.75\n",
       "2012-01-06 00:00:00+00:00  348.95  100.60   NaN  72.88\n",
       "2012-01-09 00:00:00+00:00  339.74   99.64   NaN  72.89"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.loc[prices.MCD > prices.WFM].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "组合多个布尔条件。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CMG</th>\n",
       "      <th>MCD</th>\n",
       "      <th>SHAK</th>\n",
       "      <th>WFM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-01-30 00:00:00+00:00</th>\n",
       "      <td>709.84</td>\n",
       "      <td>92.44</td>\n",
       "      <td>45.90</td>\n",
       "      <td>52.095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-02-02 00:00:00+00:00</th>\n",
       "      <td>712.55</td>\n",
       "      <td>92.51</td>\n",
       "      <td>43.99</td>\n",
       "      <td>53.150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-02-03 00:00:00+00:00</th>\n",
       "      <td>726.63</td>\n",
       "      <td>93.92</td>\n",
       "      <td>44.98</td>\n",
       "      <td>53.410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-02-04 00:00:00+00:00</th>\n",
       "      <td>676.00</td>\n",
       "      <td>94.05</td>\n",
       "      <td>41.32</td>\n",
       "      <td>53.680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-02-05 00:00:00+00:00</th>\n",
       "      <td>670.91</td>\n",
       "      <td>94.34</td>\n",
       "      <td>42.64</td>\n",
       "      <td>53.375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              CMG    MCD   SHAK     WFM\n",
       "2015-01-30 00:00:00+00:00  709.84  92.44  45.90  52.095\n",
       "2015-02-02 00:00:00+00:00  712.55  92.51  43.99  53.150\n",
       "2015-02-03 00:00:00+00:00  726.63  93.92  44.98  53.410\n",
       "2015-02-04 00:00:00+00:00  676.00  94.05  41.32  53.680\n",
       "2015-02-05 00:00:00+00:00  670.91  94.34  42.64  53.375"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.loc[(prices.MCD > prices.WFM) & ~prices.SHAK.isnull()].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 添加删除列，合并 DataFrame/Series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CMG</th>\n",
       "      <th>MCD</th>\n",
       "      <th>SHAK</th>\n",
       "      <th>WFM</th>\n",
       "      <th>TSLA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-01-03 00:00:00+00:00</th>\n",
       "      <td>341.27</td>\n",
       "      <td>98.84</td>\n",
       "      <td>NaN</td>\n",
       "      <td>69.64</td>\n",
       "      <td>28.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-04 00:00:00+00:00</th>\n",
       "      <td>348.75</td>\n",
       "      <td>99.39</td>\n",
       "      <td>NaN</td>\n",
       "      <td>71.49</td>\n",
       "      <td>27.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-05 00:00:00+00:00</th>\n",
       "      <td>350.48</td>\n",
       "      <td>99.83</td>\n",
       "      <td>NaN</td>\n",
       "      <td>72.75</td>\n",
       "      <td>27.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-06 00:00:00+00:00</th>\n",
       "      <td>348.95</td>\n",
       "      <td>100.60</td>\n",
       "      <td>NaN</td>\n",
       "      <td>72.88</td>\n",
       "      <td>26.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-09 00:00:00+00:00</th>\n",
       "      <td>339.74</td>\n",
       "      <td>99.64</td>\n",
       "      <td>NaN</td>\n",
       "      <td>72.89</td>\n",
       "      <td>27.25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              CMG     MCD  SHAK    WFM   TSLA\n",
       "2012-01-03 00:00:00+00:00  341.27   98.84   NaN  69.64  28.08\n",
       "2012-01-04 00:00:00+00:00  348.75   99.39   NaN  71.49  27.71\n",
       "2012-01-05 00:00:00+00:00  350.48   99.83   NaN  72.75  27.12\n",
       "2012-01-06 00:00:00+00:00  348.95  100.60   NaN  72.88  26.91\n",
       "2012-01-09 00:00:00+00:00  339.74   99.64   NaN  72.89  27.25"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_1 =  get_df_from_tiingo('TSLA', start, end).loc[:, 'close']\n",
    "\n",
    "prices.loc[:, 'TSLA'] = s_1\n",
    "prices.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CMG</th>\n",
       "      <th>MCD</th>\n",
       "      <th>SHAK</th>\n",
       "      <th>WFM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-01-03 00:00:00+00:00</th>\n",
       "      <td>341.27</td>\n",
       "      <td>98.84</td>\n",
       "      <td>NaN</td>\n",
       "      <td>69.64</td>\n",
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       "    <tr>\n",
       "      <th>2012-01-04 00:00:00+00:00</th>\n",
       "      <td>348.75</td>\n",
       "      <td>99.39</td>\n",
       "      <td>NaN</td>\n",
       "      <td>71.49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-05 00:00:00+00:00</th>\n",
       "      <td>350.48</td>\n",
       "      <td>99.83</td>\n",
       "      <td>NaN</td>\n",
       "      <td>72.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-06 00:00:00+00:00</th>\n",
       "      <td>348.95</td>\n",
       "      <td>100.60</td>\n",
       "      <td>NaN</td>\n",
       "      <td>72.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-09 00:00:00+00:00</th>\n",
       "      <td>339.74</td>\n",
       "      <td>99.64</td>\n",
       "      <td>NaN</td>\n",
       "      <td>72.89</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              CMG     MCD  SHAK    WFM\n",
       "2012-01-03 00:00:00+00:00  341.27   98.84   NaN  69.64\n",
       "2012-01-04 00:00:00+00:00  348.75   99.39   NaN  71.49\n",
       "2012-01-05 00:00:00+00:00  350.48   99.83   NaN  72.75\n",
       "2012-01-06 00:00:00+00:00  348.95  100.60   NaN  72.88\n",
       "2012-01-09 00:00:00+00:00  339.74   99.64   NaN  72.89"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices = prices.drop('TSLA', axis=1)\n",
    "prices.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果想将多个 DataFrame 合并为一个，可以使用 `pandas.concat()` 方法。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_1 = pd.concat(\n",
    "    [\n",
    "        get_df_from_tiingo(\n",
    "            symbol, start, end\n",
    "        ).loc[:, 'close'] for symbol in ['SPY', 'NVDA']\n",
    "    ],\n",
    "    axis=1,\n",
    "    keys=['SPY', 'VXX']\n",
    ")\n",
    "\n",
    "df_2 = pd.concat(\n",
    "    [\n",
    "        get_df_from_tiingo(\n",
    "            symbol, start, end\n",
    "        ).loc[:, 'close'] for symbol in ['MSFT', 'AAPL', 'GOOG']\n",
    "    ],\n",
    "    axis=1,\n",
    "    keys=['MSFT', 'AAPL', 'GOOG']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SPY</th>\n",
       "      <th>VXX</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>GOOG</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-01-03 00:00:00+00:00</th>\n",
       "      <td>127.50</td>\n",
       "      <td>14.04</td>\n",
       "      <td>26.765</td>\n",
       "      <td>411.23</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-04 00:00:00+00:00</th>\n",
       "      <td>127.70</td>\n",
       "      <td>14.20</td>\n",
       "      <td>27.400</td>\n",
       "      <td>413.44</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-05 00:00:00+00:00</th>\n",
       "      <td>128.04</td>\n",
       "      <td>14.71</td>\n",
       "      <td>27.680</td>\n",
       "      <td>418.03</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-06 00:00:00+00:00</th>\n",
       "      <td>127.71</td>\n",
       "      <td>14.54</td>\n",
       "      <td>28.105</td>\n",
       "      <td>422.40</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-09 00:00:00+00:00</th>\n",
       "      <td>128.02</td>\n",
       "      <td>14.54</td>\n",
       "      <td>27.740</td>\n",
       "      <td>421.73</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              SPY    VXX    MSFT    AAPL  GOOG\n",
       "2012-01-03 00:00:00+00:00  127.50  14.04  26.765  411.23   NaN\n",
       "2012-01-04 00:00:00+00:00  127.70  14.20  27.400  413.44   NaN\n",
       "2012-01-05 00:00:00+00:00  128.04  14.71  27.680  418.03   NaN\n",
       "2012-01-06 00:00:00+00:00  127.71  14.54  28.105  422.40   NaN\n",
       "2012-01-09 00:00:00+00:00  128.02  14.54  27.740  421.73   NaN"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_3 = pd.concat([df_1, df_2], axis=1)\n",
    "df_3.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 缺失的数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CMG</th>\n",
       "      <th>MCD</th>\n",
       "      <th>SHAK</th>\n",
       "      <th>WFM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-01-03 00:00:00+00:00</th>\n",
       "      <td>341.27</td>\n",
       "      <td>98.84</td>\n",
       "      <td>0.0</td>\n",
       "      <td>69.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-04 00:00:00+00:00</th>\n",
       "      <td>348.75</td>\n",
       "      <td>99.39</td>\n",
       "      <td>0.0</td>\n",
       "      <td>71.49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-05 00:00:00+00:00</th>\n",
       "      <td>350.48</td>\n",
       "      <td>99.83</td>\n",
       "      <td>0.0</td>\n",
       "      <td>72.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-06 00:00:00+00:00</th>\n",
       "      <td>348.95</td>\n",
       "      <td>100.60</td>\n",
       "      <td>0.0</td>\n",
       "      <td>72.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-09 00:00:00+00:00</th>\n",
       "      <td>339.74</td>\n",
       "      <td>99.64</td>\n",
       "      <td>0.0</td>\n",
       "      <td>72.89</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              CMG     MCD  SHAK    WFM\n",
       "2012-01-03 00:00:00+00:00  341.27   98.84   0.0  69.64\n",
       "2012-01-04 00:00:00+00:00  348.75   99.39   0.0  71.49\n",
       "2012-01-05 00:00:00+00:00  350.48   99.83   0.0  72.75\n",
       "2012-01-06 00:00:00+00:00  348.95  100.60   0.0  72.88\n",
       "2012-01-09 00:00:00+00:00  339.74   99.64   0.0  72.89"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filled0_prices = prices.fillna(0)\n",
    "filled0_prices.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>SHAK</th>\n",
       "      <th>WFM</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-01-03 00:00:00+00:00</th>\n",
       "      <td>341.27</td>\n",
       "      <td>98.84</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.64</td>\n",
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       "    <tr>\n",
       "      <th>2012-01-04 00:00:00+00:00</th>\n",
       "      <td>348.75</td>\n",
       "      <td>99.39</td>\n",
       "      <td>45.9</td>\n",
       "      <td>71.49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-05 00:00:00+00:00</th>\n",
       "      <td>350.48</td>\n",
       "      <td>99.83</td>\n",
       "      <td>45.9</td>\n",
       "      <td>72.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-06 00:00:00+00:00</th>\n",
       "      <td>348.95</td>\n",
       "      <td>100.60</td>\n",
       "      <td>45.9</td>\n",
       "      <td>72.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-09 00:00:00+00:00</th>\n",
       "      <td>339.74</td>\n",
       "      <td>99.64</td>\n",
       "      <td>45.9</td>\n",
       "      <td>72.89</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              CMG     MCD  SHAK    WFM\n",
       "2012-01-03 00:00:00+00:00  341.27   98.84  45.9  69.64\n",
       "2012-01-04 00:00:00+00:00  348.75   99.39  45.9  71.49\n",
       "2012-01-05 00:00:00+00:00  350.48   99.83  45.9  72.75\n",
       "2012-01-06 00:00:00+00:00  348.95  100.60  45.9  72.88\n",
       "2012-01-09 00:00:00+00:00  339.74   99.64  45.9  72.89"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bfilled_prices = prices.fillna(method='bfill')\n",
    "bfilled_prices.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这种情况下最好的做法是丢掉缺失的值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>CMG</th>\n",
       "      <th>MCD</th>\n",
       "      <th>SHAK</th>\n",
       "      <th>WFM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-01-30 00:00:00+00:00</th>\n",
       "      <td>709.84</td>\n",
       "      <td>92.44</td>\n",
       "      <td>45.90</td>\n",
       "      <td>52.095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-02-02 00:00:00+00:00</th>\n",
       "      <td>712.55</td>\n",
       "      <td>92.51</td>\n",
       "      <td>43.99</td>\n",
       "      <td>53.150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-02-03 00:00:00+00:00</th>\n",
       "      <td>726.63</td>\n",
       "      <td>93.92</td>\n",
       "      <td>44.98</td>\n",
       "      <td>53.410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-02-04 00:00:00+00:00</th>\n",
       "      <td>676.00</td>\n",
       "      <td>94.05</td>\n",
       "      <td>41.32</td>\n",
       "      <td>53.680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-02-05 00:00:00+00:00</th>\n",
       "      <td>670.91</td>\n",
       "      <td>94.34</td>\n",
       "      <td>42.64</td>\n",
       "      <td>53.375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              CMG    MCD   SHAK     WFM\n",
       "2015-01-30 00:00:00+00:00  709.84  92.44  45.90  52.095\n",
       "2015-02-02 00:00:00+00:00  712.55  92.51  43.99  53.150\n",
       "2015-02-03 00:00:00+00:00  726.63  93.92  44.98  53.410\n",
       "2015-02-04 00:00:00+00:00  676.00  94.05  41.32  53.680\n",
       "2015-02-05 00:00:00+00:00  670.91  94.34  42.64  53.375"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dropped_prices = prices.dropna()\n",
    "dropped_prices.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 使用 pandas 分析时序 Series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
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     "output_type": "display_data"
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   ],
   "source": [
    "prices.plot()\n",
    "plt.title('Collected Stock Prices')\n",
    "plt.ylabel('Price')\n",
    "plt.xlabel('Date');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "行 axis=0，列 axis=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CMG     501.636654\n",
       "MCD      96.621602\n",
       "SHAK     53.575708\n",
       "WFM      61.256984\n",
       "dtype: float64"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CMG     146.688736\n",
       "MCD       5.714232\n",
       "SHAK     11.968587\n",
       "WFM      22.445795\n",
       "dtype: float64"
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     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices.std(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用 `describe` 函数获得统计值汇总。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>CMG</th>\n",
       "      <th>MCD</th>\n",
       "      <th>SHAK</th>\n",
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       "      <th>count</th>\n",
       "      <td>1006.000000</td>\n",
       "      <td>1006.000000</td>\n",
       "      <td>233.000000</td>\n",
       "      <td>1006.000000</td>\n",
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       "      <th>mean</th>\n",
       "      <td>501.636654</td>\n",
       "      <td>96.621602</td>\n",
       "      <td>53.575708</td>\n",
       "      <td>61.256984</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>146.688736</td>\n",
       "      <td>5.714232</td>\n",
       "      <td>11.968587</td>\n",
       "      <td>22.445795</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>236.240000</td>\n",
       "      <td>84.050000</td>\n",
       "      <td>38.190000</td>\n",
       "      <td>29.150000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>371.555000</td>\n",
       "      <td>93.672600</td>\n",
       "      <td>44.120000</td>\n",
       "      <td>40.888750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>521.270000</td>\n",
       "      <td>96.290000</td>\n",
       "      <td>49.270000</td>\n",
       "      <td>53.955000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>646.835000</td>\n",
       "      <td>99.137500</td>\n",
       "      <td>61.670000</td>\n",
       "      <td>85.488750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>757.770000</td>\n",
       "      <td>120.070000</td>\n",
       "      <td>92.860000</td>\n",
       "      <td>105.710000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               CMG          MCD        SHAK          WFM\n",
       "count  1006.000000  1006.000000  233.000000  1006.000000\n",
       "mean    501.636654    96.621602   53.575708    61.256984\n",
       "std     146.688736     5.714232   11.968587    22.445795\n",
       "min     236.240000    84.050000   38.190000    29.150000\n",
       "25%     371.555000    93.672600   44.120000    40.888750\n",
       "50%     521.270000    96.290000   49.270000    53.955000\n",
       "75%     646.835000    99.137500   61.670000    85.488750\n",
       "max     757.770000   120.070000   92.860000   105.710000"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "prices.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "像处理 Series 那样缩放、增加标量。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
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     "execution_count": 74,
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   "source": [
    "(2 * prices - 50).head(5)"
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       "                                CMG       MCD  SHAK       WFM\n",
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    "若我们使用统计方法标准化化收益率，那么我们就可以更好地了解在 相同规模下它们是如何相对运动的。"
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   "source": [
    "norm_returns = (mult_returns - mult_returns.mean(axis=0)) / mult_returns.std(axis=0)\n",
    "norm_returns.loc['2014-01-01':'2015-01-01'].plot();"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这使得比较我们示例中包含的不同时间序列的运动更容易。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "移动平均和标准差也适用于 `DataFrame`。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "rolling_mean = prices.rolling(window=30).mean()\n",
    "rolling_mean.columns = prices.columns"
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  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": true
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   "source": [
    "rolling_mean.plot()\n",
    "plt.title('Rolling Mean of Prices')\n",
    "plt.xlabel('Date')\n",
    "plt.ylabel('Price')\n",
    "plt.legend();"
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