Kalman Filter.ipynb

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   "source": [
    "### Kalman Filter\n",
    "\n",
    "* [Section 1: Stock price](#section1)\n",
    "* [Section 2: A moving object](#section2)\n",
    "\n",
    "### Section 1: Stock price"
   ]
  },
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     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    }
   ],
   "source": [
    "#! pip install yfinance\n",
    "#! pip install pykalman\n",
    "import yfinance as yf\n",
    "data = yf.download(\"SPY\", start=\"2017-01-01\", end=\"2021-12-31\")"
   ]
  },
  {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2017-01-03</th>\n",
       "      <td>225.039993</td>\n",
       "      <td>225.830002</td>\n",
       "      <td>223.880005</td>\n",
       "      <td>225.240005</td>\n",
       "      <td>208.213501</td>\n",
       "      <td>91366500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-04</th>\n",
       "      <td>225.619995</td>\n",
       "      <td>226.750000</td>\n",
       "      <td>225.610001</td>\n",
       "      <td>226.580002</td>\n",
       "      <td>209.452240</td>\n",
       "      <td>78744400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-05</th>\n",
       "      <td>226.270004</td>\n",
       "      <td>226.580002</td>\n",
       "      <td>225.479996</td>\n",
       "      <td>226.399994</td>\n",
       "      <td>209.285812</td>\n",
       "      <td>78379000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-06</th>\n",
       "      <td>226.529999</td>\n",
       "      <td>227.750000</td>\n",
       "      <td>225.899994</td>\n",
       "      <td>227.210007</td>\n",
       "      <td>210.034561</td>\n",
       "      <td>71559900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-09</th>\n",
       "      <td>226.910004</td>\n",
       "      <td>227.070007</td>\n",
       "      <td>226.419998</td>\n",
       "      <td>226.460007</td>\n",
       "      <td>209.341278</td>\n",
       "      <td>46939700</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "                  Open        High         Low       Close   Adj Close  \\\n",
       "Date                                                                     \n",
       "2017-01-03  225.039993  225.830002  223.880005  225.240005  208.213501   \n",
       "2017-01-04  225.619995  226.750000  225.610001  226.580002  209.452240   \n",
       "2017-01-05  226.270004  226.580002  225.479996  226.399994  209.285812   \n",
       "2017-01-06  226.529999  227.750000  225.899994  227.210007  210.034561   \n",
       "2017-01-09  226.910004  227.070007  226.419998  226.460007  209.341278   \n",
       "\n",
       "              Volume  \n",
       "Date                  \n",
       "2017-01-03  91366500  \n",
       "2017-01-04  78744400  \n",
       "2017-01-05  78379000  \n",
       "2017-01-06  71559900  \n",
       "2017-01-09  46939700  "
      ]
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     "execution_count": 2,
     "metadata": {},
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   ],
   "source": [
    "data.head()"
   ]
  },
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   "execution_count": 3,
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     "data": {
      "text/plain": [
       "Date\n",
       "2017-01-03    208.213501\n",
       "2017-01-04    209.452240\n",
       "2017-01-05    209.285812\n",
       "2017-01-06    210.034561\n",
       "2017-01-09    209.341278\n",
       "                 ...    \n",
       "2021-05-14    416.579987\n",
       "2021-05-17    415.519989\n",
       "2021-05-18    411.940002\n",
       "2021-05-19    410.859985\n",
       "2021-05-20    415.279999\n",
       "Name: Adj Close, Length: 1103, dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
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   "source": [
    "X = data['Adj Close']\n",
    "X"
   ]
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   "execution_count": 4,
   "id": "b12bb825-4962-4e48-83cf-6254866c3463",
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       "array([[104.10675049],\n",
       "       [139.68701515],\n",
       "       [157.64501644],\n",
       "       ...,\n",
       "       [413.86745592],\n",
       "       [413.58137052],\n",
       "       [413.7429524 ]])"
      ]
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "from pykalman import KalmanFilter\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Construct a Kalman filter\n",
    "kf = KalmanFilter(transition_matrices = [1],    # The value for At. It is a random walk so is set to 1.0\n",
    "                  observation_matrices = [1],   # The value for Ht.\n",
    "                  initial_state_mean = 0,       # Any initial value. It will converge to the true state value.\n",
    "                  initial_state_covariance = 1, # Sigma value for the Qt in Equation (1) the Gaussian distribution\n",
    "                  observation_covariance=1,     # Sigma value for the Rt in Equation (2) the Gaussian distribution\n",
    "                  transition_covariance=.01)    # A small turbulence in the random walk parameter 1.0\n",
    "# Get the Kalman smoothing\n",
    "state_means, _ = kf.filter(data['Adj Close'].values)\n",
    "state_means"
   ]
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       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
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       "    <tr>\n",
       "      <th>2017-01-03</th>\n",
       "      <td>225.039993</td>\n",
       "      <td>225.830002</td>\n",
       "      <td>223.880005</td>\n",
       "      <td>225.240005</td>\n",
       "      <td>208.213501</td>\n",
       "      <td>91366500</td>\n",
       "      <td>104.106750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-04</th>\n",
       "      <td>225.619995</td>\n",
       "      <td>226.750000</td>\n",
       "      <td>225.610001</td>\n",
       "      <td>226.580002</td>\n",
       "      <td>209.452240</td>\n",
       "      <td>78744400</td>\n",
       "      <td>139.687015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-05</th>\n",
       "      <td>226.270004</td>\n",
       "      <td>226.580002</td>\n",
       "      <td>225.479996</td>\n",
       "      <td>226.399994</td>\n",
       "      <td>209.285812</td>\n",
       "      <td>78379000</td>\n",
       "      <td>157.645016</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-06</th>\n",
       "      <td>226.529999</td>\n",
       "      <td>227.750000</td>\n",
       "      <td>225.899994</td>\n",
       "      <td>227.210007</td>\n",
       "      <td>210.034561</td>\n",
       "      <td>71559900</td>\n",
       "      <td>168.718593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-09</th>\n",
       "      <td>226.910004</td>\n",
       "      <td>227.070007</td>\n",
       "      <td>226.419998</td>\n",
       "      <td>226.460007</td>\n",
       "      <td>209.341278</td>\n",
       "      <td>46939700</td>\n",
       "      <td>176.081344</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "                  Open        High         Low       Close   Adj Close  \\\n",
       "Date                                                                     \n",
       "2017-01-03  225.039993  225.830002  223.880005  225.240005  208.213501   \n",
       "2017-01-04  225.619995  226.750000  225.610001  226.580002  209.452240   \n",
       "2017-01-05  226.270004  226.580002  225.479996  226.399994  209.285812   \n",
       "2017-01-06  226.529999  227.750000  225.899994  227.210007  210.034561   \n",
       "2017-01-09  226.910004  227.070007  226.419998  226.460007  209.341278   \n",
       "\n",
       "              Volume     KF_mean  \n",
       "Date                              \n",
       "2017-01-03  91366500  104.106750  \n",
       "2017-01-04  78744400  139.687015  \n",
       "2017-01-05  78379000  157.645016  \n",
       "2017-01-06  71559900  168.718593  \n",
       "2017-01-09  46939700  176.081344  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "data['KF_mean'] = np.array(state_means)\n",
    "data.head()"
   ]
  },
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       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>KF_mean</th>\n",
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       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "    <tr>\n",
       "      <th>2021-05-14</th>\n",
       "      <td>413.209991</td>\n",
       "      <td>417.489990</td>\n",
       "      <td>413.179993</td>\n",
       "      <td>416.579987</td>\n",
       "      <td>416.579987</td>\n",
       "      <td>82123100</td>\n",
       "      <td>413.917658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-05-17</th>\n",
       "      <td>415.390015</td>\n",
       "      <td>416.390015</td>\n",
       "      <td>413.359985</td>\n",
       "      <td>415.519989</td>\n",
       "      <td>415.519989</td>\n",
       "      <td>65129200</td>\n",
       "      <td>414.070079</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-05-18</th>\n",
       "      <td>415.799988</td>\n",
       "      <td>416.059998</td>\n",
       "      <td>411.769989</td>\n",
       "      <td>411.940002</td>\n",
       "      <td>411.940002</td>\n",
       "      <td>59810200</td>\n",
       "      <td>413.867456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-05-19</th>\n",
       "      <td>406.920013</td>\n",
       "      <td>411.049988</td>\n",
       "      <td>405.329987</td>\n",
       "      <td>410.859985</td>\n",
       "      <td>410.859985</td>\n",
       "      <td>106355400</td>\n",
       "      <td>413.581371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-05-20</th>\n",
       "      <td>411.799988</td>\n",
       "      <td>416.619995</td>\n",
       "      <td>411.670013</td>\n",
       "      <td>415.279999</td>\n",
       "      <td>415.279999</td>\n",
       "      <td>77360973</td>\n",
       "      <td>413.742952</td>\n",
       "    </tr>\n",
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      "text/plain": [
       "                  Open        High         Low       Close   Adj Close  \\\n",
       "Date                                                                     \n",
       "2021-05-14  413.209991  417.489990  413.179993  416.579987  416.579987   \n",
       "2021-05-17  415.390015  416.390015  413.359985  415.519989  415.519989   \n",
       "2021-05-18  415.799988  416.059998  411.769989  411.940002  411.940002   \n",
       "2021-05-19  406.920013  411.049988  405.329987  410.859985  410.859985   \n",
       "2021-05-20  411.799988  416.619995  411.670013  415.279999  415.279999   \n",
       "\n",
       "               Volume     KF_mean  \n",
       "Date                               \n",
       "2021-05-14   82123100  413.917658  \n",
       "2021-05-17   65129200  414.070079  \n",
       "2021-05-18   59810200  413.867456  \n",
       "2021-05-19  106355400  413.581371  \n",
       "2021-05-20   77360973  413.742952  "
      ]
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     "execution_count": 6,
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   "source": [
    "data.tail()"
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   "id": "897514e3-26e3-4854-93a4-e9ae7b7266ea",
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    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Price')"
      ]
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     "execution_count": 7,
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data[['Adj Close','KF_mean']].plot()\n",
    "plt.title('Kalman Filter estimates for SPY')\n",
    "plt.legend(['SPY','Kalman Estimate'])\n",
    "plt.xlabel('Day')\n",
    "plt.ylabel('Price')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f36bed2e-8a12-4867-9139-f98c23cff97e",
   "metadata": {},
   "source": [
    "### Section 2: A Moving objective"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "9914593b-982e-4309-af63-4224e8271158",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pylab as pl\n",
    "from pykalman import KalmanFilter\n",
    "\n",
    "rnd = np.random.RandomState(0)\n",
    "n_timesteps = 100\n",
    "x = np.linspace(0, 3 * np.pi, n_timesteps)\n",
    "y = 20 * (np.sin(x) + 0.5 * rnd.randn(n_timesteps))\n",
    "pl.figure(figsize=(16, 6))\n",
    "pl.scatter(x,y, marker='x', color='b', label='observations')\n",
    "pl.xlabel('time')\n",
    "pl.ylabel('Position')\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "f207e96c-4b6b-4286-a27e-efaaae9cd3e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "kf = KalmanFilter(transition_matrices=np.array([[1, 1], [0, 1]]),\n",
    "                  transition_covariance=0.01 * np.eye(2))\n",
    "states_pred = kf.em(y).smooth(y)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "544aa034-0a1e-4fae-91e8-b0e630ceda58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.figure(figsize=(16, 6))\n",
    "obs_scatter = pl.scatter(x, y, marker='x', color='b',\n",
    "                         label='observations')\n",
    "position_line = pl.plot(x, states_pred[:, 0],markersize=2,\n",
    "                        linestyle='-', marker='o', color='r',\n",
    "                        label='position est.')\n",
    "velocity_line = pl.plot(x, states_pred[:, 1],markersize=2,\n",
    "                        linestyle='-', marker='o', color='g',\n",
    "                        label='velocity est.')\n",
    "pl.legend(loc='lower left',fontsize=14)\n",
    "pl.xlim(xmin=0, xmax=x.max())\n",
    "pl.xlabel('time')\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "a406dd25-ccf7-46ed-9345-67f5c9f26a78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kf = KalmanFilter(transition_matrices=[1],\n",
    "                  transition_covariance=0.01)\n",
    "states_pred = kf.em(y).smooth(y)[0]\n",
    "\n",
    "pl.figure(figsize=(16, 6))\n",
    "obs_scatter = pl.scatter(x, y, marker='x', color='b',\n",
    "                         label='observations')\n",
    "position_line = pl.plot(x, states_pred,markersize=2,\n",
    "                        linestyle='-', marker='o', color='r',\n",
    "                        label='position est.')\n",
    "pl.legend(loc='lower left',fontsize=14)\n",
    "pl.xlim(xmin=0, xmax=x.max())\n",
    "pl.xlabel('time')\n",
    "pl.ylabel('Position')\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a9648a1-0e82-47c0-8648-caecd4e0f3a9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "faabd4a1-5b61-435b-a189-656de2bf1ec2",
   "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}