linear_regression_submission.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Workbook\n",
    "By Tanay Trivedi and Jonathan Bair"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Imports and Formatting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data=pd.read_hdf('full_data.hdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data=data.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data['response']=data['fx'].pct_change()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "data['response']=data['response'].shift(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=data.copy()\n",
    "del X['fx']\n",
    "del X['response']\n",
    "y=data['response'].copy()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "newX=pd.DataFrame()\n",
    "newX['diff_inf']=X['jad_inf']-X['usd_inf']\n",
    "newX['diff_tbill']=X['jad_tbill']-X['usd_tbill']\n",
    "newX[\"diff_oir\"]=X[\"jad_oir\"]-X[\"usd_oir\"]\n",
    "newX[\"tourism\"]=X['tourism']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "newX=newX.pct_change()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "newX=newX.iloc[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "newX[\"intercept\"]=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "y=y.iloc[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_X=newX.iloc[:int(0.8*len(newX))]\n",
    "val_X=newX.iloc[int(0.8*len(newX)):int(0.9*len(newX))]\n",
    "test_X=newX.iloc[int(0.9*len(newX)):]\n",
    "\n",
    "train_y=y.iloc[:int(0.8*len(y))]\n",
    "val_y=y.iloc[int(0.8*len(y)):int(0.9*len(y))]\n",
    "test_y=y.iloc[int(0.9*len(y)):]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_X=test_X.iloc[:-1]\n",
    "test_y=test_y.iloc[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "103"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(train_X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "103"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(train_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pd.option_context('mode.use_inf_as_null', True):\n",
    "    train_X = train_X.dropna()\n",
    "    train_y=train_y.loc[train_X.index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "102"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(train_X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "features=list(train_X.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['diff_inf', 'diff_tbill', 'diff_oir', 'tourism', 'intercept']"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "features=features[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['diff_inf', 'diff_tbill', 'diff_oir', 'tourism']"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "mus=train_X[features].mean().to_dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'diff_inf': 0.0025794448862713803,\n",
       " 'diff_oir': -0.0039218389843883135,\n",
       " 'diff_tbill': -0.0020261457034433665,\n",
       " 'tourism': 0.1086817350456867}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigmas=train_X[features].std().to_dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'diff_inf': 2.523251535718829,\n",
       " 'diff_oir': 0.05796874158309547,\n",
       " 'diff_tbill': 0.10984407086814305,\n",
       " 'tourism': 0.998048225755341}"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/meltingpot/anaconda3/lib/python3.6/site-packages/pandas/core/frame.py:3140: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  self[k1] = value[k2]\n"
     ]
    }
   ],
   "source": [
    "train_X[features]=(train_X[features]-mus)/sigmas\n",
    "val_X[features]=(val_X[features]-mus)/sigmas\n",
    "test_X[features]=(test_X[features]-mus)/sigmas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "mus=train_y.mean()\n",
    "sigmas=train_y.std()\n",
    "train_y=(train_y-mus)/sigmas\n",
    "val_y=(val_y-mus)/sigmas\n",
    "test_y=(test_y-mus)/sigmas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_mat=train_X.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.linalg import inv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta_hat=np.matmul(np.matmul(inv(np.matmul(X_mat.T,X_mat)),X_mat.T),train_y.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  8.26093063e-03,   3.30132398e-01,   1.66805327e-01,\n",
       "        -8.21329001e-03,  -1.21430643e-17])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat=np.matmul(test_X.values,beta_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "mse=np.mean(np.power(test_y.values-y_hat,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.096862851855098797"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_lin=pd.DataFrame()\n",
    "y_lin['y']=test_y\n",
    "y_lin['yhat']=y_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd19d3d7320>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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X0ro8GyJ6w+hfW8MUHTHyyYlmvriKLr65vDI827pWsH+VNSY+qLX15d9rOvSc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\nZkiDv1JKNUMa/JVSqhnS4K+UUs3Q/wMgLiEIladONwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_lin.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_lin['sign']=np.sign(y_lin[\"y\"])==np.sign(y_lin[\"yhat\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4166666666666667"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(y_lin[y_lin['sign']==True])/float(len(y_lin))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ridge_solve(train_X,train_y,lambd):\n",
    "    return np.matmul(np.matmul(inv(np.matmul(train_X.T,train_X)+lambd*np.ones((train_X.shape[1],1))),train_X.T),train_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta_hat=[]\n",
    "for i in np.arange(0.1,1,0.1):\n",
    "    beta_hat.append(ridge_solve(train_X,train_y,i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(beta_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "error=pd.DataFrame(index=np.arange(0.1,1,0.1),columns=[\"mse\",\"acc\"])\n",
    "ix=0.1\n",
    "for i in range(len(beta_hat)):\n",
    "    y_hat=np.matmul(val_X.values,beta_hat[i])\n",
    "    mse=np.mean(np.power(val_y.values-y_hat,2))\n",
    "    error.iloc[i][\"mse\"]=mse\n",
    "    \n",
    "    y_lin=pd.DataFrame()\n",
    "    y_lin['y']=val_y\n",
    "    y_lin['yhat']=y_hat\n",
    "    \n",
    "    y_lin['sign']=np.sign(y_lin[\"y\"])==np.sign(y_lin[\"yhat\"])\n",
    "    error.iloc[i][\"acc\"]=len(y_lin[y_lin['sign']==True])/float(len(y_lin))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        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>mse</th>\n",
       "      <th>acc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.1</th>\n",
       "      <td>0.137659</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.2</th>\n",
       "      <td>0.137406</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.3</th>\n",
       "      <td>0.137156</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.4</th>\n",
       "      <td>0.136908</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.5</th>\n",
       "      <td>0.136663</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.6</th>\n",
       "      <td>0.13642</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.7</th>\n",
       "      <td>0.13618</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.8</th>\n",
       "      <td>0.135942</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.9</th>\n",
       "      <td>0.135707</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          mse       acc\n",
       "0.1  0.137659  0.538462\n",
       "0.2  0.137406  0.538462\n",
       "0.3  0.137156  0.538462\n",
       "0.4  0.136908  0.538462\n",
       "0.5  0.136663  0.538462\n",
       "0.6   0.13642  0.538462\n",
       "0.7   0.13618  0.538462\n",
       "0.8  0.135942  0.538462\n",
       "0.9  0.135707  0.538462"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sign Accuracy is the same for all, we should just pick by MSE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmin(error[\"mse\"].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.90000000000000002"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error.index[np.argmin(error[\"mse\"].values)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd19d2df9e8>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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incdZmZxFSbmNiFaBXDu0E1MHRDGiW1v8fDXgn88RLf/hwH5jTCqAiCwAZgBng78xZkWV\n9dcDtzigXKUarLisgtlvbiAjt5iOYUF0j2zF9EEdrQAfaQX4Tq1bODxojImN5LK+7Xnl+/1cO7QT\nUWEtHLr95uJ0YSnf7TnBkl3HWZ2SRVmFoUNoEDcN78KU/h2Ij2nrNWkYnMURwb8TcKTK7+nAiBrW\nvxNYXN0CEZkLzAXo0sXz82Ur9/XRhsNk5BYz/84RjI6NaNKy/zCtL5NeWMnTi/fx0qwhTVq2N8gr\nLmPS86vIzi+hU+sW3HZJDFMGRDEkujU+GvDrzBHBv7q/tqnmNUTkFiAeuLS65caYecA8gPj4+Gq3\noVRjFZaW88+E/VzSPbzJAz9Al/CW3DO2Oy9/v5/ZI7oyvJt33TzkbGtTssnOL+GVm4cwbUCUjpxq\nIEec06YD0VV+7wwcO38lEZkEPAZMN8aUnL9cqaby7g+HyM4v5eHLe7msDj8f15OOYUH876LdVNi0\nnVMfK5IyCQny44p+HTTwN4Ijgv8mIFZEuolIADALWFR1BREZAryOFfgzHVCmUg2SW1TG6ytTmdC7\nHcO6tnFZPVoE+PL7aX3Ym5HHxxsPu6wensYYQ0JSFmNjI/UibiM1+q9njCkH7gW+BfYCnxpjdovI\nkyIy3b7aP4BWwEIR2SYiiy6wOaWc6q3VqeQWlfHQ5DhXV4VpA6K4uHtbnv0uiVMFpa6ujkfYk5FH\n5pkSxvWKdHVVPJ5DDp3GmG+MMXHGmB7GmL/YX/ujMWaR/fkkY0x7Y8xg+2N6zVtUyvFy8kt4a81B\npg7oQP9OYa6uDiLCE9P7caa4nOeXJru6Oh4hISkLgEs1+DeanjepZuP1VakUlVW4Rau/Uu8Oodx6\ncVc+3JDGnmN5rq6O20tIyqR/p1DahWh+pMbS4K+ahRN5xbz3wyGuHtKJnu1CXF2dH3lwUhxhLfx5\nYtFujNGLvxeSW1jGlsOnGeclc+i6mgZ/1Sy88v1+KmyGBya6T6u/UlhLf35zeW82HjrJlzsyXF0d\nt7V6fxYVNsP43trl4wga/JXXO3KykAWbDjPzomi6hLd0dXWqdeNF0fTvFMpfv95LQUm5q6vjllbs\nyyKshT+Do103SsubaPBXXu/l5SmICL+a4L65dHx9hCeu6sfxvGL+mbDf1dVxOzabYWVyFmPjIjVt\ng4No8Fde7UBWPp9tSefWi7u6fR6d+Ji2XDOkE2+sOkhaToGrq+NWdh/LIzu/hHFx2uXjKBr8lVd7\nYWkyQf6+/HxcD1dXpU4endIbf1/hqa/21L5yM5KQZN0bqkM8HUeDv/Jae47l8dWODG4fFUNEq0BX\nV6dO2ocG8auJsSzbm8mKJL0ZvtKKpEwGdg7zmM/RE2jwV17r+aXJhAT5MXeMZ7T6K90+KoZuEcE8\n9eUeSqtMINNcnSooZduR04zrpUM8HUmDv/JKWw+fYtneE/xsbHfCWlY/s5a7CvTz5Y9X9SU1u4B3\n1h50dXVcblVKFjYD47XLx6E0+Cuv9Nx3ybQNDmDOqG6urkqDjO/Vjom92/Hy8hQy84pdXR2XWpmU\nRZuW/gzs3NrVVfEqGvyV11l3IIc1+7P5xbgetAp0yDTVLvH4lX0pqzA8vWSfq6viMpVDPC/VIZ4O\np8FfeRVjDM99l0T70EBuubirq6vTKDERwdw1phv/2XKUzWknXV0dl9h5NJecglLt73cC7wz+mh+l\n2UpIziIx7RS/mhBLkL+vq6vTaL8c35MOoUE8sWhPs5z0ZUVSJiIwVsf3O5z3Bf/SQnihP3xxL+xf\nDhVlrq6RaiKVrf7ObVowMz669jd4gOBAP343tTc7j+ayMPFI7W/wMglJWQzq3Jq2wQGurorX8b7g\nX5IHMaNg939h/rXwbBwsug8OrIAKzZnizZbsOs6uo3k8MCmOAL9a/rVPpcGiX8HiR92+gTB9UEcu\nimnDM98mkVvo3nV1pJz8Erann2a8dvk4hedeDbuQkA5w7TwoK4YDy2H357DrM9jyHrQMhz5XQb9r\noOto8PW+3W+uKmyG55cm0yMymGuGdLrwivlZsPo5SHzL/sZSyE6Gme9BoHuleq5UOenLVf+3hheW\nJfPE9H6urlKTWJWShTHorF1O4r3Rzz8Iek+zHmVFsH+ZdSDYsRA2vwstI6DvdPuBYBT4eH7/cHO2\naPtRUjLzefXmodWPCinOg3WvwrpXrP+HIbfApY9YDYQvH4B3p8HNCyGkfdNXvg76dQzj5hFd+GB9\nGjcN70KvDu55oHKkhKQswoMDGOAGs655I3HXySPi4+NNYmKi4zdcWnjuQJC8BMoKIbjduQNBl0v0\nQOBhyipsTHxuJcGBfnz9q9H4VA3+5SWw6S1Y/SwU5kDfq2HCHyAi9tw6yd/BwtsgOAJu+c+Pl7mR\nUwWljH8ugT4dQvno7hGIeO/QxwqbYdiflzKhVzuev3Gwq6vjUURkszEmvrb1vLflfyEBLa1A33c6\nlBZAylLrQLD1Q9j0JrRqD31nWAeC6IvBx/sui3ibf29O5/DJQt66Lf5c4LdVwI5PYMVfIfcIdB8P\nE/8InYb+dANxl8Gcr+GjmfDWZLhpAXS5uGl3og7aBAfw68t68fh/d7F413GmDohydZWcZnv6aU4X\nljGutxv095cWwLFt4BcI/i2tGBLQynru3wI89CDc/IJ/VQHB0O9q61FaAMnfWgeCLe/DxnkQEnXu\nQNB5uB4I3FBxWQUvL09hSJfWTOjdzhrmm/QNLH8SsvZBxyEw4xXoPq7mDXUaCncuhfnXwfsz4Lo3\nretDbubm4V34aMNh/vL1Xsb3akeLADc5S7XZcxA56DuSsC8TH4GxsREO2V6DHN8Fm9+BHZ9aA0mq\nJfYDQrB1UPAPPu+5fVltz/3tB5Sqz/2cO8KpeQf/qgKCof+11qMk3+oS2v05JL4DG16DkI72A8U1\n0CleDwRu4qMNh8nILea5GwYhaWth2ROQvgnCY2Hm+9Bnet1bZm27WQeAj2+ET26FKc/AiLlOrX99\nWZO+9OXGeev518oDrpmM3hjrbOroZvtjK2RsA78g6/sz8EboNKxRLeKE5CyGdGlD65ZNPMSztBB2\n/8e6Lpi+CXwD7d/7a63u4NJ8a52ywtqfF2RbjcrSAvvrBUAdu9k7DoW5K5y5pxr8qxXYCgZcbz1K\nzkCS/UCw6U1Y/08I7VzlQNC4f3LVcIWl5fwzYT83RZ9i5PqfWddyQjrC9P+DQTc3bDRXcDj8zyL4\n7C5Y/BvIS4eJT7jVwX5E93CmD+rIaysPcMOwzkS3dfLUlAU5cGwLHN1yLuAXZlvLfAOgw0AYfDPk\nZ8Lm96yz5jbdYOBMGDATIuo3g1rWmRJ2pOfy66Y8sJ3YbTX0dnwKJbkQEQeX/w0GzYKWbR1ThjHW\nYIPKA0HVg8L5z1uGO6bMGjS/C76NUZx77kBwYLk1TDAs2mpddhtr9RO30ORTTWX+NysIXfd3pvuu\ng6DWMObXMPxuqx+2sWwV8M1vrCGhA26AGa9afb5uIiO3iAnPrmRsXASv31rrtb26Ky2AjB3ngvyx\nLXDqkH2hQGQvq8HTaajVOm3f/8fdE8W5sPdLK4geXAUYa72BM6H/ddCq9j78zzan8+uF2/nqV6Pp\n78yRPqWF1nd58zvnWvl9Z0D87dbADw9t1NX1gq8G/4YqOg1Ji2HPf+HA99aBAIEOA6yhozGjrJ+O\najWoc84cp+T7p/HZ+j428Sdw9L0w8leOP/AaA2tegOV/gpgxMOtDCHKfYYevrtjPP75N4oM7hzMm\ntgFj4SvKIXPPuSB/dIv1u7H334dFnwvynYZBx8H1uxci75h1j82OT+D4ThBf69rLwJnQ+0rrDLsa\n9360hfWpJ9n4+4k/HrnlKCf2WAF/+ydWKz881gr4g27yiu+rBv+mVFYE6YmQthYOrbFaEeX2NLzt\n+v74YFCHlo+6gKLTsPYlWP8vKipK+bBsAiPm/I1ePZ08NHP7AvjilxDRC2YvhLAabiJrQsVlFVz+\n4ir8fX1YfP8Y/H1r6JoyBk6mwrGt51r1GTugvMha3qLNuSBf2bJ35P9q5j7Y+al1n03uYfBrYd2D\nM3Am9JgAvtacC+UVNob9eRmT+7bn2RsGOa780kKroZb4DqRvtLqr+s6AYbdD15Ee28qvjgZ/Vyov\nsb5kh9ZYB4TDG6DMPiF3eKz9QDDa+hna0bV19QRlRbDhdasVXnyakj7XMmP3pfToNZBXZ1czdNMZ\nDqywLgIHhcLsf0P7vk1Tbi2W7TnBXe8n8odpfbhrTPdzC8qKITUBjiZaLfpjW6DolLXMrwVEDToX\n5DsNtfromyIA2mxwZIN1INj9uVWnluHWBdWBN5JY3p3rX1/PKzcP4cqBDvhunNhjXbzdscDqkgqP\nhWFzrFZ+sPP71V1Bg787qSiDjO32M4O1cHjduaFjbWLOHQi6joI2np2G2KEqymHbfEh4Gs5kQOxl\nMOFx/rrVnzdXp/Ldg2Pp2a4J73Q9vhM+vMFqRc76ELqNabqyL8AYw5x3NrEl7RTfPzyOSP9iSHwb\n1v0TCjKtrpZ2faHTkHOt+sg+7pHapLzUuki/81OrC7W8mFOBnZlfOJw5c39DSHQDD7BlRfa+/Het\nA41vgHVdLv526zvmRa386mjwd2e2CiuQnD0Y/HCuVRYWbf2Ddh0JMaOhbXev/2f9CZsN9n4B3/8Z\ncvZb91hMegJiRnEir5ixz6xg2sAonp/pgjs/Tx+BD6+3ulCu/pc1IszFDmTlc8uLi/hL1BomnPnS\nalh0Hw+X3AtdL7GGMbu74jzY+yVbv57HoPId+GCz7tEYYL9QXJe0G5l7rYC//WN7K7+nvZV/s9e2\n8qvTpMFfRK4AXgJ8gTeNMU+ftzwQeB8YBuQANxpjDtW0Ta8O/uez2SBrr3UgSFsDaT9AQZa1rFWH\nc2cFXUdZoy289WBgDKSugGV/ssaNR/ax7srtNeXsPj/+3118vPEw3/96HF3CnTzE8UKKTsGC2dbB\n+7I/W0HWVZ/JyVT44f8o3zwfH1sZud2n0Wbyb6yLsx4mM6+Y4X9dzv+Oa8vtoZutM4KM7SA+1oXi\nATOhz5U/vuhcVmRl8N38LhxZf66VP2yO1Xjy1u9KDZosvYOI+AKvApOBdGCTiCwyxuypstqdwClj\nTE8RmQX8HbixsWV7DR8faN/PeoyYawXB7BTrQHBorRVkdn1mrdsywhpWGnsZ9JwErTw842F5qXXm\nk7TYepxOg7AucPVr1sXAKnmWjpwsZMGmw9x4UbTrAj9YF0dv+Q/89x747g+QexQu/0vT5oTK2AFr\nX7S6N3z8MINu4vpd8VTk9+DzDoM8Mld7QrLV4Bk+sC90vARG3gtZSdaw0Z2fWn/vr1pA76nWaKEj\nG37cyr/sz82uld8Yjuj4Gw7sN8akAojIAmAGUDX4zwCesD//N/CKiIhx1z4nVxOByDjrEX/HuZEa\naT9YF5FTV1h3ISLWxbrYyyB2MkQNcaubkS6o8KTV15v0jTXhTkmedXdot0th7MPWHaLVjKl/eXkK\nIsK9E+p305BT+AfBdW9bN5WtfxXyjsK1b1ivO4sx1ue/5gXrPpOAEGuI68W/wD+kA7d0SeehT7fz\n2ZZ0bvDAyWwSkjJpFxJI36jQcy9G9oKJj1vJ+I5stIaNVqZp9/G3cnQNu73ZtvIbwxHBvxNQdYqh\ndGDEhdYxxpSLSC4QDmRXXUlE5gJzAbp06eKAqnkJEQjvYT2G3mp1Ex3fASnfWY+EpyHhbxAcCT0n\nWweCHhPc64az7BSrZZ+8BA6vB1Nhz6Y6A3pNhe6X1tg3fSArn8+2pHP7qG5EhTngJi5H8PGBK/5q\nDf389jH44GqY9ZHjx4rbbNaBcs0L1uid4EirOyz+zh99xlcP7sT89Wn8fck+Lu/fgdAgf8fWw4nK\nKmysTslmav+o6rOVikCXEdbjiqet4dSRvaxMrKpBHBH8qzvcnt+ir8s6GGPmAfPA6vNvfNW8lI+P\n1afbcTBc+lvr9vv9y6wDQdI3sP0ja5RHl4vtZwWXQbs+Tdsyqii3+mArA37Ofuv19v1hzEMQN8W6\noFfHM5UXliYT5O/Lz8f1cGKlG+iSX1pDdv8zF96+Am75N7R2QOOlvBR2LrS6d7KToXVXmPYcDJ5d\n7V3MPj7Cn6b3Z/qra3h5WQp/uNI9hqPWxZa0U5wpLq/bxC1+AdZ1MNUojgj+6UDVc8zOwLELrJMu\nIn5AGHDSAWUrsPo4B91oPSrjLRW/AAAgAElEQVTKrdZh5VnBsv+1HqGdrTOCuMutawbOGAFSnGvv\nzllilV182jo17zYGRtxjld2AoLjnWB5f7cjg3vE9iWjlPikWfqTfNdaZzIKb4M1J1r0AUQMbtq2S\nfCuz7LpXrO6k9v3huresuQhqGaI5oHMYsy6K5t0fDjFreHTTDoVthITkLPx8hFGuzOLZzDR6tI89\nmCcDE4GjwCbgZmPM7irr/BIYYIy5x37B91pjzMyattusRvs4U94xa86ClO+sm35K860RETGjIfZy\n64AQ3ojW9MmDVss+abF1YdpWDi3aQtwV0OsKq/upkdMj3vVeIhsO5rDmtxMIa+nmXRmZe2H+9daB\nb+b70HNi3d9bkGMlRdv4ujWiqOtoGP2AdWG/HmdtOfkljH82gUHRrXn/juEeMenLFS+uIqyFP5/8\n7BJXV8XjNdloH3sf/r3At1hDPd82xuwWkSeBRGPMIuAt4AMR2Y/V4p/V2HJVHYV2hGG3WY/yEusG\ns5Sl1twFSx6xHuE9z1007jqq5gRmtgorlUXyYquFn7XXej2ilzXksdcU6HyRw0a+bD18imV7T/Dw\nZXHuH/jB6l67a5l1L8BHM60Mo4Nvrvk9p49Yrfwt71uZHXtNs4J+9PAGVSG8VSAPTo7jT1/uYXVK\nNmPj3HtE2PHcYvYdP8OjU3q7uirNit7k1ZydTIWUZZDyLRxcDRUl1uQS3cdZB4LYyRDW2eqGOPC9\n1bpP+c5K5+vjZ92IFjfFauG37V5baQ1yy5sb2JuRx6rfjic40A3uSq2r4jz45BY4uNIaqTLm4Z+2\n3jP3WrmKdi60fh8wE0bdD+0aHwRLyiuY8OxK2oUG8p+fj3Tr1v+CjYd59D87WfLAGHp3CK39DapG\nOo2jql3b7tZ9BSPmWikLDq22zghSvoOkr+3r9LAm7qgotTJaxl5mden0nOT00UTrDuSwZn82f5jW\nx7MCP5zLAbToXutO5dyjMPVZq8/+yEZr5E7SN9asTRfdbV00bu244ZmBfr78cnxPfv/5ThKSsxjf\ny30TCiYkZREVFkSv9p5xfcJbeNg3SjlNQEvrgmzc5dZ48qwk64zg0BqrKyfuCmv0kG/TdL0YY3ju\nuyTahwZyy8Uemu/ILwCued3qelvzApw+bGV7TVtr3Sh26aMwfK7Tbkq6flhn/pmwnxeXJjMuLtIt\nW/+l5TbW7M/mqkEXGOKpnEaDv/opEavroV1vqxvCBRKSs0hMO8Wfr+5PkL+bzFPbECJWXqLQTrD4\nt9a80Jf/DYb+zwXz2TtKgJ8Pv5rQk0c+28n3+zKZ2KcO+XGa2Oa0U+SXlDPOjc9MvJUGf+V2Klv9\n0W1bMNMD71St1vC7rbOnVu2dPjF3VdcO7cyrKw7wwrJkJvRu53at64SkTPx9hVE9dYhnU/OAXACq\nuVmy6zi7jubxwMQ4Avy86F+0dXSTBn4Af1+r9b/raB5L95xo0rLrIiEpi4ti2tLK067peAEv+mYp\nb1BhMzy/NJkekcFcPcQ9ZszydNcM6URMeEteWJaCzeY+o/uOnS4i6cSZut3VqxxOg79yK4u2HyUl\nM5+HJvfC1xnztzZDfr4+3Dcxlr0ZeXy357irq3NWQpKVxdOdRyJ5Mw3+ym2UVdh4YWkKfaNCmdK/\ng6ur41WmD+pI98hgXljqPq3/FUmZdGrdgp7tnHvhW1VPg79yG59vOcrhk4U8fHkcPtrqdyg/Xx/u\nnxhL0okzLN7l+tZ/SXkFa/dnM66Xew5BbQ40+Cu3YLMZ5q1OpV/HUO0GcJIrB3akZ7tWvLgsmQoX\nt/4TD52isLRCh3i6kAZ/5RZWJGWyPzOfuWO7a0vQSXx9hAcmxZKSmc/XOzNcWpcV+zIJ8PVhZA+d\ndctVNPgrtzBvVSodw4KYOiDK1VXxalP7R9GrfQgvubj1n5CcxfBubT0vbYcX0eCvXG77kdNsOHiS\nO0Z3w99X/yWdycfe+j+QVcCX28+fdqNpHDlZyP7MfB3i6WL6TVMu98bqVEKC/Jg1XKfubAqX9+tA\n7w4hvLQ8hfIKW5OXXzlRu/b3u5YGf+VSR04W8s3ODG4e0UXv8mwiPj7Cg5PjOJhdwBfbmr71n7Av\nk+i2LegR6YTZ5FSdafBXLvXWmoP4+gi3j+zm6qo0K5f1bU+/jqG8/H0KZU3Y+i8uq+CHAzmM7+V+\neYaaGw3+ymVOF5byaeIRpg/qRIewIFdXp1kRER6cFEdaTiGfbznaZOVuPHiSorIK7e93Axr8lct8\nuOEwhaUV3D1WW/2uMLFPOwZ2DmvS1n9CUhYBfj5c0l2zeLqaBn/lEiXlFbyz9hBj4yJ16j4XqWz9\np58q4t+b05ukzISkTC7uHk6LAA+eo8FLaPD3MGUVNkrKK1xdjUb7YusxsvNL+NlY58z9q+pmXK9I\nBke35pXv91Na7tzWf1pOAanZBYzXLh+3oMHfgxSXVXD1q2u58fX1Lr89vzEqUzn0jQrVOzxdTMQa\n+XP0dBGfJh5xalmVWTx1iKd70ODvQZ5evI/dx/LYduQ0n21pmtN0Z0hI1lQO7mRsbATDurbh1RX7\nnXpWmZCUSUx4S7pF6BBPd6DB30N8v+8E7/5wiNtHxTA4ujXPfptEQUm5q6vVIJWpHKYN1FQO7kBE\neGhyHBm5xXyyyTmt/8ohntrqdx8a/D1AZl4xDy/cQZ+oUB6d0pvHr+xL5pkSXl95wNVVq7cd6adZ\nn6qpHNzNyB7hDI9py6sr9lNc5vjW/7rUHErKbTrE043ot8/N2WyGXy/cTmFpOS/PGkygny/Durbh\nyoFRzFudyrHTRa6uYr28sfogIYF+3HiRl0zM7iUq+/5P5JXw8cbDDt/+yqQsAv18uLi7XuNxFxr8\n3dxbaw6yOiWbx6/sS2z7kLOvP3JFb2wG/vFtkgtrVz9VUzmEBPm7ujrqPJf0COfi7m35Z8IBh7f+\nVyRlMrJHOEH+OsTTXWjwd2O7jubyzLf7uLxfe24+L+lZdNuW3Dm6G59vPcr2I6ddVMP6eXvtQQSY\nMyrG1VVRF/DgpDiyzpQwf32aw7Z5MLuAtJxC7e93Mxr83VRhaTn3fbyV8OBAnr52YLWjYn4xrgcR\nrQJ46qs9GOPeQz9zC8v4ZNMRpg/uSFRYC1dXR13AiO7hjOoZzmsrD1BY6pgBBSv2ZQI6Ubu70eDv\npv60aA8Hcwp4/sZBtAkOqHadkCB/Hprci8S0U24xL2tNPtyYZqVyGKM3dbm7ByfFkZ1f6rDWf0Jy\nFt0jgukS3tIh21OOocHfDX29I4NPEo/w80t7MLJHzTlQbrwomt4dQvjb4r1ue+dvZSqHMbER9InS\nVA7uLj6mLWNiI3htZWqjhxMXlVawPlWHeLqjRgV/EWkrIktFJMX+s0016wwWkXUisltEdojIjY0p\n09sdPV3E7/6zg0HRrXlwclyt6/v6CI9N68ORk0W8u/aQ8yvYAF9sO0bWmRLmaioHj/Hg5DhOFpTy\n/rrGtf7XpWZTqkM83VJjW/6PAsuNMbHAcvvv5ysE/scY0w+4AnhRRFo3slyvVGEzPLhgGxU2w8uz\nBtd5HPyY2Egm9G7HK9/vJye/xMm1rB9jDG+sSqVPVCije2omR08xtEsbxveK5PVVB8hvROt/xb4s\nWvj7MrxbWwfWTjlCY4P/DOA9+/P3gKvPX8EYk2yMSbE/PwZkAtoMqMY/V+xn46GTPHV1f7qG1+8W\n+N9P7U1hWQUvLEt2Uu0aJiE5i5TMfOaO7aapHDzMA5PiOF1Yxns/HGrQ+40xOsTTjTU2+Lc3xmQA\n2H/W2LEnIsOBAKDaW1NFZK6IJIpIYlZWViOr5lk2p53ixeUpzBjckWuGdKr3+3u2C+GWEV34aMNh\nkk+ccUING2beylSiwoK4cmBHV1dF1dOg6NZM6tOOeatSySsuq/f7D2QVkH6qiHG9tb/fHdUa/EVk\nmYjsquYxoz4FiUgU8AFwuzGm2tyxxph5xph4Y0x8ZGTzOTnIKy7j/gVbiQoL4qmr+ze4hXz/pDiC\nA/34y9d7HVzDhtmZnsu61BzuGKWpHDzVA5PiyC0q4501h+r93oQka4jnuLjm8132JLV+I40xk4wx\n/at5fAGcsAf1yuCeWd02RCQU+Br4gzFmvSN3wNMZY/jD57vIyC3mpVlDCG3Ena9tgwO4f2IsK5Oz\nzn7xXOmN1amEBPoxa7imcvBU/TuFcVnf9ry5JpXcovq1/hOSsujZrhXRbXWIpztqbHNsEXCb/flt\nwBfnryAiAcDnwPvGmIWNLM/rfL71KIu2H+OBibEM6/qTwVL1duslXeka3pK/fL2X8iacmPt86acK\n+XpnBjdpKgeP98CkOM4Ul/PWmoN1fk9BSTkbD57UVr8ba2zwfxqYLCIpwGT774hIvIi8aV9nJjAW\nmCMi2+yPwY0s1yuk5RTw+H93MTymLb8Y39Mh2wz08+V3U/qQkpnPAiel562Lt9ccslI5jIxxWR2U\nY/TtGMqU/h14Z81BTheW1uk9PxzIobTCxnjt73dbjQr+xpgcY8xEY0ys/edJ++uJxpi77M/nG2P8\njTGDqzy2OaLynqyswsZ9C7bh6yO8MGswvj6OGwlzeb/2DO/WlheWJjfoQl1j5RaWsWDTYaYP6kjH\n1prKwRs8MCmO/NJy3lxdt9b/iqRMggN8iY9p/Nmscg69CuciLyxNZvuR0zx93UA6OThAigiPT+vL\nycJSXl2x36HbrouPNh6msLSCuzSVg9fo1SGEqQOieGftQU4V1Nz6N8awMimLkT0jCPTTIZ7uSoO/\nC/xwIJt/rTzArIuimTrAObNZDegcxrVDOvPOmkMczil0ShnVsVI5HGRMbAR9O2oqB2/ywMRYCssq\nmLc6tcb1UjLzOXq6SBO5uTkN/k3sVEEpD32ynW7hwfzxqr5OLes3l/fC10f4+5J9Ti2nqkXbjpF5\npkQTuHmh2PYhXDWwI+/9cKjGO8nPDvHUlA5uTYN/EzLG8MhnO8gpKOHlm4bQMsDPqeV1CAviZ5d2\n5+udGWw6dNKpZYE9lcPqVHp3CGFMrKZy8Eb3TYyluKyCeasu3PpfsS+LXu1D9HqPm9Pg34Q+2niY\n7/ac4JEretO/U1iTlDl3bHfahwby56/2YLM5N+f/yuQskk/kM3dsd03l4KV6tmvFjMGdeG/dIbLO\n/LT1f6a4jMS0k9rq9wAa/JtIyokzPPXVHsbERnDHqG5NVm7LAD9+e3lvtqfn8sX2o04ta96qVDqE\naioHb3ffxFjKKgyvr/xplpa1+3MoqzCawtkDaPBvAsVlFdy3YBvBAX48N3MQPg4c1lkX1wzpxIBO\nYTyzJImiUufk/N91NJcfDuRwx+gYAvz038qbdYsI5urBnfhgfRqZecU/WrYyOZNWgX46xNMD6Le0\nCTyzJIm9GXn844aBtAsJavLyfXyEP0zrQ0ZuMW/UMlKjod5YnUqrQD9mnTfXsPJO903sSbnN8K8q\nrX9jDCv2ZTG6Z4TmcvIA+gk52YqkTN5ee5A5I2OY0Lu9y+oxons4V/TrwL8SDnDivNZaYx09XcRX\nOzK4aXh0o3ITKc/RNTyY64d25sMNhzmea/0/JZ04w/G8Yu3v9xAa/J0o60wJv1m4nd4dQnh0Sm9X\nV4ffTe1Nuc3Gc98lOXS7b685iAC3N+G1DOV6907oic1m+FeCdSPhin1WGnbt7/cMGvydxGYzPLxw\nO2eKy3n5piFuMZlF1/Bg5oyMYeHmdHYdzXXINnOLyliw8TBXaSqHZie6bUtuiI/m441HOHa6iISk\nTHp3CKFDWNN3bar60+DvJO/8cIiVyVn84cq+xLUPcXV1zrp3QiytW/jzl6/3Ykzjh35+vPEwBaUV\n3DVGW/3N0b0TemIw/H3JPhLTTmkiNw+iwd8Jdh/L5e+L9zG5b3tuGeFeF0DDWvjz4OQ41qXmsHTP\niUZtq7TcxjtrDzK6ZwT9OjbNfQvKvXRq3YIbL4rmi23HqLAZTeHsQTT4O1hhaTn3fbyVNsH+/P26\ngW55s9PNw7vQs10r/rZ4H6XlDc/5v2j7MU7klXD3WE3l0Jz9cnxPAnx9CAnyY6gD5qRQTUODv4M9\n9dVeUrMLeH7mYNoGB7i6OtXy8/Xhsal9OJhdwAfr0xq0DWMMb6yyUjmM1VQOzVpUWAsem9aH+yfG\n6hBPD6KflAMt2ZXBxxsP87OxPRjV070D4rhekYyJjeDl5Sl1nqCjqlUp2SSdOMPdYzSVg4LbRsZo\nCm8Po8HfQTJyi3jks50M7BzGQ5PjXF2dWokIf5jWlzPFZby4LKXe75+36gDtQwO5apCmclDKE2nw\nd4AKm+HBT7ZRVmHj5VlDPCa9Qa8OIcwa3oX569M4kJVf5/ftOprL2v053D6qm8fsq1Lqx/Sb6wCv\nrTzA+tSTPDmjPzERwa6uTr08OCmOIH9f/vbN3jq/5017Koeb3Wwkk1Kq7jT4N9LSPSd4fmkyVw3q\nyHVDO7m6OvUWGRLIL8f3ZNneTNbuz651/WOni/hyRwazLtJUDkp5Mg3+DVRYWs5jn+/k7vcTiWsf\nwp+v7u+xFz5vHxVD5zYteOqrPVTUkvP/7TXWBN63j9abupTyZBr8G2Dr4VNMe3kNH208zM/Gdue/\nvxxJWAvPbQUH+fvy6JTe7Dt+hn9vPnLB9XKLyvh442GuGhjl8EnnlVJNS4N/PZRV2Hh+aTLXv7aO\n0nIbH999Mb+b2odAP9fn7WmsaQOiGNa1Df/4Npn8kvJq11lwNpWDDulTytNp8K+jA1n5XP+vH3h5\neQozBndk8QNjuLh7uKur5TDW0M8+ZOeX8FrCT2doslI5HGJUz/Amm4JSKeU8GvxrYYzhg3WHmPby\natJOFvLP2UN5fuZgr7zYOaRLG2YM7sgbq1M5erroR8u+3H6M43nF3K2tfqW8ggb/GmTmFTPnnU08\n/sVuRnQL57sHxjJ1QJSrq+VUv73CmnfgmSX7zr5mjOGN1an0ah/CpZq4SymvoMH/AhbvzODyF1ex\n4WAOT83ox7u3X0S7UO/PU96pdQvuHtOdL7YdY+vhUwCsTslm3/Ez3D1WUzko5S00+J8nr7iMhz7d\nxs8/3EJ025Z8fd8Ybr0kplkFvZ+P60FkSCBPfbXnbKu/fWgg0zWVg1Jew8/VFXAnG1JzeOjT7RzP\nK+a+ibH8akLPZpmlMDjQj4cvi+ORz3byj2+TWJ2SzSNX9NZUDkp5kUZ9m0WkrYgsFZEU+88LJvMW\nkVAROSoirzSmTGcoKa/gb9/sZdYb6/H3FRbecwkPTY5rloG/0vXDoukTFco/Ew4QHOCrqRyU8jKN\njW6PAsuNMbHAcvvvF/IUsLKR5TncvuN5zHhlLa+vSuWm4V345v4xDO2iE1L4+giPT+sDwKzhXTz6\nJjal1E81tttnBjDO/vw9IAF45PyVRGQY0B5YAsQ3skyHsNkMb605yD++TSK0hT9vz4lnQu/2rq6W\nWxnZM4KP7h7B4OjWrq6KUsrBGhv82xtjMgCMMRki8pPZm0XEB3gOuBWYWNPGRGQuMBegSxfndTMc\nPV3Erz/dxvrUk1zWtz1/u3YA4a0CnVaeJxvZw70npVFKNUytwV9ElgEdqln0WB3L+AXwjTHmSG0j\nZowx84B5APHx8TVnGGsAYwz/3XaUP/53NzZjeOb6gdwwrHOzGsmjlFJQh+BvjJl0oWUickJEouyt\n/iggs5rVLgHGiMgvgFZAgIjkG2Nquj7gcKcLS3ns8118vTODi2La8PzMwUS3bdmUVVBKKbfR2G6f\nRcBtwNP2n1+cv4IxZnblcxGZA8Q3deBflZzFwwu3c6qwlN9e0Yufje2Br4+29pVSzVdjg//TwKci\ncidwGLgBQETigXuMMXc1cvuNUlRawdOL9/LeujRi27Xi7TkXaVIypZQCxBiHd607RHx8vElMTGzw\n+3ekn+bBT7ZxIKuAO0Z147dX9CLI3/NTLyulVE1EZLMxptZRlV53h295hY1/JRzgpeUpRIYE8uFd\nIxjVU0esKKVUVV4X/NNPFfHKiv1MHRDFUzP6E9ZSb05SSqnzeV3wj4kI5tsHxhITEezqqiillNvy\nyuQ1GviVUqpmXhn8lVJK1UyDv1JKNUMa/JVSqhnS4K+UUs2QBn+llGqGNPgrpVQzpMFfKaWaIbfN\n7SMiWUBaIzYRBuQ6qDq16YKV2K6pNOW+NXV53rxvTV2eN+9bU5fnSfvW1RgTWetaxhivfADzmrCs\nLG/dNxf8Lb123/Rv6bnleeO+eXO3z5dNWNbpJiwLmnbfmro8b963pi7Pm/etqcvzun1z224fTyIi\niaYOKVSVUspdeHPLvynNc3UFlFKqPrTlr5RSzZC2/JVSqhnyyOAvIhUisk1EdovIdhF5SEQ8cl+q\nU2X/Kh8xNaw7TkS+akRZRkQ+qPK7n4hkNWabdSz3GnvZvZ1Yhqv2Ld+Z229ouSKSYJ9fu6Hbd/pn\ndl55j9m/4zvs34MRTi6vs4h8ISIpInJARF4SkYAa1n9ARFo2oBwjIs9V+f1hEXmigdVuME8NmEXG\nmMHGmH7AZGAq8L/OLrQJv9SV+1f5OOTEsgqA/iLSwv77ZOBofTYgIg2ZFOgmYA0wq55l1Wci5kbv\nm/qRBn1mDSEilwBXAkONMQOBScARJ5YnwH+A/xpjYoE4oBXwlxre9gBQ7+APlADXiohL55f11OB/\nljEmE5gL3CsWXxH5h4hssrcYfla5roj8VkR22s8WnnZdreuvpv0CQkXkcxHZIyKvNeAsaDEwzf78\nJuDjKuUOF5EfRGSr/Wcv++tzRGShiHwJfFfPfWkFjALuxB5I7Gcwq6rbDxHJF5EnRWQDcEkT7Ntq\nERlcZb21IjKwnvv4ozMyEXlFRObYnx8SkT+JyBb7/6PDWtI1ldvI7V7oM7vQPk4VkX0iskZEXm7A\n2VYUkG2MKQEwxmQbY46JyDARWSkim0XkWxGJspeXICIv2j/HXSIyvJ7lTQCKjTHv2MurAB4E7hCR\nYBF51v5Z7RCRX4nIfUBHYIWIrKhnWeVYg0QePH+BiHQVkeX2cpaLSBcRCbP/z1R+H1qKyBERadQc\ntR4f/AGMMalY+9IO658z1xhzEXARcLeIdBORKcDVwAhjzCDgmYaUJSKt7B9K5Rd3hv31GBHZKyJv\niHWq+l2VFmd9tZBzXT6f21+rdr/sy4YDvwYGAD2Aa+tZ3gJglogEAQOBDVWW7QPGGmOGAH8E/lpl\n2SXAbcaYCfUs72pgiTEmGTgpIkNr2Y9gYJcxZoQxZk09y2rIvr0JzAEQkTgg0Bizo57l1ibbGDMU\n+BfwsIO37QwX+sx+wv63fh2YYowZDdR+t+lPfQdEi0iyiPxTRC61B7v/A643xgwD3ubHLfNgY8xI\n4Bf2ZfXRD9hc9QVjTB7Wnft3Ad2AIfazkA+NMS8Dx4DxxpjxDdi/V4HZIhJ23uuvAO9XlgO8bIzJ\nBbYDl9rXuQr41hhT1oByz/KK4G8n9p+XAf8jItuwvujhQCzWaeM7xphCAGPMyQaWUwxcY//ijgee\nE5HKsmOBV+3dUaeB6xpYRtVun2vsr11ovwA2GmNS7a2Vj4HR9SnMHthisFrG35y3OAxYKCK7gBew\nviSVljbw73gTVlDG/vMm+/ML7UcF8FkDymnovi0ErrQHmzuAdxtSdi3+Y/+52V4/d3ehz6w6vYFU\nY8xB++8f17ButYwx+cAwrLP6LOAT4GdAf2Cp/XvwB6Bzlbd9bH/vKqyz4db1KFKA6oY+CjAWeM0Y\nU27ffkNjx1n2A8v7wH3nLboE+Mj+/APOfQc+AW60P59l/71RvGICdxHpjhUgMrE+rF8ZY749b50r\nqP7DrXdxwF9FZCxgAzoB7e3LDhpjttmfO/pLfaH9GsdP96sh+7kIeBYYh3VgqfQUsMIYc41YF54T\nqiwrqG8hIhKOdYrdX0QM4Guv7zfV1Lvy92L7AaGh6rVvxphCEVkKzABmAg25SFrOjxtXQectL7H/\nrMCx38Payq23Gj6zRRcoS3AA+2eeACSIyE7gl8BuY8yFuv4a8z3YzXmNNREJBaKB1Hpuq65eBLYA\n79SwTmW5i4C/iUhbrIPi940t3ONb/iISCbwGvGKsmxa+BX5e2R8mInEiEox1GnmH2K/O2/+IDTEb\n6zR2mDFmMHCCc//0JVXWc/SX+kL7BTDc3rXlg9U6qG/XCFinyU8aY3ae93oY5y6SzmnAds93PdZp\nbVdjTIwxJho4iNXCccR+VKch+/Ym8DKwqYEtvTSgr4gE2k/tJzZgGw3hjHIv9JlxgbL2Ad3l3Ci1\nG6knEeklIrFVXhoM7AUixboYjIj4i0jVM9Eb7a+PxuoirU9itOVASxH5H/s2fIHnsM76vgPuEfvA\nhiqx4wwQUt99q2T/v/oUq0u30g+cu6A+G/t3wH4mtBF4CfiqkY0hwHODf2Wf+G5gGdaH8yf7sjeB\nPcAW++n864CfMWYJ1tEz0X7K2NB+1jAg0xhTJiLjga6N2ZF6qHa/7MvWAU8Du7C+lJ9Xu4UaGGPS\njTEvVbPoGawWx1qsFl9j3cRP6/cZcDMO2I/qNGTfjDGbgTxqbpX9hD1AlBhjjmB9sXdg9d1ubUjd\n3aTcmj6zn5RljCnC6ndfIiJrsBpI9c1Q2Qp4T6yL/zuAvljXZa4H/i4i24FtwMgq7zklIj9gNQbv\nPH+DNbE3HK8BbhCRFCAZq4v391jfvcPADnu5N9vfNg9Y3IALvlU9B1Qd9XMfcLt9n28F7q+y7BPg\nFhzQ5QN6h2+d2b9cJ4BeWEmX/LH++UYBU+yrfWWM6W9f/2GglTHmiaavreexd189bIy50tV1ARCR\njlhdDr2NMbZ6vG8Q8IYxpr6jTRrFVeVeiIi0Msbk26+HvQqkGGNecGJ5CVj/P4nOKsPbeEWffxPp\nBxwwxmRz4eGG/SufGGOebZJaKYezn/r/BXionoH/HqyW2wPOqps7lVuLu0XkNiAA64zgdRfXR51H\nW/51UPXLZYyp15h2pQTUmsEAAALsSURBVJRyRxr8lVKqGfLUC75KKaUaQYN/NUQkWkRW2O/Y3S0i\n99tfbysiS8VK/LRURNrYX+8tIutEpMR+obfG7SillKtpt081xMoXEmWM2SIiIVg3bF2NNRb8pDHm\naRF5FGhjjHlERNphDfm8GjhVebH3QtsxxuxxwW4ppdRZ2vKvhjEmwxizxf78DNbNJZ2w7vh8z77a\ne1jBHmNMpjFmE1BWx+0opZRLafCvhf0uxSFY+XTaG2MywArsWInkGrIdpZRyKQ3+NRArje1nWEM8\n81y9HaWUchQN/hdgz6HzGVb61soMjCfkXP7wKKxEcg3ZjlJKuZQG/2rYb0l/C9hrjHm+yqJFwG32\n57cBXzRwO0op5VI62qca9qyAq4GdWGmbwUrwtAErkVUXrERPNxhjTopIByARCLWvn4+ViGpgddsx\nxpyfV14ppZqUBn+llGqGtNtHKaWaIQ3+SinVDGnwV0qpZkiDv1JKNUMa/JVSqhnS4K/UBYjIE1Wz\ntFaz/GoR6duUdVLKUTT4K9VwV2Pdz6GUx9Fx/kpVISKPAf8DHAGysNJw5wJzseaj3Q/cCgwGvrIv\nywWus2/iVSASKATuNsbsa8r6K1VXGvyVshORYcC7wAjAD9gCvAa8Y4zJsa/zZ+CEMeb/RORd4Ctj\nzL/ty5YD9xhjUkRkBPA3Y8yEpt8TpWrn5+oKKOVGxgCfG2MKAURkkf31/vag3xpoBXx7/hvtmVtH\nAgutlE4ABDq9xko1kAZ/pX6sulPhd7FmYNsuInOAcdWs4wOcNsYMdl7VlHIcveCr1DmrgGtEpIV9\n2s2r7K+HABn29Nyzq6x/xr4M+zwNB0XkBrAyuorIoKarulL1o33+SlVR5YJvGpAO7AEKgN/aX9sJ\nhBhj5ojIKOANoAS4Hitz67+AKMAfWGCMebLJd0KpOtDgr5RSzZB2+yilVDOkwV8ppZohDf5KKdUM\nafBXSqlmSIO/Uko1Qxr8lVKqGdLgr5RSzdD/A0eBErHB59Z9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_hat=np.matmul(test_X.values,beta_hat[-1])\n",
    "\n",
    "y_lin=pd.DataFrame()\n",
    "y_lin['y']=test_y\n",
    "y_lin['yhat']=y_hat\n",
    "\n",
    "y_lin.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "mse=np.mean(np.power(test_y.values-y_hat,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.096904667717962703"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4166666666666667"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_lin['sign']=np.sign(y_lin[\"y\"])==np.sign(y_lin[\"yhat\"])\n",
    "len(y_lin[y_lin['sign']==True])/float(len(y_lin))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lasso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lasso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lasso_solve(train_X,train_y,alpha):\n",
    "    lassoreg = Lasso(alpha=alpha, normalize = True )\n",
    "    lassoreg.fit(train_X.values[:,:-1],train_y)\n",
    "    return np.append(lassoreg.coef_,lassoreg.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_lasso = [1e-15, 1e-10, 1e-8, 1e-5,1e-4, 1e-3,1e-2, 1, 5, 10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta_hat=[]\n",
    "for i in alpha_lasso:\n",
    "    beta_hat.append(lasso_solve(train_X,train_y,i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "error=pd.DataFrame(index=alpha_lasso,columns=[\"mse\",\"acc\"])\n",
    "for i in range(len(beta_hat)):\n",
    "    y_hat=np.matmul(val_X.values,beta_hat[i])\n",
    "    mse=np.mean(np.power(val_y.values-y_hat,2))\n",
    "    error.iloc[i][\"mse\"]=mse\n",
    "    \n",
    "    y_lin=pd.DataFrame()\n",
    "    y_lin['y']=val_y\n",
    "    y_lin['yhat']=y_hat\n",
    "    \n",
    "    y_lin['sign']=np.sign(y_lin[\"y\"])==np.sign(y_lin[\"yhat\"])\n",
    "    error.iloc[i][\"acc\"]=len(y_lin[y_lin['sign']==True])/float(len(y_lin))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe thead th {\n",
       "        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>mse</th>\n",
       "      <th>acc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1.000000e-15</th>\n",
       "      <td>0.137914</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.000000e-10</th>\n",
       "      <td>0.137914</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.000000e-08</th>\n",
       "      <td>0.137914</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.000000e-05</th>\n",
       "      <td>0.137916</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.000000e-04</th>\n",
       "      <td>0.137938</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.000000e-03</th>\n",
       "      <td>0.138051</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.000000e-02</th>\n",
       "      <td>0.138842</td>\n",
       "      <td>0.538462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.000000e+00</th>\n",
       "      <td>0.164545</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5.000000e+00</th>\n",
       "      <td>0.164545</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.000000e+01</th>\n",
       "      <td>0.164545</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   mse       acc\n",
       "1.000000e-15  0.137914  0.538462\n",
       "1.000000e-10  0.137914  0.538462\n",
       "1.000000e-08  0.137914  0.538462\n",
       "1.000000e-05  0.137916  0.538462\n",
       "1.000000e-04  0.137938  0.538462\n",
       "1.000000e-03  0.138051  0.538462\n",
       "1.000000e-02  0.138842  0.538462\n",
       "1.000000e+00  0.164545         1\n",
       "5.000000e+00  0.164545         1\n",
       "1.000000e+01  0.164545         1"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sign accuracy is skewed here from the fact that the val set is all negative numbers. Ignore for now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmin(error[\"mse\"].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1e-08"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error.index[np.argmin(error[\"mse\"].values)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd19253be48>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Izaak3EZ4y0CuHNqJGQOiGNmtLX6+GvDP5YiW/whgjzEmHUBE5gOXAWeCvzFmeZXt1wE3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\nZkiDv1JKNUMa/JVSqhnS4K+UUs3Q/wMgLiEIladONwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_hat=np.matmul(test_X.values,beta_hat[np.argmin(error[\"mse\"].values)])\n",
    "\n",
    "y_lin=pd.DataFrame()\n",
    "y_lin['y']=test_y\n",
    "y_lin['yhat']=y_hat\n",
    "\n",
    "y_lin.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        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>y</th>\n",
       "      <th>yhat</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2011-12-01</th>\n",
       "      <td>-0.439221</td>\n",
       "      <td>0.098026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-01</th>\n",
       "      <td>-0.338465</td>\n",
       "      <td>0.045543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-02-01</th>\n",
       "      <td>-0.137423</td>\n",
       "      <td>0.013509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-03-01</th>\n",
       "      <td>-0.393778</td>\n",
       "      <td>-0.032813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-04-01</th>\n",
       "      <td>-0.075246</td>\n",
       "      <td>0.013365</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-05-01</th>\n",
       "      <td>0.203748</td>\n",
       "      <td>0.091349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-06-01</th>\n",
       "      <td>0.225244</td>\n",
       "      <td>-0.038672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-07-01</th>\n",
       "      <td>-0.021075</td>\n",
       "      <td>0.026884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-08-01</th>\n",
       "      <td>-0.306944</td>\n",
       "      <td>0.055284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-09-01</th>\n",
       "      <td>0.196775</td>\n",
       "      <td>0.011519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-01</th>\n",
       "      <td>0.244053</td>\n",
       "      <td>0.066810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-11-01</th>\n",
       "      <td>0.594338</td>\n",
       "      <td>0.061608</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   y      yhat\n",
       "date                          \n",
       "2011-12-01 -0.439221  0.098026\n",
       "2012-01-01 -0.338465  0.045543\n",
       "2012-02-01 -0.137423  0.013509\n",
       "2012-03-01 -0.393778 -0.032813\n",
       "2012-04-01 -0.075246  0.013365\n",
       "2012-05-01  0.203748  0.091349\n",
       "2012-06-01  0.225244 -0.038672\n",
       "2012-07-01 -0.021075  0.026884\n",
       "2012-08-01 -0.306944  0.055284\n",
       "2012-09-01  0.196775  0.011519\n",
       "2012-10-01  0.244053  0.066810\n",
       "2012-11-01  0.594338  0.061608"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_lin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.096862849277366492"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse=np.mean(np.power(test_y.values-y_hat,2))\n",
    "mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4166666666666667"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_lin['sign']=np.sign(y_lin[\"y\"])==np.sign(y_lin[\"yhat\"])\n",
    "len(y_lin[y_lin['sign']==True])/float(len(y_lin))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lasso Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "."
     ]
    },
    {
     "data": {
      "image/png": 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BdEvnLqLdsBJT1C9cWQO3MSbwju2Ela/Duqlw/pTTDjHoZWeyISvqF1ICmixEpD/wMs4c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\nSUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "_, _, coefs = linear_model.lars_path(train_X.values[:,:-1], train_y.values, method='lasso', verbose=True)\n",
    "\n",
    "xx = np.sum(np.abs(coefs.T), axis=1)\n",
    "xx /= xx[-1]\n",
    "\n",
    "plt.plot(xx, coefs.T)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.vlines(xx, ymin, ymax, linestyle='dashed')\n",
    "plt.xlabel('|coef| / max|coef|')\n",
    "plt.ylabel('Coefficients')\n",
    "plt.title('LASSO Path')\n",
    "plt.axis('tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Final Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "results=pd.DataFrame(columns=['mse','sign_acc'],index=['Least Squares','Ridge','Lasso'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta_hat_ls=np.matmul(np.matmul(inv(np.matmul(X_mat.T,X_mat)),X_mat.T),train_y.values)\n",
    "beta_hat_ridge=ridge_solve(train_X,train_y,0.9)\n",
    "beta_hat_lasso=lasso_solve(train_X,train_y,1e-08)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta_hats=[beta_hat_ls,beta_hat_ridge,beta_hat_lasso]\n",
    "for i in range(len(beta_hats)):\n",
    "    y_hat=np.matmul(test_X.values,beta_hats[i])\n",
    "    mse=np.mean(np.power(test_y.values-y_hat,2))\n",
    "    results.iloc[i][\"mse\"]=mse\n",
    "    \n",
    "    y_lin=pd.DataFrame()\n",
    "    y_lin['y']=test_y\n",
    "    y_lin['yhat']=y_hat\n",
    "    \n",
    "    y_lin['sign']=np.sign(y_lin[\"y\"])==np.sign(y_lin[\"yhat\"])\n",
    "    results.iloc[i][\"sign_acc\"]=len(y_lin[y_lin['sign']==True])/float(len(y_lin))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        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>mse</th>\n",
       "      <th>sign_acc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Least Squares</th>\n",
       "      <td>0.0968629</td>\n",
       "      <td>0.416667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ridge</th>\n",
       "      <td>0.0969047</td>\n",
       "      <td>0.416667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lasso</th>\n",
       "      <td>0.0968628</td>\n",
       "      <td>0.416667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     mse  sign_acc\n",
       "Least Squares  0.0968629  0.416667\n",
       "Ridge          0.0969047  0.416667\n",
       "Lasso          0.0968628  0.416667"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lasso just eked out ahead."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.6.3"
  }
 },
 "nbformat": 4,
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}