Kalman Filter-Smoothing on NVDA Dataset.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.optimize as optimize\n",
    "import scipy as sc\n",
    "import math as math\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Main \n",
    "\"\"\"\n",
    "@ Params:\n",
    "    R: a list of stock price\n",
    "    k: number of latent components\n",
    "@ Return:\n",
    "    price_tplus1\n",
    "    u_tplus1\n",
    "    u_smooth\n",
    "\"\"\"\n",
    "def KalmanFilterForecast(R, k):\n",
    "    r = 0.25*np.log(np.var(R,axis = 0,ddof=1))\n",
    "    if k == 1:\n",
    "        param0 = np.append(np.append(np.append(np.array(100),r,),100),r)\n",
    "        \n",
    "    if k == 2:\n",
    "        param0 = np.append(np.append(np.append(np.array([100,100]),4*r),[-100,-100]),[r,r])\n",
    "    def objective(params):\n",
    "        Likelihood,_ = KalmanFilter(R,k,params)\n",
    "        return Likelihood\n",
    "    params_star = optimize.fmin(objective,param0)\n",
    "    print(params_star)\n",
    "    #params_star = optimize.minimize(objective,param0,method='CG')\n",
    "    #params_star = params_star.values()[5]\n",
    "    #print(params_star)\n",
    "    u_smooth = KalmanSmoother(R, k, params_star)\n",
    "#     Z = np.array(params_star[0])\n",
    "#     H = np.exp(params_star[1]);\n",
    "#     T = np.array(params_star[2])\n",
    "#     Q = np.exp(params_star[3]);\n",
    "    Z = 2/(1+np.exp(-params_star[0]))-1;\n",
    "    H = np.exp(params_star[1]);\n",
    "    T = 2/(1+np.exp(-params_star[2]))-1;\n",
    "    Q = np.exp(params_star[3]);\n",
    "      \n",
    "    u_tplus1 = T*u_smooth[-1] + np.random.normal()*np.sqrt(Q)\n",
    "    price_tplus1 = Z*u_tplus1 + np.random.normal()*np.sqrt(H)\n",
    "    print('T*u_smooth[-1] is {}; Z*u_tplus1 is {}'.format(T*u_smooth[-1],Z*u_tplus1))\n",
    "    return price_tplus1,u_tplus1,u_smooth,params_star"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def KalmanFilter(R,k,params):\n",
    "    S_length = R.shape[0]\n",
    "    S = S_length+1\n",
    "    if k == 1:\n",
    "#         Z = np.array(params[0])\n",
    "#         H = np.array(np.exp(params[1]))\n",
    "#         T = np.array(params[2])\n",
    "#         Q = np.array(np.exp(params[3]))\n",
    "        Z = np.array(2/(1+np.exp(-params[0]))-1)\n",
    "        H = np.array(np.exp(params[1]))\n",
    "        T = np.array(2/(1+np.exp(-params[2]))-1)\n",
    "        Q = np.array(np.exp(params[3]))\n",
    "    if k == 2:\n",
    "        Z = np.array([[2/(1+np.exp(-params[0]))-1,2/(1+np.exp(-params[1]))-1]])\n",
    "        H = np.array(np.exp(params[2]))\n",
    "        T = np.array([[2/(1+np.exp(-params[3]))-1,0],[0,2/(1+np.exp(-params[4]))-1]])\n",
    "        Q = np.array([[np.exp(params[5]),0],[0,np.exp(params[6])]])\n",
    "    u_predict = np.zeros((k,S));\n",
    "    u_update = np.zeros((k,S));\n",
    "    P_predict = np.zeros((k,k,S));\n",
    "    P_update = np.zeros((k,k,S));\n",
    "    v = np.zeros((1,S));\n",
    "    F = np.zeros((1,S));\n",
    "    KF_Dens = np.zeros((1,S));\n",
    "    for i in range(S):\n",
    "        if i == 0:\n",
    "            P_update[:,:,i] = 1000*np.eye(k)\n",
    "            P_predict[:,:,i] = T.dot(np.array(P_update[0][0][0]).dot(T.T))+Q\n",
    "        else:\n",
    "            F[0][i] = Z.dot(P_predict[:,:,i-1].dot(Z.T))+H\n",
    "            v[0][i] = R.T.flatten()[i-1]-Z.dot(u_predict[:,i-1])\n",
    "            u_update[:,i] = u_predict[:,i-1]+P_predict[:,:,i-1].dot(Z.T.dot(np.linalg.inv([[F[0][i]]]).dot(v[0][i]))).flatten()\n",
    "            u_predict[:,i] = T.dot(u_update[:,i])\n",
    "            P_update[:,:,i] = P_predict[:,:,i-1]-P_predict[:,:,i-1].dot(Z.T.dot(np.linalg.inv([[F[0][i]]]).dot(Z.dot(P_predict[:,:,i-1]))))\n",
    "            P_predict[:,:,i] = T.dot(P_update[:,:,i]).dot(T.T)+Q\n",
    "            KF_Dens[0][i] = (1.0/2)*np.log(2*np.pi)+(1.0/2)*np.log(np.abs(F[0][i]))+(1.0/2)+v[0][i].T*np.linalg.inv([[F[0][i]]])*v[0][i]\n",
    "    Likelihood = np.sum(KF_Dens)-KF_Dens[0][0]\n",
    "    varargout = [u_update, P_update, P_predict, T]\n",
    "    return Likelihood, varargout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def KalmanSmoother(R,k,params_star):\n",
    "    _,vararg = KalmanFilter(R,k,params_star)\n",
    "    u_update = vararg[0]\n",
    "    P_update = vararg[1]\n",
    "    P_predict = vararg[2]\n",
    "    T = np.array(vararg[3])\n",
    "    S = R.shape[0]+1\n",
    "    u_smooth = np.zeros((k,S))\n",
    "    P_smooth = np.zeros((k,k,S))\n",
    "    u_smooth[:,S-1] = u_update[:,S-1]\n",
    "    P_smooth[:,:,S-1] = P_update[:,:,S-1]    \n",
    "    for t in reversed(range(1,S)): # 2 to S inverse sequence\n",
    "        u_smooth[:,t-1] = u_update[:,t] + P_update[:,:,t].dot(T.T.dot(np.linalg.inv(P_predict[:,:,t]).dot((u_smooth[:,t]-T.dot(u_update[:,t])))))\n",
    "        P_smooth[:,:,t-1] = P_update[:,:,t] + P_update[:,:,t].dot(T.T).dot(np.linalg.inv(P_predict[:,:,t])).dot((P_smooth[:,:,t]-P_predict[:,:,t])).dot(np.linalg.inv(P_predict[:,:,t])).dot(T).dot(P_update[:,:,t])\n",
    "    u_smooth = u_smooth.flatten()[1:]\n",
    "    return u_smooth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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       "       11119300.,  9365000., 11792700., 11002300.,  9874100.,  8775100.,\n",
       "        9524700.,  6998400.,  8671400.,  7955100., 12482400., 21724700.,\n",
       "        9798000.,  9073000.,  8857000.,  9867100.,  8420600., 10554400.,\n",
       "       13880500., 10479200., 16506200., 14237500., 16422800., 13122000.,\n",
       "       12558000., 19527200., 25551700., 14301600.,  9046200.,  8146700.,\n",
       "       14796100.,  8939600., 10708900., 13995000.,  9857500.,  9743000.,\n",
       "       11966100., 16045900., 12790400., 10203500.,  8721400., 10069500.,\n",
       "        9596800.,  8972300.,  7702000.,  9860700.,  6901000., 14548000.,\n",
       "        8291100.,  8754200., 10860700.,  7073700.,  7796700., 14601800.,\n",
       "       11136000.,  9941700.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('NVDA.csv')\n",
    "data=data.dropna()\n",
    "R=data[\"Volume\"].values\n",
    "#R=np.matrix(R)\n",
    "k=1\n",
    "R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 15765.050545\n",
      "         Iterations: 208\n",
      "         Function evaluations: 368\n",
      "[-417.68334334   31.06480284    3.97708318   31.2072884 ]\n",
      "T*u_smooth[-1] is -9904307.622553626; Z*u_tplus1 is 15608885.517690804\n"
     ]
    }
   ],
   "source": [
    "price_tplus1,u_tplus1,u_smooth,params_star = KalmanFilterForecast(R, k)\n",
    "#KalmanFilterForecast(R, k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11646927.018928336\n"
     ]
    }
   ],
   "source": [
    "print(price_tplus1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-15608885.517690804\n"
     ]
    }
   ],
   "source": [
    "print(u_tplus1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      " 14705158.28487869 15881412.54583709 15068494.5508099  13247767.5830476\n",
      " 13490046.15597404 15080807.76165934 17057073.83224357 21359219.88694073\n",
      " 26502615.84250081 18016125.76920956 14605655.27987265 12509809.90144291\n",
      " 11983223.61322422 13795679.11467711 12509076.90029941 11596187.37248672\n",
      "  9609903.60090465  9416500.20574404  9819118.00807605  9719929.69862793\n",
      " 10408773.40473559 11496148.72461264 12891251.44932939 17094923.16823926\n",
      " 16057080.49040288 16918601.2001599  15045711.24517182 15661489.80201413\n",
      " 15251012.39471546 18544752.74735666 18477070.80495002 19031994.78504072\n",
      " 17727138.4799096  15293156.41410328 15469998.06585031 13133304.88511263\n",
      " 12340283.25195047 11964082.69307803 12253187.71271148 12748173.01751292\n",
      " 15326418.98381743 12824793.94655786 12005745.79353659 11158250.66918312\n",
      " 10989017.11423198 10822915.68901147 10317197.52145478 10965931.53268303\n",
      " 10640283.45591888  9896188.26509389  9192443.63312644  9001253.18411427\n",
      "  8196050.92652371  8836172.4275999   9685973.77110524 12621557.37661304\n",
      " 15741474.46360585 11720503.25017036 10017588.72418124  9459596.22905217\n",
      "  9636314.39877243  9550281.91177072 10830104.97772061 12455216.35728384\n",
      " 12391506.96002037 14634590.38216701 14657582.26421842 15204087.00329594\n",
      " 14312936.53324117 14867667.39118723 18208383.48409155 19995824.11375214\n",
      " 15159970.25796501 11373045.71539132 10387761.07493666 12100031.91805234\n",
      " 10601622.69703684 11107855.21749743 12107319.32632    10863900.40128598\n",
      " 10840592.631842   12146536.9537685  13685566.38526511 12418079.10202019\n",
      " 10722306.81413035  9662708.47679994  9743606.41236915  9448042.90447219\n",
      "  8987667.21016373  8558319.02538866  9166167.30564082  8955414.60690414\n",
      " 11216754.77103459  9505751.02550351  9262263.74139721  9640037.23024136\n",
      "  8570002.24489442  9303356.48216261 11853526.41365047 11130170.38646562\n",
      " 10415476.22548203 10282615.02647074]\n"
     ]
    }
   ],
   "source": [
    "u_smooth=-u_smooth\n",
    "print(u_smooth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(18,10))\n",
    "#plt.plot(price_tplus1,'y',label = \"price_tplus1\")\n",
    "#plt.plot(u_tplus1,'r',label = \"u_tplus1\")\n",
    "plt.plot(u_smooth,'b',label = \"u_smooth\")\n",
    "plt.plot(R,'g',label = \"price\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "params=np.matrix([[2.34],[3.24],[5.12],[6.34]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(92082659955347.98,\n",
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       "          1.01357640e+07, 1.55476622e+07, 1.84195703e+07, 1.15995158e+07,\n",
       "          1.85562814e+07, 2.63212048e+07, 2.86974155e+07, 2.06447180e+07,\n",
       "          2.28380581e+07, 2.43693058e+07, 2.27050241e+07, 1.74916357e+07,\n",
       "          1.39467379e+07, 1.16389339e+07, 9.21200397e+06, 1.43462033e+07,\n",
       "          1.54307635e+07, 1.26931182e+07, 1.83537972e+07, 1.94705559e+07,\n",
       "          1.61632958e+07, 2.49380953e+07, 5.74996311e+07, 5.18075621e+07,\n",
       "          5.13115049e+07, 3.22558933e+07, 1.36347177e+07, 2.40524792e+07,\n",
       "          2.24664646e+07, 2.42715480e+07, 1.70872449e+07, 2.18191066e+07,\n",
       "          2.66968508e+07, 2.47340316e+07, 2.12000519e+07, 2.06911515e+07,\n",
       "          1.91713701e+07, 2.02945197e+07, 1.98523698e+07, 1.46098756e+07,\n",
       "          1.43176175e+07, 1.97542421e+07, 1.72585858e+07, 2.22800884e+07,\n",
       "          2.26925253e+07, 2.59750531e+07, 1.47503888e+07, 2.06994827e+07,\n",
       "          1.93880028e+07, 1.90743905e+07, 1.43864182e+07, 1.53588819e+07,\n",
       "          2.10332098e+07, 1.79394623e+07, 2.12861914e+07, 2.36746232e+07,\n",
       "          1.89961745e+07, 1.60379832e+07, 2.59029665e+07, 2.23487354e+07,\n",
       "          1.89120319e+07, 1.45186827e+07, 1.49293624e+07, 1.94606082e+07,\n",
       "          2.00155966e+07, 1.80344638e+07, 2.12863465e+07, 3.41953450e+07,\n",
       "          7.36809881e+07, 3.72223556e+07, 2.99735199e+07, 2.58019749e+07,\n",
       "          1.93421348e+07, 1.62132658e+07, 1.64262548e+07, 2.10070983e+07,\n",
       "          1.94080516e+07, 1.43048734e+07, 1.49667192e+07, 1.77421549e+07,\n",
       "          1.83120157e+07, 2.46792139e+07, 4.47311360e+07, 1.83540409e+07,\n",
       "          1.65096892e+07, 1.37637213e+07, 1.22679501e+07, 1.94396300e+07,\n",
       "          1.50734480e+07, 1.51562886e+07, 1.01566883e+07, 1.07865313e+07,\n",
       "          1.23304696e+07, 1.10766143e+07, 1.21626958e+07, 1.35554827e+07,\n",
       "          1.28460591e+07, 2.52882315e+07, 1.80142420e+07, 2.29958617e+07,\n",
       "          1.61627782e+07, 1.98219791e+07, 1.50536515e+07, 2.52807774e+07,\n",
       "          2.19979982e+07, 2.48091834e+07, 2.27840283e+07, 1.63168308e+07,\n",
       "          2.10305402e+07, 1.47636479e+07, 1.45675954e+07, 1.38891431e+07,\n",
       "          1.46183904e+07, 1.34360482e+07, 2.31466504e+07, 1.44014766e+07,\n",
       "          1.45887931e+07, 1.29568144e+07, 1.33124128e+07, 1.34701005e+07,\n",
       "          1.14761522e+07, 1.41322822e+07, 1.33841588e+07, 1.20524631e+07,\n",
       "          1.07201905e+07, 1.14986724e+07, 8.65931268e+06, 1.04045661e+07,\n",
       "          9.68811039e+06, 1.48158782e+07, 2.56670550e+07, 1.26794759e+07,\n",
       "          1.10967850e+07, 1.07581605e+07, 1.18918421e+07, 1.03060759e+07,\n",
       "          1.26503462e+07, 1.65844425e+07, 1.29293916e+07, 1.95987658e+07,\n",
       "          1.73959319e+07, 1.97631412e+07, 1.61317737e+07, 1.52767190e+07,\n",
       "          2.31846673e+07, 3.05232512e+07, 1.81040758e+07, 1.13814724e+07,\n",
       "          9.96366485e+06, 1.74737474e+07, 1.12231174e+07, 1.28800593e+07,\n",
       "          1.67285335e+07, 1.22278903e+07, 1.18355645e+07, 1.43511653e+07,\n",
       "          1.91558174e+07, 1.57178438e+07, 1.25642205e+07, 1.06886185e+07,\n",
       "          1.21189067e+07, 1.16622945e+07, 1.09226821e+07, 9.42922699e+06,\n",
       "          1.18072941e+07, 8.56603609e+06, 1.71092263e+07, 1.04614535e+07,\n",
       "          1.06038536e+07, 1.30173963e+07, 8.83356375e+06, 9.41593467e+06,\n",
       "          1.72200546e+07, 1.37162889e+07, 1.21489549e+07]]),\n",
       "  array([[[1000.        ,   36.68791932,   35.37526278,   35.37083735,\n",
       "             35.3708224 ,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
       "             35.37082235,   35.37082235,   35.37082235,   35.37082235,\n",
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       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203,  601.33164203,\n",
       "            601.33164203,  601.33164203,  601.33164203]]]),\n",
       "  array([[0.98811896]])])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "KalmanFilter(R, k, params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "params_star = [2.34,3.41,4.12,5.22]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       29961209.66539031, 28010139.96124369, 26985012.4925191 ,\n",
       "       21777552.89522146, 23174014.17170255, 21330027.64832508,\n",
       "       19772605.02733883, 16796427.57689054, 20897053.02030425,\n",
       "       15565659.90402722, 17140737.20368961, 14991036.16665558,\n",
       "       11716631.36173391, 13074314.54162764, 12344792.99460285,\n",
       "       13664603.89667229, 12207180.95766149, 12880477.53271937,\n",
       "       13199620.42602382, 16213185.43481313, 12229053.08756579,\n",
       "       11819127.18477314,  9969923.72693058,  8244831.866327  ,\n",
       "        8876487.96623137, 12693652.09974516, 13321370.90230694,\n",
       "       18978520.06694428, 16606992.92170437, 19577147.13186988,\n",
       "       28904704.88595939, 32921077.91304679, 20190046.83986496,\n",
       "       26021748.0757529 , 18149152.72033574, 16092609.38478125,\n",
       "       15458338.29828928, 18217027.97787324, 15792925.39759488,\n",
       "       13703239.32452933, 12779441.40796075,  9785007.46661938,\n",
       "       10769289.34843313, 12075694.03582451, 14324930.93260531,\n",
       "       13784567.44832971, 17488989.21802102, 12705407.260344  ,\n",
       "       11472837.51504887, 11151672.82404569, 10612379.74341571,\n",
       "        8711161.16838093,  9660336.02985351, 10535141.45067203,\n",
       "       12610602.61872098, 12847984.75938693, 11973709.62278848,\n",
       "       16122032.46021957, 12043949.55987501, 11532199.65649781,\n",
       "       13726594.79099011, 18331209.24702453, 14965984.8597818 ,\n",
       "       13510170.49683183, 10969523.74872237, 11518420.05526289,\n",
       "       10449962.97046156,  7697989.6828625 ,  8996564.0224456 ,\n",
       "        9057045.45785563,  9421946.7514119 , 10677397.58220291,\n",
       "       10907066.47091445, 10121652.25699212,  7813578.07719919,\n",
       "        6896791.60408975,  9936025.18488361,  8493413.16343236,\n",
       "        7371346.22671909,  7205027.43346747,  9023998.81648715,\n",
       "       10325074.3801556 ,  9790874.76633289,  9748528.1977232 ,\n",
       "        9234365.90711471,  9906514.46120413,  8805344.0963137 ,\n",
       "        8537107.56497652,  8007329.0444654 ,  6749875.01510489,\n",
       "        6574146.83293776,  7608224.35448271,  7703114.22748196,\n",
       "        6749731.88858773,  8179254.62965638, 11344978.93501058,\n",
       "       14372576.72453724, 18411283.59951562, 24537671.26303987,\n",
       "       31700492.5126649 , 26150104.05563713, 21642448.35898879,\n",
       "       22306375.10196973, 21121415.81470593, 16798943.92050266,\n",
       "       15403221.96896928, 14294565.11780335, 12670357.17577521,\n",
       "       10753188.15190254,  9879409.0699005 , 11505815.54990266,\n",
       "       11536242.08123647,  9914422.87875602,  8835250.28690339,\n",
       "        7230281.30346438,  8006661.82556822, 11506783.26073794,\n",
       "        9854655.94855729, 10733888.90920781,  7328047.7191832 ,\n",
       "        8623609.47342624,  7952179.55452942, 12144908.74954904,\n",
       "       12427964.72172479,  9424525.55500035,  8619288.55436908,\n",
       "        8317124.0968622 ,  8761912.52830672, 18901359.25652837,\n",
       "       17848089.71392678, 12444091.20669417, 10477946.83372042,\n",
       "       11763716.26068378, 12624873.59253025, 12148825.2243197 ,\n",
       "       10637917.97111176, 19185462.27833328, 20940142.54571599,\n",
       "       18161575.10495501, 14175213.85002467, 12494362.58568992,\n",
       "       11247914.67585406, 15370585.97710979, 17267228.99244418,\n",
       "       13420790.40557265, 19168741.7428043 , 25662025.13879184,\n",
       "       27215053.23525793, 21718697.23123228, 22918225.15886531,\n",
       "       23832138.24956357, 21984316.4590597 , 17437284.12945533,\n",
       "       14000607.92818805, 11704184.690308  , 10274108.35387872,\n",
       "       14023350.30314646, 14997322.42975242, 13791851.43258183,\n",
       "       17997709.05543589, 19137759.74986053, 18512981.95441803,\n",
       "       28809284.25775138, 53334973.85380419, 51249125.68115025,\n",
       "       48164964.08664349, 31605074.71764094, 17231474.50994916,\n",
       "       23189790.4069038 , 22637083.15543634, 23188513.35481982,\n",
       "       18564257.95673725, 22142383.72538992, 25807628.23558057,\n",
       "       24309648.29776299, 21458363.12664436, 20606001.52851189,\n",
       "       19479103.36542466, 20034003.32104334, 19130690.80810136,\n",
       "       15206396.53679163, 15198383.34230404, 19015563.78970843,\n",
       "       18182078.88452227, 21934377.54498892, 22826310.79044228,\n",
       "       24134613.60373028, 16623230.09978097, 20087280.78282405,\n",
       "       19305480.97558997, 18475752.32850758, 15120470.15834754,\n",
       "       16125056.09526992, 20126092.9164026 , 18688227.06905517,\n",
       "       21243556.09429836, 22684311.38986542, 19193912.36676614,\n",
       "       17750391.7430312 , 24402005.63249634, 21947029.15800642,\n",
       "       18662583.2204339 , 15178003.80419187, 15654404.00247073,\n",
       "       19100506.7797947 , 19760356.5176018 , 19135696.42498744,\n",
       "       23721357.59242126, 37846054.39184244, 64139704.25381683,\n",
       "       38889152.25197677, 30365433.15035331, 25378946.14767256,\n",
       "       19627663.53746419, 16770918.37164847, 17100520.24131339,\n",
       "       20231178.58897289, 18775398.20189395, 14987879.34258604,\n",
       "       15451392.92694288, 17786890.56332802, 19541463.10963972,\n",
       "       26380155.42967799, 38776605.34486838, 20223703.95910319,\n",
       "       16637991.69578725, 14055990.99272825, 13425714.94421289,\n",
       "       18131998.09248304, 15288093.10072943, 14489241.77206309,\n",
       "       10774722.13343388, 11013918.33816064, 12038776.19817153,\n",
       "       11377188.22639089, 12313488.13123694, 13583115.19741348,\n",
       "       14573549.67925389, 23135034.20901681, 19110746.14369519,\n",
       "       21678330.09107261, 17225717.0753498 , 19108157.98039988,\n",
       "       16917163.85636648, 23951004.55331365, 22518021.43360895,\n",
       "       24138413.77618298, 22084028.98376527, 17514674.81783495,\n",
       "       19761853.15578957, 15273504.22854546, 14600646.88844277,\n",
       "       14090486.23070228, 14594157.98424582, 14769622.69858641,\n",
       "       20950329.5631214 , 15088278.25881373, 14457904.10441065,\n",
       "       13185384.02933002, 13298013.24853097, 13226355.62308679,\n",
       "       12038656.42205265, 13767621.20962495, 13198732.60873768,\n",
       "       12004058.75748909, 10928780.86523847, 11078331.35233231,\n",
       "        9194068.17727776, 10337333.89719153, 10707819.05854038,\n",
       "       15621729.68714675, 22602937.14010352, 13511310.3424115 ,\n",
       "       11400764.87742743, 10989765.58823426, 11639077.49295391,\n",
       "       10878527.13158191, 12971696.26729675, 15795578.80808462,\n",
       "       14158198.99221188, 18732602.01626546, 17783300.89125271,\n",
       "       19042098.49423883, 16538786.31351238, 16708871.45575104,\n",
       "       23216474.97163235, 27716785.11829848, 18169482.32558935,\n",
       "       12153388.07205867, 11204847.91724862, 15934967.22846101,\n",
       "       12037889.65851774, 13267547.48918465, 15693182.13685154,\n",
       "       12622553.35525342, 12410879.2631949 , 14745875.08600593,\n",
       "       18077282.53968119, 15468773.17221044, 12668887.82110442,\n",
       "       11126478.94153552, 11936375.92186998, 11558658.00833447,\n",
       "       10832471.8619552 ,  9891938.64849179, 11311787.80025523,\n",
       "        9951082.16972483, 15372081.32957846, 11042109.29508922,\n",
       "       10941373.6062457 , 12228228.95720596,  9462824.85329355,\n",
       "       10486062.5861516 , 15925602.25316873, 13708716.53965397,\n",
       "       12358107.93216977, 12293955.11662213])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_smooth=KalmanSmoother(R, k, params_star)\n",
    "u_smooth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(R)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, varargout = KalmanFilter(R, k, params)\n",
    "u_update, P_update, P_predict, T = varargout\n",
    "P_predict = np.squeeze(np.asarray(P_predict))\n",
    "plt.plot(P_predict)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(u_smooth)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}