{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Modèles ARCH et GARCH avec la méthode de moments généralisés\n",
    "\n",
    "* [pip install cvxopt]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import cvxopt\n",
    "from functools import partial\n",
    "import math\n",
    "import numpy as np\n",
    "import scipy\n",
    "from scipy import stats\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.stats.stattools import jarque_bera\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#np.random.seed(777) #jackpot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simuler un GARCH(1,1)\n",
    "\n",
    "La dynamique de la série temporelle est donnée par :\n",
    "\n",
    "$$\n",
    "x_t = \\sigma_t \\,\\varepsilon_t\n",
    "\\quad \\text{avec } \\varepsilon_t \\sim \\mathcal{N}(0,1),\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\sigma_t^2 = a_0 + b_1\\,\\sigma_{t-1}^2 + a_1\\,x_{t-1}^2,\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\sigma_0 = \\sqrt{\\frac{a_0}{1-a_1-b_1}}.\n",
    "$$\n",
    "\n",
    "Nos paramètres sont $a_0=1$, $a_1=0.1$ et $b_1=0.8$.\n",
    "\n",
    "Nous laisserons tomber les premiers $10\\%$ des valeurs simulées (burn-in).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3]\n"
     ]
    }
   ],
   "source": [
    "# Define parameters\n",
    "a0 = 1.0\n",
    "a1 = 0.1\n",
    "b1 = 0.8\n",
    "sigma1 = np.sqrt(a0 / (1 - a1 - b1)) #sigma1=sigma_0\n",
    "\n",
    "print(list(range(1,4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_GARCH(T, a0, a1, b1, sigma1):\n",
    "    \n",
    "    # Initialize our values\n",
    "    X = np.ndarray(T)\n",
    "    sigma = np.ndarray(T)\n",
    "    sigma[0] = sigma1\n",
    "   \n",
    "    for t in range(1, T):\n",
    "     X[t-1] = sigma[t-1] * np.random.normal()\n",
    "     sigma[t] = math.sqrt(a0 + a1 * (X[t-1]**2) + b1 * (sigma[t-1]**2))\n",
    "\n",
    "    X[T-1] = sigma[T-1] * np.random.normal()\n",
    "     \n",
    "    \n",
    "    return X, sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2060236fc50>]"
      ]
     },
     "execution_count": 280,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# T=10000, faire \"burn in de 1000\", normaliser X puis faire un plot\n",
    "X, _ = simulate_GARCH(10000, a0, a1, b1, sigma1)\n",
    "# Compléter \n",
    "X= X[1000:] # burn in\n",
    "\n",
    "#scale\n",
    "X=X/np.std(X)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons maintenant comparer les queues de distribution du processus GARCH (1, 1) avec celles d'une loi normale. Nous nous attendons à voir des queues plus grosses, car le processus GARCH (1, 1) aura plus souvent des valeurs extrêmes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.52333333e-01, 2.53333333e-02, 2.33333333e-03, 1.11111111e-04],\n",
       "       [1.58655254e-01, 2.27501319e-02, 1.34989803e-03, 3.16712418e-05]])"
      ]
     },
     "execution_count": 281,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculer P(X>k) et P(G>k) pour k=1,2,3,4 \n",
    "np.random.seed(777)\n",
    "def compare_tails_to_normal(X):\n",
    "    \n",
    "    A = np.zeros((2,4))\n",
    "    for k in range(4):\n",
    "        # X tails\n",
    "        A[0, k] = np.sum(X > (k+1)) / float(len(X))\n",
    "        # Normal tails\n",
    "        \n",
    "        #G tails use stats.norm.cdf\n",
    "        A[1, k] = 1 - stats.norm.cdf(k+1)\n",
    "       \n",
    "        \n",
    "    return A\n",
    "\n",
    "compare_tails_to_normal(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les queues de distribution du processus GARCH(1, 1) sont plus épaisses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.00131494, 0.        , 0.        , 0.00065747, 0.00065747,\n",
       "        0.00131494, 0.00657471, 0.00525977, 0.00723218, 0.01512183,\n",
       "        0.02695631, 0.03353102, 0.04405055, 0.06048733, 0.08284134,\n",
       "        0.11571489, 0.16765509, 0.1742298 , 0.23603207, 0.25970102,\n",
       "        0.3030941 , 0.35766419, 0.39316762, 0.37541591, 0.40237222,\n",
       "        0.38067568, 0.35766419, 0.37738832, 0.31098376, 0.28205503,\n",
       "        0.25246884, 0.21236311, 0.1788321 , 0.14069878, 0.10059305,\n",
       "        0.07363675, 0.06180227, 0.03879079, 0.03090113, 0.01380689,\n",
       "        0.01249195, 0.00788965, 0.00394483, 0.00525977, 0.00262988,\n",
       "        0.00065747, 0.        , 0.        , 0.        , 0.00065747]),\n",
       " array([-4.17917942, -4.01018167, -3.84118392, -3.67218617, -3.50318842,\n",
       "        -3.33419066, -3.16519291, -2.99619516, -2.82719741, -2.65819966,\n",
       "        -2.4892019 , -2.32020415, -2.1512064 , -1.98220865, -1.8132109 ,\n",
       "        -1.64421314, -1.47521539, -1.30621764, -1.13721989, -0.96822214,\n",
       "        -0.79922439, -0.63022663, -0.46122888, -0.29223113, -0.12323338,\n",
       "         0.04576437,  0.21476213,  0.38375988,  0.55275763,  0.72175538,\n",
       "         0.89075313,  1.05975089,  1.22874864,  1.39774639,  1.56674414,\n",
       "         1.73574189,  1.90473965,  2.0737374 ,  2.24273515,  2.4117329 ,\n",
       "         2.58073065,  2.7497284 ,  2.91872616,  3.08772391,  3.25672166,\n",
       "         3.42571941,  3.59471716,  3.76371492,  3.93271267,  4.10171042,\n",
       "         4.27070817]),\n",
       " <BarContainer object of 50 artists>)"
      ]
     },
     "execution_count": 282,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "# Faire des histplots de X et de G\n",
    "\n",
    "X2 = np.random.normal(size=len(X))\n",
    "plt.hist(X,density=True,bins=50,alpha=0.7)\n",
    "\n",
    "plt.hist(X2,density=True,bins=50,alpha=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'sigma')"
      ]
     },
     "execution_count": 283,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = np.random.normal(size=len(X))\n",
    "both = np.matrix([X, G])\n",
    "\n",
    "# Faire un plot de X et de G et les droite +- ecart type de X et +-3* ecart type de G et conclure\n",
    "plt.figure(figsize=(10,5))\n",
    "# Compléter \n",
    "plt.plot(X,alpha=0.7)\n",
    "plt.plot(G,alpha=0.7)\n",
    "plt.axhline(y = np.std(X), color = 'y', linestyle = '-')\n",
    "plt.axhline(y = -np.std(X), color = 'y', linestyle = '-')\n",
    "plt.axhline(y = 3*np.std(G), color = 'r', linestyle = '-')\n",
    "plt.axhline(y = -3*np.std(G), color = 'r', linestyle = '-')\n",
    "\n",
    "\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('sigma')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous examinons ici le processus GARCH en bleu et le processus normal en orangé.\n",
    "Nous pouvons constater que le processus GARCH bleu a tendance à franchir la barre (3 $\\times$ écart type ) beaucoup plus souvent que la loi normale."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tester un comportement ARCH\n",
    "\n",
    "La première étape consiste à tester les conditions ARCH. Pour ce faire, nous effectuons une régression sur $ x_t $ correspondant au modèle suivant.\n",
    "\n",
    "$$x_t^2 = a_0 + a_1 x_{t-1}^2 + \\dots + a_p x_{t-p}^2$$\n",
    "\n",
    "On utilisera OLS pour estimer  $\\hat\\theta = (\\hat a_0, \\hat a_1, \\dots, \\hat a_p)$ et la matrice de covariance $\\hat\\Omega$. On peut après calculer le test statistique \n",
    "\n",
    "$$F = \\hat\\theta \\hat\\Omega^{-1} \\hat\\theta'$$\n",
    "\n",
    "Si les données $X$ suivent un modèle ARCH alors forcément F suit une loi de Chi2 avec $p$ degrés de libertés.\n",
    "\n",
    "On rejettera si $F$ est plus grand que la valeur correspendant à 95% de confiance dans ${\\chi}^2_p$ distribution. On fixe $p=20$.\n",
    "\n",
    "On utilsera OLS de statsmodel : https://www.statsmodels.org/stable/generated/statsmodels.regression.linear_model.OLS.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F = 468.7660273201326\n",
      "P( Xi2(p) >F ) =0.00000\n"
     ]
    }
   ],
   "source": [
    "# on part de données synthétiques (mais on pourrait partir de log return SPY)\n",
    "\n",
    "X, _ = simulate_GARCH(1100, a0, a1, b1, sigma1)\n",
    "X = X[100:] # Drop burn in\n",
    "\n",
    "p = 20\n",
    "\n",
    "# truncate the first 20 so we have a lag of p's\n",
    "\n",
    "Y2 = (X**2)[p:]\n",
    "\n",
    "n=1000-p\n",
    "X2 = np.ndarray((n, p))\n",
    "for i in range(p, 1000):\n",
    "    X2[i - p, :] = np.asarray((X**2)[i-p:i])[::-1] # copie backward\n",
    "\n",
    "#pour i=p on a X2[0, :] = np.asarray((X**2)[0:p])[::-1]\n",
    "#pour i=p on a X2[1, :] = np.asarray((X**2)[1:p+1])[::-1]\n",
    "#...\n",
    "#pour i=999 on a X2[979, :] = np.asarray((X**2)[979: 989])[::-1]\n",
    "\n",
    "# Y2=theta.X2  modèle arch\n",
    "\n",
    "#compléter  use sm.OLS \n",
    "model = sm.OLS(Y2, X2)\n",
    "results = model.fit()\n",
    "# model=\n",
    "\n",
    "theta = np.matrix(results.params)\n",
    "\n",
    "Omega = np.matrix(results.cov_HC0)\n",
    "\n",
    "#cov_HCO \n",
    "\n",
    "\n",
    "# F désigne la statistique use np.asscalar\n",
    "\n",
    "F = (theta*np.linalg.inv(Omega)*theta.T).item()\n",
    "\n",
    "print('F = ' + str(F)) \n",
    "\n",
    "# p-value\n",
    "chi2dist=scipy.stats.chi2(p)\n",
    "pvalue =  1- chi2dist.cdf(F)  # 1- fonction de répartition d'une chi2(p)\n",
    "print('P( Xi2(p) >F ) =' + str(\"%.5f\" % pvalue)) # P( Xi2(p) >F ) <-- p-value\n",
    "\n",
    "# p-value < alpha=0.05 donc on rejette H0 (i.e. X ne suit pas un modèle ARCH)\n",
    "\n",
    "# Faites le test avec les valeurs critiques de la chi2 ? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calibrer un modèle GARCH(1, 1) avec EMV\n",
    "Une fois que nous avons décidé que les données pourraient avoir un modèle GARCH (1, 1) sous-jacent, nous aimerions calibrer le modèle GARCH (1, 1) aux données en estimant ses paramètres.\n",
    "\n",
    "Pour ce faire, nous avons besoin de la fonction log-vraisemblance\n",
    "\n",
    "$$\\mathcal{L}(\\theta) = \\sum_{t=1}^T - \\ln \\sqrt{2\\pi} - \\frac{x_t^2}{2\\sigma_t^2} - \\frac{1}{2}\\ln(\\sigma_t^2)$$\n",
    "\n",
    "\n",
    "Pour évaluer cette fonction, nous avons besoin de $ x_t $ et $ \\sigma_t $ pour $ 1 \\leq t \\leq T $. Nous avons $ x_t $, mais nous devons calculer $ \\sigma_t $. Pour faire cela, nous devons trouver une valeur pour $ \\sigma_1 $. Notre hypothèse sera $ \\sigma_1^2 = \\hat E [x_t^2] $. Une fois que nous avons notre condition initiale, nous calculons le reste des $ \\sigma $ en utilisant l'équation\n",
    "\n",
    "\n",
    "$$\\sigma_t^2 = a_0 + a_1 x_{t-1}^2 + b_1\\sigma_{t-1}^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(777)\n",
    "# Création des données synthétiques qui pourraient être remplacées par log return SPY ou cac40\n",
    "X, _ = simulate_GARCH(100000, a0, a1, b1, sigma1)\n",
    "X = X[1000:] # burn in"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def compute_squared_sigmas(X, initial_sigma, theta):\n",
    "    \n",
    "    a0 = theta[0]\n",
    "    a1 = theta[1]\n",
    "    b1 = theta[2]\n",
    "    \n",
    "    T = len(X)\n",
    "    sigma2 = np.ndarray(T)\n",
    "    \n",
    "    sigma2[0] = initial_sigma ** 2\n",
    "    \n",
    "    for t in range(1, T):\n",
    "        sigma2[t] = a0 + a1 * (X[t-1] ** 2) + b1 * sigma2[t-1]\n",
    "        \n",
    "    \n",
    "    return sigma2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Regardons les sigmas que nous venons de simuler."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Sigma2')"
      ]
     },
     "execution_count": 301,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(len(X)), compute_squared_sigmas(X, np.sqrt(np.mean(X**2)), (1, 0.5, 0.5))) # initial guess (1, 0.5, 0.5)\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Sigma2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maintenant que nous pouvons calculer les $ \\sigma_t $, nous allons définir la fonction de vraisemblance. Cette fonction prendra en entrée nos observations $ x $ et $ \\theta $ et retournera $ - \\mathcal {L} (\\theta) $.\n",
    "\n",
    "Notez que nous re-calculons constamment les $ \\sigma_t $ dans cette fonction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {},
   "outputs": [],
   "source": [
    "def negative_log_likelihood(X, theta):\n",
    "    \n",
    "    # il faut optimiser theta\n",
    "    \n",
    "    T = len(X)\n",
    "    \n",
    "    # Estimate initial sigma squared\n",
    "    initial_sigma=np.sqrt(np.mean(X**2))\n",
    "    \n",
    "    \n",
    "    # Generate the squared sigma values\n",
    "    sigma2=compute_squared_sigmas(X, initial_sigma, theta) \n",
    "    \n",
    "    return - sum(-0.5 * (np.log(sigma2[t]) + X[t]**2 / sigma2[t]) for t in range(T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maintenant on optimise numériquement \n",
    "$$\\hat\\theta = \\arg \\max_{(a_0, a_1, b_1)}\\mathcal{L}(\\theta) = \\arg \\min_{(a_0, a_1, b_1)}-\\mathcal{L}(\\theta)$$\n",
    "\n",
    "Sous les contraintes\n",
    "\n",
    "$$a_0 \\geq 0, a_1 \\geq 0, b_1 \\geq 0, a_1+b_1 < 1$$\n",
    "\n",
    "Voir : \n",
    "https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_5048\\2794730685.py:14: RuntimeWarning: invalid value encountered in log\n",
      "  return - sum(-0.5 * (np.log(sigma2[t]) + X[t]**2 / sigma2[t]) for t in range(T))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta MLE: [ 1.23970197e-04 -2.03606125e-04  5.35710135e-06]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(777)\n",
    "\n",
    "# Make our objective function by plugging X into our log likelihood function\n",
    "objective = partial(negative_log_likelihood, X)\n",
    "\n",
    "# Define the constraints for our minimizer\n",
    "#def constraint0(theta):\n",
    "#    return  ???\n",
    "\n",
    "def constraint1(theta):\n",
    "    return np.array([1 - (theta[1] + theta[2])])  # a1 + b1 < 1\n",
    "\n",
    "def constraint2(theta):\n",
    "    return theta[1]  # a1 > 0\n",
    "\n",
    "def constraint3(theta):\n",
    "    return theta[2]  # b1 > 0\n",
    "\n",
    "def constraint4(theta):\n",
    "    return theta[0]  # a0 > 0\n",
    "\n",
    "cons = ({'type': 'ineq', 'fun': constraint1},\n",
    "        {'type': 'ineq', 'fun': constraint2},\n",
    "        {'type': 'ineq', 'fun': constraint3},\n",
    "        {'type': 'ineq', 'fun': constraint4})\n",
    "\n",
    "# Actually do the minimization scipy.optimize.minimize\n",
    "result = scipy.optimize.minimize(objective, x0=(0.1, 0.5, 0.5), method='SLSQP', constraints=cons)\n",
    "theta_mle = result.x\n",
    "print('theta MLE: ' + str(theta_mle))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maintenant, nous voudrions un moyen de vérifier notre estimation. Nous allons regarder deux choses:\n",
    "\n",
    "1. Quelle est la taille des queues de distribution ?\n",
    "2. Faire le test de normalité de  Jarque-Bera.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tails table\n",
      "[[0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
      " [1.58655254e-01 2.27501319e-02 1.34989803e-03 3.16712418e-05]]\n",
      "\n",
      "Jarque-Bera probability normal: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_5048\\3012303717.py:3: RuntimeWarning: invalid value encountered in sqrt\n",
      "  sigma = np.sqrt(compute_squared_sigmas(X, initial_sigma, theta_estimate))\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def check_theta_estimate(X, theta_estimate):\n",
    "    initial_sigma = np.sqrt(np.mean(X**2))\n",
    "    sigma = np.sqrt(compute_squared_sigmas(X, initial_sigma, theta_estimate))\n",
    "    epsilon = X / sigma\n",
    "    print('Tails table')\n",
    "    print(compare_tails_to_normal(epsilon / np.std(epsilon)))\n",
    "    print('')\n",
    "    \n",
    "    \n",
    "    _, pvalue, _, _ = jarque_bera(epsilon)\n",
    "    print('Jarque-Bera probability normal: ' + str(pvalue))\n",
    "    \n",
    "check_theta_estimate(X, theta_mle)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prédire le future\n",
    "Maintenant que nous avons calibré le modèle à nos observations, nous aimerions pouvoir prédire à quoi ressemblera la volatilité future. Pour ce faire, nous pouvons simplement simuler plus de valeurs en utilisant notre dynamique GARCH originale et les paramètres estimés.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_5048\\674691437.py:2: RuntimeWarning: invalid value encountered in sqrt\n",
      "  sigma_hats = np.sqrt(compute_squared_sigmas(X, np.sqrt(np.mean(X**2)), theta_mle))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(nan)"
      ]
     },
     "execution_count": 306,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compléter \n",
    "sigma_hats = np.sqrt(compute_squared_sigmas(X, np.sqrt(np.mean(X**2)), theta_mle))\n",
    "\n",
    "initial_sigma = sigma_hats[-1]\n",
    "initial_sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simuler des valeurs futures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {},
   "outputs": [],
   "source": [
    "a0_estimate =  theta_mle[0]\n",
    "a1_estimate = theta_mle[1]\n",
    "b1_estimate =theta_mle[2]\n",
    "\n",
    "X_forecast, sigma_forecast = simulate_GARCH(100, a0_estimate, a1_estimate, b1_estimate, initial_sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.plot(range(-100, 0), X[-100:], 'b-')\n",
    "plt.plot(range(-100, 0), sigma_hats[-100:], 'r-')\n",
    "plt.plot(range(0, 100), X_forecast, 'b--')\n",
    "plt.plot(range(0, 100), sigma_forecast, 'r--')\n",
    "plt.xlabel('Time')\n",
    "plt.legend(['X', 'sigma'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En pratique, on voudrait probablement générer des milliers de scénarios futurs, puis examiner la plage potentielle de sorties (risque de hausse de volatilité)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 313,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "x and y must have same first dimension, but have shapes (100,) and (1,)",
     "output_type": "error",
     "traceback": [
      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
      "\u001b[31mValueError\u001b[39m                                Traceback (most recent call last)",
      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[313]\u001b[39m\u001b[32m, line 22\u001b[39m\n\u001b[32m     19\u001b[39m     plt.plot(\u001b[38;5;28mrange\u001b[39m(\u001b[32m0\u001b[39m, N), sigma_forecast, \u001b[33m'\u001b[39m\u001b[33mr--\u001b[39m\u001b[33m'\u001b[39m, alpha=\u001b[32m0.05\u001b[39m)\n\u001b[32m     21\u001b[39m \u001b[38;5;66;03m# Draw the most extreme X values specially\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m22\u001b[39m \u001b[43mplt\u001b[49m\u001b[43m.\u001b[49m\u001b[43mplot\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mrange\u001b[39;49m\u001b[43m(\u001b[49m\u001b[32;43m0\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mN\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmax_X\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[33;43m'\u001b[39;49m\u001b[33;43mg--\u001b[39;49m\u001b[33;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43malpha\u001b[49m\u001b[43m=\u001b[49m\u001b[32;43m1.0\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[32m     23\u001b[39m plt.plot(\u001b[38;5;28mrange\u001b[39m(\u001b[32m0\u001b[39m, N), min_X, \u001b[33m'\u001b[39m\u001b[33mg--\u001b[39m\u001b[33m'\u001b[39m, alpha=\u001b[32m1.0\u001b[39m);\n",
      "\u001b[36mFile \u001b[39m\u001b[32mc:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\matplotlib\\pyplot.py:3838\u001b[39m, in \u001b[36mplot\u001b[39m\u001b[34m(scalex, scaley, data, *args, **kwargs)\u001b[39m\n\u001b[32m   3830\u001b[39m \u001b[38;5;129m@_copy_docstring_and_deprecators\u001b[39m(Axes.plot)\n\u001b[32m   3831\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mplot\u001b[39m(\n\u001b[32m   3832\u001b[39m     *args: \u001b[38;5;28mfloat\u001b[39m | ArrayLike | \u001b[38;5;28mstr\u001b[39m,\n\u001b[32m   (...)\u001b[39m\u001b[32m   3836\u001b[39m     **kwargs,\n\u001b[32m   3837\u001b[39m ) -> \u001b[38;5;28mlist\u001b[39m[Line2D]:\n\u001b[32m-> \u001b[39m\u001b[32m3838\u001b[39m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mgca\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mplot\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m   3839\u001b[39m \u001b[43m        \u001b[49m\u001b[43m*\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m   3840\u001b[39m \u001b[43m        \u001b[49m\u001b[43mscalex\u001b[49m\u001b[43m=\u001b[49m\u001b[43mscalex\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m   3841\u001b[39m \u001b[43m        \u001b[49m\u001b[43mscaley\u001b[49m\u001b[43m=\u001b[49m\u001b[43mscaley\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m   3842\u001b[39m \u001b[43m        \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43m(\u001b[49m\u001b[43m{\u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mdata\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m:\u001b[49m\u001b[43m \u001b[49m\u001b[43mdata\u001b[49m\u001b[43m}\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mdata\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01mis\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;129;43;01mnot\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mNone\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43m{\u001b[49m\u001b[43m}\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m   3843\u001b[39m \u001b[43m        \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m   3844\u001b[39m \u001b[43m    \u001b[49m\u001b[43m)\u001b[49m\n",
      "\u001b[36mFile \u001b[39m\u001b[32mc:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\matplotlib\\axes\\_axes.py:1777\u001b[39m, in \u001b[36mAxes.plot\u001b[39m\u001b[34m(self, scalex, scaley, data, *args, **kwargs)\u001b[39m\n\u001b[32m   1534\u001b[39m \u001b[38;5;250m\u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m   1535\u001b[39m \u001b[33;03mPlot y versus x as lines and/or markers.\u001b[39;00m\n\u001b[32m   1536\u001b[39m \n\u001b[32m   (...)\u001b[39m\u001b[32m   1774\u001b[39m \u001b[33;03m(``'green'``) or hex strings (``'#008000'``).\u001b[39;00m\n\u001b[32m   1775\u001b[39m \u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m   1776\u001b[39m kwargs = cbook.normalize_kwargs(kwargs, mlines.Line2D)\n\u001b[32m-> \u001b[39m\u001b[32m1777\u001b[39m lines = [*\u001b[38;5;28mself\u001b[39m._get_lines(\u001b[38;5;28mself\u001b[39m, *args, data=data, **kwargs)]\n\u001b[32m   1778\u001b[39m \u001b[38;5;28;01mfor\u001b[39;00m line \u001b[38;5;129;01min\u001b[39;00m lines:\n\u001b[32m   1779\u001b[39m     \u001b[38;5;28mself\u001b[39m.add_line(line)\n",
      "\u001b[36mFile \u001b[39m\u001b[32mc:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\matplotlib\\axes\\_base.py:297\u001b[39m, in \u001b[36m_process_plot_var_args.__call__\u001b[39m\u001b[34m(self, axes, data, return_kwargs, *args, **kwargs)\u001b[39m\n\u001b[32m    295\u001b[39m     this += args[\u001b[32m0\u001b[39m],\n\u001b[32m    296\u001b[39m     args = args[\u001b[32m1\u001b[39m:]\n\u001b[32m--> \u001b[39m\u001b[32m297\u001b[39m \u001b[38;5;28;01myield from\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_plot_args\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m    298\u001b[39m \u001b[43m    \u001b[49m\u001b[43maxes\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mthis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mambiguous_fmt_datakey\u001b[49m\u001b[43m=\u001b[49m\u001b[43mambiguous_fmt_datakey\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m    299\u001b[39m \u001b[43m    \u001b[49m\u001b[43mreturn_kwargs\u001b[49m\u001b[43m=\u001b[49m\u001b[43mreturn_kwargs\u001b[49m\n\u001b[32m    300\u001b[39m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n",
      "\u001b[36mFile \u001b[39m\u001b[32mc:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\matplotlib\\axes\\_base.py:494\u001b[39m, in \u001b[36m_process_plot_var_args._plot_args\u001b[39m\u001b[34m(self, axes, tup, kwargs, return_kwargs, ambiguous_fmt_datakey)\u001b[39m\n\u001b[32m    491\u001b[39m     axes.yaxis.update_units(y)\n\u001b[32m    493\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m x.shape[\u001b[32m0\u001b[39m] != y.shape[\u001b[32m0\u001b[39m]:\n\u001b[32m--> \u001b[39m\u001b[32m494\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[33mf\u001b[39m\u001b[33m\"\u001b[39m\u001b[33mx and y must have same first dimension, but \u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m    495\u001b[39m                      \u001b[33mf\u001b[39m\u001b[33m\"\u001b[39m\u001b[33mhave shapes \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mx.shape\u001b[38;5;132;01m}\u001b[39;00m\u001b[33m and \u001b[39m\u001b[38;5;132;01m{\u001b[39;00my.shape\u001b[38;5;132;01m}\u001b[39;00m\u001b[33m\"\u001b[39m)\n\u001b[32m    496\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m x.ndim > \u001b[32m2\u001b[39m \u001b[38;5;129;01mor\u001b[39;00m y.ndim > \u001b[32m2\u001b[39m:\n\u001b[32m    497\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[33mf\u001b[39m\u001b[33m\"\u001b[39m\u001b[33mx and y can be no greater than 2D, but have \u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m    498\u001b[39m                      \u001b[33mf\u001b[39m\u001b[33m\"\u001b[39m\u001b[33mshapes \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mx.shape\u001b[38;5;132;01m}\u001b[39;00m\u001b[33m and \u001b[39m\u001b[38;5;132;01m{\u001b[39;00my.shape\u001b[38;5;132;01m}\u001b[39;00m\u001b[33m\"\u001b[39m)\n",
      "\u001b[31mValueError\u001b[39m: x and y must have same first dimension, but have shapes (100,) and (1,)"
     ]
    },
    {
     "data": {
      "image/png": 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uwOL0aPxPPZWuwIlrmjgFDiEkqMD54ov67jMocEhdNvykwlTMwSGEZI0ZmvqsjsNUFDikrkhL4KigUZiDQwhJe5o4oMAhpA6t2ySgg0NI/fHJJyL//rfkBjo4VShwSF2RdYgKSX9hE/8ocAjJN2PGVFfufvllyQUUOFUocEhdkZXA6dxZpKEh2kwqChxC8gsW133wwer/33hDcgEFThUKHFJXZCVwWrWqihxAgUNIeZg1qyk3zmyrWUKBU4UCh9QVSQqc9eubxItd4NSSh8MkY0Lyy0MPNf1/7VrJBRQ4VShwSF2RpMCBVV2puAucqLVw6OAQUgyBQwcnX1DgkLoiSYGj4akOHUTatWv5fBwODgUOIflh2TKR+fPjFThRqp2bwOU1naTPKHAIKT9mVc8kBY6TewMocAgpFw8/3PzvWgUOlpJBPzF9evTPsAuazyhwCCk/ZkMvqsBhDg4h+QxPxSFwnnmmej9nTvTPsAuaz+t4PSoKHFI3FFHgIHHZdG3o4HgPNosXZ70VpF5Avp1OD99ss3iSjLUCMfL5okIHpwkKHFI3FFHg2K8IKXCceeklkX32Efn+97PeElIvLFok8uabIm3aiIwaFY+Do30UBU48UOCQuiEvAidMEiEFTjDmzave08EhaYendt+9qc3XKnDo4MQLBQ6pG7IWOFGmiVPgBOO112ofGAiJInDg3uisyTw4OOZCm4ACh5A6wGzoSQgFt5XE4wxRMcnYW+Bgf+WlFgkpL8iN0xlUCI2qwGEOTr6gwCF1Q9YODnNwkhc4cdQRIcSP558X+eADkY02Etl11/gcHAqckgmc888/XxoaGprdBg4c6PmeO++803pN+/btZdCgQXLvvfemtr2kuFDglJd//7vp/xQ4JK3w1F57VZOM27bNT4iKAidHAgfssMMOsnTp0sbbv/71L9fXzp49Ww4//HAZN26cPPfcc3LQQQdZt/lmOUlCHKDAKSfY77iaVihwSFoCB+EpQAcnn2wgOWCDDTaQXr16BXrtVVddJfvtt5+cddZZ1t8XXXSRPPDAA3LNNdfI9ddf7/ieNWvWWDdlJTMR65KkBY4KFz+Bg04M348rPz+YgxNsuq4JmzdJEuTZPPpo9f86PTyuHBzto1CcD5+lzlCUz1DqWeDkwsH597//LX369JEBAwbIkUceKW+iuIALTzzxhOyjsvkrRo8ebT3uxqRJk6RLly6Nt759+8a6/aQYJC1w9OqrY0fn5zt3Du8y0MEJl38D6OCQJHnqqWpb33RTkR13jM/BQeFAcwbUJ5/U1s+1bt3873okc4EzfPhwmTp1qsyYMUMmT54sb7zxhnzzm9+UT1yO7rJly6Rnz57NHsPfeNyNiRMnyooVKxpvS5Ysif13kPxjdh5JCBzt3Nq3d35+gw2qSYlhwlQUOP5Q4JA0Wbiwer/LLiINDdX/x5GDA8cGIqdWgaP9XLdu1ft6FjiZh6j233//xv/vtNNOluDZYost5E9/+pOVZxMH7dq1s26kvknawdHOzetUQ5jq008pcMoocIKGHUmx0RCoWQ4iDgfHXr8maqhV+7lu3UTee6++BU7mDo6drl27yjbbbCOv2Xutr0CuzvLly5s9hr+D5vCQ+iVpgaOL2vkJHECBE/8MqiiVouPi5Zer3/+zn6X/3SRdVHiYIec4cnCSEDiAi23miE8//VQWLVokvXv3dnx+9913l4dsS7giyRiPE5KVwDEXxXQLUZkJyOasHy+YZOyPXgsNG5ZdkvEjj1QHqJkz0/9uki4aOnISOLU4OHanJS6B8xkdnOw488wzZdasWbJ48WJrCvjBBx8srVu3tqaCg6OPPtrKoVFOPfVUK1/nsssukwULFlh1dJ555hk5+eSTM/wVpN4FjtmxeTk4ffpU799+O/znAjo4LQeBd9+t/n/nnbNzcDStL2reBMmGm24SmTy5dgcnjhycpBycz+pY4GSeg/PWW29ZYuaDDz6QHj16yB577CFPPvmk9X+AGVWtWjXpsBEjRsi0adPknHPOkZ/+9Key9dZby9133y07ajo7IRkIHNMG9hI4m21WvafAiXeKOLoLnRyZhcDRiZ+col4cIChOOKGa2HvUUU0TAGoJUdHByReZC5w77rjD8/lH4P3aGDNmjHUjJC9rUWnHhlkVXommKnDeeivc5yoUOM7hqa22alrMNEuBQwenOCABF6FlFTtxCJw85uB89llVxOmMr3oi8xAVIVkIHHRs2rnFnWDs1ZFEFThqgTMHJ98CB4OSOdWX5Jf332/6fxjnJSkHJy6BY58mXqnUXoCwqFDgkLrBbtXGGabyq4FTq8DZcMPqPR0c5xlUpsBJO0yEY6IhRwjQep61UjQHJy6BE0cOTlIhqnoOU1HgkLohDYHjV27pa1+r3r/zTjAHiQInmIOz9dbZOThLlzZ31piHUwzK6uBoP9elS5ObTIFDSMlJUuAEqYEDUK4JOfMQKjr7xwsKnOAhKh1w0hY49pVlKHDqQ+B06tT0mLZ7tM+ooe+4HZwOHao3p8+uFyhwSN2QhxAVEpC1JmWQMJV+rq5vRYHTxKpVVffEHqLC42nuJ7vAYaJx8QRO0LAi8lm8HBwQNd9FHRx1XWoVOB07UuBQ4JC6IQ8hqrB5OHYHh0nGLaeII9cABRRV4KTtotDBqZ8cHPQh6tA45eCE+Sw3gdO9e3YOTqVSrrXcKHBI3ZCHEFWtAocOjnN4St0x7dCzFDh0cMobotLzCi6Ltsm4BI72T+rwZiFwJk4U2WQTkaefllJAgUPqhjyEqMxEYwqc+GZQKVkkGtPBiQ7ckKxmndUicODemOUgkFen9a9qDVHVKnD0czoYAifoPn7yyapLPGeOlAIKHFI35C1EFaSacS0CBwtADh4sMn26lH4GlZJForEKHM2TooMTnO9+V2TzzYMvPpt1iMop/yaumVTaP/Xs2fy7wgBxov1ahwgOjn7nRx9JKaDAIXVzpagdj678UaQQlQ6eYXJw7r1X5IUXRP7wB6mLEFXWDs7221fv6eAE5/HHq0Jj/vziOTh2aq2FY3dwIJTDzsgyhUyHCAJH2w0FDiEFwrRotXPKKkSVVg7Op5+W21HIg8DBgKfuww47lHt/J4EO6jobLi0gHD74IF8Oju4LdXDMNhwUCpzmUODUGehIsIyXwxJfpcZs4Fq/Is58lqizqPzK+lPguB9PFYhOAictF0VXEccsLl0png5OMHCBoRcZaQsciFLTHQkrcMwaOHGtR6V9FM6lDTaIdi7pZ2BbWrVquuAKInDMKfBlETiZL7ZJ0uXuu0X+/OdqxzJypNQN2sDRcehVTVYhKh0I8Z4PP6zOWkhC4KiwKaPAef31JkFj7r+0c3A0PIU8Eh30yri/k8AcdNMWOGb+Td4cHLR1fD76hqgCR/u4DiEcHPRH2ifiu8sAHZw6QxuMac/WA2bD19kOWYWo8BqtdeGXaFxLob8yOzg6gwoJxuZslrAhKgx0F1/cPB8jqsDRQY8OTvilCdIWOPbjHVSUaFtKMskYfVTUc6kWgbPCaDNlcXAocOoMVHkFFDjZzaIKk4dTS6G/Mgscp/ybKAJn/Phq7Y9rrqktREUHpz4EThpJxriYiSpwzCniYQWO+V0UOKTQAqcsFmReBE6YEFUtAocOTnwC56WXRO65x7mWTVDo4BRT4NhDVEHrxAQJUdVaB4cOTnxQ4NSxwPFLcC0TeQpRpSVwVNigw43a6eZd4Gy5ZfPHwyQZIzTlNuDVInDKKCiToGwOTlwhqlocnLgEzqpV5egzKHDqVOBgcA87BbHIlCVEFcXBsf+/DOgA1bt388eDJhm/8Ubz+kBxCBwNUdHBCS9wcDzTHFDzKHCydnBW2r6rDC4OBU6dYQ509RSmMhu+TsHMMkSlyzWETTKOkoNTRldBf499um7QENWll1b3pdYciSJw8H4VqHRwahM4YPny9AWOni95yMGJ08HR/qJDRAcHUOCQwjo49SxwihKiQgjR7uDgsaDVTSlwnFm2TOTmm6v/v/DC6AIHAzLOodatq06S6eDUU/g3LoGTZphKj7deaMTp4ERxosw1uZIIUX0eIMeIAocUHgqc4oSoEI7SgdJcuThomIoCx5krr6wer+HDq0Uv9fPCXnlreAqDJESODkoYrIJWjq1nzL4IvPNO+g5OVIHjVegvioNjChCGqOKDAqeOO5V6miqet1lU2rGiU3HrxMyOMqzAwXvN31cmgYPfr/vbTeC4uSioYHvdddX///SnIl27NoUsw7o4Zv6NHiOtycM8nHw7OCpw9EIj6xwcc1/UInBqmSa+gg4OSYqwi6o5sWiRyLHHirzyivtr6ODkI0SFgVkHY7c8HLOj1Jh6UIFjTyouk8Axf4td4OjAAHHjlFgNcYP3Y92o73ynKki06GKtAgefxVo4xQpRhRU4XoX+asnB0X2BzzDdwLDnUVyzqMoyPlDg5IBzz62e0M8/X9vn/Pa3IlOnitxwg/trKHDyEaIKkmisn4kOz/zcIInG9SBwMBjooKKYSeT2Dhu5EQhPgQkTmlaV79EjHoEDOJMq/wIH7UrPoTAhKvQX2o/E7eDYk4OzniYO6OCQWPjb36rCQxMfo6L5HLq6sRMUOE0CJ87FNsOGqILk4ZiiCSJHoYPjngcBF8UtD+fVV6siBoPHD37Q9HicAoczqaKtvZSmwNHQPNqUzqILIkq8nMNak4zNKsZxCpz2IRbb1O/StfIocEgsaLn3v/61ttkXmB3iVfMEn80cnHyEqMIKHLgN6jgEETj2AbZMdXC8BA5wEzjazvr3b3J5AB2cbNBBXYs1piVwNP8Gi7Rqew0icPSYmn1I3A6OCpMsp4n361e9p8AhsTRyFRr/+Y/ICy/ULnDcrh5xZWGGN+rdwckyyTiswAHq4tDBCSZw7IODCpK+fZs/TgenvgSOHmccd21bQaZReyUYx5WDk4cQVT8KHBIX9sFN18ZJwsGxT8ukwMk2ByeswFHXIekcnH/+U2TcuJbnS1EEjls1Y3NhzFoFDvaNXpjQwYlH4KCuUJhClrU6OEguD+O6+AmcOGZROTk4YVz9OBbb3GKL8owPFDgZo51urQIH7ow2XAqcYoSogiYZ2wVO0g7OL38pcsstIvffL6UKUcXp4Gi7xUCk36d/m9tI/AdjOAbIncJM0qhLZqQpcNzOu1pycNySjM2SCMrChSL77y8ye7b759gFzpo1/jN16eCQ2NGOcujQaiN/9tmWoicI777b9H+3ztUucJiDU6wQVRiBYz8Hwgy4mqSe1/OjVoETh4Pj9ll0cMILHAzmm26aXphKj3MeHRwVOF41lW69VWTGDJGbbgoucPzCcOhTdHxAjhqgwImBSZMmya677iqdOnWSTTfdVA466CBZCInqwdSpU6WhoaHZrX2YS+ccoWJm551FRoxoSjaOGp7ycnD0cU1WracVxfPo4KjAwRWlU+cTRw6OvieMwNHX5rWDqzXJOEmBEzV3Ik889pjII48Ey0upBXNQ10VT0xA46uCYOThxCJxacnDswgR9tJtYxkKxTguG+gmczzzCVGb/oCGqvLb/QgmcWbNmyUknnSRPPvmkPPDAA7Ju3TrZd999ZZVPAkDnzp1l6dKljbf/IEO3gGinC9v8wAOjh6nMjsHPwdFpgBjg85pnUaTFNiE4NHcgjIOz8cZNHZBTmCqOEJVOg40icLzKDRQhB8ccGGDPm23NRN0D0wWt1cEpaogKRUL33FNk772r5+d//ZfIxRfXXqMrjwIHDk6YWVReRf7idnDM77ELnMWL3R1Wu8DZYIOmfsNL4OjFAPaHtge8PmmRW3qBM2PGDBk7dqzssMMOMnjwYMudefPNN2Xu3Lme74Nr06tXr8ZbT+3JSyBwcPXktxqyl4ODk9JpEFQxgxNYrzbyGoYokoNjdmhhBA4saK8wVRxJxjpwhBlw9b1lcnAgXnC8cWWsAt/u4EDQBT0n3Nygojs4//53837kwQdFJk4UGTKkGhZJqg5OVgLHzJvxc7ODhqhqqYNjOi5xCJygC25qW0HbwfdqeCyvfUBhBI6dFV/t6W7dunm+7tNPP5UttthC+vbtKwceeKC89NJLrq9ds2aNrFy5stktL5gd5TbbiAwcWO1kw3YmpsABTs6MPrbRRtUaEPWUaJyWwAkbKfVKNI4jB0cH86B1cMw1rNJwcHBcsHwC1oU6+WSRo48WOeggkdNOc0+KjCJw1HHB/rDXMEFXo2FbJ9u/nhwc7Q9GjxZBl/qb34jsuGP1sUcfLYeD4zRNPIgwSTIHx55kbH6POVzhddrXewkc83M6BJhJpd+BtoO2APcOUODEyPr16+W0006Tb3zjG7KjtioHtt12W7nlllvknnvukd///vfW+0aMGCFvuWRrIs+nS5cujTeIorxgt82/971oYSp7x+DUwarAwRWT6kcKnNrRDg0dg1lALghBHBx126KEqMI6OKYQSqNzQ8LkSSehjYpce63I735XPfevukrkuefiFzhOTR/HTQV/0DwcjYin4eDAWbBfwCSF9gfYH9tvL3LKKSLHH199zOMa0trXf/hDuJC3vjbLEJUpcPyESZp1cNzOJTMTA+3TfhHg5AR1CCBwtK3od1LgJABycebPny933HGH5+t23313Ofroo2XIkCGy1157yfTp06VHjx5yg8siTBMnTrScIb0tiTJNKQHMlaS149Uw1b33hhuA7R2g0xU7BU4yAifKDColTIgqSpJxWIFjvi4NB0cHza9/XeScc0QuuaRpn7iFT6MIHLeQUpREY4QIVTBpQmaS08QnT64eR4i/NAWOgoVJ/QQOSgsccYTI9dfn28GBWDQFjrmWWa0CJ85KxsApyVjDUwDixt5GvUJUnwUQONp2KHBi5uSTT5a///3vMnPmTNlMe7iAtGnTRoYOHSqvvfaa4/Pt2rWzkpLNWx7QThdiQ5X78OHVHBmccLNmRRc4fg6OdmD1nIMT11pUUWZQKWnl4EDMBel403ZwdEbI2LEiF10kcuaZIgMGeAusKEnGXg5OWIHzzjvV/YnzSEOMSU4TVycLJSSSRvsDM0NABc7rr7sPkk88Ub0POtcDg7MZTklL4ODc0VAUBA7cO+0PggqcJOrgBHVwTIFj77/RL+hFW1iBs9IIUZkCp+gXwJkLnEqlYombu+66Sx5++GHpr5PwQ/Dll1/Kiy++KL21lRQEp04XV+nf/W74MJW9Y6CD0/yqLY0QVdIOTpQcnF69Wj4W5H1pOTgqcMxm37Wr9/dn7eDoNuOzzEVQk3Jw9LPCTjyIgvYHpsDBBRf+RjtasMBZrOgsq6D9iZnwahc4SZauUPcG36liIuhyDWlWMo4icEwBY35O+wALbjJElRAISyGPZtq0aVYtnGXLllm3z4yjgXAUwkzKhRdeKPfff7+8/vrr8uyzz8oPf/hDa5r4cccdJ0XCbdqqhqmCJhqbMXrtqClwmoCQ0Vh13kJUXleucUwTh1jQzi6swEHnluRgg8/WDjspgaPb75YUXIvAcboWM5OM49p3eiyzEjiYUaMuzssvt3wPjmHY2kk6oAOcn9oO4H4k2SeZ4amwwiSNOjh+Do6ee2EETocIISo9/hQ4NTJ58mQrL2bkyJGWA6O3P/7xj42vwbRx1LpRPvroIxk/frxst912csABB1izombPni3bIyuuBAJn0KCmq/ognSQagA6yW21VvWeSsXvDT8rBiRKi0sHcafCKIwcHM+bCzOwxhTEGmyTrYGDqNgY6DKCm8IhL4OD46vbHGaLyEjg6KEFQm4N4kR0cvzwcs0ZOWIGDcxvnNe71O5MMUyUpcNKog6MXBDqN20ngQGjprMBaQ1RFFzgh53wkE6Ly4xEUhjG44oorrFvRcRM42vjQOePEhyDxQjsEnJxapMnPwdHGUw85ONqw0SmgE8pTiEo7FAxiiKGbIY84HBwVOBATYR0c7eDMq8E4UaGAPBZz32nn6iRw0F34CRz8ZhxrvBaiAJ09FnJMw8HBAIXvg8DBoOHXdvMqcMwkY6DXjk4CZ9686ALHHNDh4uD70Z95TKKNbYp4WGEStNBfLWtRBQ1RoZwIijI6CRxznwLOoiK5EjjoFLWxBKnLoeEp5FugcwdOg5kOevXq4MBhwcCXpxCVuVCjXZRGTTLGwO7k4ASphWN/TZJ5OG5CQR0cp84V+0QFnpvAsZe51/wmHH/7wB23wMH5FXctnDQFjlOSMfAKUdXi4NgFTl4dHLSpoA4Ozk+/hS2jODh4jVbbHjas+e8xP8N+QdKhhllURR8fKHByKHDQSWoDjCpwmIPjfnWUpxAV3qOxe/sAFtXBsYuAMAOuk4OTlcBxElfm9um57peHYyYYq7WflMBJYiZVWjk4aA+6f+0CRx2cRYtaDpR2gRMkrJ4ngRNkuQb0nfq7/HJw/D4rapKxujc4t7fcsvp/JwcnisBZWdIQFQVORqCxuAkcEFXgeF2tOwmcegpRJS1wojg4XotDRhU45rHHsa5F4GTp4HgJHAyM9hlMbvvUL8E4jMDBMdGq024CJ+6ZVGk5ODqYQQTqMVCwEo7TTCocI3NmD8IzXgNp1gLHXEk8jIOjAgDnnFvINkzRwChJxmZCvlOZj1oEzgpbiIpJxqQmcGJqaMNeSyOswNEOAR2EV4jKbamGsq8o7rQAXV5CVGEETtAkYxU4+L14T9QkY68ODhY86sFkJXDcwlNeAsergLkKHLRLrxAgPgvtBQORmceRlIOD/aztFudDlATWoKibi/1vF49uM6leeKFp3+p7ggyKWTs4YXNwzPCUmwtoOjhh83CChKhU4PTrF03gfB5wLSpAB4fUhLo3uDJyGhjTcnDqYUXxPIeozI4sqIPjl4Nj5t+AJBycc8+tCvNaFmBMS+D41cABOmBAvHiFbc1tdhvo4nRw7O3YzcXBOTF7dm2z3tzyb7wSjTXBeOjQcINi1gInqoPjdd7hfIg6VTxIknGtAueziCGqIl8AU+BkhFd4CtSag+M3TRwdizbGsufhhBU4GCyeeSZ4peO8hajsIsDrnIjq4MyZ41++P+hyB0kIHHNwCBKiwjmhnbpXmMov/yZuByeowJk2TeQb3xA5//z4p4grTg6O5t8MHlwMgVNriMqvCH6UqeJoz9oXOTk4EK1whPTci1vgVL6abWh+px5L/I4gIce8QoFTAoHjFKLyc3BwtVEvyzWEFThY3XrXXasrKacZorIPiLXm4NTi4Gi5ATcHR2dzRHUMMLMJvwPHQlc8V7RzxWfbP78WB8dvjV39zbUKnDgdHPtnuAmchQub3ycpcExR6yRwglwwqcAxp9EXwcHxEzhRHBy3An3mOY7zIGgOTthp4qtXN7nC2m7w3WFCjnmFAicj/DpdjREnFaIC9TKTKqzAwZo7wGVps9hDVEnl4NgFTphp4up2uHVutQoc82rUnu+B7dXwj11gRRE4bit/u7U5/W15cHCCChw9TrVcrPgJHPtMKpyH8+dXHxsyJJyDY64kbhc4eC7OpS4UbK9um1MOjte5HNbBCZODYxaENPsQ9FPaZ+H7nUJUWivN/JywDs7KlU3lFXRsQPsrQx4OBU7BHRwM0voarxAVGpwOjPUqcLQz9VtsU4VFEEGQxxBVHA6OnpduxfZUBES1r72EAjpa3Se1ChyEp3R/+Dk4QWZS5dXB0TZcS1tWceRWK8icSQWnCDecozjPsD9qDVHhc/ScTcLFMfNJTBEXxMHxK/IX5rO89oU9r0u/Dwn92s9jBXuc/9qP6XGLGqJaYYSnzO+nwCGZCxwMNGi0uArGe9yu1s1E4noVOEEdnLACJ61ZVEGTjLUzjkPgOHVuEB0qsqI6OOqSuQkFtzycsALnxRebBm27dZ+UwCmrg4PBz0w0NsNTEKW1Cpykw1R6XLGd2pbykIPjJkzM79PzGNuOc9spxcDtc9r7LLZpn0GlUOCQyPjN7AgqcDQ8hasrdDJuDo4KHAzuOsBnkYODAevaa4OF3ooicNKeRRXUwdGBNso0cS8HxwzhJOHgxCFwdJ9qmNEvPBVE4GDf6HmbloMTNMlYB6Fayj74CRx7orHOoILAAXkXOE5TxPOQg+O2L8zv0+n45nkXVOB06FCbwCnyBTAFTgbgClyLhQVxcLw6LDP/BphJxub77Pk3WTk4v/qVyMkni1x+efYCBzVGnEqqqysRdPp82g5OmiEqp8HKFAC15uAk7eDo8fULTwUROLrNaDdeA53TGkJphagQio66yGcYgWN3cIokcMwE46CVjJPMwQni4KjAQf5N3AJnpctvK0OxPwqcDMDCf3APEFbSBm1HT14MZl4dpTmDyuz48T6zkZnrUGUpcB5+uHqviZ9ZChw3FyerHBy/WVS1Jhn7CRwIb91XWTs4bgtuhhU4ShwOTpDwlLltaebgmINQVEfWLwcHOIWokGAcdkDMMkRlFzhx1cEJ+lm1ODhOAkeFW1IOzkcFFjiZryZez+EpTI91KzePqwoMUGqL208+NwfHFDDoHLXB5cHBwTY8+6z/TJW0BY5dmKQdoko6BydoHRzz96rAwTbZVzk3j10UBwfHQwewpB0cJU4Hx0/gpO3gwKUyByG05yCCrhYHR0N/CIvryt95cnAw0+umm6rnz2abVW9PPFG7wEkyydjLwdHzIIiDE3aa+AoKHBInQetyoCGqwNHF1fwEDgZBDLQYePBebcxOAiftHJynnmpyH5IQOOgo0LENGlSbg6ODdl6TjGvJwUHY0q0Cr3ai+B7kdJmdu3Z2cTg46t6ZS4bYcVtRPGwOTtEdHD2WGLRwfjsJHHyPGWqN2p6DCBydSaWv3XrrpgE1DoEDIRKmRIMdVHO+7DKRu+5yD+0nKXBqqYPj5eAoXgKn1mninTuXT+AwRJVzgQO8EnL1SkcFjlsHa65DlZWD89hjTf9PQuAcf7zITjtVO7kga1HFHaKK08HBgKXbFlcODpwYr47XFEboqLXDtXdwtTo4QZY7iNvBCSNw0N6ccrOydHB04HcSOPb2G6U941zT7fUSOOZMKjM8FZfAGTGieo9K4mEEIkJmu+9ereY8fXpV3Oy/v8jPfy7yP/8jsu++ItttV71QPOSQ5B2cKHVwgggcJhmHgw5OwQWOOjhmLg8GNlyFmgN0HkJUpsDB9mEQgcUdF3BvAGZ3aEfpdGWDThohFwz4XgIH7wuyjXHm4KjDYnaQtebgmKIWg4abELOHttDBYR/YRUacAseNuGZRhQlRaXvDeYHvtQ/0URwcL8csrMB59VVngWMXFFHas7mfTbfOLUz1r381TzA236czubx+t9ugDocC+xf7Gv3FAQcE2/5jj60uHwJhftRRIj/+cVM4zY+sQ1RBkowV1MCJKnC++KJ6My/wvAROLUnGDz0k8s9/VgXnwQdLZtDBKYnAcXJw/ASO2UCSXlANQuLJJ5v+xiASt7DSBq4z1OyPmw3fa6q42TkFmZFSa4hKOzHsE/0+cxtqdXDMCqVeV8X20JZbmKjWEFUaAgfHVwdPr2R+E+xnPRb2MBXaR1gHB++pdSHbKA5OlBCVvsdpJXE7fg4O2pRfu/FyLUaNaj4hwQ9UU4a4QftA8cHf/ja4uMlboT875vehvzbP+7ACx+2CJIkQFQQwQoX33SeZQoFTYIGDDtRJ4DgllXo5OGmsKA5XBd+hhaqSCFNp40XVz1oEjtkJBAlT1RqiwjHRQUUHMLOD1Lh+2CRjszMMkhfi5OCAIjo4QM8zrHpuv2oNm4eDQUTPBfMq2gmcZ+r61Rqm0u/EbwBJOThB8m8UUzyYDg7Om6DrF3kN6t/6VpMLEISpU6v33/lO8xyVoMS5VEMtdXCcHBzzPLf/trCF/twuSJJIMg5zPiUJBU4BBI5b0iM6e20cTgLHz8FJc0VxDU/tsUfTtsYtcJJwcMIInKgODqx8e7E//Uxspw6WUR2coAInTw6Ok7iCoLdvoxe6T4OEp/wEjm4zZj76CVnzeNaaaBzEwbEfnygOTpgBadiw6uAKcWM6Y2HWLwoicHBR5Pdb0H5/97umMFUU/FwXPK7PJRmi8nNw7O1Fxwc/gdOqVdN2RRE4UYpHUuDUKWiQmhhcq4Oj7g06e1O4eCUZm69Dh5RWHo7G7CFwdNXmpBycMALHSSyEFTi1hqicEo2dRFPSAsfujji5KPhuc9BJ08HBOawdbRgHJ8yUaT+B4xeeinu5BrvAwf62J7Bq29Wcl6QdHBybV14RmTWrZZ5NWIFj9kfmTC11iWbO9P6cGTOq/Qj6FCQVR8FPlJhtJmgdnCSSjN0cHF06xSuXp4NHorFfiAqfHdbhp8CpUxA+QScN58ReMjyqwDHdmzAOTlpTxfF7VeB885vJCRxtvLWGqMyOLkjDrjVEFVTgBEkyNl0OU+AEqYXjFqLyKiIX1sHB79PPCypwVNTo9uGK1G9dKXOfxungBBU4cTs4GqJycnF0f+rvjCJwghT5s+8np9pcQRJTzYV/3Y6jujh+eThTplTvf/jD5uUf4hQ4KgCwrX75SUkmGdsFjpkMjv3tJZQ6dAjv4GCs0H0aNkyl52DQ8ykpKHAyCk/hisxvdo6fwLFXMQ6bZAzScHCQ+IcBAwIA9rbWWEnKwcGgaCY5ppWDk5aD45WDg23X58Pm4LiFqEwXRY+ZdvTYf345QU5CAee2KcDs6HdjMNTjZwqwIDOTVBRsu23w7VPxnTcHB/tD265d4Gjb3WqrdEJUXgRxcMy26SZwgiQa4xj97W/V/48dK5HxW6ohaP5NkmtROQkc9AfaTnDMvYRS+/bhBU6YkKMdPQfp4NQZb74ZftpqVAfHHMyclmpIS+Bo/s3w4dUOIAkHxz7l2wxThRE4+BxzwE4rRGWvnRI1RGVur9lhuq0yH9bB0WOmIZOwYaqgQgHboBcAKrDCJBiDiy4SueEGkSOOKKaDgxIFZv0qt4KQeny0GGjSIaq4BA5Espvrstde1eOPiyN7yFmZNq3aFnDRZC/umYSDE0TgJFXJ2O3cU4dEl/9x+5wOLg4O3qOPOf2+qAKHIao6Rau4+s3EMAUOThanq+Q4Q1RJChwzPAVU4KBRxoW94UYVOPaOKY1ZVHHm4JiVb007PW4Hx8xrSULg4OrR/v1hBQ5EGIo/hjkuKnDs4jsLB8cMj+Lz3ASO3cHJMik0jMDBOepV6BHCxcvF0fBU1OTiJAVOlMU2nRwc7E/053jOaYaY9t9mfxdG4Kw0zk8vgRNmfDCXDqHAqVMHJ4jA0ZMDnZVTh+EXovJLMja/I8kcHHVw7AInjIOD2hannOIeDrEPspqHYzo7QQSO/XP8BA7Ehla9TTpEFSQHxyn/JmqSsZeDg9lEKriSEDjm90cVOFFwcnBwDumFSZoOjplzhHPXz8FRgYNzOmgV7qg5OHEJHC+8potjhhUW+4QjfPjhUhN5cXCc9gd+34MPVkWe0/N6vN56q+mxMAJnxVfnEj7byU2L4uBgf2mf6Fc0MmkocHLs4OCE06tYpzBVHA5O0iEqXFlgUEMn/fWvhxc4EHfnnCMyfrzINddUS7iHcXDMx6M4OH5JxubgnodZVPYwUy11cLwcHBxDvxLwXgJnwAD/19bq4MQlcCCWcUWO/W+G5pJ2cMzfC6fDz8FBzpGeL2Hbc1YOjhdmorHdkVL35sADa9/moLOoksrB8cqd0dA+bk6owNHcTny/U25nBx8Hx+23RalmrOcSjm8trnYcUOBk5OAEnbrqlYfjJnC8koztA1/SAkfDU6h4qo0oqMBBp3bmmSK//GXTY24DtN1FiEvg+F0JO1UczjLJ2K1OTJQQlZeDAyGgnVdSDk7WAgeDBo6DbjParN8smjgdHLsbp/vDzcFBW/abFekWuopb4Hj1J0EFDkpKoJ3iOOgyLNqmb789nvCUXeA47Z8sHRw/7A6Om0jq4OPgOM2Ii+rg5GUGFaDASRE0njAOjp/AcVpoM0wl4zRycMwCf4rOokLH4TY4wuL8f/9P5PLLm2+3m1vg5+DYr2xULMQlcDDwBa2Wm0YOThoOjtfMDCewr4sicLCtEDT4jfvtFy48FdeCm/bf6+TgYDv1dRiMvC5YsJYV+opJk4rh4OB5LKBphqkWLxbZc8+qgEOYFIto1orZxpxmVSadg+OVZBxW4Ljt0w5ffba9v01C4ORlBhWgwImRZ5+tzty44w7n53GS6AAUtDaHm8DBIKc2uj0HJ0qIKqkcHHv+jTYmdVCcqjTDocAKwNdfX7XmkX+zyy7V59zWuHHLwXGzf+PKwYljBlUSs6jsAidIHRw3BwfbovvRKUQV1MHB4nv4HAjcMAJHO9c0BA5+02mnVcM9eo7ob9cQaxCCCMo4BI4pPrG/vAQORAKOn1b+VXA+6WfWOigFCWmEcSzM6eIo6ofEY4Sp8T2//31wR80Ls415rdUU5LyLu5Jx0g7OSh/xFiXJOC8zqAAFTow88YTIuee6CxwNT5mDQ9ArSrvAgW0LRwidsIqgWpKMk3BwnntO5MUXWzo4EC1eYao77xS59dZq54VObNw4/3wPPwcnqMCJ6uDUGmuOK8k4jhwcfa3TVO1aHJzbbqveH3lksIEpCwcHXHFFdcDAMYDwf+klkaefFjnvvPw5OCok8H0QwF4hKs3TgJNjDuSmGKk1KTROB8fMw7nnnurK4uincLGDi8m995ZYMNuYkzDJsg6OH9r364zUuENU3WrIwaHA+Yprr71W+vXrJ+3bt5fhw4fL0+hNPLjzzjtl4MCB1usHDRok9957r+SBbbZp6kCcCBue8nJwVDhgZV/7YGF3cDCI60DuJXDiXFEcncL3v1/9zIMOahlG85oqjs4LILFYa5j4CRztsLWDh4ODMFetAscvyTiOIn9p5uB4CTanVcjtLkpUBwfnlxZlO+YYCURWAse+lAna2K67hquUG4eDYz8eTgLHPph4XbCowMH5g6UW7J+Bz68lzGoXOG79SZgBfbfdqq/T/JgTT6zm9YXpQ/3Aea6/u1aBE9bBwW/ySzL2Qvs73dd5ysHpRoEj8sc//lFOP/10Oe+88+TZZ5+VwYMHy+jRo+VdlwzU2bNny+GHHy7jxo2T5557Tg466CDrNn/+fMmLwHntNedBKGyCsZfAeeGF6r1TgSvtXDE4m8XCvHJwEDOOa0VxNDaIE+wH/Nabb275Gi8HRxMKBw5seiyog4PQBwYmCBfsMz+BY3dDsgpRZZ2D47aQpSkysC/1NaaDE0TgwNXEOYYFGnfaSQKRxTTxuEjbwdF95RVyVoFjXiDFPSDpdqD9uYWTwwgcOCIQxNifcACvu672tha2mnGSOTh4nU6priVEpSQVovqooAKnRr1eO5dffrmMHz9ejv0qHf7666+Xf/zjH3LLLbfIhAkTWrz+qquukv3220/OOuss6++LLrpIHnjgAbnmmmus92YJ8mpwgqORwK2xT4VNwsFxGix0cMOghc5EhQsGSLVQ7SuKo6HhxPQqn98MjGrI+MNoCzWH+6/+f9d0kSV/Evlma5HrfibSbcFX79GqXg0Nsl3H3nKfbOEocF5/vXllVjBw9bMyXNbKxv9uJTK3dfWyCzcotq22ahxkMRhg8IUzBBenTCGqJAUOzhPtaM33mh2c5kvhfEGHGGaauIanfrL3HJE5Di9Ab2gecAcHJ0wuRKwgm99UByZYFdJhxci0cnDsg4nXpAHzJ+gFUtxJodgVOE9xjuKccVpMM2xIBqLm6qsNpxo7AHFD9Cf2G6rh+S3y5wDaGdpO2g6O2yzPtATOioAhKrR9jCdBlkjJ0yyqTAXO2rVrZe7cuTJx4sTGx1q1aiX77LOPPIGEFgfwOBwfEzg+d999t+v3rFmzxropK2tdIMYFjLdbby0CMwlhKjeBk7SDoxVC9arcLf/GtOEx5RwnZuBtQwejmb82DvnqJnCxfuT89oOH/ViulMtbCBxsszo45nh3wszvy89lkQg0rKljkfn5xBPNhAwSRCFwkIeTlsCJy8GB0MRnJpmD49RR6e/E4+bAY4oMMzyF1wV1cFBu/6mnqtt/xJW7iVzp8CLEInXur8N3m78tdYGDNQFQr8At0Qw1EHLm4NgFDsSrm8CJc0DS9YswIGLbnOoGaX8UxrFoFobHPndLwLnpJpHjjgu51d7CJMkcnCDLVmQpcLbcsrptaIPoT4PUgcrTLKpMBc77778vX375pfTUecNfgb8XLNDL/uYsW7bM8fV43I1JkybJBRdcIGmAhf1U4Oj00ihVjL0EDgYUzfNxcnDQyWCAQweJm9s6VAoGLOw+j13o3CPgDNb50a1by5etNpC33mkta79osL4Ls7sax1ENEn9139C92jLtAge/E9uM32DOtFnZua+sXFGRjTt/Kd26rK/22Lh9tYN0kMWgi+mjyONBg9SGHVbgoDNDx5ZWiMoUJOh0anVw3HJwNC/JPrjoYIrjZk6nNx0cU+CAoA6OujdWe5jvcvLbM+XzJHBwMrg1WpdRycx5wj73W1g3bgfHHqLCsTPP9aRCVMAUOF6Dult/5AtOPIy86Evst8AWdHCBE6bQX1gHJ8iyFV5oMT3th9xEY3uXCQF6Lrn9NrwPJiUE8dy5wQQOQ1QpA4fIdH3g4PQNOk87xkTjuEJUL79c7TTRmdmniCsqcPwcHICTFiewmwvvyI47Wr0ovuMf/xD5y19EkOu9+ovq74PAaPA4wV+/VUTuaylw1L2BC2OGfX73PzMFGvWEI0QmT275eaZTow41BI6uKB12mjj2LQRO0CTjWkNU0IkYyLA//QROkCRjez9vunr4DntH6CaM3BwcEMTBwXmq05Kt5OIxiyUoWUwTdwQJZbiFQAcM7G+cQ1G2OUiScVAHR9s2XodjiYsZiBC0lSQEjrltcc4askBZXyT4xUgQByfMNPGgOTi1JBgr6Kt01mjUHJwuLg4OwNR8jA/o01E5ukgCJ9Mk4+7du0vr1q1luW0qDf7uZZ928xV4PMzrQbt27aRz587NbkmhAge2vAkGAd3sKCEqdGo6GOvVF8JTbqrfvIL0Eziq9cIIHPyeo4+udpBYC+bPf652XLiwgtjxO7ndkoxV4NjDe0FnUWHQVVFTSw6OXgmn5eDYB7C4c3A0XcktL8RNPHg5OEGmic+cWT2vIFa++10JhSmuVJg5bWMewb7RsErUPBw3Bwf7W89bHUz8koy1baN/0ral/UhSAset9ETNAicB3AQOBHpaDk5UzDBV3CEqsPPOzWe3+kGB8xVt27aVYcOGyUPGamrr16+3/t5dS1jawOPm6wGSjN1enzZuDo52MBhkwhx4dPJqb2unpfFzr9koZmG3JAQOaoLgyhwNGXlHyAdHAa5//7tpFWAv3KaJO+XfmB2A28wMew4OqCUHRzsN/O1U3dT++rwLHL/EV7fcHS8HJ8g0cQ1PHXZYeJdLB0o4VjiHiyRwcOERJA8HCyniqthcDVqx/15zgNWByb5qs5lkbE7T1raNiyvtN7QfiTtnwq92SpEEjnmBE0bg4Jz1clrjdnBqFTidO8cjcHDO5SnJOPNp4ggd3XTTTXLrrbfKK6+8IieeeKKsWrWqcVbV0Ucf3SwJ+dRTT5UZM2bIZZddZuXpnH/++fLMM8/IySefLHkSOMi3MU8mM8E4TKwV4kZPFA1TmQ6OG2YtHLd1qKIKHJQpuvTS6v//+MeqW4Xy7xA2QX+b6eCYHbHTDKqwDg5ycOISOMArTBVXiCqIwAmTZOwkArxq4biFqJwcHA0B+jk4+Ey4eQBuX1hwzPQ44dw3Z8oVgSAzqbCA7F//WnVA/Y4lBK5epNgFjt3BweBqfq+2bbR1u8CJe0BKPESVosDRfYi2F6SNm7NUg7g4WTs4KwOEqFDaAf06HHG/PE3sLxV2Wa8knguBc9hhh8mll14q5557rgwZMkTmzZtnCRhNJH7zzTdlqS66JCIjRoyQadOmyY033mjVzPnzn/9szaDaETkhOQAnmx5YM0wcJcHYLQ8niINjdq5BHRwt9+0FGi20J6xbVKRFMb8oyXEqcDBYm+Xm3RycoHVwgjo4bmtRmYOoDq5eYaokQlTodOLOwcnCwZk+vXruweGLYrDivNLvN8V3UQROEAdHxYUuLeJ3LO15OPZwAI6JHhczTGUKHL0wSjpEVUSBYz+XzRlUQfo5s70GycPJUuBUKsEEDsYNrUmGCWxe6Dlnnod1LXAA3Jf//Oc/1lTup556yqpmrDzyyCMyderUZq8fM2aMLFy40Ho9CvwdgBreOQGNwClMFSXB2EngYJBBWAffg+z2MA5OkBCVXzXjCy+sJjlDf151lUQGHYE2KjMPJ6rAccrBQWNT8RTWwcHn6D4M4uDEIXB0QMwiRBXGwQmaZKyW9ve+F00EA7vAwRVyEoXeksA8nm6oCHC6MnZy4+wCx+7guCUaOzk4mO0JsUyB4+/gBBXV5qS6IA5O2iGqz422qjP8goTfNEyFmVRFyb/JjcApG04CJ0oVYyeBo1ddEABe0yzDJBnr1D90PF4VK3Fy/+pXTcW3arW07YnG+H416+xJxmFycNDB6uCrIa+wAgcdnu4vLwcnzRCVn8AxqxFHdXDCzKLyE526LbV0dnaBUxT3JmgVWBXghkkdSuA4DShOicamwEHbwrHDYIcLirhzcMokcMLUwAEQ8mESjePYF2aFhTAOzsqVTeE3v+8PmodDgVMHJOngeBX4i5pkjMFZ8yrc8nBgtyI0hSs+hKUOsSr5xStwVIygE7c3kDAODjoZzcPRMGHYaeLopJxWZXf73jSSjP1ycLBvnKoRh3Fw7O9zqmQc1MHxq78UhLILHH3OLnBwHJ1cNfMcwfHW88R0cOzVjHG+aAgMAgfnkUb0EXJQsVTPOThuSzWEFThhi/3F7eC47dMODv2nOYPKz2HViSMUOMRT4MTl4Pit5xMmRBUk0fiSS6rfjW1BYmQc2AWOGZ6yN7gwOThAw1TqnEVxcIIInCwcHLccHHM7nY61KXrDOjjYJs0pUDHsd0z8ktuDoN+vx7FMAgfnnu4ju8AxnUq3HBwdTLSGkluICp8NwYRzXmuk6gXSo4+23N56FDhxhajMz8prDk6lEnwGlaLFujGOOa1zpuRpBhWgwElB4Jhl0tNycMKEqIIIHJ0Nc/HFkZZ6CTRV3G0GVVgHxxQ4bqvsui226ZSDE0TgpD1N3ClXynRMnCrn1pJkbH6G7ss0HBwdLIvo4NgrMdsxc3MwaJgDoh4PHEdz8DPPETP/xrwgsFcz1n2HNqHnhV4gPfJI0yBX60riZRQ4URycKCGqtHJw1q9vuqjDCiQgSHVinHdbbeWfaEwHpw7QEwGCBAccCYQ4qXClpaGTKAIHQgBLQIVxcIIs1WCe5E4CB4OpirU99pDY0KtJJwfHjnaGYR0cpRYHxyvJOItZVEBDUSZe+TdRk4zx/ea+U1EaZJp4nA5OEQWO30Bvf9xMNDYFpylenBwcu/Nid3DM/BtF+w9MGDDfE3cdHLsQx3nrt6xAWRycMCGqtBwc/U4s9XjttU01zYIQJA8nT+tQAQqcBECnpAMshIHa63gsylWSCpw5c6qdA05WexJukg4O4vf4DAg0v++NK0Tl1kBxxePkXtgdHLuQjJKDk9ckY7c8HDcXJkgdHK+O3BxATYHjN008zhwc7TjLJHDszo6TwLH/XicHxz6Y2JOMnQSO3QGOM6Sgv9sMwSmmGC6CwEk6ByetEFXbtk1CGecOVh5BPzp2rMg++wT7niAzqejg1GGYqpYEY/tyDQAJgs1W160xydhP4OiyExA3UVa8DStwnESUk8WapIOTRYjKb5q4ecydBI6bC1NLkrE9TJWVg6OUSeDYHzfzcMIIHLuDY08ydhI46FPMdeziHJAwWGv7sv9GU/DkoU5KkiGqIDk4cSQZm9Xu3T6noaGpvZ5/fjUSgFQDLdgal4NDgVMnYFVxu8CJkmDstNCyX/5N3EnGGp7S35SEwEHi7OLF/g6O24DqloPj9P44k4yzWIvKLdG4lhBV3h2cMgocu4NjChy3Y+kUonJzcPR5dZDt6wub/UicAxIGU7ffbuacRFlhvWwhqjgcHOxHXFCjf/BKgejwVXudMqV6/5vfhHPuVOBgZqpbbScKnDp0cGqpYuwkcPzyb2oJUaGasT2/Qx2cJAUOhBXEBoSHU9IbOg21WJ0Ejv1KKGqIqgizqPwcnFoEThQHx03g0MHJxsEJEqKy9yNxD0h+AidP4amiJxmD+++vpjCY7dOO+R2ojYv14cIAMaRj2Lx5zq/hLKo6Ic4QlblsQFgHxwxReQ00cDwgIGCrar0Tu8DR3xQX2hjRCS5YUP1///7O4Tdsm5mHk0YOTtqVjHXwwu9zcob8QlRBc3DCJBnbB1BzBp3XzDZsn+6bOGZRFV3gOOWNeTk4QQSO29VykBAVoMDxX6ohzEritdTBqXV/4NjqVG43OnRoao+TJ0erLu4XpqKDUyeoGMDq2hp6iRqiwoloujhJhKgw4Pfq5RymSipEhU5QXYmnnnIPTwUZUO0ODoSOV/JdXDk4cYaozE5UB0Tzc3EeqK0fJQcnSB2cqA6OfQA3RWG9Ozg4Vk4iWQWOtsu4HRwMNjg2muPmFaKK+4q7bA5OnuvgBKX3VzlXWBg56ljkJXDQB3AWVZ3Qr1918MYJrFMxozo45pUzREiQOjTaINHBaSP1u5J2ysNBg3/jjWQcHAzW+ltmz67ee83SchM4yEdRoWKGisw8nKCLbWa5VANEl72jswsnr2J/UUNU6Ih1P0TJwXEaGHRb4DqZKyzXk8Axk22dauHo4L/ddsnk4CDUrH0PjpVdxOB71RWsdwcnzkrGUaaJp5FwfeONInfcIXLSSdE/w2smFc5ZvfCiwCk56Nh0sNaclqiqGaiDEyT/xt4x6mAYReCg+B62HwOLOjxxogNmLQ6OaSubHYUZpkpqqYY4Q1ROHambwKklBwevMx0XU/BEcXCcrH0zLBp1oU37dxdN4JiroTvl4ajoUYETZpo4hII6M3YHB8dFBYTmSqBt248Dzq3tt29ekyouiiZwipxkHJSBA6t5N7Ukd6vAQUqB3ZVUwW2vnZUlFDgJYjoeuHqqJRdBBU6Q8JSeZPYp3VEEjpl/U8tA5YYOmJqV7yVw3BbcNAfXoA5OHmdRmQMYwP62102KQ+BA3Jj7UN+HfedUp8nNwcE+dEv8jmMGlW6TuW+LJHD8Eo31MRUZKOSpF0NuA6spgDW3z2mJBb2Cfv555/CUgpk0EyeKfOtbEitmsb8iC5y06uDkRRD4gYtchLrQh+i5pZiOYhJjRRQocFISOLWEp8CYMdXBP0zmuznQBQkVmDOpkp5Bpdiz/qM4OPo3BlwzEVcFDq5Y7GIvTA5OkCTjOEJUdoFjzhwLInD8rjYxqOjVm+na+L1PXQhsixnmMBO/vRycWjFdnDIJHHVw9OIBxxTVz72OiRnG9Ero1ONkOjhOjBwp8n//V1sYsawODpxv3d6k6+DkbX9ECVPlbQYVoMBJSeDUEp4C//3f1foDu+4a/D3m4IIraT9V7eTgJJVg7CZwMIsqaojKfhWkAgeP23+731pUWYWo7ALHjteK4n4ODvaBU6Kx3+wrHazQcdkdHrdif3E5OGUWOPoY8tDUodU8HK9jaZ4j5ndEcXCSQrdJB70iChyzjZQhRBUXQ4dW770cnLxAgVMQBycKZqMMMtD4haiSwIz9w/r0auh+Do7dRdEcHCf718nBMaskB00yTjJE5fSZtSQZm1ei5oDrN/tq8OCqNY3aGXbScHDMAbyMDg4EnM5wUYHj5aoFETh6Fa2h36wETpEdHA1Pwd0K076DChxzXa6ihKi0P3ASOHmbQQUocAri4ETB7uD4oZ3g2283DaBpOjhe4SmvBTfdOglN3rRXNXYTOGaHZJ8m7lTHBI8lHaKyU0sOjnlOmoW6/EJUGKwQtrz11pbPuRX7o4PjPdDj3FGBg9dEFTjY/06Do32QocCJ7uCEPeeC5uCYbSZv+yOIwJk/v3k/RAenzoCDoCduERwcXKUjBAJxgxkd6Jy06N/WW2cvcNwK/bk5OPi8Rx4RmT49vMAxQ1TYH06dFRq3U72aWjBj/WEFjl+oCQwfXr1/+ulwwsht7TM3Vy2pHJw4Pi8vA72ee7U4OG6DCQVOfA5OmPwbt89ywmwzRXJwttyyOp5AoKHOm0KBU2cg52GvvaqD0rBh+XdwMIhpWAdhKg1PwQFJamCJInDcQlROnQT2v1NtHSeBY15R4XlznzklGpuvz1MOjtcVpwocnZZfy5Vq2g4OBkW/RWbzhttAr+4N+gbsIxU4OlU8qMBxCk85JXpmKXBM97OeBI5fkrHuCzg+RTqvW7Vqms1rOsEUOHXI3XdX7X0U/ksbU5QEFShmHo6Gp5LKv4lL4NiXaQiCl4Ojs5fQ6eh3OuXh2B2fIuTgqMDBasI6iAZxftxI08EpWnjK3HZ7oT8VPHge55rdwQmaZBzEwcEAHXaQrhX9fghxFQrmeZFXgWMK9ajCP6yDUyT3xisPh7Oo6hCo87iLaCUVorILnKSniKfh4PgJHCT6ae0Rp3war0Rj7QwhOuK6Aouag4Or5CBLciAMiXwwvP6ZZ4I7P3lwcIoocPwcHH1ei2hC4ODYeB2TsA5O2u6NChhdNNe8yi+Cg6OOU1QHJ2wOThEFzpAh7gKHDg7JZYjKzcFJUuCgcSMZGIOYFjyLWugvioNjujhOU769porHPUW8FoGDv1Wo+e2H3XZrHqaKI0Tl5uDEIXB0EC+TwDEdHGA6ONh3OshGFTjmIJOFwAFf/3r1/sknmx7TthvHeREnZpvR/iBpByfuGZhZOzgfcBYVKaKDk2SISgdaJKv5dSRxOjhmPRft0Jw6nCACJ64ZVLUIHLdqzkHycIKEttxIY5q4uhtB1mArmoPjJHB0YEXoysnpCBuiykrgOOV75d3BMdt10jk4US7M8sKgQdXzE+erTkShg0MK4+CgDLxmyCfp4AAIG3O19DRzcJwcHPNzvAROEldgfrOo3JKMw+QD2WdS5T3JeL/9qisg//rXUtoQlQocnNso0+C1jlcRQlR2B0cdqXoSOEEdnCIKnI02akopgIuD40uBQwojcHDSogFCCGQxxT2tHJygISqnWVRZhqjsScbaWeJ3+S2mh1LrEErvvFNNgI/DwUkyyRg5DRMmNNniRUIFCM4Vcx/ZQ1QY8HUg1QsLN8EZxMExhU9WAgfnGc5XXOXr8i95FThoM9q2tF2nVQeniALHHqbCcVXHiknGJPchKh30t9rKeQHGLIgzB0dnSfkJHK8k46RDVE7rA/mFqIKILfymHXdsCh/k3cEpMtinep6ZLo7dwTFdnDACx83BMStxZyVw0F532ql5Hk5eBY6T80IHJ7jAUfcGfVaeji0FTomJ4uAgz8EcWJPOv8nKwXGaKh42ByeJEFXUHJywYsvMj8j7NPEiAyGtLo0pcOwOjilwNLm/FgdHjzE+I0vny55oXCSBU2uScZlzcNwETp5WEgcUOCUmioMDq1and6aRfxOGOHNwnBbcDJuDk4SDg89SgRkmByfsPjAFTt6niRcdpzwce5KxmUytAsdNHAZxcMCMGdXJAkHy25IWOJpoXCSBk7SDk0T/kYXAeeWVpvpNecq/ARQ4JSaKg2O3tIsgcOJycPIwTdwcwMLk4ITdFhU4qIWjg20UgUMHJ1qxPxU7tYaovAYUnN/2hTnTRs+zuXOrjgYFTnkcnM03r57b6D//9a/qYxQ4pFACJ08hKr/FNqM6OEFCVF5LNcQtcLRDjTJNPOg+GDiwOoBiwNH6FVHECB2c+BwcFTh+ghOiBS4f3Na8T53HGnb4/Tg/5sxpqtVUBIHDJGNvEIrSHKuZM6v3FDhfsXjxYhk3bpz0799fOnToIFtuuaWcd955stYncDly5EhpaGhodjvhhBNS2+6yh6iK4OC4LbaZhIOTdpJxUAfHLQcnqNhCqGuXXZo/FlehPwxieozo4HgLHCcHx+944Lz9/e9FpkxpLpDyOgiqi6ODYN4FjgqPtOrgFLHQnz1MpSUn8jSDCmQ2P2bBggWyfv16ueGGG2SrrbaS+fPny/jx42XVqlVy6aWXer4Xr7vwwgsb/+6Yx9aSA6KsRQU0BwedZ5bx+7RycKLWwckyRFWrgwMw8JiDTlyF/kwBSgfHWeB4JRkHOR5jxkhhQB4O8oEefrjpHDbLNOQFbTtxJRmX3cExl2zQ/ihvDk5mAme//fazbsqAAQNk4cKFMnnyZF+BA0HTSzPySOwhKiydoCdvnjLiTYGDwlK6bVnl4CR1BeYlcPwK/YXZFr2y1kEnyu9wClFpOA/Hp4jr7CQtcJA/pe5AFAenaGii8ezZ1fu8Xo+awgTui57TzMFxxz5DL28CJ1c5OCtWrJBuAfbQ7bffLt27d5cdd9xRJk6cKKvtMQsba9askZUrVza71QMYDNFp4t5c1NKPkSNF/vQnkVtukVxhDpZm55FGDk6aIapvf7tq9X7zm+EL/YV1cMzBNIqYdXLVdF9hIPMrOliPAmfFiqbnzCRg+zVbWQSOrn2m7aUIAkfdm1pycBCqtV+IlE3g7LBD84WG8yZwclLCTeS1116Tq6++2te9OeKII2SLLbaQPn36yAsvvCBnn3225fxMnz7d9T2TJk2SCy64QOqRf/6z2rGGiY1ioMujBW52jNC09vyPuBwcpxBVWpWMwXHHiYwb5yw44srBARC/yLfCVOKouTJeDg7zb5wFjubf4Hw2a07hdTh+eizLInDwu5DLp2vbFUng4PwOG04z2yCcILdCqWUQOO3bV4/tyy/nU+DEfn01YcKEFknA9hvyb0zefvttK1w1ZswYK7/Gi+OPP15Gjx4tgwYNkiOPPFJuu+02ueuuu2TRokWu74HLA3dIb0vQo9cJsBDhyJQBdDR6tWA6BlE7Cu148haiAm5uSpw5OObVddTB1MvBYf6Ns8BxmiKux9x0ccoicMwwVZ7PC1PgRE0wNj9HP6usdXCcwlSld3DOOOMMGTt2rOdrkG+jvPPOO7L33nvLiBEj5MYbbwz9fcO/8tnhAGEmlhPt2rWzbqT4YEDFAGoOqGWbReWFX6G/sKc5ms9f/kIHJ0lUyKhz4zRF3HTVsNBt2fYfzrNbby2Og1OLwMFFCMQq8gS9BE4ZHBwVOH/4Q53MourRo4d1CwKcG4ibYcOGyZQpU6RVhID9vHnzrPve9gw9UjcCJ+scnDS1s1+hv7D74OCDRX71K5H994+2PXRw/LEv1eA0RVwxu7GyOjhFEDi1rM8GcYPQIz6nXgRO3Tg4QYG4QU0b5NMg7+a9995rfE5nSOE1o0aNssJQu+22mxWGmjZtmhxwwAGyySabWDk4P/7xj2XPPfeUnbTiECk1TsX+0srBQdKgqcGzqGMRd4gKi6mi6UWdLUcHJ3qIys3BKaPAGTSo2j7RVsvu4Ohn6WyssgucIV9NFUcfUnoHJygPPPCAFVbCbTNz8SOBtVex7tetW2clEOssqbZt28qDDz4oV155pVUvp2/fvnLooYfKOeeck8lvIPko9hf3WlRODg5A52y6ElmEqOJMMlZqKQVgJnrr1H06OM4CB+csBjy/EFUZBQ7OWxSWfOyx8js49s8qc6E/AD/i17/O50VNZgIHeTp+uTr9+vVrFDsAgmbWrFkpbB3JK/aQCEI1epWUxGri+EyNp2PgdhI4RXZwakX3uU6JxT6lg9McTAXXcwjujVuSMTCTjMu2/xCmgsDJ6+8yKxnH4eCAeghRgbPOklzCKhWk0ALH7ECSqGSMgckt0TiLK7A4C/3FgbmvdH/QwWkOwppa7wbiph4dHHDiiSKHHiryox9J6UNUQdajKpPAySu5qYNDSJQcHDMXJy6BYxcJuOLEoG0XOFmGqOIo9BcH5vfhWGBQVgeHAqcJuDUQNn4OjgocU1iXhf79Rf78Z8kt5lINcYWo6iEHJ8/QwSGFzsHRTgIDv1tBrTgEDnATOHkIUWXl4GAgti9SqPspr6GIrBONvRwcrL6Nx5GUm6dlUuqBuJOM9bPcoMBJHjo4pNAhqqgzqILm4HhVMy7DLKo4wL5HR67Hgg5OMIHj5ODAMUDN0qInnhYR+1pUSScZl6XQX56hwCGFFji1DOxBcnCCODhFLvQXB/ap4kwybom6NRqmMh+zk7daIvUscJiDU2wocEgpcnDicHDcwjx5SjKOu9BfEqKTScbRQ1QkX9PEaw1RMQcnW5iDQ0qRgxOHg+MXospzDg4dnOIIHK8kY1IfdXDQfrUNMxyZHBQ4pG5zcIIstpm3EJVfknEWV4N2gUMHpyUqZpYubTpWdHDqN8m4lvIWJDgUOKQUOThxhqjccnCYZBzsmNDBcRc4b7zRVBunbHVuik6cDo5fDo65tAkdnOSgwCGlcHBqDVGhyqzGy/McospboT9ABye4wHn99eo9Cv9FWFuYFKySsVsOTi3lLUhw2MRIoZOM43JwzCutIEnGEEQs9FeFDk5wgfPuu9V7hqfyh7Z7iBt1dZMKUTHBOB0ocEihk4zjcHDghnjFxJ0cHPPKLA8hqrw4OLpmF6CD04Q9oZgJxvlDz+P33mt6LKpID5qDQ4GTLBQ4pFAkVejP7Ig0fu4lcLJKEsx7Dg72CxbeBHRw3AUNHZz8Ya/IDYGuIeGkcnAocJKFAocUiqQK/WlHhI7JXiLfKcnYSxClnYNjhsuydnBMEUgHx13Q0MHJH/a2U0sSOENU+YAChxSKpAr9ec2IcnJw9PX4jDSTRZ1ycDRJOg8OjopAbEfUq996EDh0cPKHve1Hzb8Jk2RMgZMsFDikUCRV6M8rJu6UZJxVDN0pRJX1lFMnB4fuTcvjZjoCdHDqQ+D4OTicIp4sFDikUCSdgxPUwckqJOQkcLxmgKUtcDiDyh1T1NDByR8MUZUPChxSKJLKwYkaosqDwMkqXOZ0TOjguEOBUz8ODpOM8wEFDikUSeXgeIWcvJKM0+6gnJKMs55ySgcnvMBhiKo+HBzm4GQLBQ4pFCpkMKgj0baWjsJciypIiArfpcIi6xCVmWScdWdJBycYdHDyDS4ezMT4NHJwKHCShQKHFArTqUEnkWYODtABPE8hqiyniAM6OMGgg5N/zDaUpMDJ2nWtFyhwSKEwhQzETRo5OIin64B04onVzimPs6jo4OQb07Whg5NPzPZfS4iKOTj5gAKHFApYyCpMMKCmkYMDJk+uvv6OO0RGjxZZvjwb18QrB4cOTr5hiCr/mO2fdXCKD9cxJYVMNF6xIj4Hx1yLyk0kHHaYSPfuIgcfLDJrlsiTT3q/PimYg1NcGKKqnxCVKfqdyLrN1gt0cEihi/2lUclYGTVK5LHHRPr0yVeIKo8ODgVOS1TU4DhxYCt3iErPf3PmpQkL/aUDBQ4pHKZjEHclY78OZ/BgkSeeENluu+rf3bqJ1HsOjlMlY4ao3AUO3ZvyOzhBBQ6FbrIwREUKLXDSysEx2XxzkccfF7ntNpGDDpLcCJysrgad1qKig9OSbbapLuS67bZZbwlJy8Exi4OaUOCkAwUOKXSxv7QdHAVX4aeeKqmT90J/dHDc2XJLkRdfrIY4SbkdHD3/tV6XfeFZCpx0oMAhhSOrHJw8kPckYzo43uywQ9ZbQNIMUQG0CftnZd1m6wXm4JDCoQMqOg6dhpnkauJ5FTiVSr6SjLEfV66s/p8ODqnnEBU+R9eFcwpTFaW/KToUOKSwAufjj1s+llaIKmuBY7o4WV8Nmvv+gw+q93RwSBHR9o9cqVrOYbzfaQ07Jes2Wy9kKnD69esnDQ0NzW4XX3yx53s+//xzOemkk2STTTaRjTbaSA499FBZrlXXSF3l4Hz4YdNjtTg469c3hbryLnDMWH7W62I57fv336/e08EhRUTbEM5fdWCSmElFgVMnDs6FF14oS5cubbydcsopnq//8Y9/LH/729/kzjvvlFmzZsk777wjhxxySGrbS7JHHQMVOHA1TGcjKOZ71EbOu8DJo4NjVpdGXhSgg0OKiLahWvJvgsykKkrOX9HJPMm4U6dO0qtXr0CvXbFihdx8880ybdo0+da3vmU9NmXKFNluu+3kySeflK9//esJby3Jo8CJOrDroGx2Qnm/ojIFTl4cHN1vCPUpdHBIEdE2FIfAYYgqezJ3cBCSQrhp6NChcskll8gX5vxXG3PnzpV169bJPvvs0/jYwIEDZfPNN5cnUH3NhTVr1sjKlSub3UjxBc5HHzX/uxaB88knxbiichI4eegs7d9NB4cUEW3/tSQYKwxR1bmD87//+7+y8847S7du3WT27NkyceJEK0x1+eWXO75+2bJl0rZtW+lqW6muZ8+e1nNuTJo0SS644ILYt5+Uz8HJu8Ax8wLy5ODYRSYdHFLvDk6QEBUFTsEcnAkTJrRIHLbfFixYYL329NNPl5EjR8pOO+0kJ5xwglx22WVy9dVXW45LnEA4IbyltyVLlsT6+STbJOOoDg5mOmjSrl5l5b3DMbc5rw4OXKa2bbPbFkLy4OAwRFVCB+eMM86QsWPHer5mwIABjo8PHz7cClEtXrxYtnWoZ45cnbVr18rHH3/czMXBLCqvPJ527dpZN1IO4nJw1MVBsm5RHBwVENhme5JxXhwcujek6BdPXbokG6JiHZyCCpwePXpYtyjMmzdPWrVqJZtuuqnj88OGDZM2bdrIQw89ZE0PBwsXLpQ333xTdt9995q2mxS3Dk5UB0cFDgRCUXJwVOCgg7SHqPLi4DD/hhSV//5vkdmzRcaPTy5EhQKddHBKnoODpOCnnnpK9t57b2smFf7GFPAf/vCHsvFXy+2+/fbbMmrUKLnttttkt912ky5dusi4ceOs0Bbydjp37mxNK4e44Qyq+kEFDerXxOHg5MUFibrgZh46Szo4pAxsvbXI3/4Wz2e5hai0+jqgwCmpwEHI6I477pDzzz/fyrnp37+/JXAgXhTMmIJDs1qLa4jIFVdcYbk8cHDwvtGjR8t1112X0a8gWdrISq0OjkkROhx7Dk4ekozp4BASLESlFyRF6W+KTGYCB7OnULvGr9JxRRfc+Yr27dvLtddea91IfWIXNHE4OEqRHJy8FPoDdHAICRaiMgWOvf8hJauDQ0itAidOB6dIAocODiH5xc/BQZvBrEiSHBQ4pHBQ4OQvB8f8bjo4hLjn4OShvdYLFDik8Dk4tXQU9jWsitDp5NHBMUUmHRxC/ENURehrig4FDikc9e7g5L3QHx0cQoKFqEiyUOCQwsEk4+ZJxnRwCClOiCoPdavqBQocUjjq3cExQ1R5KRrGJGNCmsMQVfZQ4JDCkZSDg/+bi1kWQeCYRcPy4uAwREUIQ1R5oADdOSHNsXcMcTk4RXBv7Dk45rq0dHAIyWeIyiznRoGTHhQ4pHDAZTE7h7gcnKIIHDMHxywalpc6OHRwCGkS+min5oVIkZaFKToUOKSQmK5NXA5OUa6ozBCVdpxt22ZbNIxJxoQ0x2wHZpiKDk56UOCQQmIOqPXq4EDg5KWzpINDSMt2qn0KBU42UOCQwhf7q7ccHCcHJ+ttp4NDSLCZVBQ46UGBQwpJEg5OUTocM8k4L50lHRxCgs2kYh2c9KDAIYUkiRycrF2QKEnGdHAIKVaxv7xclNQDFDikkDAHhw4OIXmHIapsocAhdZ2DYy62WWSBk/W208EhJFiIigInPShwSCFhDk7zJOOst12PB6aq1yI4CamXEFXWFyX1gHH9SkhxYA5O80J/WW97374ihxxSvc+yHg8heYIhqmyhwCGFhDk4+XJwIGr+8pdst4GQvMEQVbYwREUKCR2cfCUZE0JawllU2UKBQwqdZIx8FDNRuB5ycPJY6I8Q0hKGqLKFAocUEnVtak1oLaKDk8dCf4SQlrDQX7ZQ4JBCosKm1k6iiAInj4X+CCEtYYgqW5hkTApJEg5OEUNUEDlF2nZC6gmGqLKFAocUOgennh0cCJz164u17YTUE5xFlS0UOKSQMAenKnDWrq3+n50lIfmDhf6yhTk4pJB06hTPukdFFDh5LPRHCGkJQ1TZQgeHFJJRo0TGj69Wz60Fc4p5UTqcPBb6I4S0hCGqbKHAIYXNwbnxxto/p8gOTp4W2ySEtISzqLKFISpS1xRd4NDBIaQ4ISrOfKwTgfPII49IQ0OD423OnDmu7xs5cmSL159wwgmpbjspD0UUOCz0R0ixBM5nn1VnPOoFCWCbLXGIasSIEbJ06dJmj/385z+Xhx56SHbZZRfP944fP14uvPDCxr876pxhQuqoDg4L/RGSb8xJEKtXNxc4bLMlFjht27aVXr16Nf69bt06ueeee+SUU06xXBkvIGjM9xJSTw4OF9skpBigjAWGs0qlGqbS8BT6HXViSR3k4Pz1r3+VDz74QI499ljf195+++3SvXt32XHHHWXixImyGtLYgzVr1sjKlSub3Qgpg8Chg0NIfoG40QADEo15QVKns6huvvlmGT16tGy22WaerzviiCNkiy22kD59+sgLL7wgZ599tixcuFCmT5/u+p5JkybJBRdckMBWk6JTxBAVc3AIKVaYCuIGN227vCApqIMzYcIE1+RhvS1YsKDZe9566y257777ZNy4cb6ff/zxx1tCaNCgQXLkkUfKbbfdJnfddZcsWrTI9T1weVasWNF4W7JkSSy/lRSfIjs4zMEhpFgzqXhBUnAH54wzzpCxY8d6vmbAgAHN/p4yZYpssskm8r3vfS/09w0fPty6f+2112TLLbd0fE27du2sGyFlEjh0cAgpVrE/5OIAtteCCpwePXpYt6BUKhVL4Bx99NHSxhxtAjJv3jzrvnfv3qHfS0hZBE5Rtp2QehY4rb6KmVDg1EmS8cMPPyxvvPGGHHfccS2ee/vtt2XgwIHy9NNPW38jDHXRRRfJ3LlzZfHixVZiMoTRnnvuKTvttFMGW0+KThFzcFjoj5DiTRVHiIrttc6SjJFcjJo4EDJ2MHUcCcQ6SwpTyx988EG58sorZdWqVdK3b1859NBD5Zxzzslgy0kZKKKDo4mK69YxB4eQIjk4OqOKAqdOBM60adNcn+vXr58VwlIgaGbNmpXSlpF6wFxssygiQbcZ1VEVdpiE5F/gdOpU/T/ba50IHEKypGdPkSFDkDtWnMJbKnB0fRvADpOQ/IeoOCkgXShwSF0DUfPss1IoVOCYKxS3bZvZ5hBCAjo4nBSQLhQ4pO7xWRkkd6jTpAIHnWXRfgMh9Sxw6ODUySwqQkhtDg6vBgnJLwxRZQcFDiEFw6xkDNhZEpJf6OBkBwUOIQWe+QXo4BBSDIHDOjjpQoFDSMEFDjtLQvILQ1TZQYFDSMGwT2eng0NIfmGIKjsocAgpGHRwCCkOFDjZQYFDSMFgDg4hxYEhquygwCGkYNDBIaQ4sNBfdlDgEFLwHBwKHELyC0NU2UGBQ0jBYIiKkOKFqNatE1m5svp/Cpx0oMAhpGAwREVI8Rwc8OGH1Xu22XSgwCGkYNDBIaQ4YCFcbbMffFC9p8BJBwocQgoGHRxCihmmooOTLhQ4hBQMFvojpJhhqkqlek+Bkw4UOIQUDDo4hBQ3DwewzaYDBQ4hBYM5OIQUM0SlUOCkAwUOIQWDDg4hxXZweFGSDhQ4hBSMVrZWy86SkHzDEFU2UOAQUnAXh50lIfmGIapsoMAhpIBQ4BBSHOjgZAMFDiEFFzgMURFSHIHT0CDSpk2WW1M/UOAQUkDo4BBSzBAV2itEDkkeChxCCl7sjw4OIcVxcHhBkh4UOIQUEDo4hBQHCpxsoMAhpIAwB4eQYoao2F7TgwKHkAJCB4eQ4kAHJxsocAgpIMzBIaQ4UOBkAwUOIQWEDg4hxZ1FRQoucH75y1/KiBEjpGPHjtK1a1fH17z55pvy7W9/23rNpptuKmeddZZ88cUXnp/74YcfypFHHimdO3e2PnfcuHHy6aefJvQrCMknzMEhpDjQwSmZwFm7dq2MGTNGTjzxRMfnv/zyS0vc4HWzZ8+WW2+9VaZOnSrnnnuu5+dC3Lz00kvywAMPyN///nd59NFH5fjjj0/oVxCST+jgEFIcKHCywbYucXxccMEF1j1EixP333+/vPzyy/Lggw9Kz549ZciQIXLRRRfJ2WefLeeff760bdu2xXteeeUVmTFjhsyZM0d22WUX67Grr75aDjjgALn00kulT58+Sf0cQnIFBQ4hxYEhqjrLwXniiSdk0KBBlrhRRo8eLStXrrQcGrf3ICyl4gbss88+0qpVK3nqqadcv2vNmjXW55o3QooMk4wJKQ50cOpM4CxbtqyZuAH6N55zew9ydUw22GAD6datm+t7wKRJk6RLly6Nt759+8byGwjJg4PjYHYSQnIEBU4BBM6ECROkoaHB87ZgwQLJGxMnTpQVK1Y03pYsWZL1JhESi8CBe8N1bQjJNx07Nv2fjmtOc3DOOOMMGTt2rOdrBgwYEOizevXqJU8//XSzx5YvX974nNt73n333WaPYdYVZla5vQe0a9fOuhFSNoHDq0FCihFS7tBB5LPP2GZzK3B69Ohh3eJg9913t6aSQ7Bo2AkzozD9e/vtt3d9z8cffyxz586VYcOGWY89/PDDsn79ehk+fHgs20VIkXJwqNsJKU6YigKnJDk4qHEzb9486x5TwvF/3LRmzb777msJmaOOOkqef/55ue++++Scc86Rk046qdFtgcMzcOBAefvtt62/t9tuO9lvv/1k/Pjx1nOPP/64nHzyyfKDH/yAM6hIXUEHh5Bi5uGwzZZgmjjq2aC2jTJ06FDrfubMmTJy5Ehp3bq1VccGdXLgzGy44YZyzDHHyIUXXtj4ntWrV8vChQtl3bp1jY/dfvvtlqgZNWqUNXvq0EMPld/85jdJ/QxCcp+DQwgpzlRxCpwSCBzUv3GrgaNsscUWcu+997o+DyFUqVSaPYYZU9OmTYttOwkpInRwCCkWdHDSh2tREVJA6OAQUiwocNKHAoeQAicZs7MkpBj071+9Zxm29KDAIaSAMERFSLG4/HKRRx4R2X//rLekfkgsB4cQkhwMURFSLLp0Edlrr6y3or6gg0NIAaGDQwgh3lDgEFJAWOiPEEK8ocAhpIDQwSGEEG8ocAgpIMzBIYQQbyhwCCkgFDiEEOINBQ4hBeSAA0QGDBD5zney3hJCCMknnCZOSAEZNUpk0aKst4IQQvILHRxCCCGElA4KHEIIIYSUDgocQgghhJQOChxCCCGElA4KHEIIIYSUDgocQgghhJQOChxCCCGElA4KHEIIIYSUDgocQgghhJQOChxCCCGElA4KHEIIIYSUDgocQgghhJQOChxCCCGElA4KHEIIIYSUjg2kDqlUKtb9ypUrs94UQgghhAREx20dx72oS4HzySefWPd9+/bNelMIIYQQEmEc79Kli+drGipBZFDJWL9+vbzzzjvSqVMnaWhoiF1dQjgtWbJEOnfuHOtnk+ZwX6cH93V6cF+nB/d18fY1JAvETZ8+faRVK+8sm7p0cLBTNttss0S/AweQDSYduK/Tg/s6Pbiv04P7ulj72s+5UZhkTAghhJDSQYFDCCGEkNJBgRMz7dq1k/POO8+6J8nCfZ0e3NfpwX2dHtzX5d7XdZlkTAghhJByQweHEEIIIaWDAocQQgghpYMChxBCCCGlgwKHEEIIIaWDAiciv/zlL2XEiBHSsWNH6dq1q+Nr3nzzTfn2t79tvWbTTTeVs846S7744otmr3nkkUdk5513tjLLt9pqK5k6dWpKv6DYvPrqq3LggQdK9+7draJRe+yxh8ycOTP0/ifB+Mc//iHDhw+XDh06yMYbbywHHXRQs+e5r+NlzZo1MmTIEKvS+rx585o998ILL8g3v/lNad++vVUZ9te//nVm21lUFi9eLOPGjZP+/ftb5/SWW25pzfBZu3Zts9dxX8fHtddeK/369bP2JfqSp59+WpKGAiciaAhjxoyRE0880fH5L7/80urw8brZs2fLrbfeaomXc889t/E1b7zxhvWavffe2+rETjvtNDnuuOPkvvvuS/GXFJPvfOc71gD68MMPy9y5c2Xw4MHWY8uWLQu8/0kw/vKXv8hRRx0lxx57rDz//PPy+OOPyxFHHNH4PPd1/PzkJz+xStE7lbvfd999ZYsttrDO+0suuUTOP/98ufHGGzPZzqKyYMECa8meG264QV566SW54oor5Prrr5ef/vSnja/hvo6PP/7xj3L66adbIvLZZ5+1+uvRo0fLu+++K4mCaeIkOlOmTKl06dKlxeP33ntvpVWrVpVly5Y1PjZ58uRK586dK2vWrLH+/slPflLZYYcdmr3vsMMOq4wePTqFLS8u7733HkobVB599NHGx1auXGk99sADDwTe/8SfdevWVb72ta9Vfvvb37q+hvs6XrA/Bw4cWHnppZesc/q5555rfO66666rbLzxxs3269lnn13ZdtttM9ra8vDrX/+60r9//8a/ua/jY7fddqucdNJJjX9/+eWXlT59+lQmTZpUSRI6OAnxxBNPyKBBg6Rnz56Nj0Gx4qoAVwz6mn322afZ+/AaPE7c2WSTTWTbbbeV2267TVatWmU5ObgSQ2hk2LBhgfc/8QdXW2+//ba1ftvQoUOld+/esv/++8v8+fMbX8N9HR/Lly+X8ePHy+9+9zsr3GcH+3rPPfeUtm3bNtvXCxculI8++ijlrS0XK1askG7dujX+zX0dD3B24YCZYx36E/yd9FhHgZMQCJWYHT7QvzWM4vYaDAyfffZZiltbLJCX8OCDD8pzzz1nrQiPmO7ll18uM2bMsPJDgu5/4s/rr79u3cOaP+ecc+Tvf/+7tY9HjhwpH374ofUc93U8oObq2LFj5YQTTpBddtnF8TXc18nw2muvydVXXy0/+tGPGh/jvo6H999/3wpjO+3LpPcjBY7BhAkTrMHT64bYLcl2/2MgOOmkkyzH5rHHHrOS1ZD0+t3vfleWLl2a9c8o1b5GngL42c9+JoceeqjlkE2ZMsV6/s4778z6Z5RqX2OA/eSTT2TixIlZb3Jd9eFwKPfbbz8rpxLuGSkPG2S9AXnijDPOsK6gvBgwYECgz+rVq1eLLHHYz/qc3utj5mswKwiZ/fVG0P2PxGI4CbCJsa/AddddJw888ICV4IpOLsj+r2eC7msVjNtvv33j45jxh+cwcwpwX8d3XsOyt6/VAzfnyCOPtM5ttz4DcF+H78Pfeecda5IHZsTak4e5r+MBM11bt27tuC+T3o8UOAY9evSwbnGw++67W1PJkSUOpwFgAMaArIMFXnPvvfc2ex9eg8frkaD7f/Xq1Y1xXBP8rY5DkP1fzwTd13BsMOAi7wBT8cG6deusabaYXQK4r+PZ17/5zW/kF7/4RbPBFzkfmIGCabW6r+Gm4Ri0adOmcV8jJ03Ds/VMmD4czg3EjbqS9v6E+zoekMOEffzQQw81lpdAP42/Tz75ZEmURFOYS8x//vMfa3bDBRdcUNloo42s/+P2ySefWM9/8cUXlR133LGy7777VubNm1eZMWNGpUePHpWJEyc2fsbrr79e6dixY+Wss86qvPLKK5Vrr7220rp1a+u1xHsW1SabbFI55JBDrH27cOHCyplnnllp06aN9XfQ/U+Cceqpp1ozqe67777KggULKuPGjatsuummlQ8//NB6nvs6Gd54440Ws6g+/vjjSs+ePStHHXVUZf78+ZU77rjD6kNuuOGGTLe1aLz11luVrbbaqjJq1Cjr/0uXLm28KdzX8YF9165du8rUqVMrL7/8cuX444+vdO3atdnMyySgwInIMcccY3U+9tvMmTMbX7N48eLK/vvvX+nQoUOle/fulTPOOMOadmuC1w8ZMqTStm3byoABA6xp58SfOXPmWANqt27dKp06dap8/etft6bXmgTZ/8SftWvXWvsOogb7ep999rE6fBPu63QEDnj++ecre+yxhzVgQHhefPHFmW1jUUE/69R/26/5ua/j4+qrr65svvnm1liHaeNPPvlkJWka8E+yHhEhhBBCSLpwFhUhhBBCSgcFDiGEEEJKBwUOIYQQQkoHBQ4hhBBCSgcFDiGEEEJKBwUOIYQQQkoHBQ4hhBBCSgcFDiGEEEJKBwUOIaRwYEFFXdeGEEKc4GKbhJBc0dDQ4Pn8eeedJ1dddRVq6qe2TYSQ4kGBQwjJFUuXLm38P1bSPvfcc63VzJWNNtrIuhFCiBcMURFCckWvXr0ab126dLEcHfMxiBt7iGrkyJFyyimnyGmnnSYbb7yx9OzZU2666SZZtWqVHHvssdKpUyfZaqut5J///Gez75o/f77sv//+1mfiPUcddZS8//77GfxqQkjcUOAQQkrBrbfeKt27d5enn37aEjsnnniijBkzRkaMGCHPPvus7LvvvpaAWb16tfX6jz/+WL71rW/J0KFD5ZlnnpEZM2bI8uXL5fvf/37WP4UQEgMUOISQUjB48GA555xzZOutt5aJEydK+/btLcEzfvx46zGEuj744AN54YUXrNdfc801lrj5v//7Pxk4cKD1/1tuuUVmzpwpr776atY/hxBSI8zBIYSUgp122qnx/61bt5ZNNtlEBg0a1PgYQlDg3Xffte6ff/55S8w45fMsWrRIttlmm1S2mxCSDBQ4hJBS0KZNm2Z/I3fHfExnZ61fv966//TTT+W73/2u/OpXv2rxWb179058ewkhyUKBQwipS3beeWf5y1/+Iv369ZMNNmBXSEjZYA4OIaQuOemkk+TDDz+Uww8/XObMmWOFpe677z5r1tWXX36Z9eYRQmqEAocQUpf06dNHHn/8cUvMYIYV8nUwzbxr167SqhW7RkKKTkOF5UAJIYQQUjJ4mUIIIYSQ0kGBQwghhJDSQYFDCCGEkNJBgUMIIYSQ0kGBQwghhJDSQYFDCCGEkNJBgUMIIYSQ0kGBQwghhJDSQYFDCCGEkNJBgUMIIYSQ0kGBQwghhBApG/8fU04lG35bLbYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M=100 # taille des simulations des prédictions\n",
    "N = 100 # nombre de prochaines dates à prédire\n",
    "\n",
    "plt.plot(range(-N, 0), X[-N:], 'b-')\n",
    "plt.plot(range(-N, 0), sigma_hats[-N:], 'r-')\n",
    "plt.xlabel('Time')\n",
    "plt.legend(['X', 'sigma'])\n",
    "\n",
    "\n",
    "max_X = [-np.inf]\n",
    "min_X = [np.inf]\n",
    "for i in range(M):\n",
    "    X_forecast, sigma_forecast = simulate_GARCH(N, a0_estimate, a1_estimate, b1_estimate, initial_sigma)\n",
    "    if max(X_forecast) > max(max_X):\n",
    "        max_X = X_forecast\n",
    "    elif min(X_forecast) < min(max_X):\n",
    "        min_X = X_forecast\n",
    "    plt.plot(range(0, N), X_forecast, 'b--', alpha=0.05)\n",
    "    plt.plot(range(0, N), sigma_forecast, 'r--', alpha=0.05)\n",
    "\n",
    "# Draw the most extreme X values specially\n",
    "plt.plot(range(0, N), max_X, 'g--', alpha=1.0)\n",
    "plt.plot(range(0, N), min_X, 'g--', alpha=1.0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GMM pour estimer les paramètres du modèle GARCH(1, 1) \n",
    "\n",
    "Réference méthode GMM https://swopec.hhs.se/hastef/papers/hastef0434.pdf\n",
    "\n",
    "Pour cela, on a besoin de \n",
    "\n",
    "1. Le résidu $\\hat\\epsilon_t = x_t / \\hat\\sigma_t$\n",
    "2. La variance du résidu $\\hat\\epsilon_t^2$\n",
    "3. Le skew  $\\mu_3/\\hat\\sigma_t^3 = (\\hat\\epsilon_t - E[\\hat\\epsilon_t])^3 / \\hat\\sigma_t^3$\n",
    "4. Le kurtosis  $\\mu_4/\\hat\\sigma_t^4 = (\\hat\\epsilon_t - E[\\hat\\epsilon_t])^4 / \\hat\\sigma_t^4$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The n-th standardized moment\n",
    "# skewness is 3, kurtosis is 4\n",
    "def standardized_moment(x, mu, sigma, n):\n",
    "    return ((x - mu) ** n) / (sigma ** n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MMG se fait en trois étapes:\n",
    "\n",
    "Commencer par $W$ comme une matrice identité.\n",
    "\n",
    "1. Estimer $\\hat\\theta_1$ en minimisant numériquement\n",
    "\n",
    "$$\\min_{\\theta \\in \\Theta} \\left(\\frac{1}{T} \\sum_{t=1}^T g(x_t, \\hat\\theta)\\right)' W \\left(\\frac{1}{T}\\sum_{t=1}^T g(x_t, \\hat\\theta)\\right)$$\n",
    "\n",
    "2. Recalculer $W$ en se basant sur les  covariances du $\\theta$ estimé. \n",
    "$$\\hat W_{i+1} = \\left(\\frac{1}{T}\\sum_{t=1}^T g(x_t, \\hat\\theta_i)g(x_t, \\hat\\theta_i)'\\right)^{-1}$$\n",
    "\n",
    "3. Répéter jusqu'à ce que  $|\\hat\\theta_{i+1} - \\hat\\theta_i| < \\epsilon$ ou on atteint un seuil fixé.\n",
    "\n",
    "Initialiser $W$ et $T$ et définir la fonction objectif qu'on doit minimiser."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gmm_objective(X, W, theta):\n",
    "    # Compute the residuals for X and theta\n",
    "    initial_sigma = np.sqrt(np.mean(X ** 2))\n",
    "    sigma = np.sqrt(compute_squared_sigmas(X, initial_sigma, theta))\n",
    "    e = X / sigma # résidus\n",
    "    \n",
    "    # Compute the mean moments errors\n",
    "    m1 = np.mean(e)\n",
    "    m2 = np.mean(e**2) - 1\n",
    "    m3 = np.mean(standardized_moment(e, np.mean(e), np.std(e), 3))\n",
    "    m4 = np.mean(standardized_moment(e, np.mean(e), np.std(e), 4) - 3)\n",
    "    \n",
    "    G = np.matrix([m1, m2, m3, m4]).T\n",
    "    \n",
    "    return (G.T * W * G).item()\n",
    "\n",
    "def gmm_variance(X, theta):\n",
    "    # Compute the residuals for X and theta    \n",
    "    initial_sigma = np.sqrt(np.mean(X ** 2))\n",
    "    sigma = np.sqrt(compute_squared_sigmas(X, initial_sigma, theta))\n",
    "    e = X / sigma\n",
    "\n",
    "    # Compute the squared moments errors\n",
    "    m1 = np.mean(e)\n",
    "    m2 = np.mean(e**2) - 1\n",
    "    m3 = np.mean(standardized_moment(e, np.mean(e), np.std(e), 3))\n",
    "    m4 = np.mean(standardized_moment(e, np.mean(e), np.std(e), 4) - 3)\n",
    "    \n",
    "    # Compute the covariance matrix g * g'\n",
    "    T = len(X)\n",
    "    s = np.ndarray((4, 1))\n",
    "    for t in range(T):\n",
    "        G = np.matrix([m1, m2, m3, m4]).T\n",
    "        s = s + G * G.T\n",
    "    \n",
    "    return s / T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_5048\\155234857.py:4: RuntimeWarning: invalid value encountered in sqrt\n",
      "  sigma = np.sqrt(compute_squared_sigmas(X, initial_sigma, theta))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0 theta : [ 1.23970197e-04 -2.03606125e-04  5.35710135e-06]\n",
      "Iteration 1 theta : [ 1.23970197e-04 -2.03606125e-04  5.35710135e-06]\n",
      "Iteration 2 theta : [ 1.23970197e-04 -2.03606125e-04  5.35710135e-06]\n",
      "Iteration 3 theta : [ 1.23970197e-04 -2.03606125e-04  5.35710135e-06]\n",
      "Iteration 4 theta : [ 1.23970197e-04 -2.03606125e-04  5.35710135e-06]\n",
      "Iteration 5 theta : [ 1.23970197e-04 -2.03606125e-04  5.35710135e-06]\n",
      "Iteration 6 theta : [ 1.23970197e-04 -2.03606125e-04  5.35710135e-06]\n",
      "Iteration 7 theta : [ 1.23970197e-04 -2.03606125e-04  5.35710135e-06]\n",
      "Iteration 8 theta : [ 1.23970197e-04 -2.03606125e-04  5.35710135e-06]\n",
      "Iteration 9 theta : [ 1.23970197e-04 -2.03606125e-04  5.35710135e-06]\n",
      "Tails table\n",
      "[[0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
      " [1.58655254e-01 2.27501319e-02 1.34989803e-03 3.16712418e-05]]\n",
      "\n",
      "Jarque-Bera probability normal: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_5048\\3012303717.py:3: RuntimeWarning: invalid value encountered in sqrt\n",
      "  sigma = np.sqrt(compute_squared_sigmas(X, initial_sigma, theta_estimate))\n"
     ]
    }
   ],
   "source": [
    "# Initialize GMM parameters\n",
    "W = np.identity(4) # matrice identité 4x4\n",
    "\n",
    "gmm_iterations = 10 # on pourrait changer cela par un while  |theta_{i+1} -theta_i| <epsilon\n",
    "\n",
    "# First guess\n",
    "theta_gmm_estimate = theta_mle\n",
    "\n",
    "# Perform iterated GMM\n",
    "for i in range(gmm_iterations):\n",
    "    # Estimate new theta\n",
    "    objective = partial(gmm_objective, X, W)\n",
    "    result = scipy.optimize.minimize(objective, theta_gmm_estimate, constraints=cons)\n",
    "    theta_gmm_estimate = result.x\n",
    "    print('Iteration '+str(i)+ ' theta : ' + str(theta_gmm_estimate))\n",
    "    \n",
    "check_theta_estimate(X, theta_gmm_estimate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion : \n",
    "on ne peut pas rejeter $H_0$ donc on accepte les résidus sont gaussiens et que le modèle est un GARCH(1,1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prédiction avec GMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a0_estimate = theta_gmm_estimate[0]\n",
    "a1_estimate = theta_gmm_estimate[1]\n",
    "b1_estimate = theta_gmm_estimate[2]\n",
    "\n",
    "X_forecast, sigma_forecast = ??\n",
    "\n",
    "\n",
    "plt.plot(range(-100, 0), X[-100:], 'b-')\n",
    "plt.plot(range(-100, 0), sigma_hats[-100:], 'r-')\n",
    "plt.plot(range(0, 100), X_forecast, 'b--')\n",
    "plt.plot(range(0, 100), sigma_forecast, 'r--')\n",
    "plt.xlabel('Time')\n",
    "plt.legend(['X', 'sigma']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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