Bootstrap.ipynb

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   "source": [
    "# Advanced Time Series Econometrics\n",
    "## Lorenzo Mezzini - 926012"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import scipy.stats as stats\n",
    "from scipy.optimize import minimize\n",
    "import matplotlib.pyplot as plt\n",
    "import random"
   ]
  },
  {
   "source": [
    "## 1) Generation of the data sample"
   ],
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   "metadata": {}
  },
  {
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   "execution_count": 2,
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# global variables\n",
    "delta_0, rho_0, sq_0, T, x_0, B = [1, 0.7, 1, 200, 1, 399]\n",
    "\n",
    "# Generation of Data sample\n",
    "x = [x_0]\n",
    "e_t = stats.norm.rvs(loc=0, scale = sq_0, size = T, random_state = 123)\n",
    "\n",
    "for i in range(T):\n",
    "    x.append(delta_0 + rho_0 * x[-1] + e_t[i])\n",
    "\n",
    "# Plot\n",
    "fig = plt.figure(figsize = (10,5))\n",
    "plt.plot(np.linspace(0,T,T), x[1:], color = 'b',linewidth = 1, label = '$x_t$')\n",
    "plt.plot(np.linspace(0,T,T), x[:-1], color = 'g',linewidth = .5, label = '$x_{t-1}$' )\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Now I compute the MLE estimators for both the restricted and unrestricted model"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "MLE unrestricted estimaor : \n\n\tDelta : \t0.952\n\tRho : \t\t0.715\n\tSigma2 : \t1.113\n\nMLE restricted estimator : \n\n\tDelta : \t1.004\n\tRho : \t\t0.7\n\tSigma2 : \t1.113\n\nLikehood ratio: \t0.0985\np-value: \t\t0.9215\n"
     ]
    }
   ],
   "source": [
    "# this calculate the  - Log likehood, since with scipy.optimise I can only minimize.\n",
    "def log_likehood(theta, xt, xt2):\n",
    "    errors = [theta[0] + theta[1]*i for i in xt2]\n",
    "    return 0.5 * ((len(xt)-1)* np.log(theta[2]) + sum([(i-j)**2 for i , j in zip(xt, errors)])/theta[2])\n",
    "\n",
    "theta0 = [0.5,0.5,0.5] # a random guess\n",
    "bounds_un = ((None,None),(None,None), (1.e-10, None)) # Boundaries of research for the unresticted model\n",
    "bounds_re = ((None,None),(0.7,0.7), (1.e-10, None)) # Resticted model boundaries\n",
    "\n",
    "llik_un = minimize(log_likehood, theta0, args = (x[1:],x[:-1]), bounds=bounds_un) #calc log likehood unresticted\n",
    "llik_re = minimize(log_likehood, theta0, args = (x[1:],x[:-1]), bounds=bounds_re) #calc log likehood resticted\n",
    "\n",
    "# LR is inverted since the signs of the log likehoods is inverted\n",
    "LR = 2*(llik_re.fun - llik_un.fun)\n",
    "\n",
    "print(\"MLE unrestricted estimaor : \\n\\n\" + \n",
    "    \"\\tDelta : \\t\" + str(np.round(llik_un.x[0], decimals = 3)) + \"\\n\"+\n",
    "    \"\\tRho : \\t\\t\" + str(np.round(llik_un.x[1], decimals = 3)) + \"\\n\"+\n",
    "    \"\\tSigma2 : \\t\" + str(np.round(llik_un.x[2], decimals = 3)) + \"\\n\\n\" + \n",
    "    \"MLE restricted estimator : \\n\\n\" + \n",
    "    \"\\tDelta : \\t\" + str(np.round(llik_re.x[0], decimals = 3)) + \"\\n\"+\n",
    "    \"\\tRho : \\t\\t\" + str(np.round(llik_re.x[1], decimals = 3)) + \"\\n\"+\n",
    "    \"\\tSigma2 : \\t\" + str(np.round(llik_re.x[2], decimals = 3)) + \"\\n\\n\" + \n",
    "    \"Likehood ratio: \\t\" + str(np.round(LR,decimals=4)) + \"\\n\" +\n",
    "    \"p-value: \\t\\t\" + str(np.round(1 - stats.chi.cdf(LR,1), decimals=4)))"
   ]
  },
  {
   "source": [
    "### Now I save both the errors and the centered errors"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "e_hat = [i - llik_un.x[1] * j - llik_un.x[0]  for i, j in zip(x[1:], x[:-1])] \n",
    "e_tilde = [i - llik_re.x[0] * j - llik_re.x[0] for i, j in zip(x[1:], x[:-1])]\n",
    "\n",
    "m1 = sum(e_hat)/len(e_hat)\n",
    "m2 = sum(e_tilde)/len(e_tilde)\n",
    "e_hat_c = [i - m1 for i in e_hat] \n",
    "e_tilde_c = [i - m2 for i in e_tilde]"
   ]
  },
  {
   "source": [
    "## 2-3-4) Bootstrap implementation"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "LikehoodRatio_bootstrap = []\n",
    "for i in range(B):\n",
    "\n",
    "    # Creation of the Fixed regression bootstrap\n",
    "    x_bs = [llik_un.x[0] + llik_un.x[1] * i + j for i, j in zip(x[:-1], random.choices(e_hat_c, k = len(e_hat_c)))]\n",
    "\n",
    "    llik_bs_un = minimize(log_likehood, theta0, args = (x_bs, x[:-1]), bounds=bounds_un)\n",
    "    llik_bs_re = minimize(log_likehood, theta0, args = (x_bs, x[:-1]), bounds=bounds_re)\n",
    "\n",
    "    LikehoodRatio_bootstrap.append(2*(llik_bs_re.fun - llik_bs_un.fun))\n",
    "\n",
    "# Plot\n",
    "x_axys = np.linspace(-0.5,10,200)\n",
    "y_cdf = stats.chi2.cdf(x_axys,1) \n",
    "fig = plt.figure(figsize = (10,5))\n",
    "plt.hist(LikehoodRatio_bootstrap, density=True, cumulative = True, bins = 200, color='g',histtype='step', label = 'empirical CDF')\n",
    "plt.plot(x_axys, y_cdf, linewidth = .7, color = 'r', label = '$\\chi^2_1$ CDF')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "source": [
    "We can see that the LR converges to a $\\chi^2_1$, this strenghen the initial result obtained and we can accept the null hypotesis of $H_0 : \\rho = 0.7$\n",
    "\n",
    "\n",
    "\n",
    "## 5) Comparison with $\\rho_0 = 1$\n",
    "\n",
    "With the wrong $H_0$ the test statistic shouldn't converge to the $\\chi^2_1$ anymore. It could be proved algebraically, but we can see it empirically by computing the exercise above again with the new restiction.\n",
    "\n",
    "In additoin the sequence with $\\rho_0 = 1$ is not stationary."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "LikehoodRatio_bootstrap_1 = []\n",
    "bounds_re_1 = ((None,None),(1,1), (1.e-10, None)) # New bounds for rho_0 = 1\n",
    "for i in range(B):\n",
    "\n",
    "    # Creation of the Fixed regression bootstrap\n",
    "    x_bs = [llik_un.x[0] + llik_un.x[1] * i + j for i, j in zip(x[:-1], random.choices(e_hat_c, k = len(e_hat_c)))]\n",
    "\n",
    "    llik_bs_un = minimize(log_likehood, theta0, args = (x_bs, x[:-1]), bounds=bounds_un)\n",
    "    llik_bs_re = minimize(log_likehood, theta0, args = (x_bs, x[:-1]), bounds=bounds_re_1) # new boundaries \n",
    "\n",
    "    LikehoodRatio_bootstrap_1.append(2*(llik_bs_re.fun - llik_bs_un.fun))\n",
    "\n",
    "# Plot\n",
    "fig = plt.figure(figsize = (10,5))\n",
    "plt.hist(LikehoodRatio_bootstrap_1, density=True, cumulative = True, bins = 200, color='g',histtype='step', label = 'empirical CDF')\n",
    "plt.plot(x_axys, y_cdf, linewidth = .7, color = 'r', label = '$\\chi^2_1$ CDF')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}