SerieSimulada.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "superior-better",
   "metadata": {},
   "source": [
    "# Espectro de una serie simulada con un modelo AR(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "normal-vision",
   "metadata": {},
   "outputs": [],
   "source": [
    "figure(1); close(1) # en mi PC me da error al generar las figuras png embedidas en el notebook si no hago esto."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sized-reproduction",
   "metadata": {},
   "source": [
    "Con esto obtenemos las figuras de las transparencias de la clase. Aunque la serie generada tiene 2000 datos, en el gráfico solo mostramos 60 para ilustrar el comportamiento de este modelo AR(3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bound-benefit",
   "metadata": {},
   "outputs": [],
   "source": [
    "randn('seed',9.8134e+83)\n",
    "\n",
    "y = filter([1],[1 0 0 .99],randn(2000,1));\n",
    "\n",
    "fig_serie = y(720:780);\n",
    "\n",
    "fig_fac = acf(y,y,30);\n",
    "\n",
    "fig_fac = [[0:length(fig_fac)-1]',fig_fac];"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "metric-filing",
   "metadata": {},
   "source": [
    "*Para usar los datos y las estimaciones de las autocovarianzas (por ejemplo para generar los gráficos de la Sección 2 de la [presentación](LDHR-print.pdf)) hay que descomentar el siguiente código*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "realistic-timing",
   "metadata": {},
   "outputs": [],
   "source": [
    "% save fgac.1.data fig_serie\n",
    "% save fgac.2.data fig_fac"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "609b3150-5227-4708-8804-d312f0f3c121",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%plot --format png\n",
    "plot(fig_serie)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f6bca2af-c1d3-4166-b2f2-a6bd9a3d0a8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bar(fig_fac(:,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "partial-linux",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "error: 'Repetimos' undefined near line 1, column 1\r\n"
     ]
    }
   ],
   "source": [
    "Repetimos la simulación, pero en este caso generamos 50000 datos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "touched-polish",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 1500\r\n"
     ]
    }
   ],
   "source": [
    "randn('seed',9.8134e+83)\n",
    "n=1500\n",
    "y=filter([1],[1 0 0 .99],randn(50000,1));\n",
    "%[fig_fac] = acovf(y(10001:40000),n,'unbiased');\n",
    "fig_fac=acf(y(10001:50000),y(10001:50000),n);\n",
    "w=linspace (0,pi,512);\n",
    "C=cos(w'*ones(1,n+1)*diag(linspace(0,n,n+1)))*diag([fig_fac]);\n",
    "pse=cumsum(C');\n",
    "%plot(fig_fac)\n",
    "%pause\n",
    "%plot(w',pse([1,4,7,21],:)')\n",
    "%pause\n",
    "%plot(w',pse([100,400,900],:)')\n",
    "X=[w',pse([1,4,7,21,100,400,900,1200,1500],:)'];\n",
    "%%semilogy(pse([600,900],:)'+250)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "considered-toddler",
   "metadata": {},
   "source": [
    "*Para usar en otro sitio los datos de las estimaciones del espectro usando más o menos autocovarianzas (como en la Sección 2.2 de la [presentación](LDHR-print.pdf)) decomentar el siguiente código*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7864f353-f6ca-4106-9059-d6ca98977a81",
   "metadata": {},
   "outputs": [],
   "source": [
    "% save fig_espectro_ejemplo.data X"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "working-entertainment",
   "metadata": {},
   "source": [
    "Gráficos con 1, 4, 7, 21, 100, 400, 900, 1200 y 1500 autocovarianzas estimadas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "25098897-a4b3-4bde-bac3-99be1bc00752",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(X(:,[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "412a6e26-2ef0-4a24-89ac-f79298975678",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(X(:,[3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "increasing-reputation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(X(:,[4]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "french-input",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(X(:,[5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ultimate-tooth",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(X(:,[6]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "greek-relevance",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEsE6R+v99qtVqtVp7nKaUsy1qtVqfTKYqinDA3Up0AAHMWDtLFxUWtVru8vPzjjz/6/X6e55PJ5PLystvtnp2dpZTmRqoTAKBq4SA1Go2ffvrp9s3hcNhsNlNKzWazfMI0N1KdAABVCwep2Ww2Go2iKE5OTrrdbkqp0WiU75pMJuXG3Eh1AgDMWeZnSFmW9fv9Xq/XbrdTStPptByv1WrlxtxIdcKcnRlL7A8Aa7f6mXyZnyFdX1+fn58fHByklHZ3d0ejUUqpKIry0tzcSHVC1c2M5ZYBwHqtfib/ZtEHjEaj8Xjc6XTKN8/PzzudTpZl4/G41+ullNrt9uzIwcHB3AQAqNp5kicleZ7v7+/X6/UvjVQn3Nrb27u6ulp9H3huO72PKaWb06N17whsgp3exw0+mpY7sS/8DOlO1WtxcyNfulgHACV3agAgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEHiUXZ6H29Oj9a9F8AmEyQWcHN6tNP7uO69ADaTIAEQgiABEIIgARCCIAEQgiABEIIgARDCkkEaDAZZlpXbWZa1Wq1Op1MUxZ0j1QkAMGeZIJ2cnLx7967czvN8MplcXl52u92zs7PqSHUCAFQtE6T379//+OOP5fZwOGw2mymlZrOZ53l1pDoBAKqe4GdIjUaj3JhMJneOVCcAwJwnCNJ0Oi03arXanSPVCXN2Zqy+PwC8vNXP5KsGaXd3dzQapZSKoigvzc2NVCdU3cxYcX8AWIvVz+TfrLgH7Xa70+lkWTYej3u9XnXk4OBgbgIAVO08yZOSPM/39/fr9fqXRqoTbu3t7V1dXa2+Dzyr239+wr9DAU9isw+l5U7sqz5DKlWvxc2NfOliHQCU3KkBgBAECYAQBAmAEAQJgBAECYAQBAmAEAQJgBAECYAQBAmAEAQJgBAECYAQBAmAEAQJgBAECYAQBAngpW32P4a0NEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECeFE7vY/r3oWgBAmAEASJh/mGDngBggRACIIEQAiCBEAIggRACILEwrzGAXgOggRACIIEQAiCxANcoANehiABEIIgARCCILGwm9Ojnd5Hl/KApyVIAIQgSCzm5vRo3bsAXyvXFe4nSACEIEgAhCBIAIQgSNztMRe7XRCH5fhZ7J0EiftIDqyoPIgcSo8hSNxh0UPIwQasTpBYye1vyGoSsCJB4v88SVfECWa/S5s9FnZ6H8u7nKxv16ITpC01W47bI6SakyV+9Hrn3zZ3WC692xDH3Fe1L+zVvUSQsixrtVqdTqcoihf4cKEs9DX6pbP2nX9J9XR/55+zG3c+fXnCo+jBv6raqrm9uv/P9LhP0dKfc6JZ6H/rEofPg9v3f6He85Dq+Oz3dl5i9yU7Nzc3z/oB8jy/uLh4//59nueDweC3336bm7C3t/ef//6fZ92HLbHo1YDb+fc8cPZds0fR7OD9H3TpaxQubizBJ+3FLHe4bU+K9vb2rq6uFn7YzTP7/fff//zzz3L76OioOuHVq1fPvQ9fkfT3f92/PTv44APT3/915wPL7dk/byfP/Tc7Pvfh7pwwu/GlP+f26p49fOTn4THbj58QzUI7+XyTX+ajLLFLT/hlU/1CXWjy3Pad71p0dV+v5U7sLxGk4XBYbt+5i69evXrJQHLzuOP2ngPyZsFD986/Ab5Sjzx87p+8kWbP5MsF6SV+hjSdTsuNWq1254QvLYln8qXL2bfb5caDV72r0x75geDr9ZjDZzu/2lc/kz97kHZ3d0ejUUqpKIpms/ncH46ncv8RNfde4QFW981zf4B2u93pdLIsG4/HvV7vuT8cQBy+P1vIs7/KrpTn+f7+fr1er75ryRdjABDVcif2Z3+GVHKxDoD7uVMDACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCBIAIQgSACEIEgAhCNLa7OzsrHsX1mNrF562eO0WzmMsGaTBYJBlWbmdZVmr1ep0OkVR3DlSnQAAc5YJ0snJybt378rtPM8nk8nl5WW32z07O6uOVCcAQNUyQXr//v2PP/5Ybg+Hw2azmVJqNpt5nldHqhMAoOqb1f+KRqNRbkwmkztHqhPm7O3trb4bX51Xr15Z+LbZ2rVbOI/x2CBdXFwMBoP9/f23b9/OvWs6nZYbtVrtzpHqhFlXV1cL7jMAG+ixl+za7fb5+Xm1Rru7u6PRKKVUFEV5aW5upDoBAKp2bm5ulnhY+RK7sk+dTmd/f388Hvd6vYODg+pIdQIAzFkySHPyPN/f36/X618aqU4AgFlPEyQAWJE7NQAQwpqDtFU3cbjn9hYb/Hno9/utVqvVapW/hfbgfT02w3Q6PTk5KddVvqhnSxZemk6nP/zwQ7m9PQvv/L9tO8wvLi7KY7z8Uk+rLPxmfYbD4Zs3b8qNX3/9dY178gLevHnz7bff/v777zeVhW/w5+HPP/8sl/z58+ejo6PqSjd17WdnZ+XC//nPf75582Z7Fl769ddfj46Obu5a5qYu/PPnzz///PPsyJYc5v/+97/LhX/69Gn189s6nyFt1U0c7rm9xQZ/HhqNxk8//XT75oP39VjXfj65169fd7vdcrtWq23PwlNKg8GgVquVvw6/PQsfj8eNRiPLsouLi3JkSw7zwWBwfHyc5/l0Oi1fd73Kwtd8ye7BmzhsqkVvZvGVajabjUajKIqTk5PyBP3gfT02Q6PRqNfrWZadnp4eHx+nrVl4URR//fXX7C8sbs/Cr6+vDw8PP3361O/3y8EtOczPzs6Gw+GHDx9ur1UuvfAnuHXQKu6/icMGW+hmFl+1LMtufwUty7IH7+uxSd6+fdvtdlut1uvXr7dk4aenp7VaLcuyoijK09OWLLzdbrfb7ZRSs9n87rvvfvvtt7Q1h3m32y3X/t1335Xfiyy98HU+Q9ramzhsz80sLi4urq+vz8/Py1+IfvC+Huvd2yfU7/cHg0G5fX19vT0L/+WXX46Pjw8PD+v1+uHh4fYs/MOHD+X1qOl0Wp52t+Qw393d/fTpU3qiha/595C26iYO99zeYlM/D/1+fzwe335bdH5+/uB9Pda6v09mNBq9e/fu+++/H4/Hx8fH7XZ7SxZ+q9PpnJ+fp0fcyWXNO/pERqPRycnJ69evb/+Pp+04zMsXlJbreoKFP/drMB40HA4/f/687r1Yg7mFb8/nobrSjVz758+fH/xfvJELr9qehT+40g1e+KdPn+ZGlli4OzUAEII7NQAQgiABEIIgARCCIAEQwv8CL5l1sVdhuOgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(X(:,[7]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "alpine-brain",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(X(:,[8]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "pursuant-value",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(X(:,[9]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "handed-municipality",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(X(:,[10]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "criminal-abraham",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Octave",
   "language": "octave",
   "name": "octave"
  },
  "language_info": {
   "file_extension": ".m",
   "help_links": [
    {
     "text": "GNU Octave",
     "url": "https://www.gnu.org/software/octave/support.html"
    },
    {
     "text": "Octave Kernel",
     "url": "https://github.com/Calysto/octave_kernel"
    },
    {
     "text": "MetaKernel Magics",
     "url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "octave",
   "version": "6.2.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}