Holt's_linear_trend_method.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Holt's linear trend method\n",
    "fpp2 패키지의 Air Transport Passengers Australia 데이터를 가지고 **홀트의 선형지수평활법**을 실습해봅니다.\n",
    "홀트선형지수평활법은 추세가 있는 데이터를 예측할 수 있도록 단순 지수 평활을 확장한 모형이며, 두개의 평활식(수준에 관한 것, 추세에 관한 것)으로 이루어집니다.수준식은 관측값의 가중 평균이며, 추정된 추세의 이동 평균입니다.예측 함수는 더이상 평평하지 않고, 추세를 가집니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"package 'fpp2' was built under R version 3.6.3\"\n",
      "Loading required package: ggplot2\n",
      "\n",
      "Registered S3 methods overwritten by 'ggplot2':\n",
      "  method         from \n",
      "  [.quosures     rlang\n",
      "  c.quosures     rlang\n",
      "  print.quosures rlang\n",
      "\n",
      "Loading required package: forecast\n",
      "\n",
      "Warning message:\n",
      "\"package 'forecast' was built under R version 3.6.3\"\n",
      "Registered S3 method overwritten by 'xts':\n",
      "  method     from\n",
      "  as.zoo.xts zoo \n",
      "\n",
      "Registered S3 method overwritten by 'quantmod':\n",
      "  method            from\n",
      "  as.zoo.data.frame zoo \n",
      "\n",
      "Loading required package: fma\n",
      "\n",
      "Warning message:\n",
      "\"package 'fma' was built under R version 3.6.3\"\n",
      "Loading required package: expsmooth\n",
      "\n",
      "Warning message:\n",
      "\"package 'expsmooth' was built under R version 3.6.3\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "A Time Series:<br><style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>7.3187</li><li>7.3266</li><li>7.7956</li><li>9.3846</li><li>10.6647</li><li>11.0551</li><li>10.8643</li><li>11.3065</li><li>12.1223</li><li>13.0225</li><li>13.6488</li><li>13.2195</li><li>13.1879</li><li>12.6015</li><li>13.2368</li><li>14.4121</li><li>15.4973</li><li>16.8802</li><li>18.8163</li><li>15.1143</li><li>17.5534</li><li>21.8601</li><li>23.8866</li><li>26.9293</li><li>26.8885</li><li>28.8314</li><li>30.0751</li><li>30.9535</li><li>30.1857</li><li>31.5797</li><li>32.577569</li><li>33.477398</li><li>39.021581</li><li>41.386432</li><li>41.596552</li><li>44.657324</li><li>46.951775</li><li>48.728837</li><li>51.488427</li><li>50.026967</li><li>60.640913</li><li>63.3603103378</li><li>66.355274</li><li>68.197955</li><li>68.1232376693</li><li>69.7793454797</li><li>72.597700806</li></ol>\n"
      ],
      "text/latex": [
       "A Time Series:\\\\\\begin{enumerate*}\n",
       "\\item 7.3187\n",
       "\\item 7.3266\n",
       "\\item 7.7956\n",
       "\\item 9.3846\n",
       "\\item 10.6647\n",
       "\\item 11.0551\n",
       "\\item 10.8643\n",
       "\\item 11.3065\n",
       "\\item 12.1223\n",
       "\\item 13.0225\n",
       "\\item 13.6488\n",
       "\\item 13.2195\n",
       "\\item 13.1879\n",
       "\\item 12.6015\n",
       "\\item 13.2368\n",
       "\\item 14.4121\n",
       "\\item 15.4973\n",
       "\\item 16.8802\n",
       "\\item 18.8163\n",
       "\\item 15.1143\n",
       "\\item 17.5534\n",
       "\\item 21.8601\n",
       "\\item 23.8866\n",
       "\\item 26.9293\n",
       "\\item 26.8885\n",
       "\\item 28.8314\n",
       "\\item 30.0751\n",
       "\\item 30.9535\n",
       "\\item 30.1857\n",
       "\\item 31.5797\n",
       "\\item 32.577569\n",
       "\\item 33.477398\n",
       "\\item 39.021581\n",
       "\\item 41.386432\n",
       "\\item 41.596552\n",
       "\\item 44.657324\n",
       "\\item 46.951775\n",
       "\\item 48.728837\n",
       "\\item 51.488427\n",
       "\\item 50.026967\n",
       "\\item 60.640913\n",
       "\\item 63.3603103378\n",
       "\\item 66.355274\n",
       "\\item 68.197955\n",
       "\\item 68.1232376693\n",
       "\\item 69.7793454797\n",
       "\\item 72.597700806\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "A Time Series:  \n",
       "1. 7.3187\n",
       "2. 7.3266\n",
       "3. 7.7956\n",
       "4. 9.3846\n",
       "5. 10.6647\n",
       "6. 11.0551\n",
       "7. 10.8643\n",
       "8. 11.3065\n",
       "9. 12.1223\n",
       "10. 13.0225\n",
       "11. 13.6488\n",
       "12. 13.2195\n",
       "13. 13.1879\n",
       "14. 12.6015\n",
       "15. 13.2368\n",
       "16. 14.4121\n",
       "17. 15.4973\n",
       "18. 16.8802\n",
       "19. 18.8163\n",
       "20. 15.1143\n",
       "21. 17.5534\n",
       "22. 21.8601\n",
       "23. 23.8866\n",
       "24. 26.9293\n",
       "25. 26.8885\n",
       "26. 28.8314\n",
       "27. 30.0751\n",
       "28. 30.9535\n",
       "29. 30.1857\n",
       "30. 31.5797\n",
       "31. 32.577569\n",
       "32. 33.477398\n",
       "33. 39.021581\n",
       "34. 41.386432\n",
       "35. 41.596552\n",
       "36. 44.657324\n",
       "37. 46.951775\n",
       "38. 48.728837\n",
       "39. 51.488427\n",
       "40. 50.026967\n",
       "41. 60.640913\n",
       "42. 63.3603103378\n",
       "43. 66.355274\n",
       "44. 68.197955\n",
       "45. 68.1232376693\n",
       "46. 69.7793454797\n",
       "47. 72.597700806\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "A Time Series:\n",
       " [1]  7.31870  7.32660  7.79560  9.38460 10.66470 11.05510 10.86430 11.30650\n",
       " [9] 12.12230 13.02250 13.64880 13.21950 13.18790 12.60150 13.23680 14.41210\n",
       "[17] 15.49730 16.88020 18.81630 15.11430 17.55340 21.86010 23.88660 26.92930\n",
       "[25] 26.88850 28.83140 30.07510 30.95350 30.18570 31.57970 32.57757 33.47740\n",
       "[33] 39.02158 41.38643 41.59655 44.65732 46.95177 48.72884 51.48843 50.02697\n",
       "[41] 60.64091 63.36031 66.35527 68.19795 68.12324 69.77935 72.59770"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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p/Xu9RNMQRTOFf0PSWbdC1jSP/bituP\nUu1ROT536suW2aP/cYvELV/+9ku9v07ux0gv+/OVx0gL0XN/7vIrNuirnE9/r6+etVsdJhmC\nQP23OqdftT/f5H0daXt+HanbPHodqXg/33lzt66HdzbQyxbcp5yQ0rVphmAwO3CnGUJ66tLq\nadohGMffZHfLGdJuk7qn46O3CJXO8t8vY0i7c0Hb9HA47jfp5m2SnZyT1f+DjCE9nF472l5e\niT2k1RRDMJ67dX+S/S1CaXP1QfQQjGbp/yZ7SM+X+3TeIlQmK/9HWe/aPXy8neHw4C1CRbLw\nf5XzC/u6qzcS37xBsp/z8PDo77K+jrT9yKe7eXskpHlY9RHKeWdD5iH4yqKPISQurPkoQuLM\nko8jJM4s+ThC4sSKjyQkjhZ8PCFhvQMICcsdQEhY7QBCwmoHEFLzLHYEIbXOWocQUuMsdQwh\ntc1KBxFS0yx0FCE1zUJHEVLLrHMYITUlJf8y9DSE1BQLOxUhtcS6TkZILbGukxFSQyzrdITU\nEMs6HSG1w6pOSEjtsKoTElIzLOqUhNQMizolIbXCmk5KSK2wppMSUiMs6bSE1AhLOi0htcGK\nTkxIbbCiExNSEyzo1ITUBAs6NSG1wHpOTkgtsJ6TE1IDLOf0hNQAyzk9IdXPamYgpPpZzQyE\nVD2LmYOQqmcxcxBS7axlFkKqnbXMQkiVs5R5CKluVjITIdXNSmYipKpZyFyEVDPrmI2QKmYZ\n8xFSvaxiRkKqlkXMSUjVsog5CalW1jArIVXKEuYlpDpZwcyEVCULmJuQamT9shNSjaxfdkKq\nkOXLT0j1sXozEFJ9rN4MhFQdizcHIVXH4s1BSNWxeHMQUm2s3SyEVBtrN4usIb0+btLJZvs6\n1RDNs3TzyBjSYZX+WU8yBJZuJhlD2qbueXe+2r90aTvFEFi6mWQMqUu7z+td6qYYAis3k4wh\npfTTB2FDYOVm4hapLlZuJnkfI73sz1ceI03Fws0l59Pf66tn7VaHSYZonYWbS97Xkbbn15G6\nzaPXkSZh3WbjnQ01sW6zKSekdG2aIapn3WaTM6TDQ0rrl/c/xNPf8SzbfHK+Rai7vNHu8ocI\nKZ5lm0/Wp7+f3mp66s5vsxPSBCzbfLK+IHv+ad+t9kKaglWb0QxvETqs10KaglWbUcaQVunj\nRdjVWkgTsGozyhjSU3p4v9qntZDCWbQ55Xz6e/tZz8svLxU5E39g0eaU9QXZ3ebjav8gpGDW\nbFblvLMh8xCL89uaWLNZCWkhfn3blDWblZCWIf22KJZsXkJaBiEVTkiLkD5/uPk7mI2QliBd\n/XjrdzAbIS1A+vLzjd/CTIRUvvTt4uffwkyEVLzUc/Xz72EeQipe6r388fcwCyGVLv1w/dPv\nYRZCKly68dFvv0w+QipbuvnhzV8lJyEV7dtC9K6M5ZqfkEr2fR36VsZqFUBIJRsUksUqgZAK\nNuzmx2KVQEjlGvZ4yFoVQUjFGvhUt7UqgpBKNfDFV0tVBiGV6eevLB/0Ci25CalIg7/0qPmV\nKoWQSjT4a2FbX6hyCKlAv3z6Q76ugsyEVJ7fPnshFUhIxfn9kx/wpedkJqTCDPn+uel/P1EC\nIZVl0GcupPIIqSgDP/F0x+8lCyGVZOjnLaTiCKkcQx4effzWVteoWEIqxj2fdGpziQompFLc\n9znfcetFDkIqw71htLdChRNSEZr7hKsjpAK4n7Z8QppfW59tpYQ0u6Y+2WoJaWbu1tVBSPNq\n5zOtnJDm5OaoGkKaUSOfZhOENJ82PstGCGku7tZVRUgzaeBTbIqQZuHmqDZC+quU/l7DEj4/\n7iKkP3mP6I8xFf/pcTch3e//9aR7a3K3rkZCuldvB+nD3/5zFk9Id/k1lV+CklGthHSHe/51\nkr7fK6N6CWmwu78aPH35sMjPihhCGugvGVy1o6LKCWmQP3dwaUlG1RPSEKPm4z5dC4T0OyHw\nKyH9RkYMIKTbZMQgQrpFRgwkpJ/JiMGE9BMZcQch/TCD+afAkgipd/y5J8DSCKlndBlxLyF9\nG1tG3E9IX0aWEX8hpKtRvSuOv8oa0uvj5vzlo5vt61RDDNH7JawiYoyMIR1W6Z/1JEP87rOh\n6y8Jd1PEWBlD2qbueXe+2r90aTvFEL/ovyESEeNlDKlLu8/rXeqmGOLWHykYJpQxpC//GtwU\nQwwbG8K1cYskIyaW9zHSy/58lfkxkpsjJpfz6e/11bN2q8MkQ0z+h0GvvK8jbc+vI3Wbx4yv\nI+mIDGp/Z4O7dWRRTkjpWtgfGvUHwU3lhDTFEDoik6pD0hG5VBySh0fkk/WdDYMfBkUkICMy\nyhjSU9aQdEROOe/a7brbXzwRMETgnwB3yPoYaXf7jUERQ0T9AXCXvE82PF29b3WiIUL+e7hT\nlc/a6YjcagxJR2RXYUg6Ir/6QtIRM6guJB0xh9pC0hGzqCwkHTGPukLSETOpKiQdMZeaQtIR\ns6knJF9+xIzqCMm/R8zMKghJRMxv4SG5KaIMCwsp3fH16pDPwkKCMgkJAggJAggJAggJAggJ\nAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAggJAhQaEizM\nH055fDiLGPurguZiKn0KmkovIV0UNBdT6VPQVHoJ6aKguZhKn4Km0ktIFwXNxVT6FDSVXkK6\nKGguptKnoKn0EtJFQXMxlT4FTaWXkC4Kmoup9CloKr2EdFHQXEylT0FT6SWki4LmYip9CppK\nLyFdFDQXU+lT0FR6CemioLmYSp+CptJLSBcFzcVU+hQ0lV6lzw8WQUgQQEgQQEgQQEgQQEgQ\nQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQIGNITx9jbbu0fjkPfv1vlr/9arc9zDaX\n4+FqAjnn0jOVL5eZpvK06vv8Z1mV/qn8f63yHZZB8oW0+/g3/tfndh6P/0LqPn91Ndtc9t1l\nKvvMc+mZyvfLHFPZXj7/w/8H7b+cZSrf1irTYRkmW0i77n0VntL6cDw8pN3H//OSXo/H19Tt\nTr/nda65PKTt8bSFD3nn0jeVq8t8U9mlh8Np6P9//v2Xs0zlaq2yHpaBcoX0djjeV2F9/vz3\n53N7cug2x9MJPt2Veb78NTzHXN5/5fRTxrn0TuXqMt9UNr2ff//lLFO5Wquch2WoXCG9nYqr\no3r6af3+/2zS4fzj6T7VLm3mmkv3ftllnUvvVK4ucy7L5zSuBu2/nGUqV2uVfSoD5Appd/x6\nYt5H3l1umr78av65PL7ftXvMOpfeqfRfZnG4Drmsqfx8hIqQcS7vn/fq/NfJ68cqXG6Qcq9N\nz1yeTs82dE/Z5/J9KleXuY/M0+lOUxkhfZ3K1c9COnlMm8Nx93F3d3d6SHmcK6TruTxePZmY\ncy7fp3J1mXlZ9ufHq0WE9G0qx28fNh7S8fw88+Z/jxvnCulqLk+nu3aHh/Q0U0jXy/LvMu9U\nDt36arRZQ/o+le8fth7S22ntHj8+6j6P0f9+T/65rM53MQ+nFyfyzqVnWf5d5p3K+vLKzNWg\n/ZezTOXq58yHZZAZQjrbXV5O+3zm5fJEzD7XEzHf53L1t1zeufQty+dlzqnsV+v9+eJq0P7L\nWaZy8r9n7bIdlkHyh9Sd/+p/uqzC0+mu1Mnj+S7ey+erS9nncvlb7nB6+jvvXPqm8nmZcSov\nny9IXA3afznLVE4+H09mPSyD5A/p8uaBVXo+fbD5eIND5herv89lm07v3dqeNifvXPqm8nmZ\nbyr7z8M7+zsb+qdy8r5WLb+z4fi5CofLm9ouN8uXRyaXq5P1D/9thrms/00g61y+T+V6Vtmm\n8nD1BuJV71LMPZXjv7vBeQ/LIDM8Rtq/LdTm5f+/9vHm6znn8m8CWefSM5Wry2xTuX4n/qF3\nKeaeyvHqiZmsh2WQkp74gMUSEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQ\nEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQEgQQ\nEgQQEgQQ0hKkK///NugUwqYsgZCKZ1MWQ0AlszmLIaSS2ZzF+Ajp9PPb/x5T93g8blO6fHfv\np1XqnmacXeuEtBj/D+nx9HjpZX368VTS5vz4aT3rBJsmpMX4f0jrw/Hp/cfueHw5XR3W6WXe\nKTZMSIvx/5Bez1f794836fB2dUibGefXNiEtxpfHSMfrH/89Oc48rPxiCKlkVn4xboc037w4\nsQGLcSukjacZZiakxbgV0nPqdsfjkycbZiOkxbgV0vH8glLq9rPNrnVCWoybIZ3e2ZAedDQb\nIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEA\nIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUEAIUGA/wCizyCYgRsMqwAAAABJ\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(fpp2)\n",
    "ausair\n",
    "plot(ausair)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oy4sgGejOnI4+FIfX/thOSa/AwBPZ46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\ngABCAgQQEiDgf8y2johp4xh0AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Forecasts from Holt's method\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1990년 부터 데이터 분석\n",
    "air.ts <- window(ausair, start=1990)\n",
    "# h는 미래 1~15시점까지 예측\n",
    "air_holt <- holt(air.ts, h=15)\n",
    "\n",
    "plot(air_holt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'model'</li><li>'mean'</li><li>'level'</li><li>'x'</li><li>'upper'</li><li>'lower'</li><li>'fitted'</li><li>'method'</li><li>'series'</li><li>'residuals'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'model'\n",
       "\\item 'mean'\n",
       "\\item 'level'\n",
       "\\item 'x'\n",
       "\\item 'upper'\n",
       "\\item 'lower'\n",
       "\\item 'fitted'\n",
       "\\item 'method'\n",
       "\\item 'series'\n",
       "\\item 'residuals'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'model'\n",
       "2. 'mean'\n",
       "3. 'level'\n",
       "4. 'x'\n",
       "5. 'upper'\n",
       "6. 'lower'\n",
       "7. 'fitted'\n",
       "8. 'method'\n",
       "9. 'series'\n",
       "10. 'residuals'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"model\"     \"mean\"      \"level\"     \"x\"         \"upper\"     \"lower\"    \n",
       " [7] \"fitted\"    \"method\"    \"series\"    \"residuals\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Holt's method \n",
       "\n",
       "Call:\n",
       " holt(y = air.ts, h = 15) \n",
       "\n",
       "  Smoothing parameters:\n",
       "    alpha = 0.8302 \n",
       "    beta  = 1e-04 \n",
       "\n",
       "  Initial states:\n",
       "    l = 15.5715 \n",
       "    b = 2.1017 \n",
       "\n",
       "  sigma:  2.3645\n",
       "\n",
       "     AIC     AICc      BIC \n",
       "141.1291 143.9863 147.6083 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A Time Series: 28 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>l</th><th scope=col>b</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1989</th><td>15.57152</td><td>2.101717</td></tr>\n",
       "\t<tr><th scope=row>1990</th><td>17.57375</td><td>2.101705</td></tr>\n",
       "\t<tr><th scope=row>1991</th><td>21.48918</td><td>2.101924</td></tr>\n",
       "\t<tr><th scope=row>1992</th><td>23.83643</td><td>2.101953</td></tr>\n",
       "\t<tr><th scope=row>1993</th><td>26.76106</td><td>2.102052</td></tr>\n",
       "\t<tr><th scope=row>1994</th><td>27.22376</td><td>2.101855</td></tr>\n",
       "\t<tr><th scope=row>1995</th><td>28.91531</td><td>2.101805</td></tr>\n",
       "\t<tr><th scope=row>1996</th><td>30.23504</td><td>2.101711</td></tr>\n",
       "\t<tr><th scope=row>1997</th><td>31.18835</td><td>2.101573</td></tr>\n",
       "\t<tr><th scope=row>1998</th><td>30.71275</td><td>2.101262</td></tr>\n",
       "\t<tr><th scope=row>1999</th><td>31.78927</td><td>2.101139</td></tr>\n",
       "\t<tr><th scope=row>2000</th><td>32.80047</td><td>2.101008</td></tr>\n",
       "\t<tr><th scope=row>2001</th><td>33.71918</td><td>2.100865</td></tr>\n",
       "\t<tr><th scope=row>2002</th><td>38.47801</td><td>2.101185</td></tr>\n",
       "\t<tr><th scope=row>2003</th><td>41.24938</td><td>2.101266</td></tr>\n",
       "\t<tr><th scope=row>2004</th><td>41.89437</td><td>2.101091</td></tr>\n",
       "\t<tr><th scope=row>2005</th><td>44.54495</td><td>2.101157</td></tr>\n",
       "\t<tr><th scope=row>2006</th><td>46.89988</td><td>2.101187</td></tr>\n",
       "\t<tr><th scope=row>2007</th><td>48.77506</td><td>2.101160</td></tr>\n",
       "\t<tr><th scope=row>2008</th><td>51.38448</td><td>2.101221</td></tr>\n",
       "\t<tr><th scope=row>2009</th><td>50.61420</td><td>2.100875</td></tr>\n",
       "\t<tr><th scope=row>2010</th><td>59.29524</td><td>2.101668</td></tr>\n",
       "\t<tr><th scope=row>2011</th><td>63.02696</td><td>2.101865</td></tr>\n",
       "\t<tr><th scope=row>2012</th><td>66.14704</td><td>2.101987</td></tr>\n",
       "\t<tr><th scope=row>2013</th><td>68.20663</td><td>2.101982</td></tr>\n",
       "\t<tr><th scope=row>2014</th><td>68.49428</td><td>2.101764</td></tr>\n",
       "\t<tr><th scope=row>2015</th><td>69.91801</td><td>2.101682</td></tr>\n",
       "\t<tr><th scope=row>2016</th><td>72.49956</td><td>2.101740</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A Time Series: 28 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & l & b\\\\\n",
       "\\hline\n",
       "\t1989 & 15.57152 & 2.101717\\\\\n",
       "\t1990 & 17.57375 & 2.101705\\\\\n",
       "\t1991 & 21.48918 & 2.101924\\\\\n",
       "\t1992 & 23.83643 & 2.101953\\\\\n",
       "\t1993 & 26.76106 & 2.102052\\\\\n",
       "\t1994 & 27.22376 & 2.101855\\\\\n",
       "\t1995 & 28.91531 & 2.101805\\\\\n",
       "\t1996 & 30.23504 & 2.101711\\\\\n",
       "\t1997 & 31.18835 & 2.101573\\\\\n",
       "\t1998 & 30.71275 & 2.101262\\\\\n",
       "\t1999 & 31.78927 & 2.101139\\\\\n",
       "\t2000 & 32.80047 & 2.101008\\\\\n",
       "\t2001 & 33.71918 & 2.100865\\\\\n",
       "\t2002 & 38.47801 & 2.101185\\\\\n",
       "\t2003 & 41.24938 & 2.101266\\\\\n",
       "\t2004 & 41.89437 & 2.101091\\\\\n",
       "\t2005 & 44.54495 & 2.101157\\\\\n",
       "\t2006 & 46.89988 & 2.101187\\\\\n",
       "\t2007 & 48.77506 & 2.101160\\\\\n",
       "\t2008 & 51.38448 & 2.101221\\\\\n",
       "\t2009 & 50.61420 & 2.100875\\\\\n",
       "\t2010 & 59.29524 & 2.101668\\\\\n",
       "\t2011 & 63.02696 & 2.101865\\\\\n",
       "\t2012 & 66.14704 & 2.101987\\\\\n",
       "\t2013 & 68.20663 & 2.101982\\\\\n",
       "\t2014 & 68.49428 & 2.101764\\\\\n",
       "\t2015 & 69.91801 & 2.101682\\\\\n",
       "\t2016 & 72.49956 & 2.101740\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A Time Series: 28 × 2\n",
       "\n",
       "| <!--/--> | l | b |\n",
       "|---|---|---|\n",
       "| 1989 | 15.57152 | 2.101717 |\n",
       "| 1990 | 17.57375 | 2.101705 |\n",
       "| 1991 | 21.48918 | 2.101924 |\n",
       "| 1992 | 23.83643 | 2.101953 |\n",
       "| 1993 | 26.76106 | 2.102052 |\n",
       "| 1994 | 27.22376 | 2.101855 |\n",
       "| 1995 | 28.91531 | 2.101805 |\n",
       "| 1996 | 30.23504 | 2.101711 |\n",
       "| 1997 | 31.18835 | 2.101573 |\n",
       "| 1998 | 30.71275 | 2.101262 |\n",
       "| 1999 | 31.78927 | 2.101139 |\n",
       "| 2000 | 32.80047 | 2.101008 |\n",
       "| 2001 | 33.71918 | 2.100865 |\n",
       "| 2002 | 38.47801 | 2.101185 |\n",
       "| 2003 | 41.24938 | 2.101266 |\n",
       "| 2004 | 41.89437 | 2.101091 |\n",
       "| 2005 | 44.54495 | 2.101157 |\n",
       "| 2006 | 46.89988 | 2.101187 |\n",
       "| 2007 | 48.77506 | 2.101160 |\n",
       "| 2008 | 51.38448 | 2.101221 |\n",
       "| 2009 | 50.61420 | 2.100875 |\n",
       "| 2010 | 59.29524 | 2.101668 |\n",
       "| 2011 | 63.02696 | 2.101865 |\n",
       "| 2012 | 66.14704 | 2.101987 |\n",
       "| 2013 | 68.20663 | 2.101982 |\n",
       "| 2014 | 68.49428 | 2.101764 |\n",
       "| 2015 | 69.91801 | 2.101682 |\n",
       "| 2016 | 72.49956 | 2.101740 |\n",
       "\n"
      ],
      "text/plain": [
       "     l        b       \n",
       "1989 15.57152 2.101717\n",
       "1990 17.57375 2.101705\n",
       "1991 21.48918 2.101924\n",
       "1992 23.83643 2.101953\n",
       "1993 26.76106 2.102052\n",
       "1994 27.22376 2.101855\n",
       "1995 28.91531 2.101805\n",
       "1996 30.23504 2.101711\n",
       "1997 31.18835 2.101573\n",
       "1998 30.71275 2.101262\n",
       "1999 31.78927 2.101139\n",
       "2000 32.80047 2.101008\n",
       "2001 33.71918 2.100865\n",
       "2002 38.47801 2.101185\n",
       "2003 41.24938 2.101266\n",
       "2004 41.89437 2.101091\n",
       "2005 44.54495 2.101157\n",
       "2006 46.89988 2.101187\n",
       "2007 48.77506 2.101160\n",
       "2008 51.38448 2.101221\n",
       "2009 50.61420 2.100875\n",
       "2010 59.29524 2.101668\n",
       "2011 63.02696 2.101865\n",
       "2012 66.14704 2.101987\n",
       "2013 68.20663 2.101982\n",
       "2014 68.49428 2.101764\n",
       "2015 69.91801 2.101682\n",
       "2016 72.49956 2.101740"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "A Time Series:<br><style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>17.6732393089268</li><li>19.6754518481936</li><li>23.5911065364322</li><li>25.9383832722484</li><li>28.8631110244386</li><li>29.3256110378416</li><li>31.0171142067674</li><li>32.3367495539149</li><li>33.2899256635964</li><li>32.8140084393557</li><li>33.8904040109139</li><li>34.9014742193778</li><li>35.8200477056676</li><li>40.5791990101983</li><li>43.3506432881162</li><li>43.9954583003573</li><li>46.6461070079505</li><li>49.0010650514849</li><li>50.8762170029973</li><li>53.4857052985567</li><li>52.7150789799295</li><li>61.3969058273664</li><li>65.1288213290104</li><li>68.2490298732758</li><li>70.308608786473</li><li>70.5960410449372</li><li>72.0196887298931</li></ol>\n"
      ],
      "text/latex": [
       "A Time Series:\\\\\\begin{enumerate*}\n",
       "\\item 17.6732393089268\n",
       "\\item 19.6754518481936\n",
       "\\item 23.5911065364322\n",
       "\\item 25.9383832722484\n",
       "\\item 28.8631110244386\n",
       "\\item 29.3256110378416\n",
       "\\item 31.0171142067674\n",
       "\\item 32.3367495539149\n",
       "\\item 33.2899256635964\n",
       "\\item 32.8140084393557\n",
       "\\item 33.8904040109139\n",
       "\\item 34.9014742193778\n",
       "\\item 35.8200477056676\n",
       "\\item 40.5791990101983\n",
       "\\item 43.3506432881162\n",
       "\\item 43.9954583003573\n",
       "\\item 46.6461070079505\n",
       "\\item 49.0010650514849\n",
       "\\item 50.8762170029973\n",
       "\\item 53.4857052985567\n",
       "\\item 52.7150789799295\n",
       "\\item 61.3969058273664\n",
       "\\item 65.1288213290104\n",
       "\\item 68.2490298732758\n",
       "\\item 70.308608786473\n",
       "\\item 70.5960410449372\n",
       "\\item 72.0196887298931\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "A Time Series:  \n",
       "1. 17.6732393089268\n",
       "2. 19.6754518481936\n",
       "3. 23.5911065364322\n",
       "4. 25.9383832722484\n",
       "5. 28.8631110244386\n",
       "6. 29.3256110378416\n",
       "7. 31.0171142067674\n",
       "8. 32.3367495539149\n",
       "9. 33.2899256635964\n",
       "10. 32.8140084393557\n",
       "11. 33.8904040109139\n",
       "12. 34.9014742193778\n",
       "13. 35.8200477056676\n",
       "14. 40.5791990101983\n",
       "15. 43.3506432881162\n",
       "16. 43.9954583003573\n",
       "17. 46.6461070079505\n",
       "18. 49.0010650514849\n",
       "19. 50.8762170029973\n",
       "20. 53.4857052985567\n",
       "21. 52.7150789799295\n",
       "22. 61.3969058273664\n",
       "23. 65.1288213290104\n",
       "24. 68.2490298732758\n",
       "25. 70.308608786473\n",
       "26. 70.5960410449372\n",
       "27. 72.0196887298931\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "A Time Series:\n",
       " [1] 17.67324 19.67545 23.59111 25.93838 28.86311 29.32561 31.01711 32.33675\n",
       " [9] 33.28993 32.81401 33.89040 34.90147 35.82005 40.57920 43.35064 43.99546\n",
       "[17] 46.64611 49.00107 50.87622 53.48571 52.71508 61.39691 65.12882 68.24903\n",
       "[25] 70.30861 70.59604 72.01969"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 적합된 모형의 변수 확인\n",
    "names(air_holt)\n",
    "\n",
    "# 모형의 통게량(추정량 확인)\n",
    "air_holt$model\n",
    "air_holt$model$states\n",
    "\n",
    "# 적합된 값\n",
    "air_holt$fitted\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Forecast method: Holt's method\n",
      "\n",
      "Model Information:\n",
      "Holt's method \n",
      "\n",
      "Call:\n",
      " holt(y = air.ts, h = 15) \n",
      "\n",
      "  Smoothing parameters:\n",
      "    alpha = 0.8302 \n",
      "    beta  = 1e-04 \n",
      "\n",
      "  Initial states:\n",
      "    l = 15.5715 \n",
      "    b = 2.1017 \n",
      "\n",
      "  sigma:  2.3645\n",
      "\n",
      "     AIC     AICc      BIC \n",
      "141.1291 143.9863 147.6083 \n",
      "\n",
      "Error measures:\n",
      "                      ME     RMSE     MAE        MPE     MAPE      MASE\n",
      "Training set 0.008359331 2.182343 1.52892 -0.3244107 3.820787 0.6654839\n",
      "                    ACF1\n",
      "Training set -0.01335362\n",
      "\n",
      "Forecasts:\n",
      "     Point Forecast    Lo 80     Hi 80    Lo 95     Hi 95\n",
      "2017       74.60130 71.57106  77.63154 69.96695  79.23566\n",
      "2018       76.70304 72.76440  80.64169 70.67941  82.72668\n",
      "2019       78.80478 74.13092  83.47864 71.65673  85.95284\n",
      "2020       80.90652 75.59817  86.21487 72.78810  89.02494\n",
      "2021       83.00826 77.13343  88.88310 74.02348  91.99305\n",
      "2022       85.11000 78.71857  91.50143 75.33516  94.88485\n",
      "2023       87.21174 80.34235  94.08113 76.70591  97.71757\n",
      "2024       89.31348 81.99718  96.62978 78.12417 100.50280\n",
      "2025       91.41522 83.67768  99.15276 79.58168 103.24876\n",
      "2026       93.51696 85.37987 101.65405 81.07236 105.96157\n",
      "2027       95.61870 87.10069 104.13671 82.59153 108.64587\n",
      "2028       97.72044 88.83774 106.60314 84.13553 111.30535\n",
      "2029       99.82218 90.58911 109.05525 85.70141 113.94295\n",
      "2030      101.92392 92.35321 111.49463 87.28678 116.56106\n",
      "2031      104.02566 94.12874 113.92257 88.88964 119.16168\n"
     ]
    }
   ],
   "source": [
    "summary(air_holt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hKSc2PfiA0BY+Z2ZDMjIyFxj5SdmR1Z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\nJEDA/6NBQi1Mx+vuAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Forecasts from Damped Holt's method\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "air_holt_de <- holt(air.ts, damped=TRUE, h=15)\n",
    "plot(air_holt_de)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "cf) damped : 감쇠 추세법 설정을 위한 파라미터입니다.<br/>\n",
    "상승추세였다해도 미래의 데이터가 지속적으로 지금의 속도로 가파르게 상승하기만 할거라는 보장이 없습니다.<br/>\n",
    "그러다보면 적합된 추세에 너무 맞추다보니 오히려 과하게 예측할 수 있기에 파라미터 phi를 이용한 조정을 통해 그러한 문제를 방지하는 기법입니다.<br/>\n",
    "다시 말해 상승(또는 하강)을 하기는 하되 점점 감쇠하며 상승(또는 하강)하도록 설정해주는 것이라고 이해하시면 편합니다.<br/>\n",
    "보통 도메인 지식이 어느정도 있을 때 damped를 true or false 둘중 하나를 고르게 되는데, 잘 모르는 분야의 경우는 둘 다 적용하는 것이 보다 바람직합니다.<br/>\n",
    "\n",
    "cf) phi : 감쇠 지수 매개변수로 phi=1이면 holt의 선형기법과 동일한 결과를 낳습니다. default는 0.98입니다.<br/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'model'</li><li>'mean'</li><li>'level'</li><li>'x'</li><li>'upper'</li><li>'lower'</li><li>'fitted'</li><li>'method'</li><li>'series'</li><li>'residuals'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'model'\n",
       "\\item 'mean'\n",
       "\\item 'level'\n",
       "\\item 'x'\n",
       "\\item 'upper'\n",
       "\\item 'lower'\n",
       "\\item 'fitted'\n",
       "\\item 'method'\n",
       "\\item 'series'\n",
       "\\item 'residuals'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'model'\n",
       "2. 'mean'\n",
       "3. 'level'\n",
       "4. 'x'\n",
       "5. 'upper'\n",
       "6. 'lower'\n",
       "7. 'fitted'\n",
       "8. 'method'\n",
       "9. 'series'\n",
       "10. 'residuals'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"model\"     \"mean\"      \"level\"     \"x\"         \"upper\"     \"lower\"    \n",
       " [7] \"fitted\"    \"method\"    \"series\"    \"residuals\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Damped Holt's method \n",
       "\n",
       "Call:\n",
       " holt(y = air.ts, h = 15, damped = TRUE) \n",
       "\n",
       "  Smoothing parameters:\n",
       "    alpha = 0.8691 \n",
       "    beta  = 0.0409 \n",
       "    phi   = 0.98 \n",
       "\n",
       "  Initial states:\n",
       "    l = 15.373 \n",
       "    b = 2.2224 \n",
       "\n",
       "  sigma:  2.532\n",
       "\n",
       "     AIC     AICc      BIC \n",
       "145.6239 149.8239 153.3989 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A Time Series: 28 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>l</th><th scope=col>b</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1989</th><td>15.37296</td><td>2.222414</td></tr>\n",
       "\t<tr><th scope=row>1990</th><td>17.55308</td><td>2.178067</td></tr>\n",
       "\t<tr><th scope=row>1991</th><td>21.57562</td><td>2.223377</td></tr>\n",
       "\t<tr><th scope=row>1992</th><td>23.86931</td><td>2.184312</td></tr>\n",
       "\t<tr><th scope=row>1993</th><td>26.80891</td><td>2.178235</td></tr>\n",
       "\t<tr><th scope=row>1994</th><td>27.15760</td><td>2.050602</td></tr>\n",
       "\t<tr><th scope=row>1995</th><td>28.87537</td><td>1.995854</td></tr>\n",
       "\t<tr><th scope=row>1996</th><td>30.17412</td><td>1.925003</td></tr>\n",
       "\t<tr><th scope=row>1997</th><td>31.09847</td><td>1.841213</td></tr>\n",
       "\t<tr><th scope=row>1998</th><td>30.54150</td><td>1.693237</td></tr>\n",
       "\t<tr><th scope=row>1999</th><td>31.66104</td><td>1.633962</td></tr>\n",
       "\t<tr><th scope=row>2000</th><td>32.66723</td><td>1.573272</td></tr>\n",
       "\t<tr><th scope=row>2001</th><td>33.57320</td><td>1.511877</td></tr>\n",
       "\t<tr><th scope=row>2002</th><td>38.50215</td><td>1.643907</td></tr>\n",
       "\t<tr><th scope=row>2003</th><td>41.21971</td><td>1.663114</td></tr>\n",
       "\t<tr><th scope=row>2004</th><td>41.76063</td><td>1.578595</td></tr>\n",
       "\t<tr><th scope=row>2005</th><td>44.48059</td><td>1.602234</td></tr>\n",
       "\t<tr><th scope=row>2006</th><td>46.83379</td><td>1.607047</td></tr>\n",
       "\t<tr><th scope=row>2007</th><td>48.68692</td><td>1.588002</td></tr>\n",
       "\t<tr><th scope=row>2008</th><td>51.32536</td><td>1.607182</td></tr>\n",
       "\t<tr><th scope=row>2009</th><td>50.40323</td><td>1.457494</td></tr>\n",
       "\t<tr><th scope=row>2010</th><td>59.48737</td><td>1.788710</td></tr>\n",
       "\t<tr><th scope=row>2011</th><td>63.08270</td><td>1.839659</td></tr>\n",
       "\t<tr><th scope=row>2012</th><td>66.16282</td><td>1.862987</td></tr>\n",
       "\t<tr><th scope=row>2013</th><td>68.17053</td><td>1.834294</td></tr>\n",
       "\t<tr><th scope=row>2014</th><td>68.36482</td><td>1.722138</td></tr>\n",
       "\t<tr><th scope=row>2015</th><td>69.81512</td><td>1.676521</td></tr>\n",
       "\t<tr><th scope=row>2016</th><td>72.44848</td><td>1.689608</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A Time Series: 28 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & l & b\\\\\n",
       "\\hline\n",
       "\t1989 & 15.37296 & 2.222414\\\\\n",
       "\t1990 & 17.55308 & 2.178067\\\\\n",
       "\t1991 & 21.57562 & 2.223377\\\\\n",
       "\t1992 & 23.86931 & 2.184312\\\\\n",
       "\t1993 & 26.80891 & 2.178235\\\\\n",
       "\t1994 & 27.15760 & 2.050602\\\\\n",
       "\t1995 & 28.87537 & 1.995854\\\\\n",
       "\t1996 & 30.17412 & 1.925003\\\\\n",
       "\t1997 & 31.09847 & 1.841213\\\\\n",
       "\t1998 & 30.54150 & 1.693237\\\\\n",
       "\t1999 & 31.66104 & 1.633962\\\\\n",
       "\t2000 & 32.66723 & 1.573272\\\\\n",
       "\t2001 & 33.57320 & 1.511877\\\\\n",
       "\t2002 & 38.50215 & 1.643907\\\\\n",
       "\t2003 & 41.21971 & 1.663114\\\\\n",
       "\t2004 & 41.76063 & 1.578595\\\\\n",
       "\t2005 & 44.48059 & 1.602234\\\\\n",
       "\t2006 & 46.83379 & 1.607047\\\\\n",
       "\t2007 & 48.68692 & 1.588002\\\\\n",
       "\t2008 & 51.32536 & 1.607182\\\\\n",
       "\t2009 & 50.40323 & 1.457494\\\\\n",
       "\t2010 & 59.48737 & 1.788710\\\\\n",
       "\t2011 & 63.08270 & 1.839659\\\\\n",
       "\t2012 & 66.16282 & 1.862987\\\\\n",
       "\t2013 & 68.17053 & 1.834294\\\\\n",
       "\t2014 & 68.36482 & 1.722138\\\\\n",
       "\t2015 & 69.81512 & 1.676521\\\\\n",
       "\t2016 & 72.44848 & 1.689608\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A Time Series: 28 × 2\n",
       "\n",
       "| <!--/--> | l | b |\n",
       "|---|---|---|\n",
       "| 1989 | 15.37296 | 2.222414 |\n",
       "| 1990 | 17.55308 | 2.178067 |\n",
       "| 1991 | 21.57562 | 2.223377 |\n",
       "| 1992 | 23.86931 | 2.184312 |\n",
       "| 1993 | 26.80891 | 2.178235 |\n",
       "| 1994 | 27.15760 | 2.050602 |\n",
       "| 1995 | 28.87537 | 1.995854 |\n",
       "| 1996 | 30.17412 | 1.925003 |\n",
       "| 1997 | 31.09847 | 1.841213 |\n",
       "| 1998 | 30.54150 | 1.693237 |\n",
       "| 1999 | 31.66104 | 1.633962 |\n",
       "| 2000 | 32.66723 | 1.573272 |\n",
       "| 2001 | 33.57320 | 1.511877 |\n",
       "| 2002 | 38.50215 | 1.643907 |\n",
       "| 2003 | 41.21971 | 1.663114 |\n",
       "| 2004 | 41.76063 | 1.578595 |\n",
       "| 2005 | 44.48059 | 1.602234 |\n",
       "| 2006 | 46.83379 | 1.607047 |\n",
       "| 2007 | 48.68692 | 1.588002 |\n",
       "| 2008 | 51.32536 | 1.607182 |\n",
       "| 2009 | 50.40323 | 1.457494 |\n",
       "| 2010 | 59.48737 | 1.788710 |\n",
       "| 2011 | 63.08270 | 1.839659 |\n",
       "| 2012 | 66.16282 | 1.862987 |\n",
       "| 2013 | 68.17053 | 1.834294 |\n",
       "| 2014 | 68.36482 | 1.722138 |\n",
       "| 2015 | 69.81512 | 1.676521 |\n",
       "| 2016 | 72.44848 | 1.689608 |\n",
       "\n"
      ],
      "text/plain": [
       "     l        b       \n",
       "1989 15.37296 2.222414\n",
       "1990 17.55308 2.178067\n",
       "1991 21.57562 2.223377\n",
       "1992 23.86931 2.184312\n",
       "1993 26.80891 2.178235\n",
       "1994 27.15760 2.050602\n",
       "1995 28.87537 1.995854\n",
       "1996 30.17412 1.925003\n",
       "1997 31.09847 1.841213\n",
       "1998 30.54150 1.693237\n",
       "1999 31.66104 1.633962\n",
       "2000 32.66723 1.573272\n",
       "2001 33.57320 1.511877\n",
       "2002 38.50215 1.643907\n",
       "2003 41.21971 1.663114\n",
       "2004 41.76063 1.578595\n",
       "2005 44.48059 1.602234\n",
       "2006 46.83379 1.607047\n",
       "2007 48.68692 1.588002\n",
       "2008 51.32536 1.607182\n",
       "2009 50.40323 1.457494\n",
       "2010 59.48737 1.788710\n",
       "2011 63.08270 1.839659\n",
       "2012 66.16282 1.862987\n",
       "2013 68.17053 1.834294\n",
       "2014 68.36482 1.722138\n",
       "2015 69.81512 1.676521\n",
       "2016 72.44848 1.689608"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "A Time Series:<br><style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>17.5509306321809</li><li>19.6875821786778</li><li>23.754527410949</li><li>26.0099317066083</li><li>28.9435826795993</li><li>29.1671949518264</li><li>30.8313078455822</li><li>32.0606247660408</li><li>32.9028622382245</li><li>32.2008737118851</li><li>33.2623229931611</li><li>34.2090407637095</li><li>35.0548426600559</li><li>40.1131821655803</li><li>42.8495570950485</li><li>43.3076508554009</li><li>46.0507796007465</li><li>48.4086993421954</li><li>50.2431581426909</li><li>52.9004028619215</li><li>51.8315760375836</li><li>61.2403025390097</li><li>64.8855701423558</li><li>67.988550115916</li><li>69.9681423156513</li><li>70.0525156383737</li><li>71.4581062973553</li></ol>\n"
      ],
      "text/latex": [
       "A Time Series:\\\\\\begin{enumerate*}\n",
       "\\item 17.5509306321809\n",
       "\\item 19.6875821786778\n",
       "\\item 23.754527410949\n",
       "\\item 26.0099317066083\n",
       "\\item 28.9435826795993\n",
       "\\item 29.1671949518264\n",
       "\\item 30.8313078455822\n",
       "\\item 32.0606247660408\n",
       "\\item 32.9028622382245\n",
       "\\item 32.2008737118851\n",
       "\\item 33.2623229931611\n",
       "\\item 34.2090407637095\n",
       "\\item 35.0548426600559\n",
       "\\item 40.1131821655803\n",
       "\\item 42.8495570950485\n",
       "\\item 43.3076508554009\n",
       "\\item 46.0507796007465\n",
       "\\item 48.4086993421954\n",
       "\\item 50.2431581426909\n",
       "\\item 52.9004028619215\n",
       "\\item 51.8315760375836\n",
       "\\item 61.2403025390097\n",
       "\\item 64.8855701423558\n",
       "\\item 67.988550115916\n",
       "\\item 69.9681423156513\n",
       "\\item 70.0525156383737\n",
       "\\item 71.4581062973553\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "A Time Series:  \n",
       "1. 17.5509306321809\n",
       "2. 19.6875821786778\n",
       "3. 23.754527410949\n",
       "4. 26.0099317066083\n",
       "5. 28.9435826795993\n",
       "6. 29.1671949518264\n",
       "7. 30.8313078455822\n",
       "8. 32.0606247660408\n",
       "9. 32.9028622382245\n",
       "10. 32.2008737118851\n",
       "11. 33.2623229931611\n",
       "12. 34.2090407637095\n",
       "13. 35.0548426600559\n",
       "14. 40.1131821655803\n",
       "15. 42.8495570950485\n",
       "16. 43.3076508554009\n",
       "17. 46.0507796007465\n",
       "18. 48.4086993421954\n",
       "19. 50.2431581426909\n",
       "20. 52.9004028619215\n",
       "21. 51.8315760375836\n",
       "22. 61.2403025390097\n",
       "23. 64.8855701423558\n",
       "24. 67.988550115916\n",
       "25. 69.9681423156513\n",
       "26. 70.0525156383737\n",
       "27. 71.4581062973553\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "A Time Series:\n",
       " [1] 17.55093 19.68758 23.75453 26.00993 28.94358 29.16719 30.83131 32.06062\n",
       " [9] 32.90286 32.20087 33.26232 34.20904 35.05484 40.11318 42.84956 43.30765\n",
       "[17] 46.05078 48.40870 50.24316 52.90040 51.83158 61.24030 64.88557 67.98855\n",
       "[25] 69.96814 70.05252 71.45811"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 적합된 모형의 변수 확인\n",
    "names(air_holt_de)\n",
    "\n",
    "# 모형의 통게량(추정량 확인)\n",
    "air_holt_de$model\n",
    "air_holt_de$model$states\n",
    "\n",
    "# 적합된 값\n",
    "air_holt_de$fitted\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Forecast method: Damped Holt's method\n",
      "\n",
      "Model Information:\n",
      "Damped Holt's method \n",
      "\n",
      "Call:\n",
      " holt(y = air.ts, h = 15, damped = TRUE) \n",
      "\n",
      "  Smoothing parameters:\n",
      "    alpha = 0.8691 \n",
      "    beta  = 0.0409 \n",
      "    phi   = 0.98 \n",
      "\n",
      "  Initial states:\n",
      "    l = 15.373 \n",
      "    b = 2.2224 \n",
      "\n",
      "  sigma:  2.532\n",
      "\n",
      "     AIC     AICc      BIC \n",
      "145.6239 149.8239 153.3989 \n",
      "\n",
      "Error measures:\n",
      "                    ME     RMSE      MAE      MPE     MAPE      MASE\n",
      "Training set 0.3991511 2.285529 1.529037 0.560457 3.672339 0.6655348\n",
      "                    ACF1\n",
      "Training set -0.03143013\n",
      "\n",
      "Forecasts:\n",
      "     Point Forecast    Lo 80     Hi 80    Lo 95     Hi 95\n",
      "2017       74.10429 70.85945  77.34913 69.14174  79.06685\n",
      "2018       75.72699 71.34160  80.11238 69.02012  82.43386\n",
      "2019       77.31724 71.95975  82.67472 69.12367  85.51081\n",
      "2020       78.87568 72.63402  85.11733 69.32989  88.42147\n",
      "2021       80.40295 73.33096  87.47494 69.58727  91.21862\n",
      "2022       81.89967 74.03329  89.76606 69.86907  93.93028\n",
      "2023       83.36647 74.73101  92.00192 70.15968  96.57325\n",
      "2024       84.80392 75.41796  94.18988 70.44933  99.15851\n",
      "2025       86.21263 76.09013  96.33513 70.73161 101.69365\n",
      "2026       87.59316 76.74490  98.44143 71.00217 104.18415\n",
      "2027       88.94608 77.38050 100.51167 71.25805 106.63412\n",
      "2028       90.27195 77.99578 102.54811 71.49717 109.04672\n",
      "2029       91.57129 78.58999 104.55259 71.71811 111.42448\n",
      "2030       92.84465 79.16270 106.52661 71.91990 113.76940\n",
      "2031       94.09255 79.71365 108.47144 72.10192 116.08317\n"
     ]
    }
   ],
   "source": [
    "summary(air_holt_de)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "위에서 설명한 바와 같이 damped=True 설정하여 적합한 결과를 도식화해보았을 때 mean을 보면, 상승추세를 갖긴 하되 점차적으로 상승하는 속도가 느려짐을 확인하실 수 있을 겁니다.<br/>"
   ]
  }
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