\ub525\ub7ec\ub2dd\uacfc \uc2dc\uacc4\uc5f4 \ubd84\uc11d\uc740 \ud604\ub300 \ub370\uc774\ud130 \uacfc\ud559\uc758 \uc911\uc694\ud55c \ub450 \ucd95\uc785\ub2c8\ub2e4. \uc624\ub298\uc740 ARIMA \ubaa8\ub378\uc5d0 \ub300\ud574 \uc0b4\ud3b4\ubcf4\uace0, \uc774\ub97c \ud30c\uc774\ud1a0\uce58\uc640 \ud568\uaed8 \uc5b4\ub5bb\uac8c \ud65c\uc6a9\ud560 \uc218 \uc788\ub294\uc9c0\ub97c \uc54c\uc544\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. ARIMA(Autoregressive Integrated Moving Average) \ubaa8\ub378\uc740 \ubc29\ub300\ud55c \uc591\uc758 \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\ub97c \ubd84\uc11d\ud558\uace0 \uc608\uce21\ud558\ub294 \ub370 \uc720\uc6a9\ud55c \ud1b5\uacc4\uc801 \ubc29\ubc95\uc785\ub2c8\ub2e4. \uc774\ub294 \ud2b9\ud788 \uacbd\uc81c, \uae30\ud6c4, \uc8fc\uc2dd\uc2dc\uc7a5 \ub4f1 \ub2e4\uc591\ud55c \ubd84\uc57c\uc5d0\uc11c \ud65c\uc6a9\ub429\ub2c8\ub2e4.<\/p>\n
ARIMA \ubaa8\ub378\uc740 3\uac1c\uc758 \uc8fc\uc694 \uad6c\uc131 \uc694\uc18c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc2b5\ub2c8\ub2e4. \uc774\ub4e4 \uac01\uac01\uc758 \uad6c\uc131 \uc694\uc18c\ub294 \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\ub97c \ubd84\uc11d\ud558\uace0 \uc608\uce21\ud558\ub294 \ub370 \ud544\uc694\ud55c \uc815\ubcf4\ub97c \uc81c\uacf5\ud569\ub2c8\ub2e4:<\/p>\n
ARIMA \ubaa8\ub378\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \uc218\uc2dd\uc73c\ub85c \ud45c\ud604\ub429\ub2c8\ub2e4:<\/p>\n
\nY(t) = c + \u03c6_1 * Y(t-1) + \u03c6_2 * Y(t-2) + ... + \u03c6_p * Y(t-p) \n + \u03b8_1 * \u03b5(t-1) + \u03b8_2 * \u03b5(t-2) + ... + \u03b8_q * \u03b5(t-q) + \u03b5(t)\n <\/pre>\n\uc5ec\uae30\uc11c
Y(t)<\/code>\ub294 \uc2dc\uacc4\uc5f4\uc758 \ud604\uc7ac \uac12,c<\/code>\ub294 \uc0c1\uc218,\u03c6<\/code>\ub294 AR \uacc4\uc218,\u03b8<\/code>\ub294 MA \uacc4\uc218,\u03b5(t)<\/code>\ub294 \ubc31\uc0c9\uc7a1\uc74c\uc785\ub2c8\ub2e4.<\/p>\n3. ARIMA \ubaa8\ub378\uc758 \ub2e8\uacc4<\/h2>\n
ARIMA \ubaa8\ub378\uc744 \uad6c\uc131\ud558\ub294 \uc8fc\uc694 \ub2e8\uacc4\ub294 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n
\n
- \ub370\uc774\ud130 \uc218\uc9d1 \ubc0f \uc804\ucc98\ub9ac: \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\ub97c \uc218\uc9d1\ud558\uace0 \uacb0\uce21\uac12, \uc774\uc0c1\uce58\ub97c \ucc98\ub9ac\ud569\ub2c8\ub2e4.<\/li>\n
- \ub370\uc774\ud130\uc758 \uc815\uc131 \uac80\uc0ac: \ub370\uc774\ud130\uac00 \uc815\uc0c1\uc778\uc9c0 \uc544\ub2cc\uc9c0\ub97c \uac80\uc0ac\ud569\ub2c8\ub2e4.<\/li>\n
- \ubaa8\ub378 \uc120\uc815: ARIMA \ubaa8\ub378\uc758 \ucd5c\uc801 \ud30c\ub77c\ubbf8\ud130(p, d, q)\ub97c \uc120\uc815\ud569\ub2c8\ub2e4. \uc774\ub294 ACF(\uc790\uae30\uc0c1\uad00\ud568\uc218)\uc640 PACF(\ubd80\ubd84\uc790\uae30\uc0c1\uad00\ud568\uc218)\ub97c \ubd84\uc11d\ud558\uc5ec \uacb0\uc815\ub429\ub2c8\ub2e4.<\/li>\n
- \ubaa8\ub378 \uc801\ud569: \uc120\ud0dd\ud55c \ud30c\ub77c\ubbf8\ud130\ub97c \uae30\ubc18\uc73c\ub85c \ubaa8\ub378\uc744 \uc801\ud569\uc2dc\ud0b5\ub2c8\ub2e4.<\/li>\n
- \ubaa8\ub378 \uc9c4\ub2e8: \uc794\ucc28\ub97c \uac80\uc0ac\ud558\uace0 \ubaa8\ub378\uc758 \uc2e0\ub8b0\uc131\uc744 \ud3c9\uac00\ud569\ub2c8\ub2e4.<\/li>\n
- \uc608\uce21: \ubaa8\ub378\uc744 \ud1b5\ud574 \ubbf8\ub798 \uac12\uc744 \uc608\uce21\ud569\ub2c8\ub2e4.<\/li>\n<\/ol>\n
4. ARIMA \ubaa8\ub378\uc744 \ud30c\uc774\uc36c\uc73c\ub85c \uad6c\ud604\ud558\uae30<\/h2>\n
\uc774\uc81c ARIMA \ubaa8\ub378\uc744 \ud30c\uc774\uc36c\uc73c\ub85c \uad6c\ud604\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc6b0\ub9ac\ub294
statsmodels<\/code> \ub77c\uc774\ube0c\ub7ec\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec ARIMA \ubaa8\ub378\uc744 \uad6c\uc131\ud560 \uac83\uc785\ub2c8\ub2e4.<\/p>\n4.1 \ub370\uc774\ud130 \uc218\uc9d1 \ubc0f \uc804\ucc98\ub9ac<\/h3>\n
\uba3c\uc800, \ud544\uc694\ud55c \ub77c\uc774\ube0c\ub7ec\ub9ac\ub97c \uc784\ud3ec\ud2b8\ud558\uace0 \ub370\uc774\ud130\ub97c \ubd88\ub7ec\uc635\ub2c8\ub2e4. \uc608\uc81c\ub85c `AirPassengers` \ub370\uc774\ud130\ub97c \uc0ac\uc6a9\ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n
\nimport pandas as pd\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom statsmodels.tsa.arima.model import ARIMA\nfrom statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n\n# \ub370\uc774\ud130 \ubd88\ub7ec\uc624\uae30\ndata = pd.read_csv('AirPassengers.csv')\ndata['Month'] = pd.to_datetime(data['Month'])\ndata.set_index('Month', inplace=True)\ndata = data['#Passengers']\n\n# \ub370\uc774\ud130 \uc2dc\uac01\ud654\nplt.figure(figsize=(12, 6))\nplt.plot(data)\nplt.title('AirPassengers Data')\nplt.xlabel('Date')\nplt.ylabel('Number of Passengers')\nplt.show()\n <\/pre>\n4.2 \ub370\uc774\ud130 \uc815\uc0c1\uc131 \uac80\uc0ac<\/h3>\n
\ub370\uc774\ud130\uac00 \uc815\uc0c1\uc778\uc9c0 \ud655\uc778\ud558\uae30 \uc704\ud574 ADF(Augmented Dickey-Fuller) \uac80\uc815\uc744 \uc218\ud589\ud569\ub2c8\ub2e4.<\/p>\n
\nfrom statsmodels.tsa.stattools import adfuller\n\nresult = adfuller(data)\nif result[1] <= 0.05:\n print(\"\ub370\uc774\ud130\ub294 \uc815\uc0c1\uc785\ub2c8\ub2e4.\")\nelse:\n print(\"\ub370\uc774\ud130\ub294 \ube44\uc815\uc0c1\uc785\ub2c8\ub2e4.\")\n # \ucc28\ubd84\uc744 \ud1b5\ud574 \uc815\uc0c1\ud654\n data_diff = data.diff().dropna()\n plt.figure(figsize=(12, 6))\n plt.plot(data_diff)\n plt.title('Differenced Data')\n plt.xlabel('Date')\n plt.ylabel('Differenced Passengers')\n plt.show()\n result_diff = adfuller(data_diff)\n if result_diff[1] <= 0.05:\n print(\"\ucc28\ubd84 \ud6c4 \ub370\uc774\ud130\ub294 \uc815\uc0c1\uc785\ub2c8\ub2e4.\")\n else:\n print(\"\ucc28\ubd84 \ud6c4 \ub370\uc774\ud130\ub294 \uc5ec\uc804\ud788 \ube44\uc815\uc0c1\uc785\ub2c8\ub2e4.\")\n <\/pre>\n4.3 ARIMA \ubaa8\ub378\uc758 \ud30c\ub77c\ubbf8\ud130 \uc120\uc815<\/h3>\n
ACF\uc640 PACF \ud50c\ub86f\uc744 \uc0ac\uc6a9\ud558\uc5ec p, d, q \ud30c\ub77c\ubbf8\ud130\ub97c \uc120\uc815\ud569\ub2c8\ub2e4.<\/p>\n
\nplot_acf(data_diff)\nplot_pacf(data_diff)\nplt.show()\n <\/pre>\n\uc0c1\uad00 \ud568\uc218\uc758 \ud328\ud134\uc744 \ubd84\uc11d\ud558\uc5ec AR \ubc0f MA\uc758 \ucc28\uc218\ub97c \uacb0\uc815\ud569\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4, p=2, d=1, q=2\ub85c \uc120\uc815\ud588\ub2e4\uace0 \uac00\uc815\ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n
4.4 ARIMA \ubaa8\ub378 \uc801\ud569<\/h3>\n
\nmodel = ARIMA(data, order=(2, 1, 2))\nmodel_fit = model.fit()\nprint(model_fit.summary())\n <\/pre>\n4.5 \ubaa8\ub378 \uc9c4\ub2e8<\/h3>\n
\uc794\ucc28 \ubd84\uc11d\uc744 \ud1b5\ud574 \ubaa8\ub378\uc758 \uc801\ud569\uc131\uc744 \ud655\uc778\ud569\ub2c8\ub2e4.<\/p>\n
\nresiduals = model_fit.resid\nplt.figure(figsize=(12, 6))\nplt.subplot(211)\nplt.plot(residuals)\nplt.title('Residuals')\nplt.subplot(212)\nplt.hist(residuals, bins=20)\nplt.title('Residuals Histogram')\nplt.show()\n <\/pre>\n4.6 \uc608\uce21<\/h3>\n
\uc801\ud569\ub41c \ubaa8\ub378\ub85c \ubbf8\ub798 \uac12\uc744 \uc608\uce21\ud569\ub2c8\ub2e4.<\/p>\n
\nforecast = model_fit.forecast(steps=12)\nforecast_index = pd.date_range(start='1961-01-01', periods=12, freq='M')\nforecast_series = pd.Series(forecast, index=forecast_index)\n\nplt.figure(figsize=(12, 6))\nplt.plot(data, label='Historical Data')\nplt.plot(forecast_series, label='Forecast', color='red')\nplt.title('Passenger Forecast')\nplt.xlabel('Date')\nplt.ylabel('Number of Passengers')\nplt.legend()\nplt.show()\n <\/pre>\n5. ARIMA \ubaa8\ub378\uc758 \ud55c\uacc4 \ubc0f \uacb0\ub860<\/h2>\n
ARIMA \ubaa8\ub378\uc740 \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\uc758 \ud328\ud134\uc744 \uc798 \ud3ec\ucc29\ud569\ub2c8\ub2e4. \uadf8\ub7ec\ub098 \uba87 \uac00\uc9c0 \ud55c\uacc4\uac00 \uc788\uc2b5\ub2c8\ub2e4.:<\/p>\n
\n
- \uc120\ud615\uc131 \uac00\uc815: ARIMA \ubaa8\ub378\uc740 \ub370\uc774\ud130\uac00 \uc120\ud615\uc801\uc774\ub77c\ub294 \uac00\uc815\uc744 \uae30\ubc18\uc73c\ub85c \ud558\uae30 \ub54c\ubb38\uc5d0 \ube44\uc120\ud615 \uad00\uacc4\ub97c \uc798 \ud3ec\ucc29\ud558\uc9c0 \ubabb\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n
- \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\uc758 \uacc4\uc808\uc131: ARIMA \ubaa8\ub378\uc740 \uacc4\uc808\uc131\uc774 \uc788\ub294 \ub370\uc774\ud130\uc5d0 \uc801\ud569\ud558\uc9c0 \uc54a\uc2b5\ub2c8\ub2e4. \uc774 \uacbd\uc6b0 SARIMA(Seasonal ARIMA) \ubaa8\ub378\uc774 \uc0ac\uc6a9\ub429\ub2c8\ub2e4.<\/li>\n
- \ub9e4\uac1c\ubcc0\uc218 \uc120\ud0dd: \ucd5c\uc801\uc758 \ub9e4\uac1c\ubcc0\uc218\ub97c \uc120\ud0dd\ud558\ub294 \uc77c\uc740 \uc885\uc885 \uc5b4\ub824\uc6b4 \uc791\uc5c5\uc785\ub2c8\ub2e4.<\/li>\n<\/ul>\n
\ub525\ub7ec\ub2dd\uacfc ARIMA \ubaa8\ub378\uc740 \uc11c\ub85c \ubcf4\uc644\uc801\uc778 \ubd80\ubd84\uc774 \ub9ce\uc2b5\ub2c8\ub2e4. \uc5ec\ub7ec \ub370\uc774\ud130\ub97c \ubd84\uc11d\ud560 \ub54c \ub525\ub7ec\ub2dd \ubaa8\ub378\uc744 \ud65c\uc6a9\ud558\uc5ec \ube44\uc120\ud615\uc801\uc778 \ud328\ud134\uc744 \ud3ec\ucc29\ud558\uace0,ARIMA \ubaa8\ub378\uc744 \ud1b5\ud574 \ub370\uc774\ud130\uc758 \uae30\ubcf8\uc801\uc778 \ud2b8\ub80c\ub4dc\ub97c \uc774\ud574\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n
6. \ucc38\uace0 \uc790\ub8cc<\/h2>\n
\n
- Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and Practice<\/em> (2nd ed.). OTexts.<\/li>\n
- Statsmodels Documentation: https:\/\/www.statsmodels.org\/stable\/index.html<\/a><\/li>\n
- Pytorch Documentation: https:\/\/pytorch.org\/docs\/stable\/index.html<\/a><\/li>\n<\/ul>\n
<\/body><\/p>\n","protected":false},"excerpt":{"rendered":"