予約データから未来の客数を予測する：第22回 Machine Learning 15minutes! / Predict number of customers in restaurants

トレタの保持する飲食店の予約データを使って、未来のお客様の数を予測するモデルを構築します。予約データの特性と時系列モデリングの導入から説明します。
本資料は下記の勉強会で発表いたしました。
2018年3月31日「第22回 Machine Learning 15minutes! 」
https://machine-learning15minutes.connpass.com/event/78109/

Transcript

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    ະདྷͷ஋Λܭࢉ͢Δ yt = µt + ✏t <latexit sha1_base64="lhTgQbTWtsGqxDJTL2wbLQ29tWs=">AAACA3icbVA9SwNBEJ2LXzF+Re3U4jAIghByNmohBG0sEzAmkBxhbzOXLNnbO3f3hHAErPwpVoIiFjb+Cis7f4p7SQpNfLDs2/dmmJ3nRZwpXSp9WZm5+YXFpexybmV1bX0jv7l1o8JYUqzRkIey4RGFnAmsaaY5NiKJJPA41r3+ZerX71AqFoprPYjQDUhXMJ9Roo3Uzu8M2okenreCOL2PWhgpxo1hHu18oVQsjWDPEmdCCuW99+o3AFTa+c9WJ6RxgEJTTpRq+hxvhZsQqRnlOMy1YoURoX3SxaahggSo3GS0xNA+MErH9kNpjtD2SP3dkZBAqUHgmcqA6J6a9lLxP68Za//UTZiIYo2Cjgf5Mbd1aKeJ2B0mkWo+MIRQycxfbdojklBtcsuZFJzpnWdJ7bh4VnSqJo0LGCMLu7APh+DACZThCipQAwr38AjP8GI9WE/Wq/U2Ls1Yk55t+APr4wfvlJtx</latexit> <latexit sha1_base64="nD9Da+AXzw4U9g+e1E7sO1J7LQU=">AAACA3icbVDLSsNAFJ3UV62vqDsVCRZBEEriRl0IRTcuWzC20JQymd60g5NJnJkIIRTc6Ke4EhRx0Y1f4cpv8CecPhbaemCYM+fcy517/JhRqWz7y8jNzM7NL+QXC0vLK6tr5vrGtYwSQcAlEYtE3ccSGOXgKqoY1GMBOPQZ1Pybi4FfuwMhacSvVBpDM8QdTgNKsNJSy9xKW5nqnXlhMrgPPYglZdrQj5ZZtEv2ENY0ccakWN7pV78fdvuVlvnptSOShMAVYVjKRsDgljczLBQlDHoFL5EQY3KDO9DQlOMQZDMbLtGz9rXStoJI6MOVNVR/d2Q4lDINfV0ZYtWVk95A/M9rJCo4aWaUx4kCTkaDgoRZKrIGiVhtKoAolmqCiaD6rxbpYoGJ0rkVdArO5M7TxD0qnZacqk7jHI2QR9toDx0gBx2jMrpEFeQigu7RE3pBr8aj8Wy8Ge+j0pwx7tlEf2B8/ADN2ZzX</latexit> <latexit sha1_base64="nD9Da+AXzw4U9g+e1E7sO1J7LQU=">AAACA3icbVDLSsNAFJ3UV62vqDsVCRZBEEriRl0IRTcuWzC20JQymd60g5NJnJkIIRTc6Ke4EhRx0Y1f4cpv8CecPhbaemCYM+fcy517/JhRqWz7y8jNzM7NL+QXC0vLK6tr5vrGtYwSQcAlEYtE3ccSGOXgKqoY1GMBOPQZ1Pybi4FfuwMhacSvVBpDM8QdTgNKsNJSy9xKW5nqnXlhMrgPPYglZdrQj5ZZtEv2ENY0ccakWN7pV78fdvuVlvnptSOShMAVYVjKRsDgljczLBQlDHoFL5EQY3KDO9DQlOMQZDMbLtGz9rXStoJI6MOVNVR/d2Q4lDINfV0ZYtWVk95A/M9rJCo4aWaUx4kCTkaDgoRZKrIGiVhtKoAolmqCiaD6rxbpYoGJ0rkVdArO5M7TxD0qnZacqk7jHI2QR9toDx0gBx2jMrpEFeQigu7RE3pBr8aj8Wy8Ge+j0pwx7tlEf2B8/ADN2ZzX</latexit> <latexit sha1_base64="kGnQDiF59M+2vpQ1nnkBDHWZnyA=">AAACA3icbVDLSsNAFJ3UV62vqDvdBIsgCCV1oy6EohuXFYwtNCFMpjft0MkkzkyEEAqu/BRXgiJu/QpX/o2TNgttPTDMmXPu5c49QcKoVLb9bVQWFpeWV6qrtbX1jc0tc3vnTsapIOCQmMWiG2AJjHJwFFUMuokAHAUMOsHoqvA7DyAkjfmtyhLwIjzgNKQEKy355l7m52p84UZpcR+7kEjKtKEfvlm3G/YE1jxplqSOSrR988vtxySNgCvCsJS9kME993IsFCUMxjU3lZBgMsID6GnKcQTSyydLjK1DrfStMBb6cGVN1N8dOY6kzKJAV0ZYDeWsV4j/eb1UhWdeTnmSKuBkOihMmaViq0jE6lMBRLFME0wE1X+1yBALTJTOraZTaM7uPE+ck8Z5o3lj11uXZRxVtI8O0BFqolPUQteojRxE0CN6Rq/ozXgyXox342NaWjHKnl30B8bnD9+amSw=</latexit> µt = µt 1 + ⌘t <latexit sha1_base64="VhCuoI49ttBxPIJ8kwbpIA78Kos=">AAACA3icbVA9SwNBEJ2LXzF+Re20OQ1CQAw5G7UQgjaWETwTyIWwt5lLluztnbt7QjgCVv4UK0ERW8H/YOUPsXfzUWj0wTCP92bYnefHnCldLn9amZnZufmF7GJuaXlldS2/vnGtokRSdGnEI1n3iULOBLqaaY71WCIJfY41v3c+9Gu3KBWLxJXux9gMSUewgFGijdTKb3lh0kr14HTcD5zBvoeaDKVWvlAulUew/xJnQgqVneLXOwBUW/kPrx3RJEShKSdKNQKON6KZEqkZ5TjIeYnCmNAe6WDDUEFCVM10dMTA3jNK2w4iaUpoe6T+3EhJqFQ/9M1kSHRXTXtD8T+vkejguJkyEScaBR0/FCTc1pE9TMRuM4lU874hhEpm/mrTLpGEapNbzqTgTN/8l7iHpZOSc2nSOIMxsrANu1AEB46gAhdQBRco3MEDPMGzdW89Wi/W63g0Y012NuEXrLdv8aWazQ==</latexit> <latexit sha1_base64="Jps0U1ADiJim1dk2qNfvw17azig=">AAACA3icbVDLSsNAFJ34rPUVdaebaBEqYkncqAuh6MZlBWsLTQiT6U07dDKJMxOhhIIrt/6FK0ERt278BVd+iHunj4W2Hrjcwzn3MnNPkDAqlW1/GVPTM7Nz87mF/OLS8sqqubZ+LeNUEKiSmMWiHmAJjHKoKqoY1BMBOAoY1ILOed+v3YKQNOZXqpuAF+EWpyElWGnJNzfdKPUz1Tsd9gOnt++Cwn3JNwt2yR7AmiTOiBTK28Xvjwd3r+Kbn24zJmkEXBGGpWyEDG64l2GhKGHQy7uphASTDm5BQ1OOI5BeNjiiZ+1qpWmFsdDFlTVQf29kOJKyGwV6MsKqLce9vvif10hVeOxllCepAk6GD4Ups1Rs9ROxmlQAUayrCSaC6r9apI0FJkrnltcpOOM3T5LqYemk5FzqNM7QEDm0hXZQETnoCJXRBaqgKiLoDj2iZ/Ri3BtPxqvxNhydMkY7G+gPjPcfZZGb4w==</latexit> <latexit sha1_base64="Jps0U1ADiJim1dk2qNfvw17azig=">AAACA3icbVDLSsNAFJ34rPUVdaebaBEqYkncqAuh6MZlBWsLTQiT6U07dDKJMxOhhIIrt/6FK0ERt278BVd+iHunj4W2Hrjcwzn3MnNPkDAqlW1/GVPTM7Nz87mF/OLS8sqqubZ+LeNUEKiSmMWiHmAJjHKoKqoY1BMBOAoY1ILOed+v3YKQNOZXqpuAF+EWpyElWGnJNzfdKPUz1Tsd9gOnt++Cwn3JNwt2yR7AmiTOiBTK28Xvjwd3r+Kbn24zJmkEXBGGpWyEDG64l2GhKGHQy7uphASTDm5BQ1OOI5BeNjiiZ+1qpWmFsdDFlTVQf29kOJKyGwV6MsKqLce9vvif10hVeOxllCepAk6GD4Ups1Rs9ROxmlQAUayrCSaC6r9apI0FJkrnltcpOOM3T5LqYemk5FzqNM7QEDm0hXZQETnoCJXRBaqgKiLoDj2iZ/Ri3BtPxqvxNhydMkY7G+gPjPcfZZGb4w==</latexit> <latexit sha1_base64="Y7zU3dDTjwVbV5YuI4Y3xk17JdE=">AAACA3icbVBNS8NAEN3Ur1q/ot70EiyCIJbEi3oQil48VjC20ISw2U7apZtN3N0IJQQ8+VM8CYp49Vd48t+4aXvQ6oNhHu/NsDsvTBmVyra/jMrc/MLiUnW5trK6tr5hbm7dyiQTBFySsER0QiyBUQ6uoopBJxWA45BBOxxeln77HoSkCb9RoxT8GPc5jSjBSkuBuePFWZCr4nzSj5zi0AOFSykw63bDHsP6S5wpqaMpWoH56fUSksXAFWFYym7E4I77ORaKEgZFzcskpJgMcR+6mnIcg/Tz8RGFta+VnhUlQhdX1lj9uZHjWMpRHOrJGKuBnPVK8T+vm6no1M8pTzMFnEweijJmqcQqE7F6VABRbKQJJoLqv1pkgAUmSudW0yk4szf/Je5x46zhXNv15sU0jiraRXvoADnoBDXRFWohFxH0gJ7QC3o1Ho1n4814n4xWjOnONvoF4+Mb64CYjw==</latexit> ؍ଌํఔࣜ ঢ়ଶํఔࣜ աڈͷ஋͕ະདྷͷ஋ʹ༩͑ΔӨڹΛղऍ͠΍͍͢
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    MFWFM -PDBM
    MJOFBS
    USFOE 4FBTPOBM $ZDMF IUUQXXXTUBUTNPEFMTPSHEFWHFOFSBUFETUBUTNPEFMTUTBTUBUFTQBDFTUSVDUVSBM6OPCTFSWFE$PNQPOFOUTIUNM yt = µt + ✏t <latexit sha1_base64="lhTgQbTWtsGqxDJTL2wbLQ29tWs=">AAACA3icbVA9SwNBEJ2LXzF+Re3U4jAIghByNmohBG0sEzAmkBxhbzOXLNnbO3f3hHAErPwpVoIiFjb+Cis7f4p7SQpNfLDs2/dmmJ3nRZwpXSp9WZm5+YXFpexybmV1bX0jv7l1o8JYUqzRkIey4RGFnAmsaaY5NiKJJPA41r3+ZerX71AqFoprPYjQDUhXMJ9Roo3Uzu8M2okenreCOL2PWhgpxo1hHu18oVQsjWDPEmdCCuW99+o3AFTa+c9WJ6RxgEJTTpRq+hxvhZsQqRnlOMy1YoURoX3SxaahggSo3GS0xNA+MErH9kNpjtD2SP3dkZBAqUHgmcqA6J6a9lLxP68Za//UTZiIYo2Cjgf5Mbd1aKeJ2B0mkWo+MIRQycxfbdojklBtcsuZFJzpnWdJ7bh4VnSqJo0LGCMLu7APh+DACZThCipQAwr38AjP8GI9WE/Wq/U2Ls1Yk55t+APr4wfvlJtx</latexit> <latexit sha1_base64="nD9Da+AXzw4U9g+e1E7sO1J7LQU=">AAACA3icbVDLSsNAFJ3UV62vqDsVCRZBEEriRl0IRTcuWzC20JQymd60g5NJnJkIIRTc6Ke4EhRx0Y1f4cpv8CecPhbaemCYM+fcy517/JhRqWz7y8jNzM7NL+QXC0vLK6tr5vrGtYwSQcAlEYtE3ccSGOXgKqoY1GMBOPQZ1Pybi4FfuwMhacSvVBpDM8QdTgNKsNJSy9xKW5nqnXlhMrgPPYglZdrQj5ZZtEv2ENY0ccakWN7pV78fdvuVlvnptSOShMAVYVjKRsDgljczLBQlDHoFL5EQY3KDO9DQlOMQZDMbLtGz9rXStoJI6MOVNVR/d2Q4lDINfV0ZYtWVk95A/M9rJCo4aWaUx4kCTkaDgoRZKrIGiVhtKoAolmqCiaD6rxbpYoGJ0rkVdArO5M7TxD0qnZacqk7jHI2QR9toDx0gBx2jMrpEFeQigu7RE3pBr8aj8Wy8Ge+j0pwx7tlEf2B8/ADN2ZzX</latexit> <latexit sha1_base64="nD9Da+AXzw4U9g+e1E7sO1J7LQU=">AAACA3icbVDLSsNAFJ3UV62vqDsVCRZBEEriRl0IRTcuWzC20JQymd60g5NJnJkIIRTc6Ke4EhRx0Y1f4cpv8CecPhbaemCYM+fcy517/JhRqWz7y8jNzM7NL+QXC0vLK6tr5vrGtYwSQcAlEYtE3ccSGOXgKqoY1GMBOPQZ1Pybi4FfuwMhacSvVBpDM8QdTgNKsNJSy9xKW5nqnXlhMrgPPYglZdrQj5ZZtEv2ENY0ccakWN7pV78fdvuVlvnptSOShMAVYVjKRsDgljczLBQlDHoFL5EQY3KDO9DQlOMQZDMbLtGz9rXStoJI6MOVNVR/d2Q4lDINfV0ZYtWVk95A/M9rJCo4aWaUx4kCTkaDgoRZKrIGiVhtKoAolmqCiaD6rxbpYoGJ0rkVdArO5M7TxD0qnZacqk7jHI2QR9toDx0gBx2jMrpEFeQigu7RE3pBr8aj8Wy8Ge+j0pwx7tlEf2B8/ADN2ZzX</latexit> <latexit sha1_base64="kGnQDiF59M+2vpQ1nnkBDHWZnyA=">AAACA3icbVDLSsNAFJ3UV62vqDvdBIsgCCV1oy6EohuXFYwtNCFMpjft0MkkzkyEEAqu/BRXgiJu/QpX/o2TNgttPTDMmXPu5c49QcKoVLb9bVQWFpeWV6qrtbX1jc0tc3vnTsapIOCQmMWiG2AJjHJwFFUMuokAHAUMOsHoqvA7DyAkjfmtyhLwIjzgNKQEKy355l7m52p84UZpcR+7kEjKtKEfvlm3G/YE1jxplqSOSrR988vtxySNgCvCsJS9kME993IsFCUMxjU3lZBgMsID6GnKcQTSyydLjK1DrfStMBb6cGVN1N8dOY6kzKJAV0ZYDeWsV4j/eb1UhWdeTnmSKuBkOihMmaViq0jE6lMBRLFME0wE1X+1yBALTJTOraZTaM7uPE+ck8Z5o3lj11uXZRxVtI8O0BFqolPUQteojRxE0CN6Rq/ozXgyXox342NaWjHKnl30B8bnD9+amSw=</latexit> µt = µt 1 + ⌘t <latexit sha1_base64="VhCuoI49ttBxPIJ8kwbpIA78Kos=">AAACA3icbVA9SwNBEJ2LXzF+Re20OQ1CQAw5G7UQgjaWETwTyIWwt5lLluztnbt7QjgCVv4UK0ERW8H/YOUPsXfzUWj0wTCP92bYnefHnCldLn9amZnZufmF7GJuaXlldS2/vnGtokRSdGnEI1n3iULOBLqaaY71WCIJfY41v3c+9Gu3KBWLxJXux9gMSUewgFGijdTKb3lh0kr14HTcD5zBvoeaDKVWvlAulUew/xJnQgqVneLXOwBUW/kPrx3RJEShKSdKNQKON6KZEqkZ5TjIeYnCmNAe6WDDUEFCVM10dMTA3jNK2w4iaUpoe6T+3EhJqFQ/9M1kSHRXTXtD8T+vkejguJkyEScaBR0/FCTc1pE9TMRuM4lU874hhEpm/mrTLpGEapNbzqTgTN/8l7iHpZOSc2nSOIMxsrANu1AEB46gAhdQBRco3MEDPMGzdW89Wi/W63g0Y012NuEXrLdv8aWazQ==</latexit> <latexit sha1_base64="Jps0U1ADiJim1dk2qNfvw17azig=">AAACA3icbVDLSsNAFJ34rPUVdaebaBEqYkncqAuh6MZlBWsLTQiT6U07dDKJMxOhhIIrt/6FK0ERt278BVd+iHunj4W2Hrjcwzn3MnNPkDAqlW1/GVPTM7Nz87mF/OLS8sqqubZ+LeNUEKiSmMWiHmAJjHKoKqoY1BMBOAoY1ILOed+v3YKQNOZXqpuAF+EWpyElWGnJNzfdKPUz1Tsd9gOnt++Cwn3JNwt2yR7AmiTOiBTK28Xvjwd3r+Kbn24zJmkEXBGGpWyEDG64l2GhKGHQy7uphASTDm5BQ1OOI5BeNjiiZ+1qpWmFsdDFlTVQf29kOJKyGwV6MsKqLce9vvif10hVeOxllCepAk6GD4Ups1Rs9ROxmlQAUayrCSaC6r9apI0FJkrnltcpOOM3T5LqYemk5FzqNM7QEDm0hXZQETnoCJXRBaqgKiLoDj2iZ/Ri3BtPxqvxNhydMkY7G+gPjPcfZZGb4w==</latexit> <latexit sha1_base64="Jps0U1ADiJim1dk2qNfvw17azig=">AAACA3icbVDLSsNAFJ34rPUVdaebaBEqYkncqAuh6MZlBWsLTQiT6U07dDKJMxOhhIIrt/6FK0ERt278BVd+iHunj4W2Hrjcwzn3MnNPkDAqlW1/GVPTM7Nz87mF/OLS8sqqubZ+LeNUEKiSmMWiHmAJjHKoKqoY1BMBOAoY1ILOed+v3YKQNOZXqpuAF+EWpyElWGnJNzfdKPUz1Tsd9gOnt++Cwn3JNwt2yR7AmiTOiBTK28Xvjwd3r+Kbn24zJmkEXBGGpWyEDG64l2GhKGHQy7uphASTDm5BQ1OOI5BeNjiiZ+1qpWmFsdDFlTVQf29kOJKyGwV6MsKqLce9vvif10hVeOxllCepAk6GD4Ups1Rs9ROxmlQAUayrCSaC6r9apI0FJkrnltcpOOM3T5LqYemk5FzqNM7QEDm0hXZQETnoCJXRBaqgKiLoDj2iZ/Ri3BtPxqvxNhydMkY7G+gPjPcfZZGb4w==</latexit> <latexit sha1_base64="Y7zU3dDTjwVbV5YuI4Y3xk17JdE=">AAACA3icbVBNS8NAEN3Ur1q/ot70EiyCIJbEi3oQil48VjC20ISw2U7apZtN3N0IJQQ8+VM8CYp49Vd48t+4aXvQ6oNhHu/NsDsvTBmVyra/jMrc/MLiUnW5trK6tr5hbm7dyiQTBFySsER0QiyBUQ6uoopBJxWA45BBOxxeln77HoSkCb9RoxT8GPc5jSjBSkuBuePFWZCr4nzSj5zi0AOFSykw63bDHsP6S5wpqaMpWoH56fUSksXAFWFYym7E4I77ORaKEgZFzcskpJgMcR+6mnIcg/Tz8RGFta+VnhUlQhdX1lj9uZHjWMpRHOrJGKuBnPVK8T+vm6no1M8pTzMFnEweijJmqcQqE7F6VABRbKQJJoLqv1pkgAUmSudW0yk4szf/Je5x46zhXNv15sU0jiraRXvoADnoBDXRFWohFxH0gJ7QC3o1Ho1n4814n4xWjOnONvoF4+Mb64CYjw==</latexit> yt = µt + ✏t <latexit sha1_base64="lhTgQbTWtsGqxDJTL2wbLQ29tWs=">AAACA3icbVA9SwNBEJ2LXzF+Re3U4jAIghByNmohBG0sEzAmkBxhbzOXLNnbO3f3hHAErPwpVoIiFjb+Cis7f4p7SQpNfLDs2/dmmJ3nRZwpXSp9WZm5+YXFpexybmV1bX0jv7l1o8JYUqzRkIey4RGFnAmsaaY5NiKJJPA41r3+ZerX71AqFoprPYjQDUhXMJ9Roo3Uzu8M2okenreCOL2PWhgpxo1hHu18oVQsjWDPEmdCCuW99+o3AFTa+c9WJ6RxgEJTTpRq+hxvhZsQqRnlOMy1YoURoX3SxaahggSo3GS0xNA+MErH9kNpjtD2SP3dkZBAqUHgmcqA6J6a9lLxP68Za//UTZiIYo2Cjgf5Mbd1aKeJ2B0mkWo+MIRQycxfbdojklBtcsuZFJzpnWdJ7bh4VnSqJo0LGCMLu7APh+DACZThCipQAwr38AjP8GI9WE/Wq/U2Ls1Yk55t+APr4wfvlJtx</latexit> <latexit sha1_base64="nD9Da+AXzw4U9g+e1E7sO1J7LQU=">AAACA3icbVDLSsNAFJ3UV62vqDsVCRZBEEriRl0IRTcuWzC20JQymd60g5NJnJkIIRTc6Ke4EhRx0Y1f4cpv8CecPhbaemCYM+fcy517/JhRqWz7y8jNzM7NL+QXC0vLK6tr5vrGtYwSQcAlEYtE3ccSGOXgKqoY1GMBOPQZ1Pybi4FfuwMhacSvVBpDM8QdTgNKsNJSy9xKW5nqnXlhMrgPPYglZdrQj5ZZtEv2ENY0ccakWN7pV78fdvuVlvnptSOShMAVYVjKRsDgljczLBQlDHoFL5EQY3KDO9DQlOMQZDMbLtGz9rXStoJI6MOVNVR/d2Q4lDINfV0ZYtWVk95A/M9rJCo4aWaUx4kCTkaDgoRZKrIGiVhtKoAolmqCiaD6rxbpYoGJ0rkVdArO5M7TxD0qnZacqk7jHI2QR9toDx0gBx2jMrpEFeQigu7RE3pBr8aj8Wy8Ge+j0pwx7tlEf2B8/ADN2ZzX</latexit> <latexit sha1_base64="nD9Da+AXzw4U9g+e1E7sO1J7LQU=">AAACA3icbVDLSsNAFJ3UV62vqDsVCRZBEEriRl0IRTcuWzC20JQymd60g5NJnJkIIRTc6Ke4EhRx0Y1f4cpv8CecPhbaemCYM+fcy517/JhRqWz7y8jNzM7NL+QXC0vLK6tr5vrGtYwSQcAlEYtE3ccSGOXgKqoY1GMBOPQZ1Pybi4FfuwMhacSvVBpDM8QdTgNKsNJSy9xKW5nqnXlhMrgPPYglZdrQj5ZZtEv2ENY0ccakWN7pV78fdvuVlvnptSOShMAVYVjKRsDgljczLBQlDHoFL5EQY3KDO9DQlOMQZDMbLtGz9rXStoJI6MOVNVR/d2Q4lDINfV0ZYtWVk95A/M9rJCo4aWaUx4kCTkaDgoRZKrIGiVhtKoAolmqCiaD6rxbpYoGJ0rkVdArO5M7TxD0qnZacqk7jHI2QR9toDx0gBx2jMrpEFeQigu7RE3pBr8aj8Wy8Ge+j0pwx7tlEf2B8/ADN2ZzX</latexit> <latexit sha1_base64="kGnQDiF59M+2vpQ1nnkBDHWZnyA=">AAACA3icbVDLSsNAFJ3UV62vqDvdBIsgCCV1oy6EohuXFYwtNCFMpjft0MkkzkyEEAqu/BRXgiJu/QpX/o2TNgttPTDMmXPu5c49QcKoVLb9bVQWFpeWV6qrtbX1jc0tc3vnTsapIOCQmMWiG2AJjHJwFFUMuokAHAUMOsHoqvA7DyAkjfmtyhLwIjzgNKQEKy355l7m52p84UZpcR+7kEjKtKEfvlm3G/YE1jxplqSOSrR988vtxySNgCvCsJS9kME993IsFCUMxjU3lZBgMsID6GnKcQTSyydLjK1DrfStMBb6cGVN1N8dOY6kzKJAV0ZYDeWsV4j/eb1UhWdeTnmSKuBkOihMmaViq0jE6lMBRLFME0wE1X+1yBALTJTOraZTaM7uPE+ck8Z5o3lj11uXZRxVtI8O0BFqolPUQteojRxE0CN6Rq/ozXgyXox342NaWjHKnl30B8bnD9+amSw=</latexit> µt = µt 1 + t 1 + ⌘t <latexit sha1_base64="y3Xv97TeUQOPnd1cIphe8nZZwAE=">AAACD3icbZDNSsNAFIVv/K31L+rSTVSUglgaN+pCKLpxqWC00JYymd7UoZNJnJkIJeQNXPkorgRFunXtygdx77RR0NYLw3yccy8z9/gxZ0pXKh/WxOTU9MxsYa44v7C4tGyvrF6pKJEUPRrxSNZ8opAzgZ5mmmMtlkhCn+O13z0d+Nd3KBWLxKXuxdgMSUewgFGijdSydxph0kp1dpzfe2622/BRkx/OMWvZW5VyZVjOOLjfsFXdKH32AeC8Zb832hFNQhSacqJUPeB4K5opkZpRjlmxkSiMCe2SDtYNChKiaqbDhTJn2yhtJ4ikOUI7Q/X3REpCpXqhbzpDom/UqDcQ//PqiQ4OmykTcaJR0PyhIOGOjpxBOk6bSaSa9wwQKpn5q0NviCRUmwyLJgV3dOdx8PbLR2X3wqRxAnkVYB02oQQuHEAVzuAcPKBwD4/wDC/Wg/VkvVr9vHXC+p5Zgz9lvX0Bwk+fkQ==</latexit> <latexit sha1_base64="nRyzJDntVTnRi/i0rHEighbPE9Y=">AAACD3icbZDNSgMxFIUz9a/Wv6pLN6NFqYhlxo26EIpuXFawttApJZPeaUMzmTHJCGWYNxAEH8WVoIi4c+3KB3Fv2qmgrRdCPs65l+QeN2RUKsv6NDJT0zOzc9n53MLi0vJKfnXtSgaRIFAlAQtE3cUSGOVQVVQxqIcCsO8yqLm9s4FfuwEhacAvVT+Epo87nHqUYKWlVn7H8aNWrJKT9N63kz3HBYV/OMWklS9YJWtY5iTYIyiUN4tfb3fObqWV/3DaAYl84IowLGXDY3DNmzEWihIGSc6JJISY9HAHGho59kE24+FCibmtlbbpBUIfrsyh+nsixr6Ufd/VnT5WXTnuDcT/vEakvKNmTHkYKeAkfciLmKkCc5CO2aYCiGJ9DZgIqv9qki4WmCidYU6nYI/vPAnVg9Jxyb7QaZyitLJoA22hIrLRISqjc1RBVUTQLXpAT+jZuDcejRfjNW3NGKOZdfSnjPdvNjugpw==</latexit> <latexit sha1_base64="nRyzJDntVTnRi/i0rHEighbPE9Y=">AAACD3icbZDNSgMxFIUz9a/Wv6pLN6NFqYhlxo26EIpuXFawttApJZPeaUMzmTHJCGWYNxAEH8WVoIi4c+3KB3Fv2qmgrRdCPs65l+QeN2RUKsv6NDJT0zOzc9n53MLi0vJKfnXtSgaRIFAlAQtE3cUSGOVQVVQxqIcCsO8yqLm9s4FfuwEhacAvVT+Epo87nHqUYKWlVn7H8aNWrJKT9N63kz3HBYV/OMWklS9YJWtY5iTYIyiUN4tfb3fObqWV/3DaAYl84IowLGXDY3DNmzEWihIGSc6JJISY9HAHGho59kE24+FCibmtlbbpBUIfrsyh+nsixr6Ufd/VnT5WXTnuDcT/vEakvKNmTHkYKeAkfciLmKkCc5CO2aYCiGJ9DZgIqv9qki4WmCidYU6nYI/vPAnVg9Jxyb7QaZyitLJoA22hIrLRISqjc1RBVUTQLXpAT+jZuDcejRfjNW3NGKOZdfSnjPdvNjugpw==</latexit> <latexit sha1_base64="2Fm78ffK5PaYnwvakuUaImDxrUE=">AAACD3icbZDNSsNAFIUn9a/Wv6hLN8GiCGJJ3KgLoejGZQVjC00pk+lNO3QyiTMToYS8gSsfxZWgiFvXrnwbp00Ebb0wzMc59zJzjx8zKpVtfxmlufmFxaXycmVldW19w9zcupVRIgi4JGKRaPlYAqMcXEUVg1YsAIc+g6Y/vBz7zXsQkkb8Ro1i6IS4z2lACVZa6pr7Xph0U5Wd5/eRkx16Pij8wzlmXbNq1+xJWbPgFFBFRTW65qfXi0gSAleEYSnbAYM73kmxUJQwyCpeIiHGZIj70NbIcQiyk04Wyqw9rfSsIBL6cGVN1N8TKQ6lHIW+7gyxGshpbyz+57UTFZx2UsrjRAEn+UNBwiwVWeN0rB4VQBQbacBEUP1XiwywwETpDCs6BWd651lwj2tnNefartYvijjKaAftogPkoBNUR1eogVxE0AN6Qi/o1Xg0no034z1vLRnFzDb6U8bHN7wqnVM=</latexit> t = t 1 + ⇣t <latexit sha1_base64="AkZO9akPdUZZF2tHAD6npuqNIak=">AAACCHicbZA9SwNBEIbn4leMX1FLC0+DEBDDnY1aCEEbywjGBJIQ9jZzyZK9vXN3T4hHSit/ipWgiJ34F6z8IfZuPgSNvrDw8M4Ms/N6EWdKO86HlZqanpmdS89nFhaXlleyq2uXKowlxTINeSirHlHImcCyZppjNZJIAo9jxeueDuqVa5SKheJC9yJsBKQtmM8o0cZqZjfrHmrSTHT/+Jv23P5u/WbsNrM5p+AMZf8Fdwy54lb+8xUASs3se70V0jhAoSknStV8jleikRCpGeXYz9RjhRGhXdLGmkFBAlSNZHhJ394xTsv2Q2me0PbQ/TmRkECpXuCZzoDojpqsDcz/arVY+4eNhIko1ijoaJEfc1uH9iAWu8UkUs17BgiVzPzVph0iCdUmvIxJwZ28+S+U9wtHBffcpHECI6VhA7YhDy4cQBHOoARloHAL9/AIT9ad9WA9Wy+j1pQ1nlmHX7LevgDNrpzt</latexit> <latexit sha1_base64="yD9OCNIW8WmkQUrry2QI/Qmb9g8=">AAACCHicbZDLSsNAFIYnXmu9VV26MFqEilgSN+pCKLpxWcHaQhPCZHrSDp1M4sxEqKFLVy58EFeCIm77Cq58EPdOL4K2/jDw8Z9zOHN+P2ZUKsv6NKamZ2bn5jML2cWl5ZXV3Nr6tYwSQaBCIhaJmo8lMMqhoqhiUIsF4NBnUPXb5/169RaEpBG/Up0Y3BA3OQ0owUpbXm7L8UFhL1Xd0x86sLv7zt3I9XJ5q2gNZE6CPYJ8abvw1Xt09spe7sNpRCQJgSvCsJT1gMENd1MsFCUMulknkRBj0sZNqGvkOATppoNLuuaudhpmEAn9uDIH7u+JFIdSdkJfd4ZYteR4rW/+V6snKjh2U8rjRAEnw0VBwkwVmf1YzAYVQBTraMBEUP1Xk7SwwETp8LI6BXv85kmoHBZPivalTuMMDZVBm2gHFZCNjlAJXaAyqiCC7tETekGvxoPxbLwZ78PWKWM0s4H+yOh9A0GangM=</latexit> <latexit sha1_base64="yD9OCNIW8WmkQUrry2QI/Qmb9g8=">AAACCHicbZDLSsNAFIYnXmu9VV26MFqEilgSN+pCKLpxWcHaQhPCZHrSDp1M4sxEqKFLVy58EFeCIm77Cq58EPdOL4K2/jDw8Z9zOHN+P2ZUKsv6NKamZ2bn5jML2cWl5ZXV3Nr6tYwSQaBCIhaJmo8lMMqhoqhiUIsF4NBnUPXb5/169RaEpBG/Up0Y3BA3OQ0owUpbXm7L8UFhL1Xd0x86sLv7zt3I9XJ5q2gNZE6CPYJ8abvw1Xt09spe7sNpRCQJgSvCsJT1gMENd1MsFCUMulknkRBj0sZNqGvkOATppoNLuuaudhpmEAn9uDIH7u+JFIdSdkJfd4ZYteR4rW/+V6snKjh2U8rjRAEnw0VBwkwVmf1YzAYVQBTraMBEUP1Xk7SwwETp8LI6BXv85kmoHBZPivalTuMMDZVBm2gHFZCNjlAJXaAyqiCC7tETekGvxoPxbLwZ78PWKWM0s4H+yOh9A0GangM=</latexit> <latexit sha1_base64="1h2E6e+noUYAj/1XLvYuMFoiFAo=">AAACCHicbZDNSsNAFIUn/tb6F3XpwmARBLEkbtSFUHTjsoK1hSaEyfSmHTqZxJmJUEOWrnwUV4Iibn0FV76N0zaCth4Y+Dj3Xu7cEySMSmXbX8bM7Nz8wmJpqby8srq2bm5s3sg4FQQaJGaxaAVYAqMcGooqBq1EAI4CBs2gfzGsN+9ASBrzazVIwItwl9OQEqy05Zs7bgAK+5nKz37o0MkP3PvC9c2KXbVHsqbBKaCCCtV989PtxCSNgCvCsJTtkMEt9zIsFCUM8rKbSkgw6eMutDVyHIH0stElubWnnY4VxkI/rqyR+3siw5GUgyjQnRFWPTlZG5r/1dqpCk+8jPIkVcDJeFGYMkvF1jAWq0MFEMUGGjARVP/VIj0sMFE6vLJOwZm8eRoaR9XTqnNlV2rnRRwltI120T5y0DGqoUtURw1E0AN6Qi/o1Xg0no03433cOmMUM1voj4yPb8eJmq8=</latexit> ঢ়ଶʢЖʣʹϊΠζʢЏʣ͕ՃΘͬͯ஋ ͕؍ଌʢZʣ͞ΕΔ
    ঢ়ଶ͸ɺ࣌ࠁલͷঢ়ଶʹϊΠζʢБʣ ͕ՃΘͬͯߋ৽͞ΕΔ ঢ়ଶʢЖʣʹϊΠζʢЏʣ͕ՃΘͬͯ஋ ͕؍ଌʢZʣ͞ΕΔ
    ঢ়ଶ͸ɺ࣌ࠁલͷঢ়ଶʹτϨϯυ߲ ʢЌʣͱϊΠζʢБʣ͕ՃΘͬͯߋ৽͞ ΕΔ
    τϨϯυ߲͸࣌ࠁલͷτϨϯυʹϊΠ ζʢАʣ͕ՃΘͬͯߋ৽͞ΕΔ पظతͳมಈΛμϛʔม਺ͱͯ͠ද ݱͯ͠Ϟσϧʹ૊ΈࠐΉ
    4FBTPOBMͱͳ͍ͬͯΔ͕ɺࠓճͷ৔ ߹͸िͷपظతͳมಈΛઆ໌͢Δͨ Ίʹ4FBTPOBMΛ࢖༻͢Δ $ZDMF͸4FBTPOBMΑΓ௕ظతͳϏδ ωεαΠΫϧΛදݱ͢ΔͨΊʹϞσ ϧʹ૊Έࠐ·ΕΔ
    ࠓճ͸قઅมಈΛઆ໌͢ΔͨΊʹ࢖ ༻͢Δ
16. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE 
    ༧ଌϞσϧͷߏங
    ֶशͷ࣮ߦ
     w ֶश͸਺ߦͷίʔυͰ׬ྃ͢Δ
    w -PDBM
    MFWFMͰΦϓγϣϯແ͠ͷ৔߹Λ࣮ߦͯ͠ΈΔ 1 ts_training = daily_customers['2017'] 2 3 model = sm.tsa.UnobservedComponents(ts_training['customers'].to_frame(), level='local level') 4 5 result = model.fit() 6 7 print(result.summary()) 8 9 rcParams['figure.figsize'] = 15, 20 10 fig = result.plot_components() ߦ໨ɿ೥ʹظؒΛݶఆֶͯ͠शσʔλΛ༻ҙ͢Δ
    ߦ໨ɿֶशσʔλͱΦϓγϣϯΛࢦఆͯ͠ɺঢ়ଶۭؒϞσϧΛΠϯελϯεԽ
    ɹɹɹɹࠓճ͸ϩʔΧϧϨϕϧϞσϧͰΦϓγϣϯແ͠
    ߦ໨ɿσʔλʹରͯ͠ύϥϝʔλͷֶशΛ࣮ߦ
    ߦ໨ɿֶश݁ՌͷαϚϦΛίϯιʔϧʹग़ྗ
    ߦ໨ɿঢ়ଶۭؒϞσϧͷߏ੒ཁૉΛඳը -PDBM
    MFWFM
17. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE 
    ༧ଌϞσϧͷߏங
    ֶश݁Ռͷ֬ೝ
     w ໌Β͔ʹिͷมಈΛϞσϧ͕ଊ͑ΒΕ͍ͯͳ͍ ࠇઢɿ࣮σʔλ ੨ઢɿ༧ଌ஋ Ϟσϧ͕୯७͗ͯ͢
    ࣮σʔλͷಛ௃Λଊ͑ΒΕ͍ͯͳ͍
18. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE 
    ༧ଌϞσϧͷߏங
    ֶशͷ࣮ߦʢճ໨ʣ
     w -PDBM
    MJOFBS
    USFOEͰTFBTPOBMɺDZDMF5SVFͰ࣮ߦͯ͠ΈΔ 1 ts_training = daily_customers['2017'] 2 3 model = (sm.tsa.UnobservedComponents(ts_training['customers'].to_frame(), level='local linear trend' 4 , seasonal=7, cycle=True, cycle_period_bounds=(30,500))) 5 6 result = model.fit() 7 8 print(result.summary()) 9 10 rcParams['figure.figsize'] = 15, 30 11 fig = result.plot_components() ߦ໨ɿมߋ఺͸ɺMFWFMʹʮMPDBM
    MJOFBS
    USFOEʯΛࢦఆͯ͠ɺTFBTPOBMͱDZDMFͷΦϓγϣϯΛ෇͚ͨ͜ͱ
    ɹɹɹɹDZDMF@QFSJPE@CPVOET͸DZDMFͷपظΛ୳ࡧ͢ΔϨϯδ -PDBM
    MJOFBS
    USFOE
    
    TFBTPOBM
    
    DZDMF
19. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE 
    ༧ଌϞσϧͷߏங
    ֶश݁Ռͷ֬ೝʢճ໨ʣ
     w ࠇઢͷ࣮੷ͱ੨ઢͷ༧ଌ͕߹͏Α͏ʹͳͬͨ
20. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE 
    ༧ଌϞσϧͷߏங
    Ϟσϧߏ੒ཁૉͷ֬ೝ
     -FWFM 5SFOE 4FBTPOBM $ZDMF ঢ়ଶۭؒϞσϧͷʮঢ়ଶʯͷมԽ τϨϯυͷมԽ
    σʔλશମΛ௨ͯ͠ಉ͡܏޲ʹ͋Δཁૉ͕
    දݱ͞ΕΔ͜ͱ͕๬·͍͠ 4FBTPOBMΛ೔पظͱઃఆͨͨ͠Ί
    िʹΑΔมಈ͕දݱ͞Ε͍ͯΔ
    μϛʔม਺ͷͨΊɺपظత͕ͩಉҰि಺Ͱ͸ෆنଇ $ZDMF͸ࡾ֯ؔ਺Ͱදݱ͞ΕΔͨΊ
    ඇৗʹنଇਖ਼͍͠पظੑ͕දݱ͞ΕΔ
    قઅมಈΛදݱ͢ΔͨΊʹ͸
    ਺೥ʹ౉Δσʔλ͕ඞཁͦ͏
21. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE 
    ༧ଌϞσϧͷߏங
    ֶशͷ਍அ
     -PDBM
    MFWFM -PDBM
    MJOFBS
    USFOE
    
    TFBTP OBM
    
    DZDMF ࢒ࠩͷ෼෍
    ࢒ࠩ͸ϞσϧͰදݱ͖͠Ε ͳ͔ͬͨ෦෼ͳͷͰɺϗϫ ΠτϊΠζʢఆৗ෼෍ʣ͕ ๬·͍͠
    ͜͜ʹ໌Β͔ͳ܏޲͕࢒ͬ ͍ͯΔ৔߹͸ɺϞσϧʹͦ ͷ܏޲Λදݱ͢Δม਺Λ௥ Ճ͢΂͖ ࢒ࠩͷίϨϩάϥϜ
    ࣗݾ૬ؔΛ֬ೝ͢Δάϥϑ
    σϑΥϧτͰMBH·Ͱͷ ίϨϩάϥϜ͕දࣔ͞ΕΔ
    ࣗݾ૬͕ؔ͋Δ৔߹ɺ͋Δ ࣌఺ͷ஋͸ɺաڈͷ஋ʹ૬ ؔؔ܎͕͋Δ஋ͱݟͳͤΔ
    Ϟσϧ͕આ໌Ͱ͖ͳ͔ͬͨ पظੑ͕͋Δ৔߹͸ɺࣗݾ ૬͕ؔ࢒Δ
22. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE 
    ༧ଌϞσϧͷߏங
    Ϟσϧͷબ୒
     w جຊతʹ͸࣮ߦ݁ՌͰ"*$ʢ੺஑৘ใྔن४ʣͷ௿͍ϞσϧΛબ୒͢Δ Unobserved Components Results ==================================================================================== Dep. Variable: customers No. Observations: 365 Model: local linear trend Log Likelihood -1033.339 + stochastic seasonal(7) AIC 2076.679 + cycle BIC 2096.178 Date: Wed, 28 Mar 2018 HQIC 2084.428 Time: 19:56:21 Sample: 01-01-2017 - 12-31-2017 Covariance Type: opg ==================================================================================== coef std err z P>|z| [0.025 0.975] ------------------------------------------------------------------------------------ sigma2.irregular 14.6858 1.183 12.412 0.000 12.367 17.005 sigma2.level 6.23e-10 0.219 2.84e-09 1.000 -0.429 0.429 sigma2.trend 0.0024 0.002 1.551 0.121 -0.001 0.005 sigma2.seasonal 0.0061 0.015 0.393 0.694 -0.024 0.036 frequency.cycle 0.1024 0.017 5.893 0.000 0.068 0.136 =================================================================================== Ljung-Box (Q): 33.60 Jarque-Bera (JB): 2.78 Prob(Q): 0.75 Prob(JB): 0.25 Heteroskedasticity (H): 0.95 Skew: -0.15 Prob(H) (two-sided): 0.78 Kurtosis: 3.32 =================================================================================== Warnings: [1] Covariance matrix calculated using the outer product of gradients (complex-step).
23. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE "HFOEB
     ༧໿σʔλͷಛੑ
    ༧ଌϞσϧͷߏங
    ༧ଌੑೳʹ͍ͭͯ
24. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE 
    ༧ଌੑೳʹ͍ͭͯ
    ධՁࢦඪ
     MAPE = 100 n ⇥ n X i=1 | ࣮ଌ஋i ༧ଌ஋i | ࣮ଌ஋i <latexit sha1_base64="LW7fseL7eqD7VNZtaIXRf5bt2aA=">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</latexit> <latexit sha1_base64="LW7fseL7eqD7VNZtaIXRf5bt2aA=">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</latexit> <latexit sha1_base64="LW7fseL7eqD7VNZtaIXRf5bt2aA=">AAACtnicfVLBTttAEB27hdJAIdBjL6sGJA40srlQDkjQqlIvrVKpgUhJiNabcVix3rV214jI+N6/6E/10r/pxInaEKTOytbb9+Z51jOb5Eo6H0W/g/DZ87X1FxsvG5tbr7Z3mrt7l84UVmBXGGVsL+EOldTY9dIr7OUWeZYovEpuP870qzu0Thr93U9zHGZ8omUqBfdEmWYKA8ggAQP3UMIXuIAOfIIKzohPwQIHQXwMEa2KkKY3I82DJB+Cq3cOCtqNSJfkjCnnein333celqv1f+qjzj7lzH0VvFtWv/5YUR/q+v/zV6NmK2pHdbCnIF6AFiyiM2r+GoyNKDLUXijuXD+Ocj8sufVSKKwaB4PCYc7FLZ9gn6DmGbphWbe9YgfEjFlqLD3as5ptLDlKnjk3zRLKzLi/cavajPyrPS7l0/fDUuq88KjFvFJaKOYNmw2RjaVF4dWUABdW0mmZuOGWC0+jblAb4tWffgq6x+3Tdvwtap1/WPRjA97AWzik+Z3AOXymm9AFERwHvYAHSXgajkIMJ/PUMFh4XsOjCPM/gOq2rQ==</latexit> <latexit sha1_base64="LW7fseL7eqD7VNZtaIXRf5bt2aA=">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</latexit> MAD = 1 n ⇥ n X i=1 | ࣮ଌ஋i ༧ଌ஋i | <latexit sha1_base64="mVy3JroPLZoVOMoL254tzPmrOyA=">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</latexit> <latexit sha1_base64="mVy3JroPLZoVOMoL254tzPmrOyA=">AAAChnicZVFNT+MwEJ2E7/JV4LgXi4LEAUqChIDDSt2FAxdQkSggNaVyXAcsHDuyndVWoXf+xf4pLvtvmKYVKmUkS2/ee+OxZ+JMCuuC4L/nz8zOzS8sLlWWV1bX1qsbm3dW54bxFtNSm4eYWi6F4i0nnOQPmeE0jSW/j1/Oh/r9H26s0OrW9TPeSemTEolg1CGlq9cQQQoxaPgLBVzBL7iAARD4iSeCBAxQYKiEyBagSi0CBwKrONgys5Bj1kVdYN3Q+fjpfZ28v/1P7Td3kB95B3AwqV6/Tamv3WotqAdlkO8gHIMajKPZrb5HPc3ylCvHJLW2HQaZ6xTUOMEkH1R2o9zyjLIX+sTbCBVNue0U5RgHZBeZHkm0waMcKdnKREVBU2v7aYzOlLpnO60NyU/tayuXnHYKobLcccVGnZJcEqfJcCmkJwxnTvYRUGYEvpawZ2ooc7i6Co4hnP70d9A6qp/Vw5ug1vg9nsci/IBt2MONnEADLqEJLWCe7+15oXfkL/mH/rF/MrL63rhmC76E3/gArYGpug==</latexit> <latexit sha1_base64="mVy3JroPLZoVOMoL254tzPmrOyA=">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</latexit> <latexit sha1_base64="mVy3JroPLZoVOMoL254tzPmrOyA=">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</latexit> MSD = 1 n ⇥ n X i=1 | ࣮ଌ஋i ༧ଌ஋i |2 <latexit sha1_base64="GTgJwHjH3lmpxQUR/HjE7dwtEiw=">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</latexit> <latexit 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    ޡࠩͷྔΛ֓೦Խ͢Δͷʹ໾ཱͭ ෼ࢄ΍ඪ४ภࠩʹ͍ۙܭࢉࣜͱͳ͍ͬͯΔͨΊɺ ྨࣅͨ͠஋ͱଊ͑Δ͜ͱ͕Ͱ͖Δ
    ޡࠩͷࠩΛೋ৐͍ͯ͠ΔͨΊɺޡ͕ࠩେ͖͍৔߹ ʹڧௐͯ͠ܭࢉ͞Εɺ֎Ε஋ͷӨڹΛड͚΍͍͢ ฏۉઈରύʔηϯτޡࠩ
    ʢ."1&ʣ ฏۉઈରภࠩ
    ʢ."%ʣ ฏۉฏํภࠩ
    ʢ.4%ʣ ධՁࢦඪ ܭࢉࣜ ֓ཁ
25. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE 
    ༧ଌੑೳʹ͍ͭͯ
    ೥݄ͷ༧ଌൺֱ
     w ࠇઢ͕࣮੷Ͱɺ੺ઢ͕༧ଌ       -PDBM
    MFWFM -PDBM
    MJOFBS
    USFOE
    
    4FBTPOBM
    
    $ZDMF -PDBM
    MFWFM
    
    4FBTPOBM "*$ ."1& "*$ ."1& "*$ ."1& w ࣌ܥྻσʔλ͸͋Δ࣌఺Ͱαϯϓϧ਺ͷσʔλͷͨΊɺ༧ଌ͸؆୯ʹ౰ͨΒͳ͍
    w ֶश࣌ͷධՁࢦඪ͸ඞͣ͠΋༧ଌ࣌ͷੑೳΛ୲อ͠ͳ͍
    w ༧ଌ࣌ʹ͸࣮ࡍͷΞΫγϣϯΛݟਾ͑ͨධՁࢦඪʢྫ͑͹ച্ʣΛઃఆ͢΂͖
26. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE
     wԾʹ༧ଌ͕౰ͨΔͱ͢Ε͹ɺਓ͕ؒͲΜͳΞΫγϣ ϯΛͯ͠΋ະདྷ͸มΘΒͳ͍
    wਓ͕ؒΞΫγϣϯΛͨ࣌͠఺Ͱɺ༧ଌϞσϧͱ͸ҟͳΔະ དྷ͕ඳ͔Ε࢝ΊΔ ༧ଌਫ਼౓͸ߴ͍ํ͕ྑ͍ʁ w༧ଌϞσϧ͸ະདྷΛγϛϡϨʔγϣϯͯ͠ҙࢥܾఆ͢Δ ͨΊͷπʔϧ
    w༧ଌੑೳʹͩ͜ΘΔͷͰ͸ͳ͘ɺ༧ଌʹΑΔҙࢥܾఆͷ ݁Ռ͕޲্͔ͨ͠Ͳ͏͔ͷԾઆݕূ͕ॏཁ
27. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE
     σʔλΛ࢖ͬͯʮ৯ͷ࢓ࣄΛɺ͓ ΋͠Ζ͘ʯ͢Δ஥ؒΛืू
    w ը૾ॲཧʢྉཧ΍͓ళͷࣸਅʣ
    w ࣗવݴޠॲཧʢϝχϡʔɺϨ Ϗϡʔɺ104ʣ
    w Ϧίϝϯσʔγϣϯ
    w ࣌ܥྻϞσϧʢधཁ༧ଌʣ σʔλαΠΤϯςΟετืूத ҿ৯ۀσʔλϏδωεల։த ໿ສళฮɺ೥ؒສ݅ͷ༧ ໿σʔλΛ࢖ͬͯɺ৽͍͠Ϗδω εΛى͜͢ύʔτφʔΛืू
    w ϚʔέςΟϯάϦαʔν
    w धཁ༧ଌ
    w ༧໿࠷దԽ
29. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE "QQFOEJY
    
30. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE "QQFOEJY
    
     1 import numpy as np 2 import pandas as pd 3 4 from matplotlib import pylab as plt 5 from matplotlib.pylab import rcParams 6 %matplotlib inline 7 8 import statsmodels.api as sm ࣮ߦ؀ڥ w .BD
    04
    )JHI
    4JFSSB
    
    w 1ZUIPO
    
    w +VQZUFS
    
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    ϥΠϒϥϦ
31. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE "QQFOEJY
    ٙࣅσʔλੜ੒
     1 start = pd.datetime(2017, 1, 1) 2 end = pd.datetime(2018, 1, 31) 3 date_index = pd.date_range(start=start, end=end) 4 5 mu = 40 6 mu_week = [-2, -4, 0, 1, 7, 8, 3] 7 s = 4 8 9 10 def mu_season(x): 11 if (x % 365) < 31: 12 return -0.3*(x % 365) + 10 13 elif 31 <= (x % 365) < 90: 14 return 0.15*((x % 365)-31) 15 elif 90 <= (x % 365) < 212: 16 return -0.09*((x % 365)-90) + 10 17 elif 212 <= (x % 365) < 243: 18 return 0.3*((x % 365)-212) 19 elif 243 <= (x % 365) < 273: 20 return -0.3*((x % 365)-243)+10 21 elif 273 <= (x % 365): 22 return 0.11*((x % 365)-273) 23 24 25 Y = [] 26 np.random.seed(1234) 27 for i in range(len(date_index)): 28 Y.append(np.absolute(np.floor(np.random.normal(loc=mu + mu_week[i % 7] + mu_season(i), scale=s)))) 29 30 daily_customers = pd.DataFrame(data={'date': date_index, 'customers': Y}, index=date_index) ٙࣅσʔλ ੜ੒ 1 ax = daily_customers['customers'].plot(figsize=(8, 4), grid=True, color='black') 2 ax.set_ylabel('customers') 3 fig = ax.get_figure() ඳը
32. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE "QQFOEJY
    Ϟσϧͷֶश
     1 ts_training = daily_customers['2017'] 2 3 model = sm.tsa.UnobservedComponents(ts_training['customers'].to_frame(), level='local level') 4 5 result = model.fit() 6 7 print(result.summary()) -PDBM
    MFWFM
    NPEFMͷֶश 1 ts_training = daily_customers['2017'] 2 3 model = (sm.tsa.UnobservedComponents(ts_training['customers'].to_frame(), level='local linear trend' 4 , seasonal=7, cycle=True, cycle_period_bounds=(30,500))) 5 6 result = model.fit() 7 8 print(result.summary()) -PDBM
    MJOFBS
    USFOE
    
    TFBTPOBM
    
    DZDMF
    NPEFM ͷֶश 1 ts_training = daily_customers['2017'] 2 3 model = (sm.tsa.UnobservedComponents(ts_training['customers'].to_frame(), level='local linear trend', seasonal=7)) 4 5 result = model.fit() 6 7 print(result.summary()) -PDBM
    MFWFM
    
    TFBTPOBM
    NPEFMͷֶश
33. 5PSFUB
    *OD
    "MM
    SJHIU
    SFTFSWFE "QQFOEJY
    Ϟσϧͷ֬ೝɾ༧ଌͷ࣮ߦͱ."1&ͷࢉग़
     1 rcParams['figure.figsize'] = 25, 20 2 fig = result.plot_diagnostics() NPEFMͷ DPNQPOFOU TΛඳը 1 rcParams['figure.figsize'] = 15, 30 2 fig = result.plot_components() NPEFMͷ਍அ Λඳը 1 pred = result.predict(pd.to_datetime('2017-12-31'), pd.to_datetime('2018-01-31')) 2 3 ax = daily_customers['customers'].plot(figsize=(8, 4), grid=True, color='black') 4 ax.set_xlim([pd.datetime(2017, 12, 30), pd.datetime(2018, 1, 31)]) 5 ax.set_ylabel('customers') 6 ax = pred.plot(figsize=(8, 4), grid=True, color='red') 7 fig = ax.get_figure() ༧ଌͷ࣮ߦͱ ඳը 1 eval_test = daily_customers['customers']['2018'] 2 eval_pred = pred['2018'] 3 4 mape = 100 * np.sum(np.absolute(eval_test - eval_pred) / eval_test) / eval_test.shape[0] 5 print("MAPE = {0:.3f}".format(mape)) ."1&ͷࢉग़