class: center, middle, inverse, title-slide .title[ # Seminário — séries temporais<br><br><br><br> ] .subtitle[ ## Vendas no Varejo em Lojas de Artigos Esportivos. ] .author[ ### Márcio Roger Piagio <br><br><br><br><br> ] .date[ ### 23 de abril de 2023 ] --- <head> <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/animate.css/4.1.1/animate.min.css" /> </head> <style type="text/css"> .panelset { --panel-tab-foreground: currentColor; --panel-tab-active-foreground: darkslategrey; --panel-tab-hover-foreground: #d22; --panel-tabs-border-bottom: #ddd; --panel-tab-inactive-opacity: 0.3; --panel-tab-font-family: Roboto, Menlo, Consolas, Monaco, Liberation Mono, Lucida Console, monospace;\ } </style> <center><h1 class="animate__animated animate__rubberBand">Descrição do banco de dados.</h1></center> .panelset[ .panel[.panel-name[Apresentação] - Frequência: Mensal. - Tempo da série: janeiro de 2000 até Dezembro de 2022. - Quatidade de observações: 276. - Unidades: Milhões de 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overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-a1d7{background-color:#efefef;border-color:#c0c0c0;color:#000000;font-size:18px;text-align:center;vertical-align:top} .tg .tg-dzn6{background-color:#2F4F4F;border-color:#c0c0c0;color:#ffffff;font-size:26px;font-weight:bold;text-align:center; vertical-align:top} .tg .tg-0ve6{background-color:#2f4f4f;border-color:#c0c0c0;color:#ffffff;font-size:26px;font-weight:bold;text-align:center; vertical-align:top} .tg .tg-q854{background-color:#ffffff;border-color:#c0c0c0;color:#000000;font-size:18px;text-align:center;vertical-align:top} </style> <table class="tg"> <thead> <tr> <th class="tg-dzn6">Coef</th> <th class="tg-dzn6">ar<sub>1</sub></th> <th class="tg-0ve6">ma<sub>1</sub></th> <th class="tg-0ve6">ma<sub>2</sub></th> <th 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class="tg-xhcn">abr<sub>2020</sub></th> <th class="tg-xhcn">jun<sub>2020</sub></th> <th class="tg-xhcn">set<sub>2020</sub></th> <th class="tg-xhcn">abr<sub>2021</sub></th> </tr> </thead> <tbody> <tr> <td class="tg-huqt"></td> <td class="tg-huqt">-1.1563</td> <td class="tg-huqt">-0.9434</td> <td class="tg-huqt">0.8109</td> <td class="tg-lw0b">0.3711</td> <td class="tg-huqt">-0.3548</td> <td class="tg-huqt">-0.6415</td> <td class="tg-huqt">-0.1957</td> <td class="tg-huqt">-0.5318</td> <td class="tg-o9zd">0.1398</td> <td class="tg-o9zd">0.0857</td> <td class="tg-o9zd">0.1464</td> </tr> <tr> <td class="tg-e4rb">s.e.</td> <td class="tg-e4rb">0.0366</td> <td class="tg-e4rb">0.0297</td> <td class="tg-e4rb">0.0758</td> <td class="tg-i2cn">0.0954</td> <td class="tg-e4rb">0.0812</td> <td class="tg-e4rb">0.0613</td> <td class="tg-e4rb">0.0341</td> <td class="tg-e4rb">0.0297</td> <td class="tg-juur">0.0299</td> <td class="tg-juur">0.0287</td> <td class="tg-juur">0.0327</td> </tr> <tr> <td class="tg-huqt" colspan="4">sigma² = 0.001306</td> <td class="tg-lw0b" colspan="4">log likelihood = 473.67</td> <td class="tg-huqt" colspan="4">aic = -923.34</td> </tr> </tbody> </table> </div> ] .panel[.panel-name[Análise de resíduos] <div class="animate__animated animate__flipInY"> <style type="text/css"> .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-a1d7{background-color:#efefef;border-color:#c0c0c0;color:#000000;font-size:18px;text-align:center;vertical-align:top} .tg .tg-dzn6{background-color:#2F4F4F;border-color:#c0c0c0;color:#ffffff;font-size:26px;font-weight:bold;text-align:center; vertical-align:top} .tg 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table","invalidDate":null,"loading":"Loading...","months":["January","February","March","April","May","June","July","August","September","October","November","December"],"noData":"No data to display","numericSymbolMagnitude":1000,"numericSymbols":["k","M","G","T","P","E"],"printChart":"Print chart","resetZoom":"Reset zoom","resetZoomTitle":"Reset zoom level 1:1","shortMonths":["Jan","Feb","Mar","Apr","May","Jun","Jul","Aug","Sep","Oct","Nov","Dec"],"shortWeekdays":["Sat","Sun","Mon","Tue","Wed","Thu","Fri"],"thousandsSep":" ","viewData":"View data table","viewFullscreen":"View in full screen","weekdays":["Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"]}},"type":"chart","fonts":"Source+Sans+Pro","debug":false},"evals":[],"jsHooks":[]}</script> </div> ] ] --- <center><h1 class="animate__animated animate__rubberBand">Comparação de modelos </h1></center> .panelset[ .panel[.panel-name[Métricas de desempenho] <div class="animate__animated animate__flipInX"> <style type="text/css"> .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-s1h2{background-color:#efefef;border-color:#c0c0c0;font-size:18px;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-frgn{background-color:#efefef;border-color:#c0c0c0;font-size:18px;text-align:center;vertical-align:top} .tg .tg-u9x0{background-color:#2F4F4F;border-color:#c0c0c0;color:#FFF;font-size:26px;font-weight:bold;text-align:center; vertical-align:top} .tg .tg-af71{background-color:#ffffff;border-color:#c0c0c0;font-size:18px;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-mp7g{background-color:#ffffff;border-color:#c0c0c0;font-size:18px;text-align:center;vertical-align:top} </style> <table class="tg"> <thead> <tr> <th class="tg-u9x0"><span style="font-weight:bold;color:#FFF;background-color:#2F4F4F">Modelo</span></th> <th class="tg-u9x0"><span style="font-weight:bold;color:#FFF;background-color:#2F4F4F">ME</span></th> <th class="tg-u9x0"><span style="font-weight:bold;color:#FFF;background-color:#2F4F4F">RMSE</span></th> <th class="tg-u9x0"><span style="font-weight:bold;color:#FFF;background-color:#2F4F4F">MAE</span></th> <th class="tg-u9x0"><span style="font-weight:bold;color:#FFF;background-color:#2F4F4F">MPE</span></th> <th class="tg-u9x0"><span style="font-weight:bold;color:#FFF;background-color:#2F4F4F">MAPE</span></th> <th class="tg-u9x0"><span style="font-weight:bold;color:#FFF;background-color:#2F4F4F">MASE</span></th> <th class="tg-u9x0"><span style="font-weight:bold;color:#FFF;background-color:#2F4F4F">ACF1</span></th> <th class="tg-u9x0"><span style="font-weight:bold;color:#FFF;background-color:#2F4F4F">Theil’s U</span></th> </tr> </thead> <tbody> <tr> <td class="tg-af71">SARIMA(0,1,2)(0,1,1)<sub>12</sub></td> <td class="tg-mp7g">-136.02</td> <td class="tg-mp7g">232.2</td> <td class="tg-mp7g">187.2</td> <td class="tg-mp7g">-2.262</td> <td class="tg-mp7g">3.203</td> <td class="tg-mp7g">0.8117</td> <td class="tg-mp7g">0.225</td> <td class="tg-mp7g">0.1997</td> </tr> <tr> <td class="tg-s1h2">SARIMA(1,0,2)(1,1,1)<sub>12</sub></td> <td class="tg-frgn">94.617</td> <td class="tg-frgn">172.6</td> <td class="tg-frgn">109.4</td> <td class="tg-frgn">1.796</td> <td class="tg-frgn">1.986</td> <td class="tg-frgn">0.4744</td> <td class="tg-frgn">-0.016</td> <td class="tg-frgn">0.1546</td> </tr> <tr> <td class="tg-af71">ETS(M,Ad,M)</td> <td class="tg-mp7g">208.31</td> <td class="tg-mp7g">292.8</td> <td class="tg-mp7g">262.0</td> <td class="tg-mp7g">3.932</td> <td class="tg-mp7g">4.624</td> <td class="tg-mp7g">1.1361</td> <td class="tg-mp7g">0.129</td> <td class="tg-mp7g">0.2615</td> </tr> <tr> <td class="tg-s1h2">Holt - Winters Aditivo</td> <td class="tg-frgn">129.11</td> <td class="tg-frgn">252.7</td> <td class="tg-frgn">209.1</td> <td class="tg-frgn">1.847</td> <td class="tg-frgn">3.633</td> <td class="tg-frgn">0.9070</td> <td class="tg-frgn">-0.058</td> <td class="tg-frgn">0.2087</td> </tr> <tr> <td class="tg-af71">Holt - Winters Multiplicativo</td> <td class="tg-mp7g">161.35</td> <td class="tg-mp7g">214.3</td> <td class="tg-mp7g">170.6</td> <td class="tg-mp7g">2.908</td> <td class="tg-mp7g">3.075</td> <td class="tg-mp7g">0.7401</td> <td class="tg-mp7g">-0.006</td> <td class="tg-mp7g">0.1895</td> </tr> <tr> <td class="tg-s1h2">Série com intervenção</td> <td class="tg-frgn">-66.05</td> <td class="tg-frgn">236.5</td> <td class="tg-frgn">175.5</td> <td class="tg-frgn">-0.912</td> <td class="tg-frgn">2.964</td> <td class="tg-frgn">0.7375</td> <td class="tg-frgn">-0.058</td> 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<br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br> --- class: inverse, center, middle # <center> **Conclusão ** </center> <br><br><br><br><br><br><br><br><br> <center><h1 class="animate__animated animate__lightSpeedInLeft"> O modelo que deteve as melhores métricas de desempenho foi SARIMA(1,0,2)(1,1,1)<sub>12</sub> proposto por auto-arima, mas contrariando o pressupostos de independência dos resíduos.</h1></center> <br><br><br><br> --- class: inverse, center, middle # <center> **Conclusão** </center> <br><br><br><br> <center><h1 class="animate__animated animate__hinge"> O modelo que deteve as melhores métricas de desempenho foi SARIMA(1,0,2)(1,1,1)<sub>12</sub> proposto por auto-arima, mas contrariando o pressupostos de independência dos resíduos.</h1></center> <center><h1 class="animate__animated animate__rotateInUpRight"> O modelo Holt - Winters Multiplicativo tem a segundo melhor desempenho entre os modelos, com RMSE = 214.3 e Theil’s U = 0.1895.</h1></center> <br><br><br><br><br><br><br><br><br> --- class: inverse, center, middle # <center> **Conclusão** </center> <br><br><br><br> <center><h1 class="animate__animated animate__hinge"> O modelo Holt - Winters Multiplicativo tem a segundo melhor desempenho entre os modelos, com RMSE = 214.3 e Theil’s U = 0.1895.</h1></center> <center><h1 class="animate__animated animate__rotateInUpRight"> O modelo SARIMA(2,1,3)(0,1,1)<sub>12</sub> com intervenção apresentou adequação favorável não contrariando os pressupostos, com as métricas de desempenho (RMSE = 236.541 e Theil’s U = 0.207) com destaque no AIC=-923.34.</h1></center> <br><br><br><br><br><br><br><br><br>