class: center, middle, inverse, title-slide .title[ # SERIES DE TIEMPO ] .author[ ### <br> Daniel Felipe Rengifo Hurtado <br> Janer Darío Bolaños Quiñones <br> Valentina Nuñez Oviedo<br> Jose Alejandro Franco<br /> </div><br /> <br> ] .institute[ ### Universidad del Valle ] --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px # ÍNDICE <div style="text-align: left; font-size: 1.5em; line-height: 1.8;"> 1. INTRODUCCIÓN<br> 2. METODOLOGÍA<br> 3. DESCRIPCIÓN DE LA SERIE TEMPORAL<br> 4. RESULTADOS DEL MODELO ARIMA<br> 5. CONCLUSIONES<br> </div> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px # INTRODUCCIÓN <div style="height: 100vh; display: flex; justify-content: center; align-items: flex-start; padding-top: 5vh;"> <p style="max-width: 80%; font-size: 24px; text-align: justify;"> El análisis de series temporales es esencial para entender cómo evolucionan los datos en el tiempo, permitiendo hacer pronósticos y analizar tendencias. En este trabajo, utilizamos el modelo ARIMA, reconocido por su capacidad para identificar patrones y generar predicciones precisas. Nuestro estudio se enfocó en la población desempleada en Colombia, usando datos de la OCDE desde febrero de 2008 hasta septiembre de 2024. <br><br> El proceso se dividió en tres etapas: primero, un análisis exploratorio para identificar características como la estacionalidad; luego, la selección y ajuste del modelo más adecuado; y finalmente, la proyección de escenarios futuros. </p> </div> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px # METODOLOGÍA ### **Exploración Inicial de la Serie Temporal** Se generaron gráficos descriptivos para identificar tendencias y patrones en la tasa de desempleo. Esto ayudó a comprender el comportamiento general de los datos y detectar anomalías o estacionalidades. ### **División de la Serie en Ventanas** La serie se dividió en las siguientes ventanas: - **Primera ventana:** Hasta septiembre de 2024, usada para construir el modelo. - **Segunda ventana:** Datos de enero a septiembre de 2024, utilizada para validar los pronósticos. - **Tercera ventana:** Incluye datos de toda la base desde el año 2008 hasta asta septiembre del 2023. - **Cuarta ventana:** incluye datos a partir del 1 enero de 2023 Esto permitió evaluar la capacidad predictiva del modelo en períodos recientes. --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px ### **Análisis de Estacionariedad** Se realizaron pruebas de raíz unitaria y gráficos ACF para evaluar la estacionariedad de la serie. En caso de no ser estacionaria, se aplicaron diferencias. ### **Selección del Modelo ARIMA** Se utilizó el método **auto.arima** para encontrar automáticamente los mejores parámetros ( p , d , q ), calculando en criterios como el AIC (Criterio de Información de Akaike), AICc (AIC corregido para muestras pequeñas) y BIC (Criterio de Información Bayesiano). ). Estos criterios ayudan a evaluar la calidad del modelo.Además, se compararon modelos manuales con diferentes combinaciones de parámetros. La evaluación se realizó mediante el análisis de residuos, asegurando que estos no presentarán autocorrelación y mostrarán un comportamiento aleatorio, lo que indica un buen ajuste del modelo. --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px ### **Validación del Modelo** En la validación del modelo ARIMA, se evaluaron los residuos para asegurar que no hubiera autocorrelación significativa y se utilizaron métricas de precisión como el Error Absoluto Medio (MAE) y la Raíz del Error Cuadrático Medio (RMSE), que miden la precisión global y la reducción en la escala original de los datos. También se demostró el Criterio de Información de Akaike (AIC), que ayuda a seleccionar modelos con buen ajuste y baja complejidad. Estas métricas son claves para determinar el modelo más adecuado. ### **Generación de Pronósticos** Se realizaron pronósticos a corto plazo (seis meses), con intervalos de confianza del 95%. Los resultados fueron comparados con valores reales y representados gráficamente para facilitar la interpretación de la tendencia del desempleo. --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px class: middle, center # DESCRIPCIÓN DE LA SERIE TEMPORAL --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> En este gráfico se pueden observar un crecimiento inicial de 2008 a 2010, este es debido principalmente a la crisis financiera, la cual fue originada en Estados Unidos pero generó un impacto a nivel mundial, por lo que Colombia se vio afectada. Además, en estos años también contribuyó al desempleo el hecho de que se vivió una alta migración hacia las ciudades. </div> <div class="plotly html-widget html-fill-item" id="htmlwidget-9416a9f402a8d15a9824" style="width:50%;height:360px;"></div> <script type="application/json" 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De 2017 a 2019, un leve crecimiento estuvo marcado por la migración venezolana y la insuficiencia de empleos para la creciente demanda laboral. </div> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> En el año 2020 se refleja un crecimiento acelerado sobre el desempleo en Colombia, esto es debido a la pandemia de Covid-19 en la cual se implementaron muchas restricciones lo que ocasionó la caída de la actividad económica, y el cierre de muchas empresas. En los años siguientes años del 2022 y 2023 se evidencia una disminución en el desempleo, esta caída es atribuida a la recuperación económica en la cual se han recuperado más del 50% de los puestos perdidos durante el año 2020 que es el que conserva la tasa de desempleo más alta. El análisis descriptivo del desempleo durante el periodo de estudio, evidencia los siguientes resultados: </div> | **DESEMPLEO** | |---------------:| | Min: 1981 | | 1st Qu.: 2224 | | Median: 2389 | | Mean: 2508 | | 3rd Qu.: 2635 | | Max: 4480 | <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> Estos valores reflejan una distribución la cual está ligeramente sesgada hacia valores mayores que la mediana, esto indica que hay una tendencia ascendente en los niveles del desempleo. Así mismo, se ve evidenciado el hecho de que la media es mayor a la mediana lo cual puede dar indicios de que existe la presencia de valores extremos altos. </div> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px class: middle, center # RESULTADOS DEL MODELO ARIMA --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> Para el desarrollo de nuestro modelo se realizó inicialmente el plot de la serie que nos muestra el comportamiento de esta con el fin de poder analizar si esta presenta estacionalidad o estacionariedad. </div> <div class="plotly html-widget html-fill-item" id="htmlwidget-3830b0f9f79ae9779f4e" style="width:50%;height:360px;"></div> <script type="application/json" 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","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> Este gráfico nos muestra que la serie cuenta con comportamientos crecientes y decrecientes, no obstante, se refleja que estos periodos no son repetitivos por lo que se puede concluir que la base de datos que se está manejando NO presenta estacionalidad, En cuanto a la Estacionariedad de la serie nos deja como conclusión que nuestro modelo no es estacionario y esto se puede comprobar debido a que el comportamiento de la media y varianza NO es constante. </div> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> En este caso se evidencia que la base no presenta ningún tipo de estas tendencias, dándonos la obligación de diferenciar la base pero antes es necesario realizar las ventanas con el fin de trabajar con la serie y un subconjunto de la serie con el fin de poder realizar nuestros pronósticos. </div> La primera ventana es la que incluye toda la serie y para la segunda decidimos trabajar desde el mes de enero hasta septiembre del presente año. <img src="PRESENTACION_files/figure-html/unnamed-chunk-3-1.png" width="50%" style="display: block; margin: auto;" /> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> Se aplico la prueba de ACF, donde se observó un comportamiento exponencialmente decreciente, además los resagos superaban las bandas de confianza lo que indicó que la serie no era estacionaria, recomendando que la serie debe de llevar diferenciaciones para lograr tener una base que nos permita realizar las predicciones. 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(y) ","x"],"3dcc712a565c":["function (y) ","x"],"3dcc69536739":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> ] .pull-right[ <table class="table" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;"> <thead> <tr><th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Augmented Dickey-Fuller Test</div></th></tr> <tr><th style="empty-cells: hide;border-bottom:hidden;" colspan="2"></th></tr> <tr> <th style="text-align:center;"> Métrica </th> <th style="text-align:center;"> Valor </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;"> Dickey-Fuller </td> <td style="text-align:center;"> -2.3244 </td> </tr> <tr> <td style="text-align:center;"> Lag order </td> <td style="text-align:center;"> 5 </td> </tr> <tr> <td style="text-align:center;"> p-value </td> <td style="text-align:center;"> 0.4402 </td> </tr> <tr> <td style="text-align:center;"> Alternative hypothesis </td> <td style="text-align:center;"> stationary </td> </tr> </tbody> </table> ] --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> Con estos resultados se pudo comprobar que la serie efectivamente no estacionaria debido a que nuestro valor P es de **0.4402** donde: - **H0:** La serie tiene una raíz unitaria ( “No es estacionaria“). - **H1:** La serie no tiene raíz unitaria (“Estacionaria”). Una vez ya con nuestra ventana diferenciada obtuvimos la siguiente gráfica: </dib> <img src="PRESENTACION_files/figure-html/unnamed-chunk-6-1.png" style="display: block; margin: auto;" /> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> En esta ya es evidente que la media y varianza son constante dándonos a entender que tenemos una base de datos que nos sirve para poder trabajar pero antes es necesario poder realizar la prueba del ACF para poder determinar el valor de Q y ver si nuestro modelo presenta ruido blanco, además de comprobar con la prueba de dickey fuller que la serie es estacionaria. </div> .pull-left[ <div class="plotly html-widget html-fill-item" id="htmlwidget-9e60f7204687b888b486" style="width:432px;height:360px;"></div> <script type="application/json" 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(y) ","x"],"3dcc33c558df":["function (y) ","x"],"3dcc6a4254b7":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> ] .pull-right[ <table class="table" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;"> <thead> <tr><th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Resultados del ADF Test</div></th></tr> <tr><th style="empty-cells: hide;border-bottom:hidden;" colspan="2"></th></tr> <tr> <th style="text-align:center;"> Métrica </th> <th style="text-align:center;"> Valor </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;"> Dickey-Fuller </td> <td style="text-align:center;"> -6.281 </td> </tr> <tr> <td style="text-align:center;"> Lag order </td> <td style="text-align:center;"> 5 </td> </tr> <tr> <td style="text-align:center;"> p-value </td> <td style="text-align:center;"> 0.01 </td> </tr> </tbody> </table> ] --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px class: middle, center <!-- --> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 60px Ya con estos valores encontrados procedimos a armar nuestro modelo a base de estos dando (4,1,4). Pero cabe resaltar que también se hizo uso de la modelo auto arima para lograra hacer una comparación de nuestros datos. Resultados del modelo ARIMA: | Métrica | Valor | |------------------|-------------| | Modelo ARIMA | ARIMA(0,1,0)| | sigma^2 | 19208 | | Log likelihood | -1263.74 | | AIC | 2529.49 | | AICc | 2529.51 | | BIC | 2532.78 | <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> Este modelo nos arrojó los resultados (0,1,0) como posible candidato a poder predecir mejor nuestros valores. Finalmente decidimos probar modelos y dejamos al final el modelo (3,1,3) que salió de la combinación de los posibles valores observados en la gráfica del ACF y PACF. </div> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> A la hora de escoger los modelos decidimos ver los residuos para ver poder ver la diferencia entre estos y obtuvimos las siguientes gráficas : </div> **1. Modelo ARIMA(0,1,0)** <img src="PRESENTACION_files/figure-html/unnamed-chunk-10-1.png" style="display: block; margin: auto;" /> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px **2. Modelo ARIMA(4,1,4)** <img src="PRESENTACION_files/figure-html/unnamed-chunk-11-1.png" style="display: block; margin: auto;" /> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px **2. Modelo ARIMA(3,1,3)** <img src="PRESENTACION_files/figure-html/unnamed-chunk-12-1.png" style="display: block; margin: auto;" /> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> En las tres gráficas se logra evidenciar un comportamiento muy similar más a diferencia del modelo ( 0,1,0 ) que cuenta con un rezago significativo, pero aun así se puede apreciar que gracias a su media y varianza constante, la distribución normal alrededor del 0 y que en en el ACF no presentan en su mayoría valores significativos estos modelos presentan RUIDO BLANCO entonces ya para poder escoger el modelo que nos pronostique la serie que debemos realizar, usamos el accuracy para obtener las metricas y revisamos los valores del AIC, AICc y BIC del modelo. </div> **Tablas de comparación** </b> .pull-left[ <table class="table" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Métrica </th> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Modelo (0,1,0) </th> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Modelo (4,1,4) </th> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Modelo (3,1,3) </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> AIC </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2529.49 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2531.63 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2530.76 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> AICc </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2529.51 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2532.58 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2531.34 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> BIC </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2532.78 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2561.27 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2553.81 </td> </tr> </tbody> </table> ] .pull-right[ <table class="table" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Métrica </th> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Modelo (0,1,0) </th> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Modelo (4,1,4) </th> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Modelo (3,1,3) </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> ME </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 1.7853900 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 8.6770370 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 1.4844680 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> RMSE </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 138.2452000 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 131.5098000 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 133.1435000 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> MAE </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 95.5225700 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 89.6311000 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 93.1768900 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> MPE </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> -0.0433774 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 0.1726498 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> -0.0413973 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> MAPE </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 3.7305410 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 3.5325100 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 3.6480020 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> MASE </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 0.3508530 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> -0.0078674 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> -0.0163483 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> ACF1 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 0.0364369 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 0.3292137 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 0.3422373 </td> </tr> </tbody> </table> ] --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px class: middle, center # CONCLUSIÓN --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> El Modelo 5 (ARIMA(3,1,3)) es la mejor opción, ya que ofrece un buen equilibrio entre precisión y simplicidad. Presenta el menor sesgo (ME), errores relativamente bajos (RMSE y MAE), y residuos más independientes, lo que lo convierte en el modelo más confiable para representar la serie temporal.independientes entre los modelos evaluados, lo que refuerza su confiabilidad. Aunque el Modelo 2 tiene métricas de precisión más bajas en algunos aspectos, su alto ME y mayor complejidad lo hacen menos adecuado. Por lo tanto, el Modelo 5 es la mejor elección para este caso. </div> <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> Ya con nuestro los valores de nuestro modelo, decidimos realizar pruebas de este para ver si es consistente con los resultados, para ello hicimos uso de la ventana 3 y 4 con valores hasta el año 2023 dejando unos meses posteriores a esto para poder comparar los valores pronosticados con los valores reales en donde obtuvimos los siguientes resultados: </div> </b> <table class="table" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th> <th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; " colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Modelo (3,1,3)</div></th> <th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th> </tr> <tr> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Mes </th> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Intervalo. </th> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Valor.Pronosticado </th> <th style="text-align:center;font-weight: bold;background-color: rgba(254, 226, 226, 255) !important;"> Valor.Real </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> oct 2023 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.328-2.868 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.5980 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.580 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> nov 2023 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.194-2.991 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.5930 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.623 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> dic 2023 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.016-3.033 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.5255 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.732 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> ene 2024 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 1.924-3.129 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.5260 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.652 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> feb 2024 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 1.927-3.255 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.5910 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.704 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> mar 2024 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 1.851-3.305 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.5780 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.862 </td> </tr> </tbody> </table> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> En este caso hicimos nuestra predicción a seis meses con un nivel de confianza del 95%, dado que todos los valores pronosticados se encontraban en el rango de predicción logramos afirmar que nuestro modelo realiza unas predicciones correctas. </div> <img src="PRESENTACION_files/figure-html/unnamed-chunk-16-1.png" style="display: block; margin: auto;" /> --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> También se realizó el gráfico para poder observar el comportamiento de la serie en dichos meses pronosticados. </div> <div style="text-align: justify; padding-right: 80px; padding-top: 20px; margin-left: -20px;"> Una vez ya comprobado del funcionamiento de nuestro modelo decidimos realizar el pronóstico de los seis meses posteriores a septiembre del año 2024 dando los siguientes resultados: </div> </b> <table class="table" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th> <th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; " colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Modelo (3,1,3)</div></th> </tr> <tr> <th style="text-align:center;background-color: rgba(254, 226, 226, 255) !important;"> Mes </th> <th style="text-align:center;background-color: rgba(254, 226, 226, 255) !important;"> Intervalo Pronosticado </th> <th style="text-align:center;background-color: rgba(254, 226, 226, 255) !important;"> Valor Pronosticado </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> oct 2024 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.227-2.761 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.494 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> nov 2024 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.054-2.834 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.444 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> dic 2024 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 1.923-2.910 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.417 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> ene 2025 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 1.898-3.069 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.483 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> feb 2025 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 1.837-3.130 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.483 </td> </tr> <tr> <td style="text-align:center;font-weight: bold;background-color: rgba(255, 245, 245, 255) !important;"> mar 2025 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 1.731-3.145 </td> <td style="text-align:center;background-color: rgba(255, 245, 245, 255) !important;"> 2.438 </td> </tr> </tbody> </table> --- Ya con estos valores los podemos ver de la siguiente manera en el gráfico de predicción: <img src="PRESENTACION_files/figure-html/unnamed-chunk-18-1.png" style="display: block; margin: auto;" /> Con estos resultados, podemos observar que la tasa de desempleo en octubre tiende a aumentar, para luego disminuir en los meses de noviembre y diciembre. En enero, se mantendrá estable hasta febrero, y finalmente, en marzo, se prevé una caída. --- background-image: url(https://www.univalle.edu.co/images/Univalle/70_Rojo.jpg) background-position: top right background-size: 50px class: middle, center # ¡MUCHAS GRACIAS!