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Análisis exploratorio entre modelos matemáticos predictivos, aplicados a la producción de energía media= nte series temporales<= /p>

 

Exploratory analysis between predictive mathematical models, applied to energy producti= on through time series

 

 


1

Guido Javier Mazón Fierro                                       https://orcid.org/0000-0001-8745-2373

Escuela Superior Politécnica de Chimborazo (ESPO= CH), Facultad de Administración de Empresas, Riobamba, Ecuador,

guido.mazon@espoch.edu.ec

<= /span>

2

Pamela Alexandra Buñay Guisñan               <= /span>                     https://orcid.org/0000-0002-4320-6899=

Universidad Nacional de Chimborazo (ESPOCH), Facultad de Ingeniería, Riobamba, Ecuador=

pbunay@unach.edu.ec  

 

 

 

 

 

 

 

 

 <= /span>

Artículo de Investigación Científica y Tecnológica

Enviado: 11/04/2022=

Revisado: 20/05/2022

Aceptado: 27/06/2022

Publicado:13/07/2022

                             DOI: https://doi.org/10.33262/concienciadigital.v5i3.1.2223   

 

 =

 

Cítese= :

&= nbsp;

 =

Mazón Fierro, G. J., &am= p; Buñay Guisñan, P. A. (2022). Análisis exploratorio entre modelos matemáti= cos predictivos, aplicados a la producción de energía mediante series tempora= les. ConcienciaDigital, 5(3.1), 57-78. https://d= oi.org/10.33262/concienciadigital.v5i3.1.2223

 =

<= /o:p>

 

CONCIE= NCIA DIGITAL, es una revista multidisciplinar, trimestral, que se publicará en soporte electrónico tiene como misión contribuir a la   formación de profesionales competentes con visión humanística y crítica q= ue sean capaces de exponer sus resultados investigativos y científicos en la misma medida que se promueva mediante su intervención cambios positivos e= n la sociedad. https://concienciadigital.org  <= /span>

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Palabras claves:Series temporales, pronóstico, energía, modelos matemáticos.

 

Resumen

Introducción: la energía en los actuales momentos se puede considerar como un elemento esencial en la vida de las personas, así como en el desarrollo y progreso= de los países, el sector energético se constituye como estratégico debido a = que permite el funcionamiento y operabilidad de los diferentes sectores se pu= ede afirmar que la energía es indispensable en la sociedad moderna. El pronosticar o inferir que va a suceder a futuro, permite tomar decisiones oportunas y anticiparse a los acontecimientos, es así como se vuelve trascendente el conocer la producción del sector energético a futuro, ade= más, se pueden utilizar estas predicciones como elementos de partida para gene= rar documentos como planificaciones energéticas a mediano y largo plazo. Objetivos: realizar un estudio = exploratorio de las mejores técnicas que podrían asistir la predicción en la producció= n de energía primaria en Ecuador, para evaluar la eficiencia de ajuste a corto plazo mediante series temporales univariantes. Metodología: en el trabajo investigativo se pudo realizar un estudio exploratorio de cuatro modelos predictivos en el sector energétic= o de Ecuador, mediante dos técnicas, ARIMA y suavización exponencial Holt, que permitieron una aproximación confiable de predicción en la producción de energía primaria a corto plazo, en tres años hasta 2022, mediante series temporales univariantes. En cuanto a la parte metodológica empleada para cumplir los objetivos, se inició con la obtención de la serie histórica proporcionada por el Ministerio de Recursos Renovables y Energía en el documento técnico denominado Balance Energético Nacional 2019, se procesa= ron los datos y determinaron outliers mediante el criterio de Chauvenet, una = vez determinada la base de datos para el análisis, se aplicó la metodología Box-Jenkins para la obtención de modelos ARIMA y Holt. Resultados: el modelo que mejor se ajusta a las bondades de predicción de los analizados es el Modelo_a ARIMA (1,1,0) cuya expresión = es: , además, se estimó que la producción de energía primaria para el año 2022 en Ecuador, podría ser de  kilo barriles equivalentes de petróleo= , con una fluctuación superior e inferior en el intervalo de . Conclusiones: se puede afirmar = de acuerdo con los datos obtenidos que los modelos predictivos hallados son estrictamente autorregresivos es decir que son métodos iterativos explíci= tos, puesto que determinan el valor de  en dependencia con el anterior resulta= do , en el cual= no intervienen los residuos de los errores, esto indica que no interviene la componente de medias móviles. La predicción con los tres primeros modelos= a, b, c resultaron con un comportamiento creciente y con el modelo h se mant= enía constante.

 

Keywords:

Typography: Time series, forecast, energy, mathematical models.

 

Abstract

Introduction: energy at the present time can be considered as = an essential element in people's lives, as well as in the development and progress of countries, the energy sector is strategic because it allows t= he operation and operability of the different sectors. it can be said that energy is indispensable in modern society. Forecasting or inferring what = is going to happen in the future allows timely decisions to be made and to anticipate events. This is how it becomes important to know the productio= n of the energy sector in the future. In addition, these predictions can be us= ed as starting elements to generate documents such as medium and long-term energy planning. Objectives: conduct an exploratory study of the best techniques that could assist in the prediction of primary energy production in Ecuador, to evaluate the short-term adjustment efficiency through univariate time series. Methodology: in the research wo= rk it was possible to conduct an exploratory study of four predictive models in= the energy sector of Ecuador, using two techniques, ARIMA and Holt exponential smoothing, which allowed a reliable approximation of prediction in the production of primary energy in the short term, in three years until 2022, using univariate time series. As for the methodological part used to meet= the objectives, it began with obtaining the historical series provided by the Ministry of Renewable Resources and Energy in the technical document call= ed National Energy Balance 2019, the data was processed and outliers were determined using the criterion de Chauvenet, once the database for the analysis was determined, the Box-Jenkins methodology was applied to obtain ARIMA and Holt models. Results: = the model that best fits the prediction benefits of those analyzed is ARIMA Model-a (1,1,0) whose expression is: Y_t=3D3365.526+0.074 Y_(t-1)+ε_= t, in addition, it was estimated that Primary energy production for the year 20= 22 in Ecuador could be 236940.541 kilobarrels of oil equivalent (KBEP), with= a fluctuation above and below in the interval of [275511.589 .198369.493](KBEP). Conclusions:= based on the data obtained, it can be stated that the predictive models found a= re strictly autoregressive, that is, they are explicit iterative methods, si= nce they determine the value of Y_t depending on the previous result Y_(t-1),= in which they do not intervene the residuals of the errors, this indicates t= hat the component of moving averages does not intervene. The prediction with = the first three models a, b, c resulted in an increasing behavior and with mo= del h it remained constant.

 

&n= bsp;

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Introdu= cción

La energía en los actuales momentos se puede considerar como un elemento esencial en la vida de las personas y en el desarrollo y progreso de los países, el sector energético = se constituye como estratégico debido a que permite el funcionamiento y operab= ilidad de los diferentes sectores, como por ejemplo industrial, transporte, agríco= la, residencial, entre otros, entonces  se puede decir que la energía está presente y se manifiesta en la cotidianidad= de la vida de los seres humanos cuando en el ámbito productivo se opera una maquinaria, o en una residencia se utiliza energía eléctrica para iluminar = una habitación o encender un electrodoméstico, también se puede evidenciar la presencia de energía cuando se desea transportar de un lugar a otro mediant= e la utilización de un medio de transporte motorizado en síntesis se puede afirm= ar que la energía es indispensable en la sociedad moderna. <= /p>

El pronosticar o inferir q= ue va a suceder a futuro, permite tomar decisiones oportunas en el momento adecuado y anticiparse a los acontecimientos, es por esto por lo que se vue= lve trascendente el conocer la producción y el consumo del sector energético, además de esto se puede utilizar estas predicciones como elementos de parti= da para generar documentos más elaborados como una planificación energética a mediano y largo plazo. Si se asocia la predicción a una estructura matemáti= ca se puede afirmar según González (2009), que el modelo predictivo es una representación de una realidad compleja, que se diseña para analizar su comportamiento y anunciar o conjeturar lo que en determinadas condiciones h= a de suceder. El insumo con el que se debe contar para establecer proyecciones e= n un estudio son datos del pasado es decir una serie temporal, la cual es el resultado de observar los valores de una variable a lo largo del tiempo en intervalos regulares cada día, mes, año (Alonso, 2019), si a esto le añadim= os el análisis univariante o escalar según Peña (2010), es una secuencia de  datos ordenados y equidistantes cronológicamente sobre una característica de una unidad observable en diferentes momentos.

El poder desarrollar un ca= so de estudio particular con datos históricos de producción de energía primari= a en Ecuador, proporcionados por el Ministerio de Recursos Renovables y Energía, brindan un aporte al sector energético, ya que contar con valores o estimaciones futuras basados en evidencia científica siguiendo un modelo predictivo ARIMA y Holt, son insumos importantes y necesarios para realizar= una planificación adecuada en el sector, además de ser un importante indicador = en la toma de decisiones. Estas acciones permitirán tener un abastecimiento apropiado y no permitirán llegar a producir un déficit de energía, que podr= ían afectar a otros sectores del país, además de reducir el coste de importación con relación a la compra anticipada del recurso.

El problema que se pretende ayudar a solventar es estimar la producción de energía primaria en un perio= do corto de tres años para poder obtener un valor aproximado de la producción = en el año 2022.

Metodol= ogía

Recopilación <= /span>y preparación de datos

El punto de partida se fundamenta en la recopilaci= ón de los datos históricos de la producción de energías primarias en Ecuador, = la fuente de donde se tomaron los mencionados datos es el Balance Nacional de Energía (BNE), el cual es difundido por el Ministerio de Energía y Recursos Naturales no Renovables en conjunto con otras organizaciones del sector energético de Ecuador, cabe mencionar que la información es de libre acceso= la cual se encuentra en el portal web de la institución. Esta serie de datos cronológicos se los presenta de dos maneras en el Balance Nacional de Energ= ía, la primera mediante gráficas que comprende un periodo anual de 1970 hasta 2= 012, y la segunda a través de tablas de valores desde 1995 hasta el año 2019, lo= que comprende una muestra de 50 datos para el análisis.

Para poder cuantificar la serie temporal de datos = que se muestran de 1970 al 2012 en la gráfica del Balance Nacional de Energía, = se ha utilizado el programa de libre acceso webplotdigitizer. El procedimiento= que se desarrolló para la digitalización de los datos fue:

·      =    Obtener la gráfica a digitalizar en formato *.jpg para poder importar al menú principal de webplotdigitizer.

·     Definir el punto de origen de la gráfica, lo que equivale a establecer la coordenad= a

·     Determinar el valor máximo para cada eje coordenado en =

·      =    Una vez determinados estos pasos el programa establece un mallado en el cual se asignará un valor numérico cuan= do se posicione el puntero del ratón utilizando puntos donde se desee consegui= r la coordenada

·      =    Se procede a sobre escribir la gráfica= con puntos consecutivos para sacar los valores deseados.

·      =    Para finalizar se debe exportar el arc= hivo que contiene la información de la gráfica, transformada a una tabla de datos numéricos.

Una vez agrupados todos los valores de producción = de energía primaria en una serie temporal anual de 1970 hasta el 2019 se reali= za una gráfica de líneas para visualizar cómo se comporta la serie de tiempo. =

En la preparación de los datos se incluyó el análi= sis de la serie temporal, en un primer momento elaborando un diagrama de cajas y bigotes para identificar los outliers, además de esta ayuda gráfica se apli= có el criterio de Chauvenet.

Determinados los candidatos a outliers se procede = a la elección mediante el criterio de Chauvenet el cual consiste en:<= /span>

·      =    Se debe transformar una serie de datos= con tendencia a una serie temporal estacionaria.

·      =    Como siguiente paso se calcula los estadísticos descriptivos de la serie de datos estacionaria.

·     Se estima el punto crítico de Chauvenet calculado  para todos los valores de la serie tempo= ral.

·      =    A continuación, se compara cada valor = de  con el punto crítico de Chauvenet teórico , si

Una vez identificados los valores atípicos se proc= ede a entender el origen y causas de su presencia y a tomar la decisión de eliminarlo, modificarlo o trabajar con ese dato fuera de rango.<= /span>

Desarrollo y formulación de los modelos predictivos

Con los valores de la data explicados, en esta eta= pa se procede primero a graficarlos, para en primera instancia observar características propias de esta serie temporal univariante, segundo con la ayuda el software SPSS se procede al análisis de características de la serie como la función de auto correlación simple y parcial además de identificar = si la serie es estacionaria o no,  con= esta información obtenida se procede a  estructurar modelos lineales tales como ARIMA con diferentes variant= es, por otro lado con los mismos datos se aplicara modelos con suavizamiento exponencial o de Holt. El acrónimo ARIMA tiene su origen en el término anglosajón Autoregressive Integrated Moving Average que significa Au= to Regresivo (AR) Integrado (I) Medias Móviles(MA), llamado también como modelo Autorregresivo de medias móviles integrado; la publicación de George Box y Gwilym Jenkins , marcó el comienzo de una nueva generación de herramientas = de pronóstico la misma que dio origen a la  metodología de Box-Jenkins (BJ), pero que también es conocida como metodología ARIMA  (Herrera, 2019),= una de las ventajas que se puede citar es que son muy buenos para la predicción= a corto plazo debido a su capacidad de aprender de los cambios de la serie, además de lo mencionado se puede decir que la construcción de estos modelos= no posee una elaboración complicada (Millán 2019).

Mateos del Pino (2009), menciona que el método de = Holt es una técnica de alisado exponencial y se utiliza para aquellas series temporales que presentan tendencia y estacionalidad. En este tipo de suavizamiento hace uso de datos históricos para obtener una nueva serie más suave a partir de la cual se hace la predicción. Una de las ventajas del alisado exponencial radica en que se define mediante recurrencias muy simpl= es, de manera que se facilitan los cálculos y se reducen los requerimientos de almacenamiento de datos, esto es de gran ayuda cuando se desarrollan series= con grandes datos.

El objetivo que persigue esta etapa es identificar patrones y estimar un modelo estadístico que es la base para generar la información de la muestra, si se desea realizar la predicción de los datos futuros se debe asegurar que las características de la serie son constantes= en el tiempo, es decir que la predicción se realizara sobre datos estrictamente estacionarios (Sánchez, 2018).

Validación de = los modelos

La longitud de la serie de producción de energía primaria es de , se considera= rá este valor poblacional en vista de que es el histórico de los datos existen= tes, la validación de los modelos se efectuará mediante el criterio de Error Med= io Absoluto Porcentual (MAPE), el Error Cuadrático Medio (RMSE) y el Criterio = de información Bayesiana normalizado (BIC). Las estimaciones se consideran aceptables si se encuentran en el intervalo de confianza del 5%, se ha de seleccionar el modelo que mejor se ajuste con un error mínimo. Una prueba d= el modelo seleccionado es ver si los residuales estimados a partir de este mod= elo son de ruido blanco; si lo son, aceptamos el ajuste particular; si no lo so= n, debemos empezar de nuevo. Por tanto, la metodología es un proceso iterativo (Gujarati & Porter 2010).

Interpretación= y comparación de resultados

La construcción de modelos ARIMA para pronosticar = es una de las técnicas más empleadas en diferentes ámbitos, gracias a que en c= orto plazo su capacidad predictiva es muy cercana a la realidad y la interpretac= ión del modelo emplea entre otras medidas el Error Cuadrático Medio (MSE) y el Error Absoluto Medio (MAE) (Pineda et al., 2017).

De acuerdo con los resultados de Error Medio Absol= uto Porcentual (MAPE) y el Error Cuadrático Medio (RMSE) y el Criterio de información Bayesiana normalizado (BIC), se procederá a la interpretación y comparación de resultados, para determinar y seleccionar un modelo que pres= ente las mejores condiciones de diferencia de errores.

Predicción a c= orto plazo

Se pretende en este caso utilizar el mejor modelo predictivo seleccionado para realizar una estimación a corto plazo de los siguientes 3 años de la serie estocástica. Un proceso estocástico es un conjunto de variables que se generan de forma aleatoria, además se encuentr= an ordenadas a la vez equiespaciadas con relación al tiempo, las cuales pueden= ser referidas a una o varias características de la variable observable en diferentes momentos (Mauricio, 2007).

Una vez construido el modelo ARIMA su gran aplicac= ión son los pronósticos. En muchos casos, los pronósticos obtenidos por este mé= todo son más confiables que los obtenidos de modelos econométricos tradicionales= , en particular en el caso de pronósticos de corto plazo (Espino, 2017).

Figura 1

Metodología del trabajo

Resultados

En la primera parte se digitaliza la gráfica de da= tos históricos con la ayuda del programa webplotdigitizer para obtener datos cu= antitativos y así poder obtener la serie temporal de análisis, una vez digitalizado se añaden los datos que se presentan mediante tablas en el Balance Nacional de Energía, para obtener una data de cincuenta observaciones.

Debido a que se han estimado 25 valores de producc= ión de energía primaria a través de la figura que nos ofrece el Balance Naciona= l de Energía a una tabla de valores numéricos, se procedió a encontrar el error porcentual de la utilización de esta aplicación de libre acceso para la dig= italización de imágenes llamada webplotdigitizer, en cuyo caso se encontró un error porcentual promedio de digitalización menor al 1% siendo este igual a 0.48%= .

Una vez obtenidos estos valores se procede a tabularlos y graficarlos (figura 2), se observa que se puede describir la presencia de tendencia creciente en la producción de energía primaria, en o= tras palabras, se puede notar que está presente una pendiente positiva, se perci= be también que, en el año 1975, 1988, 2004, se generan saltos que acentúan una= línea que termina en un vértice o pico. Las unidades de la producción de energía primaria son kilo barriles equivalentes de petróleo (KBEP).

Figura 2=

Serie histórica de producción de energía primaria en Ecuador

 

Fuente: Balance Energético Naciona= l (2019)

En relación con la preparación de los datos se ini= ció confeccionando un diagrama de cajas y bigotes, el cual nos permitirá visual= izar los candidatos a outliers y los seleccionaremos a través del criterio de Chauvenet (Barrios et al., 2016). De acuerdo con este análisis se afirma que existen candidatos a outliers o valores atípicos en: tres (3), cuatro (4), dieciocho (18), diecinueve (19), treinta y cinco (35) en total 5 candidatos estos valores son atribuidos a los siguientes años 1972,1973, 1987, 1988 y = 2004. Una vez determinados los candidatos a outliers se procede a la elección mediante el criterio de Chauvenet según este criterio de Puntos Críticos de Chauvenet (  el valor para el número de datos igual a= 49 es , el cual permitirá realizar el contraste con los coeficientes encontrados o calculad= os y así establecer los outliers o valores atípicos. Si se realiza la comparación para cada valor de la serie temporal se puede observar que existen valores = de coeficiente calculado de Chauvenet  mayores al punto crítico  , entonces se afirma que existen outlier= s o valores atípicos en, cuatro (4), dieciocho (18), diecinueve (19), treinta y cinco (35), descartando el valor de tres (3), estos espacios temporales son atribuidos a los siguientes años 1973, 1987, 1988 y 2004.=

Con la finalidad de que estos valores no degeneren= ni distorsionen los estadísticos descriptivos, mediante la ayuda del software estadístico SPSS se los va a modificar con la opción detección automática de valores atípicos y su transformación (Marqués, 2015), los tipos de outliers= que permite seleccionar son: aditivo, cambio de nivel, innovador, transitorio, tendencial local y parche aditivo.

Para obtener los diferentes modelos predictivos, s= e ha trabajado previamente con los datos para no eliminar los outliers y detecta= rlos automáticamente con el software SPSS y que los transforme o modifique, la segunda acción que se hizo fue transformar la serie de tiempo a una estacionaria, a partir de esta base de datos se determinará la gráfica de autocorrelación simple (FAS) figura 3 y la gráfica de autocorrelación parci= al (FAP) figura 4. Vamos a comprobar si estamos ante una serie temporal estacionaria, para ello deberemos ver cómo se comporta a lo largo del año, = y si el comportamiento entre periodos del mismo año es el mismo en el resto (Gar= cía, 2020).

Se evidencia en la gráfica de autocorrelación simp= le que las barras de coeficientes o barras de significancia muestran una tende= ncia decreciente suavizada es decir no presentan saltos e interrupciones en cada paso o número de retardo, que comparándolo con las gráficas teóricas de autocorrelación simple determinan que se está en la presencia de un modelo autorregresivo, también se debe hacer la comparación de la gráfica obtenida= de autocorrelación parcial con la teórica, la cual nos dará el valor del parám= etro del modelo autorregresivo. Si visualizamos con detenimiento la figura 4 se notará que solo existe una barra que sobresale las bandas de confianza lo c= ual implica que el modelo depende o se explica únicamente con un rezago anterior del tiempo.

 

 

Figura 3

Autocorrelación simple: límite de confianza superi= or=

La autocorrelación parcial indica que el valor de integración o diferencia del modelo ARIMA es <= span lang=3DES-MX style=3D'font-size:11.0pt;line-height:107%;font-family:"Calibr= i",sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareas= t-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times Ne= w Roman"; mso-bidi-theme-font:minor-bidi;position:relative;top:4.0pt;mso-text-raise:-= 4.0pt; mso-ansi-language:ES-MX;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'= > , es decir que= se conseguirá obtener una serie temporal estacionaria mediante una diferencia = de sus valores y de esa manera poder realizar diversas apreciaciones estadísti= cas.

Figura 4

Autocorrelación parcial: límite de confianza super= ior

 

En concordancia con los datos obtenidos de los dos correlogramas se establece en general el modelo lineal auto regresivo como:=

Donde:

 Pronóstico para cualquier valor futuro. =

 Constante del modelo

 Constante del modelo Autorregresivo AR

 Valor real anterior para el periodo de t= iempo.

 Error en el instante t.

Como siguiente paso y con la ayuda del software estadístico SPSS se obtienen los valores de los coeficientes: . <= /span>

Tabla 1

Parámetros modelo a ARIMA (1,1,0)

Parámetros Modelo_a ARIM= A (1,1,0)

Modelo

Estimación<= /o:p>

SE

t

Sig.<= /span>

Producción de Energía Primaria

Constante

3365,526

962,622

3,496<= /p>

0,001<= /p>

AR Retardo 1<= /span>

0,074=

0,147=

0,507=

0,615=

Diferencia

1

 =

 =

 =

De acuerdo con los parámetros de la tabla 1 ARIMA = (1,1,0) obtenemos el siguiente modelo:

Del modelo a descrito se puede mencionar:

·     El valor autorregresivo del modelo , significa que el modelo va a estar en función de datos del pasado anterior

·     La componente de medias móviles  , indica que no se considera el error en el instante pasado  lo que implica que existe una ponderación no muy significativa con el valor anterior para el periodo de tiempo.

·     La significancia o el p valor para el constante cumple con:  por lo que este término tiene un peso preponderante en el modelo.

Tabla 2

Estadísticos de ajuste del Modelo_a ARIMA (1,1,0)

Estadísticos de ajuste del Modelo_a ARIMA (1,1,0) <= /p>

RMSE<= /span>

MAPE<= /span>

BIC normalizado<= o:p>

5998,179

3,360<= /p>

18,034=

De la tabla 2 se evidencia que el error medio abso= luto (MAPE) es igual a 3,360 % que es un valor menor que en el intervalo de confianza del 5%.

Tabla 3

Predicción Modelo_a ARIMA (1,1,0)

Predicción Modelo_a ARIMA (1,1,0)

Modelo

2020<= /span>

2021<= /span>

2022<= /span>

Producción de Energía Primaria

Predicción

226679,447

231809,994

236940,541

UCL

248948,452<= /o:p>

263303,123<= /o:p>

275511,589<= /o:p>

LCL

204410,442

200316,865

198369,493

Si se contempla la tabla 3, se puede decir que la estimación de producción de energía para el año 2022 es de un valor de 236940,541 (KBEP) en un intervalo máximo y mínimo de [275511,589; 198369,49= 3] (KBEP).

Figura 5

Modelo ARIMA (1,1,0)

=

De la figura 5 se infiere que, la predicción de la producción de energía primaria es creciente con el ajuste mediante Modelo A= RIMA (1,1,0), en la primera parte desde el año 1971 hasta 1990 se sobrepone la s= erie histórica observada y el ajuste, y posteriormente se encuentran cercanas en= tre las dos, esto indica que el ajuste es aceptable.

A continuación, se procede a variar los parámetros para realizar un modelo ARIMA con diferentes características, se encuentra = un modelo ARIMA con (0,1,0).

Tabla 4

Modelo_b ARIMA (0,1,0)

Parámetros Modelo_b ARIM= A (0,1,0)

Modelo

Estimación<= /o:p>

SE

t

Sig.<= /span>

Producción de Energía Primaria

Constante

3425,813

879,185

3,897<= /p>

0,000<= /p>

Diferencia

1

 

 

 

&nbs= p;

Del modelo_b descrito se puede mencionar:

·     El valor autorregresivo del modelo , significa que el modelo no va a depe= nder de los datos del pasado anterior  , indica que no se considera el error en el instante pasado  por lo que este término tiene un peso preponderante en el modelo.

Tabla 5

Estadísticos de ajuste del Modelo_b ARIMA (0,1,0)

Estadísticos de ajuste del Modelo_b ARIMA (0,1,0) <= /p>

RMSE<= /span>

MAPE<= /span>

BIC normalizado<= o:p>

5943,322

3,419<= /p>

17,936=

De la tabla 5 se evidencia que el error medio abso= luto (MAPE) es igual a 3,419 % que es un valor menor que en el intervalo de confianza del 5%.

Tabla 6

Predicción Modelo b ARIMA (0,1,0)

Predicción Modelo_b ARIMA (0,1,0)

Modelo

2020<= /span>

2021<= /span>

2022<= /span>

Producción de Energía Primaria

Predicción

226178,361

229068,254

232027,704

UCL

238172,471<= /o:p>

246030,487<= /o:p>

252802,111<= /o:p>

LCL

214184,252

212106,022

211253,297

 

Si se contempla la tabla 6, se puede decir que la estimación de producción de energía para el año 2022 es de un valor de 232027,704 (KBEP) en un intervalo máximo y mínimo de [252802,111; 211253,29= 7] (KBEP).

Figura 6

Modelo AR= IMA (0,1,0)

De la figura 6 se infiere que, la predicción de la producción de energía primaria es creciente con el ajuste mediante Modelo A= RIMA (0,1,0), en la primera parte desde el año 1971 hasta 1974 se sobrepone la s= erie histórica observada y el ajuste, y posteriormente se encuentran cercanas en= tre las dos, esto indica que el ajuste es aceptable.

El siguiente modelo por obtener es en el cual interviene los promedios móviles (MA), los parámetros a considerar son:

Donde:

 Pronóstico para cualquier valor futuro. =

 Constante del modelo

 Constante del modelo de medias móviles M= A

 Valor del error anterior para el periodo= de tiempo.

 Error en el instante t.

Tabla 71

Modelo_c ARIMA (0,1,1)

Parámetros Modelo_c ARIM= A (0,1,1)

Modelo

Estimación<= /o:p>

SE

t

Sig.<= /span>

Producción de Energía Primaria

Constante

3373,909

952,627

3,542<= /p>

0,001<= /p>

Diferencia

1

 

 

 

MA

Retardo 1

-0,070=

0,151<= /p>

-0,465=

0,644<= /p>

&n= bsp;

Del modelo_c descrito se puede mencionar:

·     El valor autorregresivo del modelo , significa que el modelo no va a depe= nder de los datos del pasado anterior  , indica que se debe considerar el error en el instante pasado es negativa y muy cercana a cero lo que implica que existe una tendencia creciente en el modelo.<= /p>

·     La significancia o el p valor para el constante cumple con:   por lo que este término tiene un peso preponderante en el modelo.

Tabla 8

Estadísticos de ajuste del Modelo_c ARIMA (0,1,1)

Estadísticos de ajuste del Modelo_c ARIMA (0,1,1) <= /p>

RMSE<= /span>

MAPE<= /span>

BIC normalizado<= o:p>

5999,570

3,365<= /p>

18,034=

De la tabla 8 se evidencia que el error medio abso= luto (MAPE) es igual a 3,365 % que es un valor menor que en el intervalo de confianza del 5%.

Tabla 9

Predicción Modelo_c ARIMA (0,1,1)

Predicción Modelo_c ARIMA (0,1,1))

Modelo

2020<= /span>

2021<= /span>

2022<= /span>

Producción de Energía Primaria

Predicción

226499,069

229342,437

232253,897

UCL

238615,286<= /o:p>

247087,285<= /o:p>

254230,170<= /o:p>

LCL

214382,853

211597,589

210277,625

 

Si se contempla la tabla 9, se puede decir que la estimación de producción de energía para el año 2022 es de un valor de 232253,897 (KBEP) en un intervalo máximo y mínimo de [254230,170; 210277,62= 5] (KBEP).

Figura 7

Modelo AR= IMA (0,1,1)

De la figura 7 se infiere que, la predicción de la producción de energía primaria es creciente con el ajuste mediante Modelo A= RIMA (0,1,1), en la primera parte desde el año 1971 hasta 1974 se sobrepone la s= erie histórica observada y el ajuste, y posteriormente se encuentran cercanas en= tre las dos, esto indica que el ajuste es aceptable.

Ahora corresponde encontrar un modelo aplicando suavizamiento exponencial o modelo Holt, la ecuación que la rige es:

Tabla 10

Modelo_h Suavizamiento Exponencial Holt<= i>

Parámetros Modelo_h Suavizamiento Exponencial Holt

Modelo

Estimación<= /o:p>

SE

t

Sig.<= /span>

Producción de Energía Primaria

Alfa (nivel)<= /span>

0,970<= /p>

0,143<= /p>

6,780<= /p>

0,000<= /p>

&n= bsp;

Del modelo_h descrito se puede mencionar:

·      =    El valor que influye con mayor pondera= ción en el modelo va a depender de los datos del pasado anterior , es decir del inmediato anterior con = un valor de  

·     La significancia o el p valor para la constante Alpha de suavizamiento con:   por lo que este término tiene un peso preponderante en el modelo.

·      =    Los valores atípicos, mediante este mé= todo no han sido identificados por el sistema en el software SPSS.

Tabla 11

Estadísticos de ajuste del Modelo_h Holt=

Estadísticos de ajuste del Modelo_h Holt

RMSE<= /span>

MAPE<= /span>

BIC normalizado<= o:p>

14631,702

7,769<= /p>

19,260=

De la tabla 11 se evidencia que el error medio absoluto (MAPE) es igual a 7,769 % que es un valor mayor que en el interval= o de confianza del 5%.

Tabla 12

Predicción Modelo_h Holt

Predicción Modelo_h Holt

Modelo

2020<= /span>

2021<= /span>

2022<= /span>

Producción de Energía Primaria

Predicción

223153,660

223153,660

223153,660

UCL

252557,167<= /o:p>

264117,847<= /o:p>

273069,219<= /o:p>

LCL

193750,153

182189,473

173238,102

Si se contempla la tabla 12, se puede decir que la estimación de producción de energía para el año 2022 es de un valor de 223153,660 (KBEP) en un intervalo máximo y mínimo de [273069,219; 173238,10= 2] (KBEP).

Figura 8<= /o:p>

Modelo Holt

 

 

 

 

 

 

 

De la figura 8 se infiere que, la predicción de la producción de energía primaria se mantiene constante no es creciente con el ajuste mediante Modelo Holt, en toda la serie no se sobrepone la serie histórica observada y el ajuste siempre se encuentran cercanas entre las do= s, esto indica que el ajuste es aceptable.

Tabla 13

Modelos Predictivos

 

RMSE

MAPE

BIC

Expresión

Modelo_a ARIMA (1,1,0)

5998,179

3,360

18,034

 

Modelo_b ARIMA (0,1,0)

5943,322

3,419

17,936

 =

Modelo_c ARIMA (0,1,1)

5999,570

3,365

18,034

 

Modelo_h Holt

14631,702

7,769

19,260

=

 =

 

A la luz de los resultados se puede afirmar que:

·      =    El error cuadrado medio RMSE se encuen= tra en un mismo rango en la familia de los modelos ARIMA puesto que los valores atípicos, fueron detectados y remplazados automáticamente por el sistema, mientras que en el modelo Holt no fueron identificados datos atípicos. Adem= ás, se debe indicar que el RMSE es menor para el modelo_b

·      =    El error medio absoluto porcentual MAP= E, que tiene una bondad de ajuste con menor error es el modelo_a.

·      =    El Criterio de información Bayesiana B= IC normalizado es exactamente igual en el modelo_a y modelo_c, pero el menor v= alor lo obtiene el modelo_b puesto que no depende de componentes autorregresivas= y de promedios móviles.

Conclusiones

·      =    Se puede concluir que Modelo_a ARIMA (1,1,0), presenta el menor error medio absoluto porcentual (MAPE) igual 3.3= 6 % que se encuentra dentro de los intervalos de confianza establecidos para los modelos predictivos en un 5%. Si se observan los datos del MAPE de la tabla= 13, se verifica que no hay diferencias marcadas entre la familia de los modelos ARIMA, cada uno de los modelos predictivos construidos se encuentran en porcentajes inferiores a 3.419%.

·      =    Se puede afirmar de acuerdo con los da= tos obtenidos que los modelos predictivos hallados son estrictamente autorregresivos es decir que son métodos iterativos explícitos, puesto que determinan el valor de  en dependencia con el anterior resultado , en el cual no intervienen los residu= os de los errores, esto indica que no interviene la componente de medias móvil= es.

·      =    El modelo que mejor se ajusta a las bondades de predicción de los analizados es Modelo_a ARIMA (1,1,0) cuya expresión es: .

·      =    Se puede estimar en base al modelo pre= dictivo ARIMA (1,1,0), que la energía para el año 2022 en Ecuador podría ser de  kilo barriles equivalentes de petróleo <= /span> , con una fluctuación superior e infer= ior en el intervalo de

 

Referen= cias bibliográficas

Alonso, A. M. (2019). Introducción al Análisis de Series Temporales.

Balance Energético Nacional. (2019). Ministerio de recursos renovables y energía. https://www.recursosyenergia.gob.ec/wp-content/uploads/2020/12/Balance-Ener= getico-Nacional-2019-1.pdf

Barrios, R., Castañeda, M., Pedra= za, C., Vásquez, J. D. H., & Ibañez, I. (2016). Eliminación de outliers: una estrategia para reducir la incertidumbre tipo a en la calibración de balanz= as. In Simposio de metrología.

del Pino, Mateo. (2009). Previsión de ventas en una gran cadena de tiendas (Master's thesis, Universitat Politécnica de Catalunya).<= /o:p>

Espino Timón, C. (2017). Análisis predictivo: técnicas y modelos utiliz= ados y aplicaciones de este-herramientas Open Source que permiten su uso.

García Corona, J. (2020). Una visión didáctica de modelos predictivos p= ara una serie de demanda eléctrica en España.

González Casimiro, M. P. (2009). Análisis de series temporales: Modelos ARIMA.

Gujarati, D., & Porter, D. (2010). Econometría. 673-773, ISBN: 978-607-15-0294-0.

Herrera Granda, D. E. (2019). Predicción de demanda eléctrica medi= ante la aplicación de modelos ARIMA y SARIMA en lenguaje de programación R–caso = de estudio en la Empresa Eléctrica Quito (Bachelor's thesis, Quito, 2019.= ).

Marqués, M. P. (2015). Mi= nería de datos: a través de ejemplos. Alpha Editorial.

Mauricio, J. A. (2007). Análisis de series temporales. Universidad Complutence de Madrid.

Millán Gordo, E. A. (2019). Pronóstico de la demanda de pasajeros aéreo= s en nueve aeropuertos regionales colombianos.

Peña, D. M. (2010). Análisis de series temporales. Editorial Alian= za.

Pineda, S. E. P., Aguilar, J. A. H., & Arroyo-Figueroa, G. (2017). Aplicación de modelos auto regresivos para la predicción de generación de e= nergía eléctrica a partir de datos eólicos. Res. Comput. Sci., 139, 59-7= 0.

Sánchez Sánchez, D. A. (2018). Modelo ARIMA para el pronóstico de la producción de cacao en el Perú 2012-2018.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

El artículo que se publica es de exclusiva responsabilidad de los autor= es y no necesariamente reflejan el pensamiento de la Revista Conciencia Digital.


 

 

 

El artículo queda en propiedad de la revista= y, por tanto, su publicación parcial y/o total en otro medio tiene que ser autorizado por el director de la R= evista Conciencia Digital.

 

 

 

 


 

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ISSN: <= b>2600-5859

Vol. 5 = No 3.1,  pp.= 5778 , julio 2022

 

 

www= .concienciadigital.org

 

 

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