PRONÓSTICO DE LAS VENTAS NETAS : ARIMA
Luis Zavalaga Rodrigo
2023-02-17
1 EVOLUCIÓN DE LAS VENTAS NETAS
Hemos escogido para este estudio un extracto de datos referente a la “Evolucion mensual de las Ventas Netas de Estilos S.R.L, en el periodo entre el 1 Enero del 2019 y 15 Febrero del 2023. Fuente: Cubo Empresa al 15 de febrero del 2023
De este mismo extracto vamos a pronosticar las ventas netas de los siguientes 100 dias.
Una vez hecha las predicciones y comparados todos los modelos con los resultados reales, procederemos a estimar el error de cada modelo, para posteriormente elegir el mejor o los mejores modelos de pronostico de todos los que hemos representado.
2 MODELO ARIMA
- Un modelo autorregresivo integrado de promedio movil o ARIMA es un modelo estadistico que utiliza variaciones y regresiones de datos estadisticos con el fin de encontrar patrones para una prediccion hacia el futuro. Se trata de un modelo dinamico de series temporales, es decir, las estimaciones futuras vienen explicadas por los datos del pasado y no por variables independientes.
3 CUESTIONES IMPORTANTES A TENER EN CUENTA
Para definir un modelo ARIMA, debemos tener en cuenta que los datos deben ser estacionarios,es decir cuando su distribucion y sus parametros no varian con el tiempo.
Otra cuestion para tener en cuenta es que los datos deben ser univariantes, ARIMA trabaja en una sola variable.
La regresion automatica tiene que ver con los valores pasados, es decir necesitamos un historico de los datos para poder realizar el modelo y asi predecir datos futuros.
4 PROCESO DEL MODELO
- Comenzamos cargando las librerias previamente instaladas, que nos hacen falta para ejecutar el modelo tal como “tidyverse” para realizar transformaciones en general de nuestro conjunto de datos, ademas de otras funciones asociadas ,“readxl” para leer los datos de un archivo excel, “lubridate” para hacer transformaciones en un campo fecha, y forecast que es una libreria empleada para pronosticos de series de tiempo
library(forecast) ## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(openxlsx)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2
## ──## ✔ ggplot2 3.4.1 ✔ purrr 1.0.1
## ✔ tibble 3.1.8 ✔ dplyr 1.1.0
## ✔ tidyr 1.3.0 ✔ stringr 1.5.0
## ✔ readr 2.1.4 ✔ forcats 1.0.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()library(readxl)
library(lubridate)##
## Attaching package: 'lubridate'
##
## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, unionlibrary(tseries)
library(ggplot2)
library(astsa)##
## Attaching package: 'astsa'
##
## The following object is masked from 'package:forecast':
##
## gasA continuación vamos a cargar nuestros conjunto de datos del archivo excel que los contiene:
Pronostico_2019_2023 <- read_excel("C:/Users/lzavalaga/Desktop/Pronostico 2019-2023.xlsx")
Pronostico_2019_2023- Ahora vamos a hacer las transformaciones dentro del dataset en el campo “Fecha” correspondientes para separar mes, año y luego añadir la variable objetivo de pronostico “Venta Neta”, para configurar nuestro conjunto de datos del cual vamos a partir para iniciar nuestro pronostico, todo ello guardado en la variable STventas, donde mostramos los resultados de la transformación
Pronostico_2019_2023 %>%
mutate_at(vars(Fecha), list(year=year, month=month, day=day))%>%
select("Venta Neta")-> STventas
STventasAhora es necesario convertir nuestro dataset en una serie de tiempo
Ventas<-ts(STventas, start = c(2019,1,1),frequency = 365)
Ventas## Time Series:
## Start = c(2019, 1)
## End = c(2023, 43)
## Frequency = 365
## Venta Neta
## [1,] 25.38
## [2,] 755835.71
## [3,] 554626.22
## [4,] 621512.79
## [5,] 789422.43
## [6,] 685766.56
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## [1252,] 723401.88
## [1253,] 1082410.46
## [1254,] 1376802.09
## [1255,] 1378041.78
## [1256,] 574362.77
## [1257,] 568671.70
## [1258,] 678759.20
## [1259,] 790565.56
## [1260,] 1021105.52
## [1261,] 1818080.96
## [1262,] 986233.70
## [1263,] 581171.62
## [1264,] 498756.69
## [1265,] 645097.44
## [1266,] 526084.15
## [1267,] 675138.17
## [1268,] 895052.60
## [1269,] 764654.12
## [1270,] 593087.08
## [1271,] 569375.20
## [1272,] 695369.57
## [1273,] 1114387.50
## [1274,] 546956.27
## [1275,] 816890.05
## [1276,] 635876.92
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## [1278,] 478510.99
## [1279,] 645933.45
## [1280,] 682459.12
## [1281,] 721305.42
## [1282,] 875590.75
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## [1284,] 551275.49
## [1285,] 503204.93
## [1286,] 560927.51
## [1287,] 685860.53
## [1288,] 896541.93
## [1289,] 1404419.23
## [1290,] 1330197.06
## [1291,] 715318.57
## [1292,] 682336.15
## [1293,] 721393.62
## [1294,] 717194.94
## [1295,] 890473.81
## [1296,] 1068926.83
## [1297,] 923769.09
## [1298,] 754743.78
## [1299,] 1342611.56
## [1300,] 948266.84
## [1301,] 1057379.51
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## [1303,] 1153981.57
## [1304,] 1037563.34
## [1305,] 691771.98
## [1306,] 610381.33
## [1307,] 631661.91
## [1308,] 664027.29
## [1309,] 678231.43
## [1310,] 934094.64
## [1311,] 769823.60
## [1312,] 580836.46
## [1313,] 585207.82
## [1314,] 651974.49
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## [1319,] 536325.21
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## [1321,] 566068.58
## [1322,] 555378.20
## [1323,] 604791.74
## [1324,] 867663.13
## [1325,] 795071.79
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## [1327,] 501904.45
## [1328,] 606036.66
## [1329,] 650093.27
## [1330,] 715020.10
## [1331,] 1060196.93
## [1332,] 844898.96
## [1333,] 867983.49
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## [1336,] 571716.61
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## [1338,] 978125.19
## [1339,] 927117.10
## [1340,] 523405.25
## [1341,] 501566.31
## [1342,] 557306.20
## [1343,] 558389.52
## [1344,] 616560.51
## [1345,] 805067.42
## [1346,] 742438.64
## [1347,] 518129.29
## [1348,] 430139.33
## [1349,] 642199.08
## [1350,] 552494.38
## [1351,] 569745.04
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## [1353,] 765214.44
## [1354,] 543654.65
## [1355,] 510399.92
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## [1357,] 576881.73
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## [1359,] 1048147.32
## [1360,] 992604.59
## [1361,] 552254.93
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## [1390,] 761503.70
## [1391,] 753119.36
## [1392,] 707260.67
## [1393,] 786232.04
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## [1397,] 466995.39
## [1398,] 472838.43
## [1399,] 465969.52
## [1400,] 555297.65
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## [1403,] 523789.96
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## [1405,] 436092.57
## [1406,] 549957.10
## [1407,] 614454.40
## [1408,] 838532.80
## [1409,] 721642.02
## [1410,] 568748.47
## [1411,] 656209.98
## [1412,] 798024.25
## [1413,] 1001158.31
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## [1415,] 1411256.64
## [1416,] 1347840.29
## [1417,] 457103.20
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## [1420,] 667811.33
## [1421,] 985541.49
## [1422,] 1239633.30
## [1423,] 1177759.78
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## [1425,] 722074.44
## [1426,] 955427.47
## [1427,] 423641.63
## [1428,] 575217.49
## [1429,] 1009738.58
## [1430,] 1073932.04
## [1431,] 512668.08
## [1432,] 530381.69
## [1433,] 590481.52
## [1434,] 915119.64
## [1435,] 885595.65
## [1436,] 992229.79
## [1437,] 1023163.65
## [1438,] 552644.91
## [1439,] 474718.08
## [1440,] 891745.17
## [1441,] 950145.77
## [1442,] 1082212.28
## [1443,] 1621280.96
## [1444,] 1716999.96
## [1445,] 1069993.10
## [1446,] 1620026.52
## [1447,] 1724307.62
## [1448,] 2060094.07
## [1449,] 2863770.06
## [1450,] 3533457.04
## [1451,] 1068309.64
## [1452,] 1058423.18
## [1453,] 946910.98
## [1454,] 821616.69
## [1455,] 1024040.23
## [1456,] 1422091.06
## [1457,] 1838921.52
## [1458,] 6275.55
## [1459,] 868238.07
## [1460,] 698254.17
## [1461,] 591843.54
## [1462,] 577914.89
## [1463,] 638854.52
## [1464,] 853411.89
## [1465,] 717583.58
## [1466,] 627933.72
## [1467,] 521990.46
## [1468,] 470785.76
## [1469,] 379898.07
## [1470,] 544701.16
## [1471,] 720741.35
## [1472,] 652290.73
## [1473,] 604720.69
## [1474,] 496968.71
## [1475,] 511103.26
## [1476,] 311580.49
## [1477,] 482448.13
## [1478,] 725868.82
## [1479,] 602534.74
## [1480,] 562300.35
## [1481,] 592590.18
## [1482,] 481878.53
## [1483,] 548663.77
## [1484,] 611216.88
## [1485,] 711802.21
## [1486,] 621027.34
## [1487,] 512292.10
## [1488,] 594959.78
## [1489,] 474381.73
## [1490,] 510496.15
## [1491,] 673021.03
## [1492,] 963059.43
## [1493,] 627395.31
## [1494,] 594324.70
## [1495,] 651107.89
## [1496,] 608331.53
## [1497,] 677134.99
## [1498,] 548706.93
## [1499,] 936610.25
## [1500,] 878128.34
## [1501,] 593876.65
## [1502,] 555956.03
## [1503,] 602964.26plot(Ventas)
Luego vamos a descomponer nuestra serie temporal
descomp = decompose(Ventas)
autoplot(descomp)
En “data” podemos apreciar la grafica de los datos, en “seasonal” que es la estacionalidad, apreciamos el patron de los datos que se repite cada año, que es el patron que se mantiene constante.
Por otro lado “trend” representa la tendencia, que es como se puede ver tiene primero una pequeña subida luego baja y luego a partir de ese punto toma una tendencia ascendente, y “remainder”, representa la configuracion de los residuos que va dejando el modelo, cuando disminuyen y cuando aumentan. Si sumamos las graficas de seasonal, trend y remainder nos da la grafica total data de la serie temporal- Vamos a comprobar ahora para asegurarnos si nuestra serie temporal es estacionaria o no a traves del test de Dickey-Fuller, si cumple en su ejecucion que el p-valor>0.05 la serie cumple la hipotesis nula en la cual la serie no es estacionaria, si por el contrario el p-valor<0.05 no se cumple la hipotesis nula con lo cual la serie es estacionaria, Asi pues lo comprobamos:
adf.test(Ventas)## Warning in adf.test(Ventas): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: Ventas
## Dickey-Fuller = -6.1955, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationaryY vemos que el p-valor nos sale 0.01<0.05 por tanto se rechaza la hipotesis nula y la serie es estacionaria. Cabe destacar que se recomienda siempre realizar una diferenciacion para poder decir con mas certeza que nuestros parametros no variaN en el tiempo.- Ahora vamos a utilizar 2 parametros “acf” y “pacf” que miden el nivel de residuos, de forma que los podemos ver graficamente. En la grafica aparece el nivel de los residuos y los rezagos(Lags), para identificar la serie de tiempo que sea autoregresiva los valores no deberian sobrepasar el nivel de significancia establecido representado por las lineas de rayas horizontales entrecortadas, como podemos ver los niveles de significancia.
Acf(Ventas)
pacf(Ventas)
Vamos a ver con el comando ndiffs(), que diferencias hay para poder arreglar nuestra serie temporal y poder convertirla a estacionaria y asi poder aplicar el modelo ARIMA.
ndiffs(Ventas)## [1] 1El comando ndiffs nos indica que hay una diferencia, que tenemos que arreglar, vamos a determinar la grafica que nos da cuando aplicamos la diferencia en el tiempo a la serie.
DSventas <- diff(Ventas, lag = 1)
plot(DSventas, main="Ventas Neta Estilos", xlab="Dias",ylab="Ventas")
autoplot(DSventas) +
ggtitle("Ventas Neta Estilos") +
ylab("ventas")
Si aplicamos ahora el test de Dickey-Fuller despues de la diferenciacion nos confirma y nos da un resultado < 0.05 lo que confirma que la serie ahora si es estacionaria.
adf.test(DSventas)## Warning in adf.test(DSventas): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: DSventas
## Dickey-Fuller = -13.852, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationary-Pasamos a continuacion a elaborar el modelo de pronostico ARIMA, con la funcion auto.arima. la funcion auto.arima esta diseñada para una estimacion rapida del modelo ARIMA probando varias series de tiempo.
-La funcion auto.arima, realiza la funcion ARIMA de forma automatica, va a ir iterando, va a ir buscando el modelo que mas se ajusta a los datos, y nos da respuesta del mejor modelo, como puede verse al ejecutar el print del mismo. El resultado despues de sucesivas iteraciones, se queda con el modelo que tuvo el menor valor de AIC.
#Modelo Arima con : Autorima
model <- auto.arima(Ventas, stepwise = T, approximation =T, seasonal=T,trace = T)##
## Fitting models using approximations to speed things up...
##
## ARIMA(2,1,2)(1,0,1)[365] with drift : Inf
## ARIMA(0,1,0) with drift : 41990.12
## ARIMA(1,1,0)(1,0,0)[365] with drift : Inf
## ARIMA(0,1,1)(0,0,1)[365] with drift : Inf
## ARIMA(0,1,0) : 41988.11
## ARIMA(0,1,0)(1,0,0)[365] with drift : Inf
## ARIMA(0,1,0)(0,0,1)[365] with drift : Inf
## ARIMA(0,1,0)(1,0,1)[365] with drift : Inf
## ARIMA(1,1,0) with drift : 41832.63
## ARIMA(1,1,0)(0,0,1)[365] with drift : Inf
## ARIMA(1,1,0)(1,0,1)[365] with drift : Inf
## ARIMA(2,1,0) with drift : 41792.53
## ARIMA(2,1,0)(1,0,0)[365] with drift : Inf
## ARIMA(2,1,0)(0,0,1)[365] with drift : Inf
## ARIMA(2,1,0)(1,0,1)[365] with drift : Inf
## ARIMA(3,1,0) with drift : 41753.83
## ARIMA(3,1,0)(1,0,0)[365] with drift : Inf
## ARIMA(3,1,0)(0,0,1)[365] with drift : Inf
## ARIMA(3,1,0)(1,0,1)[365] with drift : Inf
## ARIMA(4,1,0) with drift : 41705.17
## ARIMA(4,1,0)(1,0,0)[365] with drift : Inf
## ARIMA(4,1,0)(0,0,1)[365] with drift : Inf
## ARIMA(4,1,0)(1,0,1)[365] with drift : Inf
## ARIMA(5,1,0) with drift : 41637.24
## ARIMA(5,1,0)(1,0,0)[365] with drift : Inf
## ARIMA(5,1,0)(0,0,1)[365] with drift : Inf
## ARIMA(5,1,0)(1,0,1)[365] with drift : Inf
## ARIMA(5,1,1) with drift : 41576.97
## ARIMA(5,1,1)(1,0,0)[365] with drift : Inf
## ARIMA(5,1,1)(0,0,1)[365] with drift : Inf
## ARIMA(5,1,1)(1,0,1)[365] with drift : Inf
## ARIMA(4,1,1) with drift : 41616.22
## ARIMA(5,1,2) with drift : 41440.29
## ARIMA(5,1,2)(1,0,0)[365] with drift : Inf
## ARIMA(5,1,2)(0,0,1)[365] with drift : Inf
## ARIMA(5,1,2)(1,0,1)[365] with drift : Inf
## ARIMA(4,1,2) with drift : 41574.1
## ARIMA(5,1,3) with drift : 41410.93
## ARIMA(5,1,3)(1,0,0)[365] with drift : Inf
## ARIMA(5,1,3)(0,0,1)[365] with drift : Inf
## ARIMA(5,1,3)(1,0,1)[365] with drift : Inf
## ARIMA(4,1,3) with drift : 41502.08
## ARIMA(5,1,4) with drift : 41326.19
## ARIMA(5,1,4)(1,0,0)[365] with drift : Inf
## ARIMA(5,1,4)(0,0,1)[365] with drift : Inf
## ARIMA(5,1,4)(1,0,1)[365] with drift : Inf
## ARIMA(4,1,4) with drift : Inf
## ARIMA(5,1,5) with drift : 41317.11
## ARIMA(5,1,5)(1,0,0)[365] with drift : Inf
## ARIMA(5,1,5)(0,0,1)[365] with drift : Inf
## ARIMA(5,1,5)(1,0,1)[365] with drift : Inf
## ARIMA(4,1,5) with drift : 41405.8
## ARIMA(5,1,5) : 41315.08
## ARIMA(5,1,5)(1,0,0)[365] : Inf
## ARIMA(5,1,5)(0,0,1)[365] : Inf
## ARIMA(5,1,5)(1,0,1)[365] : Inf
## ARIMA(4,1,5) : 41403.77
## ARIMA(5,1,4) : 41324.16
## ARIMA(4,1,4) : Inf
##
## Now re-fitting the best model(s) without approximations...
##
## ARIMA(5,1,5) : 41345.48
##
## Best model: ARIMA(5,1,5)print(model)## Series: Ventas
## ARIMA(5,1,5)
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 ma1 ma2 ma3
## 0.3525 -1.0342 0.1706 -0.5839 -0.3714 -0.8816 1.2406 -0.8301
## s.e. 0.0956 0.0921 0.1356 0.0844 0.0708 0.1002 0.1399 0.1704
## ma4 ma5
## 0.7220 -0.1489
## s.e. 0.1344 0.0682
##
## sigma^2 = 5.226e+10: log likelihood = -20661.65
## AIC=41345.3 AICc=41345.48 BIC=41403.76Ahra revisamos los resultados para los residuos
checkresiduals(model)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(5,1,5)
## Q* = 1903.1, df = 291, p-value < 2.2e-16
##
## Model df: 10. Total lags used: 301error=residuals(model)
plot(error)
tsdiag(model)
Ahora vamos a realizar un forecast para 100 días en el futuro
mod1 <- forecast(model, 100, level = 95)
autoplot(forecast(model, 100))
checkresiduals(model)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(5,1,5)
## Q* = 1903.1, df = 291, p-value < 2.2e-16
##
## Model df: 10. Total lags used: 301plot(mod1)
# Revisamos los pronosticos para los 100 dias
mod1## Point Forecast Lo 95 Hi 95
## 2023.1178 553947.7 105902.262 1001993
## 2023.1205 653501.6 158276.562 1148727
## 2023.1233 796706.6 254869.593 1338544
## 2023.1260 745758.4 177057.050 1314460
## 2023.1288 607146.0 14058.911 1200233
## 2023.1315 595487.5 -10093.405 1201068
## 2023.1342 605449.8 -27916.807 1238816
## 2023.1370 573935.3 -118070.383 1265941
## 2023.1397 650389.2 -88343.374 1389122
## 2023.1425 769910.1 6066.409 1533754
## 2023.1452 726106.1 -60671.038 1512883
## 2023.1479 614806.9 -190496.960 1420111
## 2023.1507 608334.4 -208687.802 1425357
## 2023.1534 615504.0 -222745.067 1453753
## 2023.1562 586926.0 -291990.885 1465843
## 2023.1589 649587.1 -263169.247 1562343
## 2023.1616 747562.1 -185774.154 1680898
## 2023.1644 710633.9 -242290.083 1663558
## 2023.1671 621009.5 -348396.455 1590416
## 2023.1699 618352.7 -362441.355 1599147
## 2023.1726 623327.1 -375646.714 1622301
## 2023.1753 597714.1 -432609.082 1628037
## 2023.1781 649132.6 -407994.122 1706259
## 2023.1808 729427.0 -345625.781 1804480
## 2023.1836 698264.4 -394317.644 1790847
## 2023.1863 626122.9 -481658.966 1733905
## 2023.1890 626112.1 -492904.769 1745129
## 2023.1918 629421.0 -505881.941 1764724
## 2023.1945 606666.9 -554239.343 1767573
## 2023.1973 648917.7 -534329.196 1832165
## 2023.2000 714702.8 -484676.371 1914082
## 2023.2027 688384.7 -527051.564 1903821
## 2023.2055 630341.0 -599349.594 1860032
## 2023.2082 632104.7 -608695.822 1872905
## 2023.2110 634162.2 -621587.217 1889912
## 2023.2137 614096.9 -663370.189 1891564
## 2023.2164 648861.8 -647878.794 1945602
## 2023.2192 702742.7 -608810.781 2014296
## 2023.2219 680501.0 -645965.865 2006968
## 2023.2247 633822.6 -706135.399 1973781
## 2023.2274 636717.8 -714212.005 1987648
## 2023.2301 637846.6 -727012.050 2002705
## 2023.2329 620263.4 -763529.636 2004056
## 2023.2356 648906.9 -751938.004 2049752
## 2023.2384 693023.5 -721608.927 2107656
## 2023.2411 674216.4 -754395.513 2102828
## 2023.2438 636697.7 -804756.522 2078152
## 2023.2466 640255.9 -812009.767 2092522
## 2023.2493 640706.1 -824669.303 2106081
## 2023.2521 625381.6 -856852.365 2107615
## 2023.2548 649012.5 -848601.583 2146627
## 2023.2575 685122.0 -825451.029 2195695
## 2023.2603 669211.9 -854553.266 2192977
## 2023.2630 639073.1 -896966.056 2175112
## 2023.2658 642958.2 -903711.102 2189627
## 2023.2685 642922.5 -916174.720 2202020
## 2023.2712 629629.8 -944729.300 2203989
## 2023.2740 649150.2 -939292.863 2237593
## 2023.2767 678695.4 -922017.486 2279408
## 2023.2795 665231.5 -947995.692 2278459
## 2023.2822 641036.4 -983957.791 2266031
## 2023.2849 645012.1 -990414.526 2280439
## 2023.2877 644638.2 -1002634.040 2291910
## 2023.2904 633156.1 -1028119.063 2294431
## 2023.2932 649301.1 -1025028.170 2323630
## 2023.2959 673466.2 -1012546.728 2359479
## 2023.2986 662069.5 -1035865.300 2360004
## 2023.3014 642659.4 -1066584.897 2351904
## 2023.3041 646564.4 -1072903.600 2366032
## 2023.3068 645964.5 -1084842.115 2376771
## 2023.3096 636083.3 -1107712.750 2379879
## 2023.3123 649452.7 -1106561.890 2405467
## 2023.3151 669209.5 -1097981.257 2436400
## 2023.3178 659561.1 -1119028.136 2438150
## 2023.3205 644001.6 -1145481.348 2433485
## 2023.3233 647729.8 -1151761.532 2447221
## 2023.3260 646988.4 -1163393.668 2457370
## 2023.3288 638513.3 -1184027.553 2461054
## 2023.3315 649597.0 -1184471.758 2483666
## 2023.3342 665743.1 -1179056.412 2510543
## 2023.3370 657574.0 -1198157.460 2513305
## 2023.3397 645111.6 -1221133.653 2511357
## 2023.3425 648597.9 -1227438.049 2524634
## 2023.3452 647777.7 -1238748.668 2534304
## 2023.3479 640530.6 -1257462.945 2538524
## 2023.3507 649729.6 -1259211.764 2558671
## 2023.3534 662919.2 -1256357.356 2582196
## 2023.3562 656002.4 -1273787.413 2585792
## 2023.3589 646029.8 -1293925.370 2585985
## 2023.3616 649238.4 -1300290.359 2598767
## 2023.3644 648385.4 -1311272.806 2608044
## 2023.3671 642205.4 -1328335.909 2612747
## 2023.3699 649848.3 -1331146.448 2630843
## 2023.3726 660617.7 -1330357.336 2651593
## 2023.3753 654761.6 -1346348.936 2655872
## 2023.3781 646789.2 -1364165.873 2657744
## 2023.3808 649705.4 -1370609.252 2670020
## 2023.3836 648852.6 -1381263.591 2678969
## 2023.3863 643595.9 -1396903.859 2684096
## 2023.3890 649952.2 -1400573.929 27004785 CONCLUSIONES
- El modelo Arima no logra capturar la tendencia diaria, lo cual no nos permite tener un mejor modelo(BIC)
- El Modelo que logra mejor precision es el ARIMA(5,1,5)
- El Modelo no cumple a cabalidad con un supuesto ya que los residuos tienen correlacion y el modelo no ha captado información
- Se recomienda realizar el modelaje Arima para series mensuales y anuales con data mayor a 75 datos.