Se cargan los datos

library(readxl)
Table_IMAE <- read_excel("C:/Users/SANCHEZ/Desktop/GABRIEL2021/Universidad/Ciclo V/Econometria/Table_IMAE.xlsx", 
    sheet = "Hoja1", col_types = c("skip", 
        "numeric"), skip = 5)
names(Table_IMAE)<-c("IMAE")

Se convierte en serie temporal

Table_IMAE.ts<-ts(data = Table_IMAE$IMAE,start = c(2019,1),frequency = 12) |> print()
##         Jan    Feb    Mar    Apr    May    Jun    Jul    Aug    Sep    Oct
## 2019 107.83 106.07 112.65 109.70 114.75 114.66 111.05 113.16 111.80 108.84
## 2020 109.05 109.55 103.92  87.43  89.84  96.18  97.82 103.72 107.63 105.61
## 2021 107.19 107.58 113.34 110.63 115.79 117.57 112.28 115.19 114.58 111.55
## 2022 110.98 112.08 120.22 112.86 121.77 119.19 115.94 120.09 117.75 115.39
## 2023 114.63 114.24 125.03 116.47 128.29 126.58 121.44 122.39 118.13 116.64
## 2024 120.22                                                               
##         Nov    Dec
## 2019 116.81 122.66
## 2020 111.45 120.52
## 2021 118.60 126.27
## 2022 121.54 129.59
## 2023 128.23 133.66
## 2024

Calculo de Pronóstico modelo Holt-Winters

library(forecast)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
#Estimar el modelo
ModeloHW<-HoltWinters(x = Table_IMAE.ts,
                      seasonal = "multiplicative",
                      optim.start = c(0.9,0.9,0.9))
ModeloHW
## Holt-Winters exponential smoothing with trend and multiplicative seasonal component.
## 
## Call:
## HoltWinters(x = Table_IMAE.ts, seasonal = "multiplicative", optim.start = c(0.9,     0.9, 0.9))
## 
## Smoothing parameters:
##  alpha: 1
##  beta : 0
##  gamma: 0
## 
## Coefficients:
##            [,1]
## a   115.6959521
## b    -0.9824213
## s1    1.0532405
## s2    1.0045275
## s3    0.8476272
## s4    0.8739906
## s5    0.9384891
## s6    0.9978989
## s7    1.0150932
## s8    1.0048430
## s9    0.9895984
## s10   1.0811708
## s11   1.1544178
## s12   1.0391029
#Generar el pronóstico:
PronosticosHW<-forecast(object = ModeloHW,h = 5,level = c(0.98))
PronosticosHW
##          Point Forecast     Lo 98    Hi 98
## Feb 2024      120.82094 105.35674 136.2851
## Mar 2024      114.24603  92.87611 135.6159
## Apr 2024       95.56886  71.81392 119.3238
## May 2024       97.68267  68.71568 126.6497
## Jun 2024      103.96943  69.23267 138.7062
#Gráfico de la serie original y del pronóstico.
PronosticosHW %>% autoplot()

Segun el modelo Holt-Winters se espera una caída constante hasta mayo, a lo que en junio le seguriria un rebote

Calculo de forma automatica modelo SARIMA

library(forecast)
library(TSstudio)
IMAE.arima.automatico<-auto.arima(y = Table_IMAE.ts)
summary(IMAE.arima.automatico)
## Series: Table_IMAE.ts 
## ARIMA(0,1,1)(1,0,0)[12] 
## 
## Coefficients:
##          ma1    sar1
##       0.3623  0.8440
## s.e.  0.1552  0.0585
## 
## sigma^2 = 17.31:  log likelihood = -177.2
## AIC=360.4   AICc=360.82   BIC=366.68
## 
## Training set error measures:
##                      ME     RMSE    MAE         MPE     MAPE      MASE
## Training set 0.06770115 4.056577 3.1059 0.006669302 2.776455 0.4312283
##                     ACF1
## Training set -0.05881266

Pronostico automatico

library(forecast)
#tabla
pronostico.arima.automatico<-forecast(object = IMAE.arima.automatico,h = 5,level = c(.98)) |> print()
##          Point Forecast    Lo 98    Hi 98
## Feb 2024       120.0607 110.3827 129.7387
## Mar 2024       129.1674 112.8123 145.5224
## Apr 2024       121.9428 100.9354 142.9502
## May 2024       131.9188 107.1169 156.7206
## Jun 2024       130.4755 102.3872 158.5639
#Grafico
IMAE.arima.automatico |> forecast(h = 5,level = c(.98)) |> autoplot()

Con el modelo SARIMA se espera un crecimiento en el IMAE para junio del 2024