1. Presentacion de la serie temporal

    #carga del archivo fuente
       library(dplyr)
    library(tidyr)
    library(forecast)
     library(readxl)
    IVAE_03_22 <- read_excel("C:/Users/Familia/Downloads/IVAE_03_22.xlsx", 
        col_names = FALSE, skip = 6, n_max = 10)

    data.ivae<-pivot_longer(data = IVAE_03_22[1,],names_to = "vars",cols = 2:160,values_to = "indice") %>% select("indice")
    data.ivae.ts<- data.ivae %>% ts(start = c(2009,1),frequency = 12)
    data.ivae.ts %>% 
      autoplot(main ="IVAE ENE 2009- MAR 2022",
               xlab="Años/Meses",
               ylab="Indice")

2. Pronóstico Modelo de Holt Winters (usando Stats y forecast)

library(forecast)
Yt <-data.ivae.ts 

#Estimar el modelo
ModeloHW<-HoltWinters(x=Yt,
                      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 = Yt, seasonal = "multiplicative", optim.start = c(0.9,     0.9, 0.9))
## 
## Smoothing parameters:
##  alpha: 0.8472467
##  beta : 0
##  gamma: 1
## 
## Coefficients:
##            [,1]
## a   118.3719784
## b     0.1600947
## s1    0.9529095
## s2    1.0192349
## s3    1.0440936
## s4    0.9962326
## s5    1.0009929
## s6    0.9838373
## s7    0.9554392
## s8    1.0145286
## s9    1.0872315
## s10   0.9748891
## s11   0.9626701
## s12   1.0059813
#Generar el pronóstico:
PronosticosHW<-forecast(object = ModeloHW,h = 12,level = c(0.99))
PronosticosHW
##          Point Forecast     Lo 99    Hi 99
## Apr 2022       112.9503 105.74127 120.1594
## May 2022       120.9752 111.24635 130.7040
## Jun 2022       124.0929 112.43504 135.7507
## Jul 2022       118.5640 105.82229 131.3057
## Aug 2022       119.2908 105.11081 133.4708
## Sep 2022       117.4038 102.17086 132.6368
## Oct 2022       114.1680  98.13733 130.1986
## Nov 2022       121.3911 103.35822 139.4240
## Dec 2022       130.2643 110.05064 150.4779
## Jan 2023       116.9603  97.75887 136.1617
## Feb 2023       115.6485  95.71905 135.5779
## Mar 2023       121.0126  71.31613 170.7091
#Gráfico de la serie original y del pronóstico.
PronosticosHW %>% autoplot(main ="Modelo Holt Winters",
               xlab="Años/Meses",
               ylab="Indice")

3. Usando Forecast (Aproximación por Espacios de los Estados ETS )

library(forecast)

#Generar el pronóstico:
PronosticosHW2<-hw(y = Yt,
                   h = 12,
                   level = c(0.99),
                   seasonal = "multiplicative",
                   initial = "optimal")
PronosticosHW2
##          Point Forecast     Lo 99    Hi 99
## Apr 2022       111.9184 102.94778 120.8891
## May 2022       119.3664 107.94336 130.7895
## Jun 2022       122.8422 109.43169 136.2528
## Jul 2022       118.4498 104.08648 132.8131
## Aug 2022       120.0189 104.13415 135.9036
## Sep 2022       118.4260 101.52944 135.3226
## Oct 2022       114.3087  96.88911 131.7282
## Nov 2022       120.2837 100.84531 139.7221
## Dec 2022       127.9776 106.17022 149.7849
## Jan 2023       114.4558  93.98669 134.9249
## Feb 2023       113.5923  92.35405 134.8306
## Mar 2023       119.3883  96.12773 142.6488
#Gráfico de la serie original y del pronóstico.
PronosticosHW2 %>% autoplot(main ="Modelo Holt Winters",
               xlab="Años/Meses",
               ylab="Indice")