library(readxl)
library(tidyr)
library(dplyr)
library(forecast)
IVAE_03_22 <- read_excel("C:/Users/erick/Desktop/IVAE.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)
library(forecast)
descompocicion_aditiva<-decompose(data.ivae.ts,type = "additive")
Yt<-descompocicion_aditiva$x
TC1<-descompocicion_aditiva$trend
library(forecast)

#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(0.95))
PronosticosHW
##          Point Forecast     Lo 95    Hi 95
## Apr 2022       112.9503 107.46492 118.4358
## May 2022       120.9752 113.57246 128.3779
## Jun 2022       124.0929 115.22236 132.9634
## Jul 2022       118.5640 108.86876 128.2592
## Aug 2022       119.2908 108.50116 130.0804
## Sep 2022       117.4038 105.81297 128.9947
## Oct 2022       114.1680 101.97016 126.3657
## Nov 2022       121.3911 107.66977 135.1125
## Dec 2022       130.2643 114.88360 145.6450
## Jan 2023       116.9603 102.34981 131.5708
## Feb 2023       115.6485 100.48405 130.8129
## Mar 2023       121.0126  83.19827 158.8270
#Gráfico de la serie original y del pronóstico.
PronosticosHW %>% autoplot()