#Cargamos la Base de Datos

library(readxl)
## Warning: package 'readxl' was built under R version 4.1.3
library(forecast)
## Warning: package 'forecast' was built under R version 4.1.3
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
IVAE_SLV <- read_excel("C:/Users/Administrador/Desktop/ECO/Practica de pronostico de series temporales.xlsx",
                       col_types = c("skip", "numeric"),
                       skip = 0)
#Serie                      
serie.ivae.ts<- ts(data = IVAE_SLV, start = c(2009,1),
                      frequency = 12)

Yt<-serie.ivae.ts

Pronóstico de series temporales, enfoque deterministico (clásico)

#Pronóstico Modelo de Holt Winters

Usando forecast

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: 0.8540065
##  beta : 0
##  gamma: 1
## 
## Coefficients:
##            [,1]
## a   118.3463237
## b     0.1600306
## s1    0.9501653
## s2    1.0195813
## s3    1.0450993
## s4    0.9926690
## s5    1.0000193
## s6    0.9831838
## s7    0.9576173
## s8    1.0161329
## s9    1.0897384
## s10   0.9766794
## s11   0.9611902
## s12   1.0061994
#Generar el pronóstico:
PronosticosHW<-forecast(object = ModeloHW,h = 12,level = c(0.99))
PronosticosHW
##          Point Forecast     Lo 99    Hi 99
## Apr 2022       112.6006 105.38558 119.8157
## May 2022       120.9900 111.20364 130.7764
## Jun 2022       124.1854 112.44318 135.9276
## Jul 2022       118.1142 105.31817 130.9101
## Aug 2022       119.1488 104.86844 133.4291
## Sep 2022       117.3002 101.95238 132.6481
## Oct 2022       114.4032  98.21202 130.5944
## Nov 2022       121.5565 103.35310 139.7599
## Dec 2022       130.5361 110.11647 150.9556
## Jan 2023       117.1494  97.76725 136.5316
## Feb 2023       115.4453  95.38900 135.5017
## Mar 2023       121.0123  71.17910 170.8454
#Gráfico de la serie original y del pronóstico.
PronosticosHW %>% autoplot()

#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       108.8405  98.74090 118.9401
## May 2022       116.0057 105.22824 126.7832
## Jun 2022       116.7806 105.91726 127.6440
## Jul 2022       110.1399  99.88030 120.3995
## Aug 2022       113.0900 102.54043 123.6395
## Sep 2022       112.0135 101.54846 122.4785
## Oct 2022       110.3025  99.98080 120.6242
## Nov 2022       116.2842 105.38441 127.1839
## Dec 2022       124.6094 112.90864 136.3102
## Jan 2023       112.4516 101.87284 123.0304
## Feb 2023       109.0939  98.81107 119.3768
## Mar 2023       115.6973 104.76982 126.6247
#Gráfico de la serie original y del pronóstico.

PronosticosHW2 %>% autoplot()

###COMPONENTE ADITIVO

Pronóstico de series temporales, enfoque deterministico (clásico)

#Pronóstico Modelo de Holt Winters

Usando Stats

library(stats)

#Estimar el modelo

ModeloHW<-HoltWinters(x = Yt,
                      seasonal = "additive",
                      optim.start = c(0.9,0.9,0.9))
ModeloHW
## Holt-Winters exponential smoothing with trend and additive seasonal component.
## 
## Call:
## HoltWinters(x = Yt, seasonal = "additive", optim.start = c(0.9,     0.9, 0.9))
## 
## Smoothing parameters:
##  alpha: 0.9146823
##  beta : 0
##  gamma: 1
## 
## Coefficients:
##            [,1]
## a   118.0432658
## b     0.1600306
## s1   -4.1500211
## s2    3.0407453
## s3    4.0089319
## s4   -1.7834041
## s5   -0.5668506
## s6   -1.8386626
## s7   -3.9271859
## s8    2.3220630
## s9    9.7452166
## s10  -2.7534648
## s11  -4.5519143
## s12   1.0367342
#Generar el pronóstico:
PronosticosHW<-forecast(object = ModeloHW,h = 12,level = c(0.99))
PronosticosHW
##          Point Forecast     Lo 99    Hi 99
## Apr 2022       114.0533 107.13982 120.9667
## May 2022       121.4041 112.03477 130.7734
## Jun 2022       122.5323 111.22866 133.8359
## Jul 2022       116.9000 103.94776 129.8522
## Aug 2022       118.2766 103.86310 132.6900
## Sep 2022       117.1648 101.42515 132.9044
## Oct 2022       115.2363  98.27386 132.1987
## Nov 2022       121.6456 103.54275 139.7484
## Dec 2022       129.2288 110.05324 148.4043
## Jan 2023       116.8901  96.69881 137.0814
## Feb 2023       115.2517  94.09332 136.4101
## Mar 2023       121.0004  98.91724 143.0835
#Gráfico de la serie original y del pronóstico.
PronosticosHW %>% autoplot()

#Usando stats (Aproximación por Espacios de los Estados ETS )

library(stats)

#Generar el pronóstico:
PronosticosHW2<-hw(y = Yt,
                   h = 12,
                   level = c(0.99),
                   seasonal = "additive",
                   initial = "optimal")
PronosticosHW2
##          Point Forecast     Lo 99    Hi 99
## Apr 2022       114.3037 107.84818 120.7592
## May 2022       120.9815 111.77049 130.1924
## Jun 2022       121.7880 110.40646 133.1696
## Jul 2022       116.2790 103.02019 129.5378
## Aug 2022       118.6236 103.66922 133.5780
## Sep 2022       117.6387 101.11353 134.1639
## Oct 2022       116.1333  98.12866 134.1379
## Nov 2022       122.3865 102.97220 141.8007
## Dec 2022       129.6508 108.88178 150.4198
## Jan 2023       118.1562  96.07668 140.2357
## Feb 2023       115.6203  92.26651 138.9742
## Mar 2023       121.7770  97.17883 146.3751
#Gráfico de la serie original y del pronóstico.

PronosticosHW2 %>% autoplot()