Descomposicion de Series Temporales

#Importando Base de datos
library(readxl)
library(forecast)
serie.ivae<-read_excel("C:/Users/KENNYA/Desktop/R/Parcial3/IVAE-K-SLV.xlsx",
           col_types = c("skip", "numeric"), skip = 5)
library(magrittr)
library(ggplot2)
serie.ivae.ts <- ts(data = serie.ivae, start = c(2009, 1), frequency = 12)
serie.ivae.ts %>% autoplot(main = "Gráfica 1: El Salvador - IVAE Periodo 2009 (Enero) - 2021 (Marzo)",
                           xlab = "Años/Meses",  ylab = "Indice") + 
                  scale_fill_brewer(palette = "Accent") + 
                  theme(plot.title = element_text(hjust = 0.5))

Modelo Aditivo

Componente Tendencial

ma2_12<-ma(serie.ivae.ts, 12, centre = TRUE)
autoplot(serie.ivae.ts,
         main = "Gráfica 2: El Salvador - IVAE Periodo 2009 (Enero) - 2021 (Marzo)",
         xlab = "Años/Meses", ylab = "Indice") + autolayer(ma2_12, series = "Tt") +
         theme(plot.title = element_text(hjust = 0.5))

Componentes Estacionales

library(magrittr)
library(ggplot2)
Yt <- serie.ivae.ts 
Tt <- ma2_12 
SI <- Yt - Tt
St <- tapply(SI, cycle(SI), mean, na.rm = TRUE)
St <- St - sum(St) / 12 
St<-rep(St, len = length(Yt)) %>% ts(start = c(2009, 1), frequency = 12) 
autoplot(St, main = "Gráfica 3: Factores Estacionales IVAE 2009-2021",
         xlab = "Años/Meses", ylab = "Factor Estacional") + 
         theme(plot.title = element_text(hjust = 0.5))

Componente Irregular

It<-Yt/(Tt*St)
autoplot(It, main = "Gráfica 4: Componente Irregular", xlab = "Años/Meses", ylab = "It") + theme(plot.title = element_text(hjust = 0.5))

Descomposicion Aditiva

Libreria Feasts

library(tsibble)
library(feasts)
library(ggplot2)
Yt %>% as_tsibble() %>% 
model(classical_decomposition(value, type = "additive")) %>%
components() %>% autoplot() + 
labs(title = "Gráfica 5: Descomposición Clásica Aditiva, IVAE", 
     caption = "Fuente: Elaboración Propia en base a datos del BCR")+
xlab("Años/Meses") + theme(plot.title = element_text(hjust = 0.5))

Modelo Multiplicativo

Componente Tendencial

library(ggplot2)
Tt<- ma(serie.ivae.ts, 12, centre = TRUE)
autoplot(Tt,main = "Gráfica 6: Componente Tendencia [Ciclo]", xlab = "Años/Meses",ylab = "Tt")+
theme(plot.title = element_text(hjust = 0.5))

Componentes Estacionales

SI<-Yt/Tt 
St<-tapply(SI, cycle(SI), mean, na.rm = TRUE) 
St<-St*12/sum(St) 
St<-rep(St, len = length(Yt)) %>% ts(start = c(2009, 1), frequency = 12) 
autoplot(St, main = "Gráfica 7: Factores Estacionales",
         xlab = "Años/Meses",
         ylab = "Factor Estacional") +
         theme(plot.title = element_text(hjust = 0.5))

Componente Irregular

It<-Yt/(Tt*St)
autoplot(It, main = "Gráfica 8: Componente Irregular",
         xlab = "Años/Meses", ylab = "It") +
         theme(plot.title = element_text(hjust = 0.5))

Descomposicion Multiplicativa

Libreria Feasts

library(tsibble)
library(feasts)
library(ggplot2)
Yt %>% as_tsibble() %>%
  model(classical_decomposition(value, type = "multiplicative")) %>%
  components() %>%
  autoplot() +
  labs(title = "Gráfica 9: Descomposición Clásica Multiplicativa, IVAE") + xlab("Años/Meses") +
  theme(plot.title = element_text(hjust = 0.5))