Descomposición de Series Temporales

GT-03 Alejandra Eunice Ramirez Urquiza DUE: RU18002

1/7/2021

1. Descomposición de Series Temporales (Enfoque Tradicional)

library(readxl)
library(forecast)
serie.IVAE <- read_excel("C:/Users/Eunice/Desktop/IVAE_SLV_C.xlsx", 
                       col_types = c("skip", "numeric"),
                       skip = 5)

serie.IVAE.ts <- ts(data = serie.IVAE,
                    start = c(2009, 1),
                    frequency = 12)

serie.IVAE.ts %>%
  autoplot(main = "IVAE, El Salvador 2009-2021[marzo]",
           xlab = "Años/Meses",
           ylab = "Indice")

1.1 Modelo Aditivo

1.1.1 Componente de Tendencia Tt [Componente TCt]

ma2_12<- ma(serie.IVAE.ts, 12, centre = TRUE)
autoplot(serie.IVAE.ts,main = "IVAE, El Salvador 2009-2021[marzo]",
         xlab = "Años/Meses", 
         ylab = "Indice")+
  autolayer(ma2_12,series = "Tt")

1.1.2 Cálculo de los Factores Estacionales [Componente St]

library(magrittr)
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 = "Factores Estacionales", 
         xlab = "Años/Meses", 
         ylab = "Factor Estacional")

1.1.3 Cálculo del Componente Irregular It.

It<-Yt-Tt-St
autoplot(It,
         main = "Componente Irregular",
         xlab = "Años/Meses",
         ylab = "It")

1.1.4 Descomposición Aditiva (usando la libreria stats):

descomposicion_aditiva<-decompose(serie.IVAE.ts,type = "additive")
autoplot(descomposicion_aditiva,main="Descomposición Aditiva",xlab="Años/Meses")

1.1.5 Descomposición Aditiva usando libreria feasts

library(tsibble)
library(feasts)
library(ggplot2)
Yt %>% as_tsibble() %>%
  model(
    classical_decomposition(value, type = "additive")
  ) %>%
  components() %>%
  autoplot() +
  labs(title = "Descomposición Clásica Aditiva, IVAE")+xlab("Años/Meses")

1.2 Modelo Multiplicativo

1.2.1 Componente Tendencia Ciclo [Tt=TCt]

Tt<- ma(serie.IVAE.ts, 12, centre = TRUE)
autoplot(Tt,main = "Componente Tendencia [Ciclo]", 
         xlab = "Años/Meses",
         ylab = "Tt")

1.2.2 Cálculo de Factores Estacionales [St]

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 = "Factores Estacionales",
         xlab = "Años/Meses",
         ylab = "Factor Estacional")

1.2.3 Cálculo del Componente Irregular [It]

It<-Yt/(Tt*St)
autoplot(It,
         main = "Componente Irregular",
         xlab = "Años/Meses",
         ylab = "It")

1.2.4 Descomposición Multiplicativa (usando la libreria stats):

descomposicion_multiplicatica<-decompose(serie.IVAE.ts,type = "multiplicative")
autoplot(descomposicion_multiplicatica,main="Descomposición Multiplicativa",xlab="Años/Meses")

1.2.5 Descomposición Multiplicativa usando libreria feasts

library(tsibble)
library(feasts)
library(ggplot2)
Yt %>% as_tsibble() %>%
  model(classical_decomposition(value, type = "multiplicative")) %>%
  components() %>%
  autoplot() +
  labs(title = "Descomposición Clásica Multiplicativa, IVAE") + xlab("Años/Meses")