Descomposición de Series Temporales (Enfoque Tradicional)

library(readxl)
library(forecast)

serie.ivae<-
  read_excel("IMAE.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 Modelo Aditivo.

1.1. Componente de Tendencia Tt [Componente TCt]

library(forecast)
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")

1.2. Cálculo de los Factores Estacionales [Componente St]

library(magrittr)
library(plyr)

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 = "Año/Meses",
         ylab = "Factor Estacional")

1.3 Cálculo del Componente Irregular It

It<-Yt-Tt-St

autoplot(It,
         main = "Componente Irregular",
         xlab = "Años/Meses",
         ylab = "It")

1.4. Descomposición Aditiva (usando la libreria stats):

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

2 Modelo Multiplicativo.

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")

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")

2.3. Cálculo del Componente Irregular [It]

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

2.4. Descomposición Multiplicativa (usando la libreria stats):

descompisicion_multiplicativa<-decompose(serie.ivae.ts, type = "multiplicative")
autoplot(descompisicion_multiplicativa, main = "Descomposicion Multiplicativa", xlab = "Años/Meses")

2.5. Descomposición Multiplicativa usando libreria feasts

library(feasts)
library(ggplot2)
library(tsibble)

Yt_tsibble <- as_tsibble(Yt)
model_result <- model(Yt_tsibble, classical_decomposition(value, type = "multiplicative"))
decomposition <- components(model_result)
autoplot(decomposition) + labs(title = "Descomposicion Clásica Multiplicativa, IVAE", x = "Años/Meses")

3 Descomposición usando la libreria TSstudio

3.1. Modelo aditivo

library(TSstudio)
ts_decompose(Yt, type = "additive", showline = TRUE)
ts_seasonal(Yt, type = "box", title = "Analsis de Valores Estacionales")

3.2. Modelo Multiplicativo

library(TSstudio)
ts_decompose(Yt, type = "multiplicative", showline = TRUE)
ts_seasonal(Yt, type = "box", title = "Analsis de Valores Estacionales")