Descomposición De Series Temporales

1. Descomposición de Series Temporales

library(readxl)
library(forecast)
serie.imae<- read_excel("C:/Users/USER/Desktop/Descomposición de Series Temporales/tableExport_IMAE.xlsx",
            col_types = c("skip", "numeric"),
            skip = 5)
serie.imae.ts<- ts(data = serie.imae,
                start = c(2018, 1),
                frequency = 12)

serie.imae.ts %>%
  autoplot(main = "IMAE, EL SALVADOR 2018-2024[marzo]",
           xlab ="Años/Meses",
           ylab = "Indice")

2. Modelo Aditivo.

2.1.1 Componente de Tendencia Tt [Componente TCt]

library(forecast)
ma2_12<- ma(serie.imae.ts, 12, centre = TRUE)
autoplot(serie.imae.ts,main = "IMAE, EL Salvador 2018-2024[marzo]",
         xlab = "Años/Meses",
         ylab = "Indice")+
  autolayer(ma2_12,series = "Tt")

2.1.2 Cálculo de los Factores Estacionales [Componente St]

library(magrittr)
Yt <- serie.imae.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(2018, 1), frequency = 12) 
 autoplot(St, 
          main = "Factores Estacionales", 
          xlab = "Años/Meses",
          ylab = "Factor Estacional")

2.1.3 Cáculo del Componente Irregular [It]

\(It = Yt -Tt - St\)

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

2.1.4 Descomposición Aditiva (usando stats)

library(stats)
descomposición_aditiva <- decompose(serie.imae.ts, type = "additive")
autoplot (descomposición_aditiva, main= "Descomposición Aditiva", xlab = "Años/Meses")

2.1.5 Descomposición Aditiva (usando feasts)

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

2.2 Modelo Multiplicativo

2.2.1 Componente Tendencia Ciclo [Tt=TCt]

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

2.2.2 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(2018, 1), frequency = 12)
autoplot(St,
         main = "Factores Estacionales",
         xlab = "Años/Meses",
         ylab = "Factor Estacional")

2.2.3 Cálculo del Componente Irregular [It]

\(It = Yt/Tt*St\)

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

2.2.4 Descomposición Multiplicativa (usando stast)

library(stats)
descomposición_multiplicativa <- decompose(serie.imae.ts, type = "multiplicative")
autoplot(descomposición_multiplicativa, main ="Descomposición Multiplicativa", xlab="Años/Meses")

2.2.5 Descomposición Multiplicativa (usando feasts)

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

2.3 Descomposición (usando TSstudio)

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