Descompocición de series temporales

Descomposición de Series Temporales (Enfoque Tradicional)

library(readxl)
library(forecast)
library(dplyr)
Ivae <- read_excel("C:/Users/DELL/Desktop/Programacion-en-R/Econometria/Tareas_Tercer_Parcial/IVAE.xlsx", col_types = c("skip", "numeric"), skip = 5)

Serie.Ivae <- ts(data = Ivae, start = c(2009,1), frequency = 12)

Serie.Ivae %>% autoplot(main = "IVAE de El Salvador 2009-2021[Marzo]", 
                        xlab = "años", 
                        ylab = "Indice")

1. Modelo Aditivo

1.1. Componente Tendencia Ciclo TCt

ma2_12 <- ma(Serie.Ivae, 12, centre = TRUE)
autoplot(Serie.Ivae, main = "IVAE de El Salvador", xlab = "Años", ylab = "Indice") + 
  autolayer(ma2_12, series = "Tt")

1.2. Factores Estacionales | Componente St

library(magrittr)
Yt <- Serie.Ivae
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 Estacinales",
         xlab = "Años",
         ylab = "Factor Estacional")

1.3. Componente Irregular

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

1.4. Descompocición aditiva

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

1.5. Descomposición 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")

2. Modelo Multiplicativo

2.1. Componente Tendencia Ciclo (Tt = TCt)

Tt <- ma(Serie.Ivae, 12, centre = TRUE)
autoplot(Tt, main = "Componente Tendencial (Ciclo)", xlab = "Años", ylab = "Tt")

2.2. Factores 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 = "Factores Estacionales",
         xlab = "Años", ylab = "St")

2.3. Componente Irregular(It)

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

2.4. Descompocción Multiplicativa Usando Stats

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

2.5. Descomposición Usando Librería 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")