INSTALAR LAS LIBRERIAS

library(tseries)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
library(forecast)
library(ggplot2)
library(readxl)

IMPORTAR LOS DATOS

url="https://raw.githubusercontent.com/vmoprojs/DataLectures/master/pib_ec_const.csv"
datos1=read.delim(url,sep = ";")
GCFH=datos1$GCFH
plot(GCFH)

GCFH_s=ts(GCFH,start = c(2000,1),frequency = 4)
HoltWinters(GCFH_s)
## Holt-Winters exponential smoothing with trend and additive seasonal component.
## 
## Call:
## HoltWinters(x = GCFH_s)
## 
## Smoothing parameters:
##  alpha: 1
##  beta : 0.0456811
##  gamma: 0.4931984
## 
## Coefficients:
##            [,1]
## a  10390297.250
## b      8133.386
## s1    31203.250
## s2    -6893.000
## s3   -19194.000
## s4    -5116.250
plot(GCFH_s)

GCFH_s=diff(GCFH_s,4)
adf.test(GCFH_s)
## 
##  Augmented Dickey-Fuller Test
## 
## data:  GCFH_s
## Dickey-Fuller = -2.6077, Lag order = 4, p-value = 0.327
## alternative hypothesis: stationary
mod=auto.arima(GCFH_s,trace = T)
## 
##  ARIMA(2,1,2)(1,0,1)[4] with drift         : Inf
##  ARIMA(0,1,0)           with drift         : 2167.968
##  ARIMA(1,1,0)(1,0,0)[4] with drift         : 2160.704
##  ARIMA(0,1,1)(0,0,1)[4] with drift         : 2153.329
##  ARIMA(0,1,0)                              : 2166.297
##  ARIMA(0,1,1)           with drift         : 2170.122
##  ARIMA(0,1,1)(1,0,1)[4] with drift         : 2155.278
##  ARIMA(0,1,1)(0,0,2)[4] with drift         : 2155.086
##  ARIMA(0,1,1)(1,0,0)[4] with drift         : 2160.727
##  ARIMA(0,1,1)(1,0,2)[4] with drift         : Inf
##  ARIMA(0,1,0)(0,0,1)[4] with drift         : 2151.343
##  ARIMA(0,1,0)(1,0,1)[4] with drift         : 2153.25
##  ARIMA(0,1,0)(0,0,2)[4] with drift         : 2153.05
##  ARIMA(0,1,0)(1,0,0)[4] with drift         : 2158.7
##  ARIMA(0,1,0)(1,0,2)[4] with drift         : Inf
##  ARIMA(1,1,0)(0,0,1)[4] with drift         : 2153.337
##  ARIMA(1,1,1)(0,0,1)[4] with drift         : Inf
##  ARIMA(0,1,0)(0,0,1)[4]                    : 2150.961
##  ARIMA(0,1,0)(1,0,1)[4]                    : 2152.741
##  ARIMA(0,1,0)(0,0,2)[4]                    : 2152.445
##  ARIMA(0,1,0)(1,0,0)[4]                    : 2157.332
##  ARIMA(0,1,0)(1,0,2)[4]                    : 2152.473
##  ARIMA(1,1,0)(0,0,1)[4]                    : 2153.058
##  ARIMA(0,1,1)(0,0,1)[4]                    : 2153.061
##  ARIMA(1,1,1)(0,0,1)[4]                    : 2155.086
## 
##  Best model: ARIMA(0,1,0)(0,0,1)[4]
mod
## Series: GCFH_s 
## ARIMA(0,1,0)(0,0,1)[4] 
## 
## Coefficients:
##          sma1
##       -0.7047
## s.e.   0.1243
## 
## sigma^2 = 3.629e+10:  log likelihood = -1073.4
## AIC=2150.8   AICc=2150.96   BIC=2155.54

\((y_t-y{t-0})-(y_{t-4}-y_{t-5})=--0.7047 E_{t-1}0 E_{t-0}\)

GCFH_sw = HoltWinters(GCFH_s, gamma = F)
GCFH_sp = predict(GCFH_sw, 3)
plot(GCFH_sw, GCFH_sp, main = "Gasto de Consumo final Hogares: 2000:2025")