Solucionario_T10

Ejercicio 4

Construya modelos ARIMA o ARMA, el que sea más adecuado, para las siguientes variables trimestrales Colombianas

• PIB real trimestral desestacionalizado

  library(forecast)

  ## Warning: package 'forecast' was built under R version 3.6.3

  ## Registered S3 method overwritten by 'xts':
  ##   method     from
  ##   as.zoo.xts zoo

  ## Registered S3 method overwritten by 'quantmod':
  ##   method            from
  ##   as.zoo.data.frame zoo

  #Modelo sin restricciones
  m_PIB<-auto.arima(PIB$PIB)
  summary(m_PIB)

  ## Series: PIB$PIB 
  ## ARIMA(0,1,0) with drift 
  ## 
  ## Coefficients:
  ##           drift
  ##       3088.6068
  ## s.e.   280.8908
  ## 
  ## sigma^2 estimated as 4814312:  log likelihood=-546.24
  ## AIC=1096.49   AICc=1096.7   BIC=1100.68
  ## 
  ## Training set error measures:
  ##                    ME     RMSE      MAE         MPE      MAPE      MASE
  ## Training set 1.284436 2157.885 1475.564 -0.07309312 0.8729784 0.4424969
  ##                     ACF1
  ## Training set -0.06440184

  #Modelo sin drift
  m_PIB2<-auto.arima(PIB$PIB,allowdrift=FALSE)
  summary(m_PIB2)

  ## Series: PIB$PIB 
  ## ARIMA(2,1,0) 
  ## 
  ## Coefficients:
  ##          ar1     ar2
  ##       0.3216  0.5000
  ## s.e.  0.1310  0.1328
  ## 
  ## sigma^2 estimated as 6188158:  log likelihood=-553.82
  ## AIC=1113.64   AICc=1114.06   BIC=1119.92
  ## 
  ## Training set error measures:
  ##                    ME     RMSE      MAE       MPE     MAPE      MASE       ACF1
  ## Training set 465.8613 2425.659 1650.831 0.3424838 1.026997 0.4950566 -0.1187033

• Tasa de desempleo promedio trimestral desestacionalizada

  m_TD<-auto.arima(TD$TD)
  summary(m_TD)

  ## Series: TD$TD 
  ## ARIMA(0,1,5) 
  ## 
  ## Coefficients:
  ##           ma1     ma2     ma3      ma4     ma5
  ##       -0.0351  0.2424  0.1028  -0.3887  0.1900
  ## s.e.   0.1245  0.1098  0.1198   0.1023  0.1234
  ## 
  ## sigma^2 estimated as 0.17:  log likelihood=-38.51
  ## AIC=89.03   AICc=90.25   BIC=103.01
  ## 
  ## Training set error measures:
  ##                       ME      RMSE       MAE        MPE     MAPE      MASE
  ## Training set -0.04996637 0.3958958 0.2898513 -0.4190405 2.496315 0.8574606
  ##                     ACF1
  ## Training set -0.00364443

• DTF promedio trimestral

  #la serie viene por defecto mensual, la convertimos en formato xts
  library(xts)

  ## Loading required package: zoo

  ## 
  ## Attaching package: 'zoo'

  ## The following objects are masked from 'package:base':
  ## 
  ##     as.Date, as.Date.numeric

  DTF_xts<-xts(DTF, order.by = DTF$mes)
  #eliminamos la columna de mes
  DTF_xts<-DTF_xts[,-1]
  #Generamos la serie trimestral
  DTF_Q<-to.period(DTF_xts,period="quarters",OHLC = FALSE)
  DTF_mq<-DTF_Q[,1]
  DTF_mq<-data.frame(DTF_mq)
  #Ahora sí generamos el modelo
  m_DTF<-auto.arima(DTF_mq)
  summary(m_DTF)

  ## Series: DTF_mq 
  ## ARIMA(2,1,4) 
  ## 
  ## Coefficients:
  ##           ar1     ar2     ma1      ma2      ma3      ma4
  ##       -0.2932  0.6621  0.6135  -0.4951  -0.4547  -0.2422
  ## s.e.   0.1391  0.1310  0.1526   0.1639   0.0886   0.0940
  ## 
  ## sigma^2 estimated as 55.44:  log likelihood=-466.74
  ## AIC=947.48   AICc=948.35   BIC=967.92
  ## 
  ## Training set error measures:
  ##                      ME     RMSE      MAE       MPE     MAPE      MASE
  ## Training set -0.9724365 7.254774 4.922157 -12.38908 20.18791 0.9444475
  ##                     ACF1
  ## Training set -0.02212227

  Y así sucesivamente con las otras bases de datos
• Inflación fin de trimestre anualizada desestacionalizada
• Producción agropecuaria trimestral desestacionalizada

Ejercicio 5

Realice pronósticos de las variables de arriba por tres periodos y muestre un gráfico con las bandas de pronóstico

# Pronóstico PIB
f_PIB<-forecast(m_PIB,h=3)
plot(f_PIB)

f_PIB2<-forecast(m_PIB2,h=3)
plot(f_PIB2)

# Pronóstico Desempleo
f_TD<-forecast(m_TD,h=3)
plot(f_TD)

# Pronóstico DTF
f_DTF<-forecast(m_DTF,h=3)
plot(f_DTF)