Primeiro exemplo

Número mensal de mortos por doenças do pulmão, como bronquite, efisema e asma, etc. no Reino Unido entre janeiro de 1974 e dezembro de 1979. O arquivo e composto por 3 séries: ambos os sexos (ldeaths), sexo feminino (fdeaths) e sexo masculino (mdeaths) 

data(UKLungDeaths)
par(mfrow=c(1,1), mar=c(3,2,3,1)+.5, mgp=c(1.6,.6,0), pch=19)
plot(ldeaths, ylim=c(500,4500), type="b", main="Número mensal de mortos por doenças do pulmão no Reino Unido", ylab="", xlab="")
lines(fdeaths, col="red", type="b")
lines(mdeaths, col="blue", type="b")
legend("topright", legend = c("ambos sexos","feminino","masculino"), col = c("black","red","blue"), lwd = 2)
grid()

Modelo aditivo

m1=HoltWinters(ldeaths,seasonal='addit') 
p1=predict(m1,n.ahead=12,prediction.interval=T)
library(forecast)
plot(m1,p1, main="Holt-Winters: modelo aditivo", type="b", pch=19)

plot(forecast(m1, h=12), main="Holt-Winters: modelo aditivo", type="b", pch=19)
abline(v=1980, lty=2)
grid()

Modelo multiplicativo

m2=HoltWinters(ldeaths,seasonal='multiplicative')
plot(forecast(m2, h=12), main="Holt-Winters: modelo multiplicativo", type="b", pch=19)
abline(v=1980, lty=2)
grid()

Performance preditiva

m3 = HoltWinters(ts(ldeaths[1:60],start=c(1,1974),freq=12),seasonal='additive')
accuracy(forecast(m3),ldeaths[61:72])
##                     ME     RMSE      MAE       MPE     MAPE      MASE      ACF1
## Training set -37.74839 270.6590 189.8017 -3.630661 9.160960 0.5953376 0.1701072
## Test set      50.73755 173.8575 135.1195  2.913078 7.230091 0.4238197        NA
m4 = HoltWinters(ts(ldeaths[1:60],start=c(1,1974),freq=12),seasonal='multiplicative')
accuracy(forecast(m4),ldeaths[61:72])
##                     ME     RMSE      MAE       MPE     MAPE      MASE      ACF1
## Training set -26.01843 271.1368 188.9341 -3.256784 8.957214 0.5926164 0.1746961
## Test set      61.66665 176.0174 118.0794  2.651880 5.804528 0.3703712        NA

Segundo exemplo:

Totais mensais de passageiros em linhas aéreas internacionais nos EUA entre 1949 e 1960. 

data(AirPassengers)
par(mfrow=c(1,1), mar=c(3,2,3,1)+.5, mgp=c(1.6,.6,0), pch=19)
plot(AirPassengers, type="b", main="No. mensal de passageiros em linhas aéreas internacionais nos EUA", ylab="", xlab="")
grid()

m5=HoltWinters(AirPassengers,seasonal='addit') 
plot(forecast(m5, h=12), main="Holt-Winters: modelo aditivo", type="b", pch=19)
abline(v=1961, lty=2)
grid()

m6=HoltWinters(AirPassengers,seasonal='multiplicative')
plot(forecast(m6, h=12), main="Holt-Winters: modelo multiplicativo", type="b", pch=19)
abline(v=1961, lty=2)
grid()

Performance preditiva

m5 = HoltWinters(ts(AirPassengers[1:132],start=c(1,1949),freq=12),seasonal='additive')
accuracy(forecast(m5),AirPassengers[133:144])
##                      ME     RMSE       MAE        MPE     MAPE      MASE
## Training set  1.9402762 12.29076  9.368199  0.4661812 3.442364 0.3889807
## Test set     -0.7984502 15.95565 11.564418 -0.4802758 2.519996 0.4801708
##                   ACF1
## Training set 0.5145714
## Test set            NA
m6 = HoltWinters(ts(AirPassengers[1:132],start=c(1,1949),freq=12),seasonal='multiplicative')
accuracy(forecast(m6),AirPassengers[133:144])
##                    ME     RMSE       MAE       MPE     MAPE      MASE      ACF1
## Training set 1.593595 13.15560  9.908093 0.4159226 3.498458 0.4113978 0.2472298
## Test set     9.266676 31.98247 24.172357 1.3219527 4.891075 1.0036700        NA