Peramalan terhadap banyak turis yang datang ke Spanyol akan dilakukan pada April sampai Desember 1989.

Library dan Visualisasi Data

library(readxl)
tugas1=read_xlsx("D:/Semester6/MPDW/spain.xlsx",sheet = "Sheet1") 
ddw=ts(tugas1$SPAIN, start=c(1970,1),end=c(1989,3), freq=12)
plot(ddw, main = 'Banyak Turis di Spanyol 1970-1989')

Dilihat dari grafik diatas, terlihat bahwa data deret waktu ini berpola seasonal. Karena itu, metode pemulusan yang akan digunakan adalah metode Winter’s Aditif dan Multiplikatif.

Metode Pemulusan

Seasonal Aditif

library(forecast)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
aditif<-HoltWinters(ddw, alpha=NULL, beta=NULL, gamma=NULL,seasonal = "additive")
aditif
## Holt-Winters exponential smoothing with trend and additive seasonal component.
## 
## Call:
## HoltWinters(x = ddw, alpha = NULL, beta = NULL, gamma = NULL,     seasonal = "additive")
## 
## Smoothing parameters:
##  alpha: 0.1903305
##  beta : 0.00662229
##  gamma: 0.49067
## 
## Coefficients:
##            [,1]
## a    4767500.51
## b      15197.63
## s1  -1026667.59
## s2   -551853.16
## s3    108644.58
## s4   3677465.62
## s5   4783380.52
## s6    920199.25
## s7   -777091.02
## s8  -2106869.05
## s9  -1321152.01
## s10 -2147239.26
## s11 -2218414.42
## s12 -1613631.38
head(aditif$fitted, n = 5L)
##               xhat   level    trend     season
## Jan 1971  827482.3 1964719 22409.74 -1159646.1
## Feb 1971  858582.7 2016754 22605.93 -1180777.4
## Mar 1971 1147419.3 2062511 22759.24  -937850.7
## Apr 1971 1825931.5 2102139 22870.96  -299078.6
## May 1971 1886605.3 2138859 22962.67  -275216.4
plot(aditif)
points(ddw)

Forecast

aditif.ramal=forecast(aditif, h=9)
aditif.ramal
##          Point Forecast   Lo 80    Hi 80   Lo 95    Hi 95
## Apr 1989        3756031 3315440  4196621 3082206  4429856
## May 1989        4246043 3797439  4694647 3559962  4932123
## Jun 1989        4921738 4465158  5378318 4223459  5620017
## Jul 1989        8505757 8041236  8970277 7795333  9216180
## Aug 1989        9626869 9154440 10099298 8904351 10349387
## Sep 1989        5778886 5298579  6259192 5044320  6513452
## Oct 1989        4096793 3608636  4584949 3350222  4843364
## Nov 1989        2782213 2286233  3278192 2023677  3540748
## Dec 1989        3583127 3079349  4086906 2812664  4353590
plot(aditif.ramal, main = 'Peramalan Banyak Turis ke Spanyol')
points(ddw)

Akurasi Seasonal Smoothing Aditif

SSE1 <- aditif$SSE
MSE1 <- aditif$SSE/length(ddw)
RMSE1 <- sqrt(MSE1)
akurasi1 <- matrix(c(SSE1,MSE1,RMSE1))
row.names(akurasi1)<- c("SSE", "MSE", "RMSE")
colnames(akurasi1) <- c("Akurasi Seasonal Smoothing Aditif)")
akurasi1
##      Akurasi Seasonal Smoothing Aditif)
## SSE                        2.591595e+13
## MSE                        1.121903e+11
## RMSE                       3.349482e+05

Seasonal Multiplikatif

multiplikatif<-HoltWinters(ddw, alpha=NULL, beta=NULL, gamma=NULL,seasonal = "multiplicative")
multiplikatif
## Holt-Winters exponential smoothing with trend and multiplicative seasonal component.
## 
## Call:
## HoltWinters(x = ddw, alpha = NULL, beta = NULL, gamma = NULL,     seasonal = "multiplicative")
## 
## Smoothing parameters:
##  alpha: 0.3302993
##  beta : 0.01050499
##  gamma: 0.6117378
## 
## Coefficients:
##             [,1]
## a   5.324835e+06
## b   1.833930e+04
## s1  6.883228e-01
## s2  7.891719e-01
## s3  9.300434e-01
## s4  1.701529e+00
## s5  1.957480e+00
## s6  1.157175e+00
## s7  7.963876e-01
## s8  5.101529e-01
## s9  6.694654e-01
## s10 4.908254e-01
## s11 4.633247e-01
## s12 5.848328e-01
head(multiplikatif$fitted, n = 5L)
##               xhat   level    trend    season
## Jan 1971  899273.5 1964719 22409.74 0.4525493
## Feb 1971  926723.5 2048337 23052.74 0.4473922
## Mar 1971 1196945.8 2110882 23467.61 0.5608011
## Apr 1971 1858425.9 2157381 23709.56 0.8520625
## May 1971 1917712.4 2196701 23873.54 0.8636110
plot(multiplikatif)
points(ddw)

Forecast

multiplikatif.ramal=forecast(multiplikatif, h=9)
multiplikatif.ramal
##          Point Forecast   Lo 80    Hi 80   Lo 95    Hi 95
## Apr 1989        3677829 3333663  4021995 3151473  4204185
## May 1989        4231156 3843694  4618618 3638584  4823728
## Jun 1989        5003497 4559837  5447158 4324977  5682017
## Jul 1989        9185181 8501863  9868499 8140136 10230226
## Aug 1989       10602752 9814679 11390826 9397498 11808006
## Sep 1989        6289100 5735828  6842371 5442944  7135256
## Oct 1989        4342869 3873241  4812497 3624636  5061103
## Nov 1989        2791327 2377708  3204945 2158752  3423902
## Dec 1989        3675291 3172888  4177694 2906931  4443650
plot(multiplikatif.ramal, main = 'Peramalan Banyak Turis ke Spanyol')
points(ddw)

Akurasi Seasonal Smoothing Multiplikatif

SSE2 <- multiplikatif$SSE
MSE2 <- multiplikatif$SSE/length(ddw)
RMSE2 <- sqrt(MSE2)
akurasi2 <- matrix(c(SSE2,MSE2,RMSE2))
row.names(akurasi2)<- c("SSE", "MSE", "RMSE")
colnames(akurasi2) <- c("Akurasi Seasonal Smoothing Multiplikatif")
akurasi2
##      Akurasi Seasonal Smoothing Multiplikatif
## SSE                              2.913402e+13
## MSE                              1.261213e+11
## RMSE                             3.551356e+05

Akurasi

akurasi <-cbind(akurasi1, akurasi2)
akurasi
##      Akurasi Seasonal Smoothing Aditif)
## SSE                        2.591595e+13
## MSE                        1.121903e+11
## RMSE                       3.349482e+05
##      Akurasi Seasonal Smoothing Multiplikatif
## SSE                              2.913402e+13
## MSE                              1.261213e+11
## RMSE                             3.551356e+05

Karena nilai MSE, RMSE, dan SSE dari metode Winter’s Aditif lebih kecil daripada metode Winter’s Multiplikatif, maka lebih baik kita menggunakan metode Winter’s Aditif untuk data deret waktu ini.

Note: Proyek ini adaalah hasil tugas individu mata kuliah Metode Peramalan Deret Waktu.