Tugas Individu Minggu 2 MPDW
Fathiyya Mufida
2024-08-25
library("forecast")## Warning: package 'forecast' was built under R version 4.3.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary("graphics")
library("TTR")
library("TSA")## Warning: package 'TSA' was built under R version 4.3.3## Registered S3 methods overwritten by 'TSA':
## method from
## fitted.Arima forecast
## plot.Arima forecast##
## Attaching package: 'TSA'## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tarPenyiapan Data
library(readxl)
data_mpdw <- read_xlsx('C:/semester 5/MPDW/Data MPDW Kel 9 101.xlsx')
data_mpdw$Date <- as.Date(data_mpdw$Date)
View(data_mpdw)data_mpdw.ts <- ts(data_mpdw$kurs)
summary(data_mpdw.ts)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 13105 13331 13512 13768 14074 15329Pembagian Data
Pembagian data latih dan data uji dilakukan dengan perbandingan 80% data latih dan 20% data uji.
#membagi data latih dan data uji
training_ma <- data_mpdw[1:80,]
testing_ma <- data_mpdw[81:100,]
train_ma.ts <- ts(training_ma$kurs)
test_ma.ts <- ts(testing_ma$kurs)Eksplorasi Data
Plot time series
Eksplorasi data dilakukan pada keseluruhan data, data latih serta data uji menggunakan plot data deret waktu.
#eksplorasi keseluruhan data
plot(data_mpdw.ts, col="red",main="Plot semua data")
points(data_mpdw.ts)
#eksplorasi data latih
plot(train_ma.ts, col="blue",main="Plot data latih")
points(train_ma.ts)
#eksplorasi data uji
plot(test_ma.ts, col="blue",main="Plot data uji")
points(test_ma.ts)
#Eksplorasi dengan GGPLOT
library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.3.3ggplot() +
geom_line(data = training_ma, aes(x = Date, y = kurs, col = "Data Latih")) +
geom_line(data = testing_ma, aes(x = Date, y = kurs, col = "Data Uji")) +
labs(x = "Periode Waktu", y = "Sales", color = "Legend") +
scale_colour_manual(name="Keterangan:", breaks = c("Data Latih", "Data Uji"),
values = c("blue", "red")) +
theme_bw() + theme(legend.position = "bottom",
plot.caption = element_text(hjust=0.5, size=12))
Single Moving Average & Double Moving Average
Single Moving Average (SMA)
data.sma<-SMA(train_ma.ts, n=4)
data.sma## Time Series:
## Start = 1
## End = 80
## Frequency = 1
## [1] NA NA NA 13349.00 13345.75 13351.25 13337.25 13336.75
## [9] 13321.75 13324.50 13319.50 13318.50 13332.75 13339.50 13328.75 13275.00
## [17] 13271.75 13261.75 13270.75 13326.50 13318.00 13310.75 13303.75 13291.00
## [25] 13290.00 13288.50 13316.75 13330.50 13325.75 13331.25 13306.50 13311.25
## [33] 13333.75 13338.50 13344.00 13305.50 13279.75 13271.50 13305.00 13380.00
## [41] 13440.00 13492.50 13524.00 13519.75 13528.50 13526.50 13503.25 13514.75
## [49] 13517.50 13532.50 13544.75 13532.50 13500.75 13432.50 13379.25 13334.75
## [57] 13334.75 13412.50 13467.00 13555.25 13640.25 13685.25 13736.75 13768.00
## [65] 13767.25 13761.50 13764.25 13780.75 13803.25 13845.25 13888.00 13960.75
## [73] 14012.75 13985.50 13983.75 13967.75 13978.25 14091.00 14192.00 14267.75data.ramal<-c(NA,data.sma)
data.ramal #forecast 1 periode ke depan## [1] NA NA NA NA 13349.00 13345.75 13351.25 13337.25
## [9] 13336.75 13321.75 13324.50 13319.50 13318.50 13332.75 13339.50 13328.75
## [17] 13275.00 13271.75 13261.75 13270.75 13326.50 13318.00 13310.75 13303.75
## [25] 13291.00 13290.00 13288.50 13316.75 13330.50 13325.75 13331.25 13306.50
## [33] 13311.25 13333.75 13338.50 13344.00 13305.50 13279.75 13271.50 13305.00
## [41] 13380.00 13440.00 13492.50 13524.00 13519.75 13528.50 13526.50 13503.25
## [49] 13514.75 13517.50 13532.50 13544.75 13532.50 13500.75 13432.50 13379.25
## [57] 13334.75 13334.75 13412.50 13467.00 13555.25 13640.25 13685.25 13736.75
## [65] 13768.00 13767.25 13761.50 13764.25 13780.75 13803.25 13845.25 13888.00
## [73] 13960.75 14012.75 13985.50 13983.75 13967.75 13978.25 14091.00 14192.00
## [81] 14267.75data.gab<-cbind(aktual=c(train_ma.ts,rep(NA,20)),pemulusan=c(data.sma,rep(NA,20)),ramalan=c(data.ramal,rep(data.ramal[length(data.ramal)],19)))
data.gab #forecast 20 periode ke depan## aktual pemulusan ramalan
## [1,] 13351 NA NA
## [2,] 13313 NA NA
## [3,] 13406 NA NA
## [4,] 13326 13349.00 NA
## [5,] 13338 13345.75 13349.00
## [6,] 13335 13351.25 13345.75
## [7,] 13350 13337.25 13351.25
## [8,] 13324 13336.75 13337.25
## [9,] 13278 13321.75 13336.75
## [10,] 13346 13324.50 13321.75
## [11,] 13330 13319.50 13324.50
## [12,] 13320 13318.50 13319.50
## [13,] 13335 13332.75 13318.50
## [14,] 13373 13339.50 13332.75
## [15,] 13287 13328.75 13339.50
## [16,] 13105 13275.00 13328.75
## [17,] 13322 13271.75 13275.00
## [18,] 13333 13261.75 13271.75
## [19,] 13323 13270.75 13261.75
## [20,] 13328 13326.50 13270.75
## [21,] 13288 13318.00 13326.50
## [22,] 13304 13310.75 13318.00
## [23,] 13295 13303.75 13310.75
## [24,] 13277 13291.00 13303.75
## [25,] 13284 13290.00 13291.00
## [26,] 13298 13288.50 13290.00
## [27,] 13408 13316.75 13288.50
## [28,] 13332 13330.50 13316.75
## [29,] 13265 13325.75 13330.50
## [30,] 13320 13331.25 13325.75
## [31,] 13309 13306.50 13331.25
## [32,] 13351 13311.25 13306.50
## [33,] 13355 13333.75 13311.25
## [34,] 13339 13338.50 13333.75
## [35,] 13331 13344.00 13338.50
## [36,] 13197 13305.50 13344.00
## [37,] 13252 13279.75 13305.50
## [38,] 13306 13271.50 13279.75
## [39,] 13465 13305.00 13271.50
## [40,] 13497 13380.00 13305.00
## [41,] 13492 13440.00 13380.00
## [42,] 13516 13492.50 13440.00
## [43,] 13591 13524.00 13492.50
## [44,] 13480 13519.75 13524.00
## [45,] 13527 13528.50 13519.75
## [46,] 13508 13526.50 13528.50
## [47,] 13498 13503.25 13526.50
## [48,] 13526 13514.75 13503.25
## [49,] 13538 13517.50 13514.75
## [50,] 13568 13532.50 13517.50
## [51,] 13547 13544.75 13532.50
## [52,] 13477 13532.50 13544.75
## [53,] 13411 13500.75 13532.50
## [54,] 13295 13432.50 13500.75
## [55,] 13334 13379.25 13432.50
## [56,] 13299 13334.75 13379.25
## [57,] 13411 13334.75 13334.75
## [58,] 13606 13412.50 13334.75
## [59,] 13552 13467.00 13412.50
## [60,] 13652 13555.25 13467.00
## [61,] 13751 13640.25 13555.25
## [62,] 13786 13685.25 13640.25
## [63,] 13758 13736.75 13685.25
## [64,] 13777 13768.00 13736.75
## [65,] 13748 13767.25 13768.00
## [66,] 13763 13761.50 13767.25
## [67,] 13769 13764.25 13761.50
## [68,] 13843 13780.75 13764.25
## [69,] 13838 13803.25 13780.75
## [70,] 13931 13845.25 13803.25
## [71,] 13940 13888.00 13845.25
## [72,] 14134 13960.75 13888.00
## [73,] 14046 14012.75 13960.75
## [74,] 13822 13985.50 14012.75
## [75,] 13933 13983.75 13985.50
## [76,] 14070 13967.75 13983.75
## [77,] 14088 13978.25 13967.75
## [78,] 14273 14091.00 13978.25
## [79,] 14337 14192.00 14091.00
## [80,] 14373 14267.75 14192.00
## [81,] NA NA 14267.75
## [82,] NA NA 14267.75
## [83,] NA NA 14267.75
## [84,] NA NA 14267.75
## [85,] NA NA 14267.75
## [86,] NA NA 14267.75
## [87,] NA NA 14267.75
## [88,] NA NA 14267.75
## [89,] NA NA 14267.75
## [90,] NA NA 14267.75
## [91,] NA NA 14267.75
## [92,] NA NA 14267.75
## [93,] NA NA 14267.75
## [94,] NA NA 14267.75
## [95,] NA NA 14267.75
## [96,] NA NA 14267.75
## [97,] NA NA 14267.75
## [98,] NA NA 14267.75
## [99,] NA NA 14267.75
## [100,] NA NA 14267.75ts.plot(data_mpdw.ts, xlab="Time Period ", ylab="Nilai Kurs", main= "SMA N=4 Data Kurs Rupiah")
points(data_mpdw.ts)
lines(data.gab[,2],col="green",lwd=2)
lines(data.gab[,3],col="red",lwd=2)
legend("topleft",c("data aktual","data pemulusan","data peramalan"), lty=8, col=c("black","green","red"), cex=0.5)
#Menghitung nilai keakuratan data latih
error_train.sma = train_ma.ts-data.ramal[1:length(train_ma.ts)]
SSE_train.sma = sum(error_train.sma[5:length(train_ma.ts)]^2)
MSE_train.sma = mean(error_train.sma[5:length(train_ma.ts)]^2)
MAPE_train.sma = mean(abs((error_train.sma[5:length(train_ma.ts)]/train_ma.ts[5:length(train_ma.ts)])*100))
akurasi_train.sma <- matrix(c(SSE_train.sma, MSE_train.sma, MAPE_train.sma))
row.names(akurasi_train.sma)<- c("SSE", "MSE", "MAPE")
colnames(akurasi_train.sma) <- c("Akurasi m = 4")
akurasi_train.sma## Akurasi m = 4
## SSE 8.543863e+05
## MSE 1.124192e+04
## MAPE 5.616509e-01MAPE: 0,5% < 10% (sangat baik)
#Menghitung nilai keakuratan data uji
error_test.sma = test_ma.ts-data.gab[81:100,3]
SSE_test.sma = sum(error_test.sma^2)
MSE_test.sma = mean(error_test.sma^2)
MAPE_test.sma = mean(abs((error_test.sma/test_ma.ts*100)))
akurasi_test.sma <- matrix(c(SSE_test.sma, MSE_test.sma, MAPE_test.sma))
row.names(akurasi_test.sma)<- c("SSE", "MSE", "MAPE")
colnames(akurasi_test.sma) <- c("Akurasi m = 4")
akurasi_test.sma## Akurasi m = 4
## SSE 6.408315e+06
## MSE 3.204158e+05
## MAPE 3.251814e+00MAPE: 3,25% < 10% (sangat baik)
Double Moving Average (DMA)
dma <- SMA(data.sma, n = 4)
At <- 2*data.sma - dma
Bt <- 2/(4-1)*(data.sma - dma)
data.dma<- At+Bt
data.ramal2<- c(NA, data.dma)
t = 1:20
f = c()
for (i in t) {
f[i] = At[length(At)] + Bt[length(Bt)]*(i)
}
data.gab2 <- cbind(aktual = c(train_ma.ts,rep(NA,20)), pemulusan1 = c(data.sma,rep(NA,20)),pemulusan2 = c(data.dma, rep(NA,20)),At = c(At, rep(NA,20)), Bt = c(Bt,rep(NA,20)),ramalan = c(data.ramal2, f[-1]))
data.gab2## aktual pemulusan1 pemulusan2 At Bt ramalan
## [1,] 13351 NA NA NA NA NA
## [2,] 13313 NA NA NA NA NA
## [3,] 13406 NA NA NA NA NA
## [4,] 13326 13349.00 NA NA NA NA
## [5,] 13338 13345.75 NA NA NA NA
## [6,] 13335 13351.25 NA NA NA NA
## [7,] 13350 13337.25 13322.98 13328.69 -5.7083333 NA
## [8,] 13324 13336.75 13326.75 13330.75 -4.0000000 13322.98
## [9,] 13278 13321.75 13296.75 13306.75 -10.0000000 13326.75
## [10,] 13346 13324.50 13315.23 13318.94 -3.7083333 13296.75
## [11,] 13330 13319.50 13309.29 13313.38 -4.0833333 13315.23
## [12,] 13320 13318.50 13314.23 13315.94 -1.7083333 13309.29
## [13,] 13335 13332.75 13347.65 13341.69 5.9583333 13314.23
## [14,] 13373 13339.50 13359.40 13351.44 7.9583333 13347.65
## [15,] 13287 13328.75 13326.88 13327.62 -0.7500000 13359.40
## [16,] 13105 13275.00 13201.67 13231.00 -29.3333333 13326.88
## [17,] 13322 13271.75 13218.42 13239.75 -21.3333333 13201.67
## [18,] 13333 13261.75 13224.15 13239.19 -15.0416667 13218.42
## [19,] 13323 13270.75 13272.31 13271.69 0.6250000 13224.15
## [20,] 13328 13326.50 13399.52 13370.31 29.2083333 13272.31
## [21,] 13288 13318.00 13357.58 13341.75 15.8333333 13399.52
## [22,] 13304 13310.75 13317.83 13315.00 2.8333333 13357.58
## [23,] 13295 13303.75 13285.42 13292.75 -7.3333333 13317.83
## [24,] 13277 13291.00 13266.21 13276.12 -9.9166667 13285.42
## [25,] 13284 13290.00 13275.21 13281.12 -5.9166667 13266.21
## [26,] 13298 13288.50 13280.48 13283.69 -3.2083333 13275.21
## [27,] 13408 13316.75 13350.40 13336.94 13.4583333 13280.48
## [28,] 13332 13330.50 13370.60 13354.56 16.0416667 13350.40
## [29,] 13265 13325.75 13343.04 13336.12 6.9166667 13370.60
## [30,] 13320 13331.25 13339.90 13336.44 3.4583333 13343.04
## [31,] 13309 13306.50 13278.17 13289.50 -11.3333333 13339.90
## [32,] 13351 13311.25 13298.85 13303.81 -4.9583333 13278.17
## [33,] 13355 13333.75 13355.52 13346.81 8.7083333 13298.85
## [34,] 13339 13338.50 13365.17 13354.50 10.6666667 13355.52
## [35,] 13331 13344.00 13364.21 13356.12 8.0833333 13365.17
## [36,] 13197 13305.50 13263.94 13280.56 -16.6250000 13364.21
## [37,] 13252 13279.75 13217.77 13242.56 -24.7916667 13263.94
## [38,] 13306 13271.50 13223.69 13242.81 -19.1250000 13217.77
## [39,] 13465 13305.00 13329.27 13319.56 9.7083333 13223.69
## [40,] 13497 13380.00 13498.23 13450.94 47.2916667 13329.27
## [41,] 13492 13440.00 13591.46 13530.88 60.5833333 13498.23
## [42,] 13516 13492.50 13639.38 13580.62 58.7500000 13591.46
## [43,] 13591 13524.00 13632.12 13588.88 43.2500000 13639.38
## [44,] 13480 13519.75 13562.56 13545.44 17.1250000 13632.12
## [45,] 13527 13528.50 13549.02 13540.81 8.2083333 13562.56
## [46,] 13508 13526.50 13529.52 13528.31 1.2083333 13549.02
## [47,] 13498 13503.25 13476.17 13487.00 -10.8333333 13529.52
## [48,] 13526 13514.75 13508.92 13511.25 -2.3333333 13476.17
## [49,] 13538 13517.50 13520.83 13519.50 1.3333333 13508.92
## [50,] 13568 13532.50 13558.33 13548.00 10.3333333 13520.83
## [51,] 13547 13544.75 13573.71 13562.12 11.5833333 13558.33
## [52,] 13477 13532.50 13533.65 13533.19 0.4583333 13573.71
## [53,] 13411 13500.75 13455.96 13473.88 -17.9166667 13533.65
## [54,] 13295 13432.50 13315.62 13362.38 -46.7500000 13455.96
## [55,] 13334 13379.25 13242.58 13297.25 -54.6666667 13315.62
## [56,] 13299 13334.75 13206.31 13257.69 -51.3750000 13242.58
## [57,] 13411 13334.75 13275.48 13299.19 -23.7083333 13206.31
## [58,] 13606 13412.50 13491.15 13459.69 31.4583333 13275.48
## [59,] 13552 13467.00 13599.92 13546.75 53.1666667 13491.15
## [60,] 13652 13555.25 13743.38 13668.12 75.2500000 13599.92
## [61,] 13751 13640.25 13842.75 13761.75 81.0000000 13743.38
## [62,] 13786 13685.25 13849.10 13783.56 65.5416667 13842.75
## [63,] 13758 13736.75 13874.04 13819.12 54.9166667 13849.10
## [64,] 13777 13768.00 13868.73 13828.44 40.2916667 13874.04
## [65,] 13748 13767.25 13813.81 13795.19 18.6250000 13868.73
## [66,] 13763 13761.50 13766.71 13764.62 2.0833333 13813.81
## [67,] 13769 13764.25 13762.58 13763.25 -0.6666667 13766.71
## [68,] 13843 13780.75 13801.27 13793.06 8.2083333 13762.58
## [69,] 13838 13803.25 13846.27 13829.06 17.2083333 13801.27
## [70,] 13931 13845.25 13923.38 13892.12 31.2500000 13846.27
## [71,] 13940 13888.00 13985.81 13946.69 39.1250000 13923.38
## [72,] 14134 13960.75 14104.81 14047.19 57.6250000 13985.81
## [73,] 14046 14012.75 14156.19 14098.81 57.3750000 14104.81
## [74,] 13822 13985.50 14025.08 14009.25 15.8333333 14156.19
## [75,] 13933 13983.75 13980.52 13981.81 -1.2916667 14025.08
## [76,] 14070 13967.75 13934.94 13948.06 -13.1250000 13980.52
## [77,] 14088 13978.25 13977.31 13977.69 -0.3750000 13934.94
## [78,] 14273 14091.00 14234.02 14176.81 57.2083333 13977.31
## [79,] 14337 14192.00 14416.58 14326.75 89.8333333 14234.02
## [80,] 14373 14267.75 14493.58 14403.25 90.3333333 14416.58
## [81,] NA NA NA NA NA 14493.58
## [82,] NA NA NA NA NA 14583.92
## [83,] NA NA NA NA NA 14674.25
## [84,] NA NA NA NA NA 14764.58
## [85,] NA NA NA NA NA 14854.92
## [86,] NA NA NA NA NA 14945.25
## [87,] NA NA NA NA NA 15035.58
## [88,] NA NA NA NA NA 15125.92
## [89,] NA NA NA NA NA 15216.25
## [90,] NA NA NA NA NA 15306.58
## [91,] NA NA NA NA NA 15396.92
## [92,] NA NA NA NA NA 15487.25
## [93,] NA NA NA NA NA 15577.58
## [94,] NA NA NA NA NA 15667.92
## [95,] NA NA NA NA NA 15758.25
## [96,] NA NA NA NA NA 15848.58
## [97,] NA NA NA NA NA 15938.92
## [98,] NA NA NA NA NA 16029.25
## [99,] NA NA NA NA NA 16119.58
## [100,] NA NA NA NA NA 16209.92ts.plot(data_mpdw.ts, xlab="Time Period ", ylab="Nilai Kurs", main= "SMA N=4 Data Kurs Rupiah")
points(data_mpdw.ts)
lines(data.gab2[,3],col="green",lwd=2)
lines(data.gab2[,6],col="red",lwd=2)
legend("topleft",c("data aktual","data pemulusan","data peramalan"), lty=8, col=c("black","green","red"), cex=0.5)
#Menghitung nilai keakuratan data latih
error_train.dma = train_ma.ts-data.ramal2[1:length(train_ma.ts)]
SSE_train.dma = sum(error_train.dma[8:length(train_ma.ts)]^2)
MSE_train.dma = mean(error_train.dma[8:length(train_ma.ts)]^2)
MAPE_train.dma = mean(abs((error_train.dma[8:length(train_ma.ts)]/train_ma.ts[8:length(train_ma.ts)])*100))
akurasi_train.dma <- matrix(c(SSE_train.dma, MSE_train.dma, MAPE_train.dma))
row.names(akurasi_train.dma)<- c("SSE", "MSE", "MAPE")
colnames(akurasi_train.dma) <- c("Akurasi m = 4")
akurasi_train.dma## Akurasi m = 4
## SSE 8.618807e+05
## MSE 1.180659e+04
## MAPE 5.896164e-01MAPE: 0,5% < 10% (sangat baik)
#Menghitung nilai keakuratan data uji
error_test.dma = test_ma.ts-data.gab2[81:100,6]
SSE_test.dma = sum(error_test.dma^2)
MSE_test.dma = mean(error_test.dma^2)
MAPE_test.dma = mean(abs((error_test.dma/test_ma.ts*100)))
akurasi_test.dma <- matrix(c(SSE_test.dma, MSE_test.dma, MAPE_test.dma))
row.names(akurasi_test.dma)<- c("SSE", "MSE", "MAPE")
colnames(akurasi_test.dma) <- c("Akurasi m = 4")
akurasi_test.dma## Akurasi m = 4
## SSE 1.240136e+07
## MSE 6.200680e+05
## MAPE 4.077252e+00MAPE: 4% < 10% (sangat baik)
Kesimpulan
Baik SMA maupun DMA memberikan hasil sangat baik, namun pada DMA memberikan nilai MAPE data uji yang lebih besar, sehingga pada kasus ini SMA lebih baik digunakan
Single Exponential Smoothing & Double Exponential Smoothing
Single Exponential Smoothing (SES)
#Cara 1 (fungsi ses)
ses.1 <- ses(train_ma.ts, h = 20, alpha = 0.3)
plot(ses.1)
ses.1## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 81 14225.3 14091.72 14358.88 14021.01 14429.59
## 82 14225.3 14085.84 14364.76 14012.02 14438.58
## 83 14225.3 14080.20 14370.40 14003.39 14447.21
## 84 14225.3 14074.77 14375.83 13995.08 14455.52
## 85 14225.3 14069.52 14381.08 13987.06 14463.54
## 86 14225.3 14064.45 14386.15 13979.30 14471.30
## 87 14225.3 14059.54 14391.06 13971.79 14478.82
## 88 14225.3 14054.76 14395.84 13964.48 14486.12
## 89 14225.3 14050.12 14400.48 13957.38 14493.22
## 90 14225.3 14045.59 14405.01 13950.46 14500.14
## 91 14225.3 14041.18 14409.42 13943.71 14506.89
## 92 14225.3 14036.87 14413.73 13937.12 14513.48
## 93 14225.3 14032.65 14417.95 13930.67 14519.93
## 94 14225.3 14028.53 14422.07 13924.37 14526.24
## 95 14225.3 14024.49 14426.11 13918.19 14532.41
## 96 14225.3 14020.53 14430.07 13912.13 14538.47
## 97 14225.3 14016.65 14433.95 13906.19 14544.41
## 98 14225.3 14012.83 14437.77 13900.36 14550.24
## 99 14225.3 14009.09 14441.51 13894.63 14555.97
## 100 14225.3 14005.41 14445.20 13889.00 14561.60ses.2<- ses(train_ma.ts, h = 20, alpha = 0.9)
plot(ses.2)
ses.2## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 81 14368.57 14265.70 14471.45 14211.24 14525.90
## 82 14368.57 14230.17 14506.97 14156.90 14580.24
## 83 14368.57 14202.06 14535.09 14113.91 14623.24
## 84 14368.57 14178.05 14559.10 14077.19 14659.95
## 85 14368.57 14156.74 14580.40 14044.61 14692.54
## 86 14368.57 14137.39 14599.75 14015.01 14722.13
## 87 14368.57 14119.54 14617.60 13987.71 14749.43
## 88 14368.57 14102.89 14634.26 13962.24 14774.90
## 89 14368.57 14087.22 14649.93 13938.28 14798.87
## 90 14368.57 14072.37 14664.77 13915.58 14821.57
## 91 14368.57 14058.24 14678.90 13893.96 14843.18
## 92 14368.57 14044.72 14692.42 13873.29 14863.85
## 93 14368.57 14031.75 14705.39 13853.45 14883.70
## 94 14368.57 14019.26 14717.89 13834.34 14902.80
## 95 14368.57 14007.19 14729.95 13815.89 14921.25
## 96 14368.57 13995.52 14741.62 13798.04 14939.10
## 97 14368.57 13984.20 14752.94 13780.73 14956.41
## 98 14368.57 13973.21 14763.93 13763.92 14973.22
## 99 14368.57 13962.51 14774.63 13747.56 14989.58
## 100 14368.57 13952.09 14785.05 13731.62 15005.52autoplot(ses.1) +
autolayer(fitted(ses.1), series="Fitted") +
ylab("Membaca") + xlab("Periode")
#Cara 2 (fungsi Holtwinter)
ses1<- HoltWinters(train_ma.ts, gamma = FALSE, beta = FALSE, alpha = 0.2)
plot(ses1)
#ramalan
ramalan1<- forecast(ses1, h=20)
ramalan1## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 81 14146.92 14006.74 14287.10 13932.53 14361.31
## 82 14146.92 14003.96 14289.88 13928.28 14365.56
## 83 14146.92 14001.24 14292.60 13924.12 14369.72
## 84 14146.92 13998.57 14295.28 13920.03 14373.81
## 85 14146.92 13995.94 14297.90 13916.01 14377.83
## 86 14146.92 13993.36 14300.48 13912.07 14381.77
## 87 14146.92 13990.82 14303.02 13908.19 14385.66
## 88 14146.92 13988.32 14305.52 13904.37 14389.48
## 89 14146.92 13985.86 14307.98 13900.60 14393.24
## 90 14146.92 13983.44 14310.40 13896.90 14396.94
## 91 14146.92 13981.05 14312.79 13893.25 14400.59
## 92 14146.92 13978.70 14315.14 13889.65 14404.19
## 93 14146.92 13976.38 14317.46 13886.10 14407.74
## 94 14146.92 13974.09 14319.75 13882.60 14411.24
## 95 14146.92 13971.83 14322.01 13879.15 14414.69
## 96 14146.92 13969.60 14324.24 13875.74 14418.11
## 97 14146.92 13967.40 14326.44 13872.37 14421.47
## 98 14146.92 13965.22 14328.62 13869.04 14424.80
## 99 14146.92 13963.07 14330.77 13865.75 14428.09
## 100 14146.92 13960.95 14332.89 13862.50 14431.34ses2<- HoltWinters(train_ma.ts, gamma = FALSE, beta = FALSE, alpha = 0.9)
plot(ses2)
#ramalan
ramalan2<- forecast(ses2, h=20)
ramalan2## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 81 14368.57 14267.37 14469.78 14213.79 14523.35
## 82 14368.57 14232.41 14504.73 14160.34 14576.81
## 83 14368.57 14204.76 14532.39 14118.04 14619.10
## 84 14368.57 14181.14 14556.01 14081.92 14655.23
## 85 14368.57 14160.18 14576.97 14049.86 14687.28
## 86 14368.57 14141.14 14596.00 14020.75 14716.40
## 87 14368.57 14123.58 14613.56 13993.89 14743.25
## 88 14368.57 14107.20 14629.95 13968.83 14768.31
## 89 14368.57 14091.78 14645.36 13945.26 14791.89
## 90 14368.57 14077.18 14659.96 13922.92 14814.22
## 91 14368.57 14063.27 14673.87 13901.66 14835.48
## 92 14368.57 14049.98 14687.17 13881.32 14855.82
## 93 14368.57 14037.21 14699.93 13861.80 14875.34
## 94 14368.57 14024.92 14712.22 13843.00 14894.14
## 95 14368.57 14013.06 14724.09 13824.86 14912.29
## 96 14368.57 14001.57 14735.57 13807.30 14929.85
## 97 14368.57 13990.44 14746.70 13790.27 14946.88
## 98 14368.57 13979.62 14757.52 13773.73 14963.42
## 99 14368.57 13969.10 14768.04 13757.63 14979.51
## 100 14368.57 13958.85 14778.30 13741.95 14995.19#SES
ses.opt <- ses(train_ma.ts, h = 20, alpha = NULL)
plot(ses.opt)
ses.opt## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 81 14371.79 14269.12 14474.45 14214.77 14528.80
## 82 14371.79 14228.88 14514.69 14153.23 14590.34
## 83 14371.79 14197.71 14545.87 14105.56 14638.02
## 84 14371.79 14171.32 14572.25 14065.21 14678.37
## 85 14371.79 14148.03 14595.54 14029.58 14713.99
## 86 14371.79 14126.94 14616.63 13997.33 14746.24
## 87 14371.79 14107.53 14636.04 13967.64 14775.93
## 88 14371.79 14089.45 14654.12 13940.00 14803.58
## 89 14371.79 14072.46 14671.11 13914.01 14829.56
## 90 14371.79 14056.39 14687.18 13889.43 14854.15
## 91 14371.79 14041.10 14702.48 13866.04 14877.54
## 92 14371.79 14026.48 14717.10 13843.68 14899.89
## 93 14371.79 14012.45 14731.12 13822.23 14921.34
## 94 14371.79 13998.96 14744.62 13801.59 14941.98
## 95 14371.79 13985.93 14757.64 13781.67 14961.90
## 96 14371.79 13973.33 14770.24 13762.40 14981.17
## 97 14371.79 13961.12 14782.45 13743.73 14999.85
## 98 14371.79 13949.26 14794.31 13725.59 15017.99
## 99 14371.79 13937.72 14805.85 13707.95 15035.63
## 100 14371.79 13926.49 14817.09 13690.76 15052.81#Lamda Optimum Holt Winter
sesopt<- HoltWinters(train_ma.ts, gamma = FALSE, beta = FALSE,alpha = NULL)
sesopt## Holt-Winters exponential smoothing without trend and without seasonal component.
##
## Call:
## HoltWinters(x = train_ma.ts, alpha = NULL, beta = FALSE, gamma = FALSE)
##
## Smoothing parameters:
## alpha: 0.9682997
## beta : FALSE
## gamma: FALSE
##
## Coefficients:
## [,1]
## a 14371.79plot(sesopt)
#ramalan
ramalanopt<- forecast(sesopt, h=20)
ramalanopt## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 81 14371.79 14270.58 14473.00 14217.00 14526.58
## 82 14371.79 14230.90 14512.67 14156.32 14587.25
## 83 14371.79 14200.17 14543.41 14109.32 14634.26
## 84 14371.79 14174.16 14569.42 14069.54 14674.04
## 85 14371.79 14151.19 14592.39 14034.41 14709.16
## 86 14371.79 14130.40 14613.18 14002.62 14740.96
## 87 14371.79 14111.26 14632.31 13973.35 14770.23
## 88 14371.79 14093.44 14650.14 13946.09 14797.48
## 89 14371.79 14076.69 14666.89 13920.48 14823.10
## 90 14371.79 14060.84 14682.73 13896.24 14847.34
## 91 14371.79 14045.76 14697.81 13873.18 14870.40
## 92 14371.79 14031.35 14712.22 13851.14 14892.44
## 93 14371.79 14017.53 14726.05 13829.99 14913.59
## 94 14371.79 14004.22 14739.36 13809.64 14933.94
## 95 14371.79 13991.38 14752.20 13790.00 14953.57
## 96 14371.79 13978.96 14764.62 13771.01 14972.57
## 97 14371.79 13966.92 14776.66 13752.59 14990.99
## 98 14371.79 13955.22 14788.35 13734.71 15008.87
## 99 14371.79 13943.85 14799.73 13717.31 15026.26
## 100 14371.79 13932.77 14810.80 13700.37 15043.21#Keakuratan Metode
#Pada data training
SSE1<-ses1$SSE
MSE1<-ses1$SSE/length(train_ma.ts)
RMSE1<-sqrt(MSE1)
akurasi1 <- matrix(c(SSE1,MSE1,RMSE1))
row.names(akurasi1)<- c("SSE", "MSE", "RMSE")
colnames(akurasi1) <- c("Akurasi lamda=0.2")
akurasi1## Akurasi lamda=0.2
## SSE 1133744.8128
## MSE 14171.8102
## RMSE 119.0454SSE2<-ses2$SSE
MSE2<-ses2$SSE/length(train_ma.ts)
RMSE2<-sqrt(MSE2)
akurasi2 <- matrix(c(SSE2,MSE2,RMSE2))
row.names(akurasi2)<- c("SSE", "MSE", "RMSE")
colnames(akurasi2) <- c("Akurasi lamda=0.9")
akurasi2## Akurasi lamda=0.9
## SSE 502617.60406
## MSE 6282.72005
## RMSE 79.26361Hasil akurasi dari data latih didapatkan skenario 2 dengan lamda=0.9 memiliki hasil yang lebih baik. Namun untuk kedua skenario dapat dikategorikan peramalan sangat baik berdasarkan nilai MAPE-nya.
#Cara Manual
fitted1<-ramalan1$fitted
sisaan1<-ramalan1$residuals
head(sisaan1)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA -38.0000 62.6000 -29.9200 -11.9360 -12.5488resid1<-training_ma$kurs -ramalan1$fitted
head(resid1)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA -38.0000 62.6000 -29.9200 -11.9360 -12.5488#Cara Manual
SSE.1=sum(sisaan1[2:length(train_ma.ts)]^2)
SSE.1## [1] 1133745MSE.1 = SSE.1/length(train_ma.ts)
MSE.1## [1] 14171.81MAPE.1 = sum(abs(sisaan1[2:length(train_ma.ts)]/train_ma.ts[2:length(train_ma.ts)])*
100)/length(train_ma.ts)
MAPE.1## [1] 0.6301266akurasi.1 <- matrix(c(SSE.1,MSE.1,MAPE.1))
row.names(akurasi.1)<- c("SSE", "MSE", "MAPE")
colnames(akurasi.1) <- c("Akurasi lamda=0.2")
akurasi.1## Akurasi lamda=0.2
## SSE 1.133745e+06
## MSE 1.417181e+04
## MAPE 6.301266e-01fitted2<-ramalan2$fitted
sisaan2<-ramalan2$residuals
head(sisaan2)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA -38.0000 89.2000 -71.0800 4.8920 -2.5108resid2<-training_ma$kurs-ramalan2$fitted
head(resid2)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA -38.0000 89.2000 -71.0800 4.8920 -2.5108SSE.2=sum(sisaan2[2:length(train_ma.ts)]^2)
SSE.2## [1] 502617.6MSE.2 = SSE.2/length(train_ma.ts)
MSE.2## [1] 6282.72MAPE.2 = sum(abs(sisaan2[2:length(train_ma.ts)]/train_ma.ts[2:length(train_ma.ts)])*
100)/length(train_ma.ts)
MAPE.2## [1] 0.4145306akurasi.2 <- matrix(c(SSE.2,MSE.2,MAPE.2))
row.names(akurasi.2)<- c("SSE", "MSE", "MAPE")
colnames(akurasi.2) <- c("Akurasi lamda=0.9")
akurasi.2## Akurasi lamda=0.9
## SSE 5.026176e+05
## MSE 6.282720e+03
## MAPE 4.145306e-01# Akurasi Data Uji
selisih1<-ramalan1$mean-testing_ma$kurs
SSEtesting1<-sum(selisih1^2)
MSEtesting1<-SSEtesting1/length(testing_ma$kurs)
selisih2<-ramalan2$mean-testing_ma$kurs
SSEtesting2<-sum(selisih2^2)
MSEtesting2<-SSEtesting2/length(testing_ma$kurs)
selisihopt<-ramalanopt$mean-testing_ma$kurs
SSEtestingopt<-sum(selisihopt^2)
MSEtestingopt<-SSEtestingopt/length(testing_ma$kurs)
akurasitesting1 <- matrix(c(SSEtesting1,SSEtesting2,SSEtestingopt))
row.names(akurasitesting1)<- c("SSE1", "SSE2", "SSEopt")
akurasitesting1## [,1]
## SSE1 9045615
## SSE2 4654666
## SSEopt 4605407akurasitesting2 <- matrix(c(MSEtesting1,MSEtesting2,MSEtestingopt))
row.names(akurasitesting2)<- c("MSE1", "MSE2", "MSEopt")
akurasitesting2## [,1]
## MSE1 452280.8
## MSE2 232733.3
## MSEopt 230270.4accuracy(ramalanopt,testing_ma$kurs)## ME RMSE MAE MPE MAPE MASE
## Training set 13.3444 79.60162 57.2760 0.09454685 0.4218534 0.9975318
## Test set 381.2114 479.86494 386.2903 2.54633925 2.5818036 6.7277190
## ACF1
## Training set -0.02692445
## Test set NADouble Exponential Smoothing (DES)
#Lamda=0.2 dan gamma=0.2
des.1<- HoltWinters(train_ma.ts, gamma = FALSE, beta = 0.3, alpha = 0.4)
plot(des.1)
#ramalan
ramalandes1<- forecast(des.1, h=20)
ramalandes1## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 81 14406.58 14283.47 14529.69 14218.29 14594.86
## 82 14474.97 14336.21 14613.73 14262.76 14687.19
## 83 14543.37 14383.80 14702.94 14299.33 14787.41
## 84 14611.77 14426.79 14796.74 14328.87 14894.66
## 85 14680.16 14465.79 14894.53 14352.31 15008.01
## 86 14748.56 14501.35 14995.76 14370.49 15126.63
## 87 14816.96 14533.90 15100.01 14384.05 15249.86
## 88 14885.35 14563.75 15206.95 14393.51 15377.20
## 89 14953.75 14591.17 15316.32 14399.24 15508.26
## 90 15022.14 14616.36 15427.92 14401.56 15642.73
## 91 15090.54 14639.48 15541.60 14400.70 15780.38
## 92 15158.94 14660.64 15657.23 14396.86 15921.01
## 93 15227.33 14679.97 15774.70 14390.21 16064.46
## 94 15295.73 14697.54 15893.92 14380.88 16210.59
## 95 15364.13 14713.43 16014.82 14368.97 16359.28
## 96 15432.52 14727.71 16137.34 14354.61 16510.44
## 97 15500.92 14740.43 16261.41 14337.86 16663.98
## 98 15569.32 14751.65 16386.98 14318.81 16819.82
## 99 15637.71 14761.41 16514.01 14297.53 16977.90
## 100 15706.11 14769.76 16642.46 14274.08 17138.14#Lamda=0.6 dan gamma=0.3
des.2<- HoltWinters(train_ma.ts, gamma = FALSE, beta = 0.4, alpha = 0.7)
plot(des.2)
#ramalan
ramalandes2<- forecast(des.2, h=20)
ramalandes2## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 81 14465.51 14351.43 14579.59 14291.04 14639.98
## 82 14543.89 14384.16 14703.61 14299.60 14788.17
## 83 14622.26 14407.38 14837.14 14293.63 14950.89
## 84 14700.63 14423.07 14978.19 14276.15 15125.12
## 85 14779.00 14432.38 15125.62 14248.90 15309.11
## 86 14857.38 14436.03 15278.73 14212.98 15501.78
## 87 14935.75 14434.50 15437.00 14169.15 15702.35
## 88 15014.12 14428.17 15600.07 14117.99 15910.25
## 89 15092.49 14417.35 15767.64 14059.95 16125.04
## 90 15170.87 14402.26 15939.47 13995.39 16346.35
## 91 15249.24 14383.11 16115.37 13924.61 16573.87
## 92 15327.61 14360.08 16295.15 13847.90 16807.33
## 93 15405.99 14333.31 16478.67 13765.46 17046.51
## 94 15484.36 14302.93 16665.78 13677.52 17291.19
## 95 15562.73 14269.08 16856.39 13584.26 17541.21
## 96 15641.10 14231.85 17050.36 13485.83 17796.38
## 97 15719.48 14191.34 17247.61 13382.39 18056.56
## 98 15797.85 14147.65 17448.05 13274.08 18321.62
## 99 15876.22 14100.85 17651.60 13161.02 18591.42
## 100 15954.60 14051.03 17858.17 13043.34 18865.85#Visually evaluate the prediction
plot(data_mpdw.ts)
lines(des.2$fitted[,1], lty=2, col="blue")
lines(ramalandes2$mean, col="red")
plot(data_mpdw.ts)
lines(des.1$fitted[,1], lty=2, col="blue")
lines(ramalandes1$mean, col="red")
#Lamda dan gamma optimum
des.opt<- HoltWinters(train_ma.ts, gamma = FALSE)
des.opt## Holt-Winters exponential smoothing with trend and without seasonal component.
##
## Call:
## HoltWinters(x = train_ma.ts, gamma = FALSE)
##
## Smoothing parameters:
## alpha: 0.9232134
## beta : 0.06502607
## gamma: FALSE
##
## Coefficients:
## [,1]
## a 14372.63063
## b 34.90352plot(des.opt)
#ramalan
ramalandesopt<- forecast(des.opt, h=20)
ramalandesopt## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 81 14407.53 14304.92 14510.15 14250.60 14564.47
## 82 14442.44 14298.53 14586.34 14222.35 14662.52
## 83 14477.34 14297.98 14656.70 14203.04 14751.64
## 84 14512.24 14300.15 14724.34 14187.87 14836.62
## 85 14547.15 14303.76 14790.53 14174.92 14919.37
## 86 14582.05 14308.20 14855.90 14163.23 15000.87
## 87 14616.96 14313.08 14920.83 14152.22 15081.69
## 88 14651.86 14318.18 14985.54 14141.54 15162.18
## 89 14686.76 14323.33 15050.19 14130.94 15242.58
## 90 14721.67 14328.43 15114.90 14120.26 15323.07
## 91 14756.57 14333.40 15179.74 14109.38 15403.75
## 92 14791.47 14338.18 15244.77 14098.21 15484.73
## 93 14826.38 14342.72 15310.03 14086.69 15566.06
## 94 14861.28 14347.00 15375.56 14074.76 15647.80
## 95 14896.18 14350.99 15441.38 14062.38 15729.98
## 96 14931.09 14354.67 15507.50 14049.54 15812.64
## 97 14965.99 14358.03 15573.95 14036.19 15895.79
## 98 15000.89 14361.05 15640.74 14022.34 15979.45
## 99 15035.80 14363.73 15707.87 14007.96 16063.64
## 100 15070.70 14366.06 15775.35 13993.04 16148.36#Akurasi Data Training
ssedes.train1<-des.1$SSE
msedes.train1<-ssedes.train1/length(train_ma.ts)
sisaandes1<-ramalandes1$residuals
head(sisaandes1)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA NA 131.00000 20.88000 44.30240 38.03955mapedes.train1 <- sum(abs(sisaandes1[3:length(train_ma.ts)]/train_ma.ts[3:length(train_ma.ts)])
*100)/length(train_ma.ts)
akurasides.1 <- matrix(c(ssedes.train1,msedes.train1,mapedes.train1))
row.names(akurasides.1)<- c("SSE", "MSE", "MAPE")
colnames(akurasides.1) <- c("Akurasi alpha=0.4 dan beta=0.3")
akurasides.1## Akurasi alpha=0.4 dan beta=0.3
## SSE 7.206543e+05
## MSE 9.008179e+03
## MAPE 5.048453e-01ssedes.train2<-des.2$SSE
msedes.train2<-ssedes.train2/length(train_ma.ts)
sisaandes2<-ramalandes2$residuals
head(sisaandes2)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA NA 131.000000 -39.380000 12.532400 9.597048mapedes.train2 <- sum(abs(sisaandes2[3:length(train_ma.ts)]/train_ma.ts[3:length(train_ma.ts)])
*100)/length(train_ma.ts)
akurasides.2 <- matrix(c(ssedes.train2,msedes.train2,mapedes.train2))
row.names(akurasides.2)<- c("SSE", "MSE", "MAPE")
colnames(akurasides.2) <- c("Akurasi alpha=0.7 dan beta=0.4")
akurasides.2## Akurasi alpha=0.7 dan beta=0.4
## SSE 6.123523e+05
## MSE 7.654404e+03
## MAPE 4.531769e-01Hasil akurasi dari data latih didapatkan skenario 2 dengan beta=0.7 dan alpha=0.4 memiliki hasil yang lebih baik. Namun untuk kedua skenario dapat dikategorikan peramalan sangat baik berdasarkan nilai MAPE-nya.
#Akurasi Data Testing
selisihdes1<-ramalandes1$mean-testing_ma$kurs
selisihdes1## Time Series:
## Start = 81
## End = 100
## Frequency = 1
## [1] -78.42385 100.97264 69.36913 133.76562 102.16210 84.55859
## [7] 93.95508 72.35157 213.74805 210.14454 200.54103 50.93752
## [13] -71.66600 -33.26951 154.12698 486.52347 822.91995 964.31644
## [19] 1104.71293 1385.10942SSEtestingdes1<-sum(selisihdes1^2)
MSEtestingdes1<-SSEtestingdes1/length(testing_ma$kurs)
MAPEtestingdes1<-sum(abs(selisihdes1/testing_ma$kurs)*100)/length(testing_ma$kurs)
selisihdes2<-ramalandes2$mean-testing_ma$kurs
selisihdes2## Time Series:
## Start = 81
## End = 100
## Frequency = 1
## [1] -19.48758 169.88520 148.25799 222.63077 201.00356 193.37635
## [7] 212.74913 201.12192 352.49470 358.86749 359.24027 219.61306
## [13] 106.98584 155.35863 352.73141 695.10420 1041.47699 1192.84977
## [19] 1343.22256 1633.59534SSEtestingdes2<-sum(selisihdes2^2)
MSEtestingdes2<-SSEtestingdes2/length(testing_ma$kurs)
MAPEtestingdes2<-sum(abs(selisihdes2/testing_ma$kurs)*100)/length(testing_ma$kurs)
selisihdesopt<-ramalandesopt$mean-testing_ma$kurs
selisihdesopt## Time Series:
## Start = 81
## End = 100
## Frequency = 1
## [1] -77.46585 68.43766 3.34118 34.24470 -30.85179 -81.94827
## [7] -106.04475 -161.14123 -53.23772 -90.33420 -133.43068 -316.52716
## [13] -472.62365 -467.72013 -313.81661 -14.91309 287.99042 395.89394
## [19] 502.79746 749.70098SSEtestingdesopt<-sum(selisihdesopt^2)
MSEtestingdesopt<-SSEtestingdesopt/length(testing_ma$kurs)
MAPEtestingdesopt<-sum(abs(selisihdesopt/testing_ma$kurs)*100)/length(testing_ma$kurs)
akurasitestingdes <-
matrix(c(SSEtestingdes1,MSEtestingdes1,MAPEtestingdes1,SSEtestingdes2,MSEtestingdes2,
MAPEtestingdes2,SSEtestingdesopt,MSEtestingdesopt,MAPEtestingdesopt),
nrow=3,ncol=3)
row.names(akurasitestingdes)<- c("SSE", "MSE", "MAPE")
colnames(akurasitestingdes) <- c("des ske1","des ske2","des opt")
akurasitestingdes## des ske1 des ske2 des opt
## SSE 5.216086e+06 8.318234e+06 1.781101e+06
## MSE 2.608043e+05 4.159117e+05 8.905507e+04
## MAPE 2.202018e+00 3.132716e+00 1.474111e+00Perbandingan SES dan DES
MSEfull <-
matrix(c(MSEtesting1,MSEtesting2,MSEtestingopt,MSEtestingdes1,MSEtestingdes2,
MSEtestingdesopt),nrow=3,ncol=2)
row.names(MSEfull)<- c("ske 1", "ske 2", "ske opt")
colnames(MSEfull) <- c("ses","des")
MSEfull## ses des
## ske 1 452280.8 260804.31
## ske 2 232733.3 415911.68
## ske opt 230270.4 89055.07Metode Double Exponential Smoothing (DES) menunjukkan performa yang lebih baik pada dua dari tiga skenario (ske 1 dan ske opt), oleh karena itu DES lebih baik digunakan
#Winter
#membagi data latih dan data uji
training<-data_mpdw[1:80,2]
testing<-data_mpdw[81:100,2]
training.ts<-ts(training, frequency = 12) #12 bulan dalam setahun
testing.ts<-ts(testing, frequency = 12)Winter Aditif
#Pemulusan dengan winter aditif
winter1 <- HoltWinters(training.ts,alpha=0.2,beta=0.1,gamma=0.1,seasonal = "additive")
winter1$fitted## xhat level trend season
## Jan 2 13365.43 13335.67 -3.3148310 33.079861
## Feb 2 13394.38 13326.27 -3.9234902 72.038194
## Mar 2 13299.17 13318.07 -4.3511144 -14.545139
## Apr 2 13111.48 13311.28 -4.5945248 -195.211806
## May 2 13325.66 13305.39 -4.7240293 24.996528
## Jun 2 13334.38 13299.94 -4.7973190 39.246528
## Jul 2 13311.49 13294.86 -4.8250044 21.454861
## Aug 2 13281.36 13292.34 -4.5948192 -6.378472
## Sep 2 13243.49 13297.07 -3.6621081 -49.920139
## Oct 2 13331.79 13302.31 -2.7718637 32.246528
## Nov 2 13316.78 13293.98 -3.3275642 26.121528
## Dec 2 13299.41 13286.30 -3.7630733 16.871528
## Jan 3 13304.49 13278.05 -4.2112192 30.645224
## Feb 3 13335.45 13269.75 -4.6209854 70.327698
## Mar 3 13236.75 13257.63 -5.3700281 -15.518781
## Apr 3 13088.84 13286.51 -1.9449322 -195.729824
## May 3 13360.82 13333.20 2.9182641 24.703369
## Jun 3 13357.09 13316.96 1.0017919 39.135786
## Jul 3 13333.17 13310.54 0.2599300 22.375602
## Aug 3 13303.09 13305.96 -0.2235544 -2.647628
## Sep 3 13269.70 13315.32 0.7345938 -46.359161
## Oct 3 13365.58 13333.12 2.4406511 30.023726
## Nov 3 13356.53 13330.24 1.9090262 24.379491
## Dec 3 13343.52 13327.04 1.3984304 15.078944
## Jan 4 13326.61 13299.14 -1.5320039 29.006159
## Feb 4 13346.99 13282.68 -3.0242555 67.331527
## Mar 4 13265.80 13271.46 -3.8440791 -1.818397
## Apr 4 13131.32 13307.46 0.1399421 -176.277039
## May 4 13405.22 13380.73 7.4535331 17.037481
## Jun 4 13450.90 13405.54 9.1890448 36.168339
## Jul 4 13458.68 13427.75 10.4910561 20.441664
## Aug 4 13479.03 13464.71 13.1373775 1.184965
## Sep 4 13451.66 13478.04 13.1568211 -39.534932
## Oct 4 13548.82 13506.26 14.6636375 27.897226
## Nov 4 13548.95 13512.76 13.8471747 22.337108
## Dec 4 13532.60 13516.42 12.8282633 3.357207
## Jan 5 13563.66 13527.93 12.6961669 23.037153
## Feb 5 13611.73 13535.49 12.1829676 64.052232
## Mar 5 13564.35 13538.93 11.3084472 14.117688
## Apr 5 13410.70 13546.77 10.9613528 -147.022675
## May 5 13607.25 13570.99 12.2872575 23.979527
## Jun 5 13593.76 13544.02 8.3621921 41.376384
## Jul 5 13526.05 13492.63 2.3869587 31.026950
## Aug 5 13456.42 13456.61 -1.4539784 1.262739
## Sep 5 13385.56 13423.67 -4.6023644 -33.507666
## Oct 5 13444.70 13424.16 -4.0936177 24.631375
## Nov 5 13469.72 13452.33 -0.8675289 18.261463
## Dec 5 13471.52 13467.91 0.7780910 2.828822
## Jan 6 13530.16 13504.79 4.3876780 20.984356
## Feb 6 13622.70 13553.34 8.8044832 60.554151
## Mar 6 13619.61 13594.81 12.0704419 12.729310
## Apr 6 13507.68 13634.56 14.8382968 -141.719056
## May 6 13731.76 13703.26 20.2247821 8.279266
## Jun 6 13764.76 13726.73 20.5495083 17.475451
## Jul 6 13783.11 13746.93 20.5143754 15.663201
## Aug 6 13773.52 13764.62 20.2322265 -11.330805
## Sep 6 13788.90 13798.75 21.6217430 -31.472680
## Oct 6 13890.33 13830.19 22.6037589 37.535730
## Nov 6 13909.19 13860.93 23.4171282 24.843942
## Dec 6 13931.81 13890.51 24.0333168 17.267170
## Jan 7 14021.71 13954.98 28.0771368 38.651577
## Feb 7 14090.10 13987.92 28.5629620 73.617985
## Mar 7 14009.86 13962.86 23.2010347 23.800730
## Apr 7 13872.18 13970.69 21.6638172 -120.173115
## May 7 14067.11 14031.92 25.6202438 9.578170
## Jun 7 14105.09 14061.71 26.0379545 17.334919
## Jul 7 14165.26 14121.33 29.3962291 14.534606
## Aug 7 14212.14 14185.08 32.8309303 -5.772739xhat1 <- winter1$fitted[,2]
winter1.opt<- HoltWinters(training.ts, alpha= NULL, beta = NULL, gamma = NULL, seasonal = "additive")## Warning in HoltWinters(training.ts, alpha = NULL, beta = NULL, gamma = NULL, :
## optimization difficulties: ERROR: ABNORMAL_TERMINATION_IN_LNSRCHwinter1.opt## Holt-Winters exponential smoothing with trend and additive seasonal component.
##
## Call:
## HoltWinters(x = training.ts, alpha = NULL, beta = NULL, gamma = NULL, seasonal = "additive")
##
## Smoothing parameters:
## alpha: 0.6206322
## beta : 0.04298124
## gamma: 1
##
## Coefficients:
## [,1]
## a 14357.493882
## b 27.666630
## s1 22.651109
## s2 91.279845
## s3 36.777788
## s4 98.238049
## s5 26.809064
## s6 -44.183749
## s7 59.241365
## s8 83.875977
## s9 5.125245
## s10 29.112277
## s11 16.171503
## s12 15.506118winter1.opt$fitted## xhat level trend season
## Jan 2 13365.43 13335.67 -3.3148310 33.079861
## Feb 2 13381.38 13313.47 -4.1266467 72.038194
## Mar 2 13285.24 13304.14 -4.3501070 -14.545139
## Apr 2 13101.36 13300.88 -4.3032784 -195.211806
## May 2 13319.62 13298.83 -4.2062882 24.996528
## Jun 2 13331.21 13296.10 -4.1428723 39.246528
## Jul 2 13310.43 13293.07 -4.0949965 21.454861
## Aug 2 13286.64 13296.78 -3.7597507 -6.378472
## Sep 2 13266.11 13318.69 -2.6564289 -49.920139
## Oct 2 13359.79 13329.62 -2.0725266 32.246528
## Nov 2 13315.48 13292.92 -3.5607589 26.121528
## Dec 2 13289.41 13276.65 -4.1070533 16.871528
## Jan 3 13281.93 13264.84 -4.4381529 21.534578
## Feb 3 13326.16 13261.68 -4.3830319 68.860242
## Mar 3 13220.81 13239.82 -5.1341812 -13.879163
## Apr 3 13156.89 13350.86 -0.1407574 -193.832455
## May 3 13489.83 13459.40 4.5303519 25.898401
## Jun 3 13362.86 13324.40 -1.4671310 39.927396
## Jul 3 13319.94 13296.33 -2.6103223 26.222577
## Aug 3 13293.34 13286.93 -2.9022279 9.312482
## Sep 3 13276.83 13319.81 -1.3640901 -41.616139
## Oct 3 13378.76 13366.96 0.7210684 11.081548
## Nov 3 13361.02 13343.00 -0.3396727 18.352372
## Dec 3 13335.06 13324.03 -1.1403803 12.162776
## Jan 4 13254.71 13237.21 -4.8231347 22.318485
## Feb 4 13283.99 13230.71 -4.8953474 58.177730
## Mar 4 13292.30 13239.47 -4.3082420 57.135094
## Apr 4 13215.24 13342.35 0.2986360 -127.402010
## May 4 13465.93 13517.51 7.8146156 -59.395140
## Jun 4 13573.69 13541.51 8.5099789 23.669437
## Jul 4 13543.26 13514.21 6.9711892 22.071225
## Aug 4 13590.25 13550.82 8.2447607 31.187195
## Sep 4 13483.98 13490.64 5.3038204 -11.961939
## Oct 4 13525.09 13522.64 6.4514174 -4.003842
## Nov 4 13531.45 13518.49 5.9955617 6.965064
## Dec 4 13468.62 13503.72 5.1033329 -40.211724
## Jan 5 13572.37 13544.44 6.6340976 21.291508
## Feb 5 13601.99 13529.75 5.7173265 66.527282
## Mar 5 13641.83 13514.37 4.8105978 122.652068
## Apr 5 13442.09 13460.32 2.2809433 -20.513081
## May 5 13437.98 13484.27 3.2121486 -49.505993
## Jun 5 13475.02 13470.74 2.4925479 1.785453
## Jul 5 13399.38 13361.51 -2.3095258 40.183395
## Aug 5 13303.93 13318.62 -4.0536096 -10.637554
## Sep 5 13311.68 13311.51 -4.1850941 4.358676
## Oct 5 13356.94 13368.96 -1.5357071 -10.486820
## Nov 5 13521.39 13522.00 5.1080935 -5.723818
## Dec 5 13533.59 13546.11 5.9247410 -18.441867
## Jan 6 13642.86 13625.52 9.0833203 8.253597
## Feb 6 13767.32 13701.72 11.9680437 53.632189
## Mar 6 13824.42 13725.28 12.4663061 86.676443
## Apr 6 13699.95 13696.52 10.6943966 -7.269891
## May 6 13708.05 13755.04 12.7498173 -59.739835
## Jun 6 13739.89 13792.58 13.8155429 -66.507509
## Jul 6 13850.55 13820.74 14.4319722 15.379808
## Aug 6 13784.31 13784.56 12.2565094 -12.507468
## Sep 6 13889.10 13833.24 13.8221585 42.037083
## Oct 6 13911.81 13815.35 12.4590184 83.998365
## Nov 6 13858.58 13839.72 12.9710214 5.890180
## Dec 6 13944.84 13903.22 15.1429080 26.478046
## Jan 7 14105.23 14035.76 20.1887695 49.278854
## Feb 7 14098.52 14019.19 18.6087884 60.718255
## Mar 7 13938.89 13866.18 11.2325208 61.477132
## Apr 7 13906.80 13873.76 11.0753111 21.961391
## May 7 13956.97 13986.12 15.4288843 -44.583559
## Jun 7 14044.06 14082.87 18.9241982 -57.740924
## Jul 7 14253.36 14243.89 25.0313498 -15.558658
## Aug 7 14357.85 14320.83 27.2624812 9.758498xhat1.opt <- winter1.opt$fitted[,2]#Forecast
forecast1 <- predict(winter1, n.ahead = 20)
forecast1.opt <- predict(winter1.opt, n.ahead = 20)plot(training.ts,main="Winter 0.2;0.1;0.1",type="l",col="black",
xlim=c(1,10),pch=12)
lines(xhat1,type="l",col="red")
lines(xhat1.opt,type="l",col="blue")
lines(forecast1,type="l",col="red")
lines(forecast1.opt,type="l",col="blue")
legend("topleft",c("Actual Data",expression(paste(winter1)),
expression(paste(winter1.opt))),cex=0.5,
col=c("black","red","blue"),lty=1)
#Akurasi data training
SSE1<-winter1$SSE
MSE1<-winter1$SSE/length(training.ts)
RMSE1<-sqrt(MSE1)
akurasi1 <- matrix(c(SSE1,MSE1,RMSE1))
row.names(akurasi1)<- c("SSE", "MSE", "RMSE")
colnames(akurasi1) <- c("Akurasi")
akurasi1## Akurasi
## SSE 1043885.6333
## MSE 13048.5704
## RMSE 114.2303SSE1.opt<-winter1.opt$SSE
MSE1.opt<-winter1.opt$SSE/length(training.ts)
RMSE1.opt<-sqrt(MSE1.opt)
akurasi1.opt <- matrix(c(SSE1.opt,MSE1.opt,RMSE1.opt))
row.names(akurasi1.opt)<- c("SSE1.opt", "MSE1.opt", "RMSE1.opt")
colnames(akurasi1.opt) <- c("Akurasi")
akurasi1.opt## Akurasi
## SSE1.opt 692027.55495
## MSE1.opt 8650.34444
## RMSE1.opt 93.00723akurasi1.train = data.frame(Model_Winter = c("Winter 1","Winter1 optimal"),
Nilai_SSE=c(SSE1,SSE1.opt),
Nilai_MSE=c(MSE1,MSE1.opt),Nilai_RMSE=c(RMSE1,RMSE1.opt))
akurasi1.train## Model_Winter Nilai_SSE Nilai_MSE Nilai_RMSE
## 1 Winter 1 1043885.6 13048.570 114.23034
## 2 Winter1 optimal 692027.6 8650.344 93.00723#Akurasi Data Testing
forecast1<-data.frame(forecast1)
testing.ts<-data.frame(testing.ts)
selisih1<-forecast1-testing.ts
SSEtesting1<-sum(selisih1^2)
MSEtesting1<-SSEtesting1/length(testing.ts)
RMSEtest1<-sqrt(MSEtesting1)
forecast1.opt<-data.frame(forecast1.opt)
selisih1.opt<-forecast1.opt-testing.ts
SSEtesting1.opt<-sum(selisih1.opt^2)
MSEtesting1.opt<-SSEtesting1.opt/length(testing.ts)
RMSEtest1.opt<-sqrt(MSEtesting1.opt)
akurasi1.test <- matrix(c(SSEtesting1,MSEtesting1,RMSEtest1))
row.names(akurasi1)<- c("SSE", "MSE", "RMSE")
colnames(akurasi1) <- c("Akurasi")
akurasi1## Akurasi
## SSE 1043885.6333
## MSE 13048.5704
## RMSE 114.2303akurasi1.test = data.frame(Model_Winter = c("Winter 1","Winter1 optimal"),
Nilai_SSE=c(SSEtesting1,SSEtesting1.opt),
Nilai_MSE=c(MSEtesting1,MSEtesting1.opt),Nilai_RMSE=c(RMSEtest1,RMSEtest1.opt))
akurasi1.test## Model_Winter Nilai_SSE Nilai_MSE Nilai_RMSE
## 1 Winter 1 2012713 2012713 1418.701
## 2 Winter1 optimal 1762844 1762844 1327.721winter multiplikatif
#Pemulusan dengan winter multiplikatif
winter2 <- HoltWinters(training.ts,alpha=0.2,beta=0.1,gamma=0.3,seasonal = "multiplicative")
winter2$fitted## xhat level trend season
## Jan 2 13365.50 13335.67 -3.3148310 1.0024863
## Feb 2 13394.49 13326.27 -3.9233563 1.0054155
## Mar 2 13299.15 13318.07 -4.3508681 0.9989060
## Apr 2 13111.38 13311.29 -4.5941983 0.9853221
## May 2 13325.67 13305.40 -4.7236342 1.0018792
## Jun 2 13334.38 13299.94 -4.7968501 1.0029515
## Jul 2 13311.44 13294.87 -4.8244589 1.0016100
## Aug 2 13281.40 13292.35 -4.5936446 0.9995219
## Sep 2 13243.63 13297.08 -3.6612986 0.9962548
## Oct 2 13331.77 13302.33 -2.7706285 1.0024219
## Nov 2 13316.78 13294.02 -3.3246177 1.0019630
## Dec 2 13299.42 13286.34 -3.7593928 1.0012678
## Jan 3 13299.61 13278.11 -4.2073012 1.0019370
## Feb 3 13332.97 13270.78 -4.5188963 1.0050282
## Mar 3 13236.69 13259.30 -5.2147692 0.9986869
## Apr 3 13090.07 13288.40 -1.7839741 0.9852071
## May 3 13363.04 13335.73 3.1273589 1.0018130
## Jun 3 13359.43 13319.28 1.1701460 1.0029265
## Jul 3 13337.18 13312.59 0.3837520 1.0018187
## Aug 3 13312.00 13307.35 -0.1789246 1.0003629
## Sep 3 13276.35 13314.96 0.6008794 0.9970552
## Oct 3 13359.13 13331.34 2.1784377 1.0019206
## Nov 3 13352.20 13329.50 1.7766416 1.0015696
## Dec 3 13339.89 13327.04 1.3532576 1.0008625
## Jan 4 13320.35 13299.84 -1.5021379 1.0016547
## Feb 4 13340.20 13284.69 -2.8668101 1.0043952
## Mar 4 13295.11 13275.02 -3.5479136 1.0017810
## Apr 4 13166.34 13305.39 -0.1560554 0.9895611
## May 4 13379.21 13372.06 6.5269117 1.0000465
## Jun 4 13439.64 13401.15 8.7826085 1.0022156
## Jul 4 13453.08 13425.17 10.3064654 1.0013104
## Aug 4 13490.45 13463.02 13.0612803 1.0010659
## Sep 4 13466.23 13474.00 12.8525652 0.9984711
## Oct 4 13534.15 13499.02 14.0698822 1.0015582
## Nov 4 13537.48 13507.87 13.5477543 1.0011877
## Dec 4 13503.08 13513.53 12.7591510 0.9982839
## Jan 5 13549.79 13530.88 13.2183788 1.0004200
## Feb 5 13605.92 13541.74 12.9826957 1.0037768
## Mar 5 13625.10 13547.17 12.2271302 1.0048455
## Apr 5 13493.47 13543.85 10.6726572 0.9954958
## May 5 13589.58 13551.22 10.3416995 1.0020664
## Jun 5 13581.15 13525.92 6.7774206 1.0035807
## Jul 5 13527.54 13475.67 1.0748571 1.0037691
## Aug 5 13447.22 13438.18 -2.7813498 1.0008799
## Sep 5 13394.03 13405.78 -5.7431435 0.9995516
## Oct 5 13412.68 13403.43 -5.4035613 1.0010937
## Nov 5 13441.65 13436.65 -1.5414405 1.0004866
## Dec 5 13440.21 13457.17 0.6645353 0.9986905
## Jan 6 13508.00 13500.25 4.9058736 1.0002110
## Feb 6 13605.62 13553.74 9.7647816 1.0031050
## Mar 6 13659.95 13599.47 13.3611660 1.0034615
## Apr 6 13582.23 13632.37 15.3153315 0.9952040
## May 6 13690.95 13686.83 19.2294057 0.9988977
## Jun 6 13717.03 13717.48 20.3716409 0.9984844
## Jul 6 13772.66 13747.06 21.2923949 1.0003126
## Aug 6 13764.38 13767.62 21.2192769 0.9982263
## Sep 6 13825.39 13804.59 22.7943861 0.9998554
## Oct 6 13915.94 13829.91 23.0466637 1.0045466
## Nov 6 13913.37 13855.95 23.3464968 1.0024547
## Dec 6 13942.64 13884.61 23.8777849 1.0024556
## Jan 7 14037.44 13946.67 27.6955137 1.0045138
## Feb 7 14092.00 13976.07 27.8658916 1.0062883
## Mar 7 14045.26 13950.27 22.4997324 1.0051877
## Apr 7 13951.41 13950.44 20.2661523 0.9986192
## May 7 14015.63 13994.45 22.6411841 0.9998958
## Jun 7 14045.63 14031.57 24.0886547 0.9992869
## Jul 7 14133.32 14101.16 28.6392069 1.0002488
## Aug 7 14197.46 14170.53 32.7118272 0.9995931xhat2 <- winter2$fitted[,2]
winter2.opt<- HoltWinters(training.ts, alpha= NULL, beta = NULL, gamma = NULL, seasonal = "multiplicative")
winter2.opt$fitted## xhat level trend season
## Jan 2 13365.50 13335.67 -3.3148310 1.0024863
## Feb 2 13381.64 13313.67 -4.1125233 1.0054155
## Mar 2 13285.40 13304.29 -4.3377707 0.9989060
## Apr 2 13101.47 13300.93 -4.2957168 0.9853221
## May 2 13319.62 13298.84 -4.2018017 1.0018792
## Jun 2 13331.19 13296.09 -4.1394646 1.0029515
## Jul 2 13310.37 13293.07 -4.0920444 1.0016100
## Aug 2 13286.60 13296.72 -3.7614210 0.9995219
## Sep 2 13265.84 13318.38 -2.6754773 0.9962548
## Oct 2 13359.55 13329.37 -2.0922864 1.0024219
## Nov 2 13315.79 13293.25 -3.5451672 1.0019630
## Dec 2 13289.70 13276.96 -4.0892419 1.0012678
## Jan 3 13281.91 13265.09 -4.4218381 1.0016019
## Feb 3 13326.05 13261.95 -4.3670506 1.0051648
## Mar 3 13221.48 13240.45 -5.0987651 0.9989525
## Apr 3 13155.20 13349.98 -0.2036759 0.9854246
## May 3 13490.66 13459.93 4.5001927 1.0019484
## Jun 3 13364.78 13326.15 -1.4045462 1.0030042
## Jul 3 13321.04 13297.34 -2.5750065 1.0019768
## Aug 3 13294.08 13287.38 -2.8901682 1.0007220
## Sep 3 13276.68 13319.41 -1.3990895 0.9968966
## Oct 3 13377.71 13366.25 0.6605926 1.0008086
## Nov 3 13360.93 13343.16 -0.3535850 1.0013584
## Dec 3 13335.28 13324.45 -1.1371407 1.0008981
## Jan 4 13255.74 13238.49 -4.7592636 1.0016628
## Feb 4 13284.08 13231.44 -4.8571759 1.0043469
## Mar 4 13293.23 13239.99 -4.2849705 1.0043462
## Apr 4 13214.11 13340.70 0.1990044 0.9904956
## May 4 13461.88 13516.25 7.6868617 0.9954110
## Jun 4 13574.09 13542.52 8.4802305 1.0017041
## Jul 4 13544.35 13515.39 6.9598493 1.0016268
## Aug 4 13591.28 13550.95 8.1808469 1.0023716
## Sep 4 13484.88 13490.97 5.2701784 0.9991587
## Oct 4 13524.28 13522.12 6.3753295 0.9996885
## Nov 4 13531.09 13518.50 5.9484333 1.0004913
## Dec 4 13466.88 13504.14 5.0813808 0.9968656
## Jan 5 13573.33 13545.63 6.6362917 1.0015537
## Feb 5 13603.82 13530.62 5.7116045 1.0049860
## Mar 5 13645.18 13514.44 4.7771847 1.0093170
## Apr 5 13442.55 13459.50 2.2269174 0.9985757
## May 5 13435.73 13482.91 3.1312955 0.9962697
## Jun 5 13473.88 13470.80 2.4804998 1.0000448
## Jul 5 13400.74 13363.46 -2.2090796 1.0029558
## Aug 5 13305.62 13320.39 -3.9537201 0.9991871
## Sep 5 13313.05 13312.38 -4.1273125 1.0003611
## Oct 5 13356.42 13368.36 -1.5603702 0.9992236
## Nov 5 13518.99 13520.15 4.9879527 0.9995454
## Dec 5 13531.63 13545.41 5.8539021 0.9985506
## Jan 6 13641.73 13625.28 9.0143752 1.0005458
## Feb 6 13767.56 13701.34 11.8774894 1.0039628
## Mar 6 13826.15 13724.49 12.3590411 1.0065009
## Apr 6 13699.86 13695.28 10.5837517 0.9995620
## May 6 13704.74 13753.24 12.6070519 0.9955610
## Jun 6 13735.55 13792.53 13.7461574 0.9948772
## Jul 6 13851.82 13823.22 14.4696490 1.0010214
## Aug 6 13785.33 13786.89 12.3005848 0.9989953
## Sep 6 13892.62 13834.63 13.8141498 1.0031896
## Oct 6 13915.21 13815.02 12.3867032 1.0063501
## Nov 6 13856.57 13837.04 12.7979704 1.0004863
## Dec 6 13943.31 13901.03 14.9841369 1.0019613
## Jan 7 14103.77 14032.86 19.9737351 1.0036245
## Feb 7 14098.86 14017.50 18.4646440 1.0044815
## Mar 7 13941.54 13866.74 11.2384621 1.0045797
## Apr 7 13907.76 13872.76 11.0157051 1.0017273
## May 7 13953.28 13983.21 15.2618861 0.9967717
## Jun 7 14038.83 14081.45 18.8052115 0.9956439
## Jul 7 14251.11 14244.65 24.9712335 0.9987024
## Aug 7 14358.33 14322.43 27.2260844 1.0006046xhat2.opt <- winter2.opt$fitted[,2]#Forecast
forecast2 <- predict(winter2, n.ahead = 20)
forecast2.opt <- predict(winter2.opt, n.ahead = 20)#Plot time series
plot(training.ts,main="Winter 0.2;0.1;0.1",type="l",col="black",
xlim=c(0,10),pch=12)
lines(xhat2,type="l",col="red")
lines(xhat2.opt,type="l",col="blue")
lines(forecast2,type="l",col="red")
lines(forecast2.opt,type="l",col="blue")
legend("topleft",c("Actual Data",expression(paste(winter2)),
expression(paste(winter2.opt))),cex=0.5,
col=c("black","red","blue"),lty=1)
#Akurasi data training
SSE2<-winter2$SSE
MSE2<-winter2$SSE/length(training.ts)
RMSE2<-sqrt(MSE2)
akurasi2 <- matrix(c(SSE2,MSE2,RMSE2))
row.names(akurasi2)<- c("SSE2", "MSE2", "RMSE2")
colnames(akurasi2) <- c("Akurasi lamda=0.2")
akurasi2## Akurasi lamda=0.2
## SSE2 1019201.1904
## MSE2 12740.0149
## RMSE2 112.8717SSE2.opt<-winter2.opt$SSE
MSE2.opt<-winter2.opt$SSE/length(training.ts)
RMSE2.opt<-sqrt(MSE2.opt)
akurasi2.opt <- matrix(c(SSE2.opt,MSE2.opt,RMSE2.opt))
row.names(akurasi2.opt)<- c("SSE2.opt", "MSE2.opt", "RMSE2.opt")
colnames(akurasi2.opt) <- c("Akurasi")
akurasi2.opt## Akurasi
## SSE2.opt 700506.81234
## MSE2.opt 8756.33515
## RMSE2.opt 93.57529akurasi2.train = data.frame(Model_Winter = c("Winter 2","winter2 optimal"),
Nilai_SSE=c(SSE2,SSE2.opt),
Nilai_MSE=c(MSE2,MSE2.opt),Nilai_RMSE=c(RMSE2,RMSE2.opt))
akurasi2.train## Model_Winter Nilai_SSE Nilai_MSE Nilai_RMSE
## 1 Winter 2 1019201.2 12740.015 112.87167
## 2 winter2 optimal 700506.8 8756.335 93.57529#Akurasi Data Testing
forecast2<-data.frame(forecast2)
testing.ts<-data.frame(testing.ts)
selisih2<-forecast2-testing.ts
SSEtesting2<-sum(selisih2^2)
MSEtesting2<-SSEtesting2/length(testing.ts)
RMSEtest2<-sqrt(MSEtesting2)
forecast2.opt<-data.frame(forecast2.opt)
selisih2.opt<-forecast2.opt-testing.ts
SSEtesting2.opt<-sum(selisih2.opt^2)
MSEtesting2.opt<-SSEtesting2.opt/length(testing.ts)
RMSEtest2.opt<-sqrt(MSEtesting2)
akurasi2.test <- matrix(c(SSEtesting2,MSEtesting2,RMSEtest2))
row.names(akurasi2)<- c("SSE", "MSE","RMSE")
colnames(akurasi2) <- c("Akurasi")
akurasi2## Akurasi
## SSE 1019201.1904
## MSE 12740.0149
## RMSE 112.8717akurasi2.test = data.frame(Model_Winter = c("Winter 2","Winter2 optimal"),
Nilai_SSE=c(SSEtesting2,SSEtesting2.opt),
Nilai_MSE=c(MSEtesting2,MSEtesting2.opt), Nilai_RMSE=c(RMSEtest2,RMSEtest2.opt))
akurasi2.test## Model_Winter Nilai_SSE Nilai_MSE Nilai_RMSE
## 1 Winter 2 1989420 1989420 1410.468
## 2 Winter2 optimal 1762684 1762684 1410.468Kesimpulan Winter
winter.dt = data.frame(winter_conclusion = c("Winter 1","Winter1 optimal","Winter 2","Winter2 optimal"), Nilai_SSE=c(SSEtesting1, SSEtesting1.opt, SSEtesting2,SSEtesting2.opt), Nilai_MSE=c(MSEtesting1, MSEtesting1.opt, MSEtesting2,MSEtesting2.opt), Nilai_RMSE=c(RMSEtest1, RMSEtest1.opt, RMSEtest2,RMSEtest2.opt))
winter.dt## winter_conclusion Nilai_SSE Nilai_MSE Nilai_RMSE
## 1 Winter 1 2012713 2012713 1418.701
## 2 Winter1 optimal 1762844 1762844 1327.721
## 3 Winter 2 1989420 1989420 1410.468
## 4 Winter2 optimal 1762684 1762684 1410.468Metode Winter multiplikatif lebih cocok digunakan dilihat dari nilai SSE, MSE, dan RMSE yang lebih kecil