library.
library("forecast")## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary("graphics")
library("TTR")
library("TSA")## 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':
##
## tarImpor Data
library(rio)
data <- import("https://raw.githubusercontent.com/DindaKhamila/mpdw/main/Data/DataTugas.csv")Eksplorasi Data
View(data) #untuk melihat data
str(data) #untuk melihat struktur data## 'data.frame': 359 obs. of 2 variables:
## $ Waktu : int 1 2 3 4 5 6 7 8 9 10 ...
## $ PowerConsumed: num 85.8 85.5 83.5 79.2 76.6 71.1 69 89.2 92.8 79.5 ...dim(data) #untuk melihat dimensi data## [1] 359 2Mengubah data agar terbaca sebagai data deret waktu dengan fungsi
ts() .
data.ts <- ts(data$PowerConsumed)
data.ts## Time Series:
## Start = 1
## End = 359
## Frequency = 1
## [1] 85.8 85.5 83.5 79.2 76.6 71.1 69.0 89.2 92.8 79.5 92.6 89.4
## [13] 82.2 77.8 111.8 115.6 117.9 121.9 121.7 112.2 108.0 109.3 111.9 114.2
## [25] 112.7 105.0 100.5 96.4 41.8 43.1 42.9 44.9 43.8 43.5 44.1 60.3
## [37] 63.2 68.4 67.6 69.0 64.8 61.2 71.8 71.7 72.7 71.6 71.3 69.2
## [49] 67.0 111.8 114.9 121.6 128.1 131.6 132.2 132.7 69.0 72.1 71.8 71.1
## [61] 73.0 68.0 67.3 111.7 121.6 128.0 132.7 132.6 129.7 113.9 57.8 51.2
## [73] 58.4 63.0 66.1 69.6 68.3 62.5 63.5 62.6 62.4 63.5 60.4 57.2
## [85] 61.7 64.3 65.9 67.4 71.8 73.9 69.1 61.4 64.1 66.1 66.1 65.4
## [97] 63.0 60.2 123.2 126.1 135.1 135.2 133.5 136.7 136.0 63.9 63.6 63.8
## [109] 62.5 63.8 60.3 57.9 74.2 76.9 76.9 79.2 82.0 80.4 78.0 98.5
## [121] 99.3 102.4 102.6 100.9 94.6 84.7 116.6 129.0 130.4 115.2 109.3 100.7
## [133] 98.9 91.9 99.3 106.7 111.4 109.7 103.2 98.7 46.1 48.7 46.0 46.1
## [145] 44.1 44.4 42.4 78.4 75.9 74.2 75.9 76.0 69.1 60.8 67.9 67.7
## [157] 70.8 70.4 72.5 58.6 63.7 102.8 110.8 114.0 114.5 105.5 109.2 99.9
## [169] 77.7 75.9 76.6 75.0 76.0 71.4 60.3 103.8 110.9 117.8 115.7 117.0
## [181] 110.1 102.1 57.8 59.9 56.8 58.6 59.9 59.5 62.2 61.5 62.6 63.6
## [193] 63.4 64.0 60.4 58.0 61.6 61.7 60.1 46.1 54.4 57.9 58.2 64.2
## [205] 65.0 65.3 65.0 65.6 61.1 59.2 114.8 99.3 106.4 112.0 122.7 118.5
## [217] 121.0 75.7 78.7 81.3 82.3 84.8 91.7 95.2 62.6 64.0 65.1 63.6
## [229] 64.3 60.7 59.4 67.6 70.2 70.2 73.2 74.8 70.7 70.0 124.6 125.1
## [241] 121.0 113.9 113.4 108.1 94.0 59.2 60.2 60.7 60.6 63.4 59.1 118.5
## [253] 108.0 91.6 100.6 108.6 111.1 105.6 97.2 89.2 73.7 74.4 75.2 78.7
## [265] 79.2 85.8 86.0 88.3 87.9 86.4 80.7 75.3 68.9 72.2 72.3 72.2
## [277] 73.9 66.2 64.6 110.5 106.0 102.7 101.8 100.9 88.4 89.8 74.9 74.9
## [289] 75.4 76.4 77.3 73.3 71.7 115.5 117.8 113.9 98.7 107.7 99.2 89.1
## [301] 52.4 56.4 60.8 62.8 63.0 65.2 62.1 63.2 59.9 62.0 63.2 60.6
## [313] 60.4 58.5 61.2 61.4 62.2 61.4 64.2 59.4 57.5 66.8 67.1 66.5
## [325] 67.0 68.5 64.9 61.6 136.7 139.1 135.2 136.1 134.7 130.7 117.9 69.4
## [337] 67.7 71.8 73.1 72.2 72.0 73.3 68.5 69.5 68.8 66.8 66.8 62.6
## [349] 61.1 62.8 62.9 65.4 64.8 66.8 63.8 62.0 128.5 126.9 134.9Menampilkan ringkasan data
summary(data.ts)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 41.80 63.40 72.50 82.06 102.25 139.10Membuat plot data deret waktu
ts.plot(data.ts, xlab="Time Period", ylab="PowerConsumed",
main = "Time Series Plot")
points(data.ts)
Kemungkinan pola yang terbentuk dari data adalah pola stasioner atau musiman. Untuk itu, saya akan coba bandingkan dengan metode SMA dan SES untuk pola stasioner serta Winter Multiplikatif untuk pola musiman.
Single Moving Average
Pembagian 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[1:287,]
testing_ma <- data[288:359,]
train_ma.ts <- ts(training_ma$PowerConsumed)
test_ma.ts <- ts(testing_ma$PowerConsumed)Eksplorasi Data
Eksplorasi data dilakukan pada keseluruhan data, data latih serta data uji menggunakan plot data deret waktu.
#eksplorasi keseluruhan data
plot(data.ts, col="red",main="Plot semua data")
points(data.ts)
#eksplorasi data latih
plot(train_ma.ts, col="purple",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 data juga dapat dilakukan menggunakan package
ggplot2 dengan terlebih dahulu memanggil library
package ggplot2.
#Eksplorasi dengan GGPLOT
library(ggplot2)
ggplot() +
geom_line(data = training_ma, aes(x = Waktu, y = PowerConsumed, col = "Data Latih")) +
geom_line(data = testing_ma, aes(x = Waktu, y = PowerConsumed, col = "Data Uji")) +
labs(x = "Periode Waktu", y = "Power Consumed", 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 (SMA)
Ide dasar dari Single Moving Average (SMA) adalah data suatu periode dipengaruhi oleh data periode sebelumnya. Metode pemulusan ini cocok digunakan untuk pola data stasioner atau konstan. Prinsip dasar metode pemulusan ini adalah data pemulusan pada periode ke-t merupakan rata rata dari m buah data pada periode ke-t hingga periode ke (t-m+1). Data pemulusan pada periode ke-t selanjutnya digunakan sebagai nilai peramalan pada periode ke t+1
Pemulusan menggunakan metode SMA dilakukan dengan fungsi
SMA(). Dalam hal ini akan dilakukan pemulusan dengan
parameter m=4.
data.sma<-SMA(train_ma.ts, n=4)
data.sma## Time Series:
## Start = 1
## End = 287
## Frequency = 1
## [1] NA NA NA 83.500 81.200 77.600 73.975 76.475 80.525
## [10] 82.625 88.525 88.575 85.925 85.500 90.300 96.850 105.775 116.800
## [19] 119.275 118.425 115.950 112.800 110.350 110.850 112.025 110.950 108.100
## [28] 103.650 85.925 70.450 56.050 43.175 43.675 43.775 44.075 47.925
## [37] 52.775 59.000 64.875 67.050 67.450 65.650 66.700 67.375 69.350
## [46] 71.950 71.825 71.200 69.775 79.825 90.725 103.825 119.100 124.050
## [55] 128.375 131.150 116.375 101.500 86.400 71.000 72.000 70.975 69.850
## [64] 80.000 92.150 107.150 123.500 128.725 130.750 127.225 108.500 88.150
## [73] 70.325 57.600 59.675 64.275 66.750 66.625 65.975 64.225 62.750
## [82] 63.000 62.225 60.875 60.700 60.900 62.275 64.825 67.350 69.750
## [91] 70.550 69.050 67.125 65.175 64.425 65.425 65.150 63.675 77.950
## [100] 93.125 111.150 129.900 132.475 135.125 135.350 117.525 100.050 81.825
## [109] 63.450 63.425 62.600 61.125 64.050 67.325 71.475 76.800 78.750
## [118] 79.625 79.900 84.725 89.050 94.550 100.700 101.300 100.125 95.700
## [127] 99.200 106.225 115.175 122.800 120.975 113.900 106.025 100.200 97.700
## [136] 99.200 102.325 106.775 107.750 105.750 89.425 74.175 59.875 46.725
## [145] 46.225 45.150 44.250 52.325 60.275 67.725 76.100 75.500 73.800
## [154] 70.450 68.450 66.375 66.800 69.200 70.350 68.075 66.300 74.400
## [163] 83.975 97.825 110.525 111.200 110.800 107.275 98.075 90.675 82.525
## [172] 76.300 75.875 74.750 70.675 77.875 86.600 98.200 112.050 115.350
## [181] 115.150 111.225 96.750 82.475 69.150 58.275 58.800 58.700 60.050
## [190] 60.775 61.450 62.475 62.775 63.400 62.850 61.450 61.000 60.425
## [199] 60.350 57.375 55.575 54.625 54.150 58.675 61.325 63.175 64.875
## [208] 65.225 64.250 62.725 75.175 83.600 94.925 108.125 110.100 114.900
## [217] 118.550 109.475 98.475 89.175 79.500 81.775 85.025 88.500 83.575
## [226] 78.375 71.725 63.825 64.250 63.425 62.000 63.000 64.475 66.850
## [235] 70.300 72.100 72.225 72.175 85.025 97.600 110.175 121.150 118.350
## [244] 114.100 107.350 93.675 80.375 68.525 60.175 61.225 60.950 75.400
## [253] 87.250 94.300 104.675 102.200 102.975 106.475 105.625 100.775 91.425
## [262] 83.625 78.125 75.500 76.875 79.725 82.425 84.825 87.000 87.150
## [271] 85.825 82.575 77.825 74.275 72.175 71.400 72.650 71.150 69.225
## [280] 78.800 86.825 95.950 105.250 102.850 98.450 95.225 88.500Data pemulusan pada periode ke-t selanjutnya digunakan sebagai nilai peramalan pada periode ke t+1 sehingga hasil peramalan 1 periode kedepan adalah sebagai berikut.
data.ramal<-c(NA,data.sma)
data.ramal #forecast 1 periode ke depan## [1] NA NA NA NA 83.500 81.200 77.600 73.975 76.475
## [10] 80.525 82.625 88.525 88.575 85.925 85.500 90.300 96.850 105.775
## [19] 116.800 119.275 118.425 115.950 112.800 110.350 110.850 112.025 110.950
## [28] 108.100 103.650 85.925 70.450 56.050 43.175 43.675 43.775 44.075
## [37] 47.925 52.775 59.000 64.875 67.050 67.450 65.650 66.700 67.375
## [46] 69.350 71.950 71.825 71.200 69.775 79.825 90.725 103.825 119.100
## [55] 124.050 128.375 131.150 116.375 101.500 86.400 71.000 72.000 70.975
## [64] 69.850 80.000 92.150 107.150 123.500 128.725 130.750 127.225 108.500
## [73] 88.150 70.325 57.600 59.675 64.275 66.750 66.625 65.975 64.225
## [82] 62.750 63.000 62.225 60.875 60.700 60.900 62.275 64.825 67.350
## [91] 69.750 70.550 69.050 67.125 65.175 64.425 65.425 65.150 63.675
## [100] 77.950 93.125 111.150 129.900 132.475 135.125 135.350 117.525 100.050
## [109] 81.825 63.450 63.425 62.600 61.125 64.050 67.325 71.475 76.800
## [118] 78.750 79.625 79.900 84.725 89.050 94.550 100.700 101.300 100.125
## [127] 95.700 99.200 106.225 115.175 122.800 120.975 113.900 106.025 100.200
## [136] 97.700 99.200 102.325 106.775 107.750 105.750 89.425 74.175 59.875
## [145] 46.725 46.225 45.150 44.250 52.325 60.275 67.725 76.100 75.500
## [154] 73.800 70.450 68.450 66.375 66.800 69.200 70.350 68.075 66.300
## [163] 74.400 83.975 97.825 110.525 111.200 110.800 107.275 98.075 90.675
## [172] 82.525 76.300 75.875 74.750 70.675 77.875 86.600 98.200 112.050
## [181] 115.350 115.150 111.225 96.750 82.475 69.150 58.275 58.800 58.700
## [190] 60.050 60.775 61.450 62.475 62.775 63.400 62.850 61.450 61.000
## [199] 60.425 60.350 57.375 55.575 54.625 54.150 58.675 61.325 63.175
## [208] 64.875 65.225 64.250 62.725 75.175 83.600 94.925 108.125 110.100
## [217] 114.900 118.550 109.475 98.475 89.175 79.500 81.775 85.025 88.500
## [226] 83.575 78.375 71.725 63.825 64.250 63.425 62.000 63.000 64.475
## [235] 66.850 70.300 72.100 72.225 72.175 85.025 97.600 110.175 121.150
## [244] 118.350 114.100 107.350 93.675 80.375 68.525 60.175 61.225 60.950
## [253] 75.400 87.250 94.300 104.675 102.200 102.975 106.475 105.625 100.775
## [262] 91.425 83.625 78.125 75.500 76.875 79.725 82.425 84.825 87.000
## [271] 87.150 85.825 82.575 77.825 74.275 72.175 71.400 72.650 71.150
## [280] 69.225 78.800 86.825 95.950 105.250 102.850 98.450 95.225 88.500Selanjutnya akan dilakukan peramalan sejumlah data uji yaitu 24 periode. Pada metode SMA, hasil peramalan 24 periode ke depan akan bernilai sama dengan hasil peramalan 1 periode kedepan. Dalam hal ini akan dilakukan pengguabungan data aktual train, data hasil pemulusan dan data hasil ramalan 24 periode kedepan.
data.gab<-cbind(aktual=c(train_ma.ts,rep(NA,72)),pemulusan=c(data.sma,rep(NA,72)),ramalan=c(data.ramal,rep(data.ramal[length(data.ramal)],71)))
data.gab #forecast 72 periode ke depan## aktual pemulusan ramalan
## [1,] 85.8 NA NA
## [2,] 85.5 NA NA
## [3,] 83.5 NA NA
## [4,] 79.2 83.500 NA
## [5,] 76.6 81.200 83.500
## [6,] 71.1 77.600 81.200
## [7,] 69.0 73.975 77.600
## [8,] 89.2 76.475 73.975
## [9,] 92.8 80.525 76.475
## [10,] 79.5 82.625 80.525
## [11,] 92.6 88.525 82.625
## [12,] 89.4 88.575 88.525
## [13,] 82.2 85.925 88.575
## [14,] 77.8 85.500 85.925
## [15,] 111.8 90.300 85.500
## [16,] 115.6 96.850 90.300
## [17,] 117.9 105.775 96.850
## [18,] 121.9 116.800 105.775
## [19,] 121.7 119.275 116.800
## [20,] 112.2 118.425 119.275
## [21,] 108.0 115.950 118.425
## [22,] 109.3 112.800 115.950
## [23,] 111.9 110.350 112.800
## [24,] 114.2 110.850 110.350
## [25,] 112.7 112.025 110.850
## [26,] 105.0 110.950 112.025
## [27,] 100.5 108.100 110.950
## [28,] 96.4 103.650 108.100
## [29,] 41.8 85.925 103.650
## [30,] 43.1 70.450 85.925
## [31,] 42.9 56.050 70.450
## [32,] 44.9 43.175 56.050
## [33,] 43.8 43.675 43.175
## [34,] 43.5 43.775 43.675
## [35,] 44.1 44.075 43.775
## [36,] 60.3 47.925 44.075
## [37,] 63.2 52.775 47.925
## [38,] 68.4 59.000 52.775
## [39,] 67.6 64.875 59.000
## [40,] 69.0 67.050 64.875
## [41,] 64.8 67.450 67.050
## [42,] 61.2 65.650 67.450
## [43,] 71.8 66.700 65.650
## [44,] 71.7 67.375 66.700
## [45,] 72.7 69.350 67.375
## [46,] 71.6 71.950 69.350
## [47,] 71.3 71.825 71.950
## [48,] 69.2 71.200 71.825
## [49,] 67.0 69.775 71.200
## [50,] 111.8 79.825 69.775
## [51,] 114.9 90.725 79.825
## [52,] 121.6 103.825 90.725
## [53,] 128.1 119.100 103.825
## [54,] 131.6 124.050 119.100
## [55,] 132.2 128.375 124.050
## [56,] 132.7 131.150 128.375
## [57,] 69.0 116.375 131.150
## [58,] 72.1 101.500 116.375
## [59,] 71.8 86.400 101.500
## [60,] 71.1 71.000 86.400
## [61,] 73.0 72.000 71.000
## [62,] 68.0 70.975 72.000
## [63,] 67.3 69.850 70.975
## [64,] 111.7 80.000 69.850
## [65,] 121.6 92.150 80.000
## [66,] 128.0 107.150 92.150
## [67,] 132.7 123.500 107.150
## [68,] 132.6 128.725 123.500
## [69,] 129.7 130.750 128.725
## [70,] 113.9 127.225 130.750
## [71,] 57.8 108.500 127.225
## [72,] 51.2 88.150 108.500
## [73,] 58.4 70.325 88.150
## [74,] 63.0 57.600 70.325
## [75,] 66.1 59.675 57.600
## [76,] 69.6 64.275 59.675
## [77,] 68.3 66.750 64.275
## [78,] 62.5 66.625 66.750
## [79,] 63.5 65.975 66.625
## [80,] 62.6 64.225 65.975
## [81,] 62.4 62.750 64.225
## [82,] 63.5 63.000 62.750
## [83,] 60.4 62.225 63.000
## [84,] 57.2 60.875 62.225
## [85,] 61.7 60.700 60.875
## [86,] 64.3 60.900 60.700
## [87,] 65.9 62.275 60.900
## [88,] 67.4 64.825 62.275
## [89,] 71.8 67.350 64.825
## [90,] 73.9 69.750 67.350
## [91,] 69.1 70.550 69.750
## [92,] 61.4 69.050 70.550
## [93,] 64.1 67.125 69.050
## [94,] 66.1 65.175 67.125
## [95,] 66.1 64.425 65.175
## [96,] 65.4 65.425 64.425
## [97,] 63.0 65.150 65.425
## [98,] 60.2 63.675 65.150
## [99,] 123.2 77.950 63.675
## [100,] 126.1 93.125 77.950
## [101,] 135.1 111.150 93.125
## [102,] 135.2 129.900 111.150
## [103,] 133.5 132.475 129.900
## [104,] 136.7 135.125 132.475
## [105,] 136.0 135.350 135.125
## [106,] 63.9 117.525 135.350
## [107,] 63.6 100.050 117.525
## [108,] 63.8 81.825 100.050
## [109,] 62.5 63.450 81.825
## [110,] 63.8 63.425 63.450
## [111,] 60.3 62.600 63.425
## [112,] 57.9 61.125 62.600
## [113,] 74.2 64.050 61.125
## [114,] 76.9 67.325 64.050
## [115,] 76.9 71.475 67.325
## [116,] 79.2 76.800 71.475
## [117,] 82.0 78.750 76.800
## [118,] 80.4 79.625 78.750
## [119,] 78.0 79.900 79.625
## [120,] 98.5 84.725 79.900
## [121,] 99.3 89.050 84.725
## [122,] 102.4 94.550 89.050
## [123,] 102.6 100.700 94.550
## [124,] 100.9 101.300 100.700
## [125,] 94.6 100.125 101.300
## [126,] 84.7 95.700 100.125
## [127,] 116.6 99.200 95.700
## [128,] 129.0 106.225 99.200
## [129,] 130.4 115.175 106.225
## [130,] 115.2 122.800 115.175
## [131,] 109.3 120.975 122.800
## [132,] 100.7 113.900 120.975
## [133,] 98.9 106.025 113.900
## [134,] 91.9 100.200 106.025
## [135,] 99.3 97.700 100.200
## [136,] 106.7 99.200 97.700
## [137,] 111.4 102.325 99.200
## [138,] 109.7 106.775 102.325
## [139,] 103.2 107.750 106.775
## [140,] 98.7 105.750 107.750
## [141,] 46.1 89.425 105.750
## [142,] 48.7 74.175 89.425
## [143,] 46.0 59.875 74.175
## [144,] 46.1 46.725 59.875
## [145,] 44.1 46.225 46.725
## [146,] 44.4 45.150 46.225
## [147,] 42.4 44.250 45.150
## [148,] 78.4 52.325 44.250
## [149,] 75.9 60.275 52.325
## [150,] 74.2 67.725 60.275
## [151,] 75.9 76.100 67.725
## [152,] 76.0 75.500 76.100
## [153,] 69.1 73.800 75.500
## [154,] 60.8 70.450 73.800
## [155,] 67.9 68.450 70.450
## [156,] 67.7 66.375 68.450
## [157,] 70.8 66.800 66.375
## [158,] 70.4 69.200 66.800
## [159,] 72.5 70.350 69.200
## [160,] 58.6 68.075 70.350
## [161,] 63.7 66.300 68.075
## [162,] 102.8 74.400 66.300
## [163,] 110.8 83.975 74.400
## [164,] 114.0 97.825 83.975
## [165,] 114.5 110.525 97.825
## [166,] 105.5 111.200 110.525
## [167,] 109.2 110.800 111.200
## [168,] 99.9 107.275 110.800
## [169,] 77.7 98.075 107.275
## [170,] 75.9 90.675 98.075
## [171,] 76.6 82.525 90.675
## [172,] 75.0 76.300 82.525
## [173,] 76.0 75.875 76.300
## [174,] 71.4 74.750 75.875
## [175,] 60.3 70.675 74.750
## [176,] 103.8 77.875 70.675
## [177,] 110.9 86.600 77.875
## [178,] 117.8 98.200 86.600
## [179,] 115.7 112.050 98.200
## [180,] 117.0 115.350 112.050
## [181,] 110.1 115.150 115.350
## [182,] 102.1 111.225 115.150
## [183,] 57.8 96.750 111.225
## [184,] 59.9 82.475 96.750
## [185,] 56.8 69.150 82.475
## [186,] 58.6 58.275 69.150
## [187,] 59.9 58.800 58.275
## [188,] 59.5 58.700 58.800
## [189,] 62.2 60.050 58.700
## [190,] 61.5 60.775 60.050
## [191,] 62.6 61.450 60.775
## [192,] 63.6 62.475 61.450
## [193,] 63.4 62.775 62.475
## [194,] 64.0 63.400 62.775
## [195,] 60.4 62.850 63.400
## [196,] 58.0 61.450 62.850
## [197,] 61.6 61.000 61.450
## [198,] 61.7 60.425 61.000
## [199,] 60.1 60.350 60.425
## [200,] 46.1 57.375 60.350
## [201,] 54.4 55.575 57.375
## [202,] 57.9 54.625 55.575
## [203,] 58.2 54.150 54.625
## [204,] 64.2 58.675 54.150
## [205,] 65.0 61.325 58.675
## [206,] 65.3 63.175 61.325
## [207,] 65.0 64.875 63.175
## [208,] 65.6 65.225 64.875
## [209,] 61.1 64.250 65.225
## [210,] 59.2 62.725 64.250
## [211,] 114.8 75.175 62.725
## [212,] 99.3 83.600 75.175
## [213,] 106.4 94.925 83.600
## [214,] 112.0 108.125 94.925
## [215,] 122.7 110.100 108.125
## [216,] 118.5 114.900 110.100
## [217,] 121.0 118.550 114.900
## [218,] 75.7 109.475 118.550
## [219,] 78.7 98.475 109.475
## [220,] 81.3 89.175 98.475
## [221,] 82.3 79.500 89.175
## [222,] 84.8 81.775 79.500
## [223,] 91.7 85.025 81.775
## [224,] 95.2 88.500 85.025
## [225,] 62.6 83.575 88.500
## [226,] 64.0 78.375 83.575
## [227,] 65.1 71.725 78.375
## [228,] 63.6 63.825 71.725
## [229,] 64.3 64.250 63.825
## [230,] 60.7 63.425 64.250
## [231,] 59.4 62.000 63.425
## [232,] 67.6 63.000 62.000
## [233,] 70.2 64.475 63.000
## [234,] 70.2 66.850 64.475
## [235,] 73.2 70.300 66.850
## [236,] 74.8 72.100 70.300
## [237,] 70.7 72.225 72.100
## [238,] 70.0 72.175 72.225
## [239,] 124.6 85.025 72.175
## [240,] 125.1 97.600 85.025
## [241,] 121.0 110.175 97.600
## [242,] 113.9 121.150 110.175
## [243,] 113.4 118.350 121.150
## [244,] 108.1 114.100 118.350
## [245,] 94.0 107.350 114.100
## [246,] 59.2 93.675 107.350
## [247,] 60.2 80.375 93.675
## [248,] 60.7 68.525 80.375
## [249,] 60.6 60.175 68.525
## [250,] 63.4 61.225 60.175
## [251,] 59.1 60.950 61.225
## [252,] 118.5 75.400 60.950
## [253,] 108.0 87.250 75.400
## [254,] 91.6 94.300 87.250
## [255,] 100.6 104.675 94.300
## [256,] 108.6 102.200 104.675
## [257,] 111.1 102.975 102.200
## [258,] 105.6 106.475 102.975
## [259,] 97.2 105.625 106.475
## [260,] 89.2 100.775 105.625
## [261,] 73.7 91.425 100.775
## [262,] 74.4 83.625 91.425
## [263,] 75.2 78.125 83.625
## [264,] 78.7 75.500 78.125
## [265,] 79.2 76.875 75.500
## [266,] 85.8 79.725 76.875
## [267,] 86.0 82.425 79.725
## [268,] 88.3 84.825 82.425
## [269,] 87.9 87.000 84.825
## [270,] 86.4 87.150 87.000
## [271,] 80.7 85.825 87.150
## [272,] 75.3 82.575 85.825
## [273,] 68.9 77.825 82.575
## [274,] 72.2 74.275 77.825
## [275,] 72.3 72.175 74.275
## [276,] 72.2 71.400 72.175
## [277,] 73.9 72.650 71.400
## [278,] 66.2 71.150 72.650
## [279,] 64.6 69.225 71.150
## [280,] 110.5 78.800 69.225
## [281,] 106.0 86.825 78.800
## [282,] 102.7 95.950 86.825
## [283,] 101.8 105.250 95.950
## [284,] 100.9 102.850 105.250
## [285,] 88.4 98.450 102.850
## [286,] 89.8 95.225 98.450
## [287,] 74.9 88.500 95.225
## [288,] NA NA 88.500
## [289,] NA NA 88.500
## [290,] NA NA 88.500
## [291,] NA NA 88.500
## [292,] NA NA 88.500
## [293,] NA NA 88.500
## [294,] NA NA 88.500
## [295,] NA NA 88.500
## [296,] NA NA 88.500
## [297,] NA NA 88.500
## [298,] NA NA 88.500
## [299,] NA NA 88.500
## [300,] NA NA 88.500
## [301,] NA NA 88.500
## [302,] NA NA 88.500
## [303,] NA NA 88.500
## [304,] NA NA 88.500
## [305,] NA NA 88.500
## [306,] NA NA 88.500
## [307,] NA NA 88.500
## [308,] NA NA 88.500
## [309,] NA NA 88.500
## [310,] NA NA 88.500
## [311,] NA NA 88.500
## [312,] NA NA 88.500
## [313,] NA NA 88.500
## [314,] NA NA 88.500
## [315,] NA NA 88.500
## [316,] NA NA 88.500
## [317,] NA NA 88.500
## [318,] NA NA 88.500
## [319,] NA NA 88.500
## [320,] NA NA 88.500
## [321,] NA NA 88.500
## [322,] NA NA 88.500
## [323,] NA NA 88.500
## [324,] NA NA 88.500
## [325,] NA NA 88.500
## [326,] NA NA 88.500
## [327,] NA NA 88.500
## [328,] NA NA 88.500
## [329,] NA NA 88.500
## [330,] NA NA 88.500
## [331,] NA NA 88.500
## [332,] NA NA 88.500
## [333,] NA NA 88.500
## [334,] NA NA 88.500
## [335,] NA NA 88.500
## [336,] NA NA 88.500
## [337,] NA NA 88.500
## [338,] NA NA 88.500
## [339,] NA NA 88.500
## [340,] NA NA 88.500
## [341,] NA NA 88.500
## [342,] NA NA 88.500
## [343,] NA NA 88.500
## [344,] NA NA 88.500
## [345,] NA NA 88.500
## [346,] NA NA 88.500
## [347,] NA NA 88.500
## [348,] NA NA 88.500
## [349,] NA NA 88.500
## [350,] NA NA 88.500
## [351,] NA NA 88.500
## [352,] NA NA 88.500
## [353,] NA NA 88.500
## [354,] NA NA 88.500
## [355,] NA NA 88.500
## [356,] NA NA 88.500
## [357,] NA NA 88.500
## [358,] NA NA 88.500
## [359,] NA NA 88.500Adapun plot data deret waktu dari hasil peramalan yang dilakukan adalah sebagai berikut.
ts.plot(data.ts, xlab="Time Period", ylab="Power Consumed", main= "SMA N=4 Data Power Consumption New Delhi")
points(data.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)
Selanjutnya perhitungan akurasi dilakukan dengan ukuran akurasi Sum Squares Error (SSE), Mean Square Error (MSE) dan Mean Absolute Percentage Error (MAPE). Perhitungan akurasi dilakukan baik pada data latih maupun pada data uji.
#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 113437.9662
## MSE 400.8409
## MAPE 17.2256Dalam hal ini nilai MAPE data latih pada metode pemulusan SMA kurang dari 20%, yaitu sebesar 17,2256%, nilai ini dapat dikategorikan sebagai nilai akurasi yang baik. Selanjutnya dilakukan perhitungan nilai MAPE data uji pada metode pemulusan SMA.
#Menghitung nilai keakuratan data uji
error_test.sma = test_ma.ts-data.gab[288:359,3]
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 52868.27000
## MSE 734.28153
## MAPE 33.63032Perhitungan akurasi menggunakan data latih menghasilkan nilai MAPE sebesar 33,63% sehingga nilai akurasi ini dapat dikategorikan sebagai cukup baik (layak).
Single Exponential Smoothing & Double Exponential Smoothing
Metode Exponential Smoothing adalah metode pemulusan dengan melakukan pembobotan menurun secara eksponensial. Nilai yang lebih baru diberi bobot yang lebih besar dari nilai terdahulu. Terdapat satu atau lebih parameter pemulusan yang ditentukan secara eksplisit, dan hasil pemilihan parameter tersebut akan menentukan bobot yang akan diberikan pada nilai pengamatan. Ada dua macam model, yaitu model tunggal dan ganda.
Pembagian Data
Pembagian data latih dan data uji dilakukan dengan perbandingan 80% data latih dan 20% data uji.
#membagi training dan testing
training<-data[1:287,]
testing<-data[288:359,]
train.ts <- ts(testing$PowerConsumed)
test.ts <- ts(testing$PowerConsumed)Eksplorasi
Eksplorasi dilakukan dengan membuat plot data deret waktu untuk keseluruhan data, data latih, dan data uji.
#eksplorasi data
plot(data.ts, col="black",main="Plot semua data")
points(data.ts)
plot(train.ts, col="red",main="Plot data latih")
points(train.ts)
plot(test.ts, col="blue",main="Plot data uji")
points(test.ts)
Eksplorasi data juga dapat dilakukan menggunakan package
ggplot2 .
#Eksplorasi dengan GGPLOT
library(ggplot2)
ggplot() +
geom_line(data = training, aes(x = Waktu, y = PowerConsumed, col = "Data Latih")) +
geom_line(data = testing, aes(x = Waktu, y = PowerConsumed, col = "Data Uji")) +
labs(x = "Periode Waktu", y = "Power Comsumed", 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))
SES
Single Exponential Smoothing merupakan metode pemulusan yang tepat digunakan untuk data dengan pola stasioner atau konstan.
Nilai pemulusan pada periode ke-t didapat dari persamaan:
\[ \tilde{y}_T=\lambda y_t+(1-\lambda)\tilde{y}_{T-1} \]
Nilai parameter \(\lambda\) adalah nilai antara 0 dan 1.
Nilai pemulusan periode ke-t bertindak sebagai nilai ramalan pada periode ke-\((T+\tau)\).
\[ \tilde{y}_{T+\tau}(T)=\tilde{y}_T \]
Pemulusan dengan metode SES dapat dilakukan dengan dua fungsi dari
packages berbeda, yaitu (1) fungsi ses() dari
packages forecast dan (2) fungsi
HoltWinters dari packages stats .
#Cara 1 (fungsi ses)
ses.1<- ses(train.ts, h = 72, alpha = 0.2)
plot(ses.1)
ses.1## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 73 96.97275 67.94058 126.0049 52.571884 141.3736
## 74 96.97275 67.36563 126.5799 51.692573 142.2529
## 75 96.97275 66.80164 127.1439 50.830016 143.1155
## 76 96.97275 66.24799 127.6975 49.983290 143.9622
## 77 96.97275 65.70415 128.2413 49.151554 144.7939
## 78 96.97275 65.16960 128.7759 48.334038 145.6115
## 79 96.97275 64.64390 129.3016 47.530038 146.4155
## 80 96.97275 64.12660 129.8189 46.738904 147.2066
## 81 96.97275 63.61733 130.3282 45.960039 147.9855
## 82 96.97275 63.11572 130.8298 45.192887 148.7526
## 83 96.97275 62.62143 131.3241 44.436937 149.5086
## 84 96.97275 62.13415 131.8113 43.691711 150.2538
## 85 96.97275 61.65359 132.2919 42.956765 150.9887
## 86 96.97275 61.17949 132.7660 42.231686 151.7138
## 87 96.97275 60.71159 133.2339 41.516086 152.4294
## 88 96.97275 60.24964 133.6959 40.809604 153.1359
## 89 96.97275 59.79344 134.1521 40.111898 153.8336
## 90 96.97275 59.34276 134.6027 39.422650 154.5228
## 91 96.97275 58.89742 135.0481 38.741561 155.2039
## 92 96.97275 58.45723 135.4883 38.068345 155.8771
## 93 96.97275 58.02201 135.9235 37.402738 156.5428
## 94 96.97275 57.59160 136.3539 36.744486 157.2010
## 95 96.97275 57.16585 136.7796 36.093350 157.8521
## 96 96.97275 56.74460 137.2009 35.449106 158.4964
## 97 96.97275 56.32772 137.6178 34.811538 159.1340
## 98 96.97275 55.91507 138.0304 34.180444 159.7650
## 99 96.97275 55.50652 138.4390 33.555629 160.3899
## 100 96.97275 55.10196 138.8435 32.936911 161.0086
## 101 96.97275 54.70128 139.2442 32.324114 161.6214
## 102 96.97275 54.30435 139.6411 31.717071 162.2284
## 103 96.97275 53.91109 140.0344 31.115624 162.8299
## 104 96.97275 53.52138 140.4241 30.519620 163.4259
## 105 96.97275 53.13514 140.8104 29.928914 164.0166
## 106 96.97275 52.75227 141.1932 29.343367 164.6021
## 107 96.97275 52.37269 141.5728 28.762846 165.1826
## 108 96.97275 51.99631 141.9492 28.187225 165.7583
## 109 96.97275 51.62306 142.3224 27.616381 166.3291
## 110 96.97275 51.25285 142.6926 27.050197 166.8953
## 111 96.97275 50.88562 143.0599 26.488561 167.4569
## 112 96.97275 50.52128 143.4242 25.931366 168.0141
## 113 96.97275 50.15979 143.7857 25.378506 168.5670
## 114 96.97275 49.80106 144.1444 24.829883 169.1156
## 115 96.97275 49.44505 144.5004 24.285401 169.6601
## 116 96.97275 49.09168 144.8538 23.744967 170.2005
## 117 96.97275 48.74089 145.2046 23.208493 170.7370
## 118 96.97275 48.39264 145.5528 22.675892 171.2696
## 119 96.97275 48.04687 145.8986 22.147082 171.7984
## 120 96.97275 47.70353 146.2420 21.621983 172.3235
## 121 96.97275 47.36256 146.5829 21.100518 172.8450
## 122 96.97275 47.02392 146.9216 20.582613 173.3629
## 123 96.97275 46.68756 147.2579 20.068196 173.8773
## 124 96.97275 46.35344 147.5921 19.557196 174.3883
## 125 96.97275 46.02151 147.9240 19.049548 174.8959
## 126 96.97275 45.69172 148.2538 18.545185 175.4003
## 127 96.97275 45.36404 148.5815 18.044046 175.9014
## 128 96.97275 45.03843 148.9071 17.546068 176.3994
## 129 96.97275 44.71485 149.2306 17.051193 176.8943
## 130 96.97275 44.39326 149.5522 16.559363 177.3861
## 131 96.97275 44.07363 149.8719 16.070524 177.8750
## 132 96.97275 43.75591 150.1896 15.584620 178.3609
## 133 96.97275 43.44008 150.5054 15.101600 178.8439
## 134 96.97275 43.12610 150.8194 14.621413 179.3241
## 135 96.97275 42.81395 151.1315 14.144010 179.8015
## 136 96.97275 42.50358 151.4419 13.669343 180.2762
## 137 96.97275 42.19497 151.7505 13.197366 180.7481
## 138 96.97275 41.88809 152.0574 12.728032 181.2175
## 139 96.97275 41.58291 152.3626 12.261299 181.6842
## 140 96.97275 41.27940 152.6661 11.797123 182.1484
## 141 96.97275 40.97754 152.9680 11.335463 182.6100
## 142 96.97275 40.67729 153.2682 10.876279 183.0692
## 143 96.97275 40.37864 153.5669 10.419530 183.5260
## 144 96.97275 40.08156 153.8639 9.965179 183.9803ses.2<- ses(train.ts, h = 72, alpha = 0.7)
plot(ses.2)
ses.2## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 73 130.8689 109.908132 151.8296 98.81218603 162.9256
## 74 130.8689 105.283028 156.4547 91.73869994 169.9990
## 75 130.8689 101.374496 160.3632 85.76111640 175.9766
## 76 130.8689 97.926483 163.8113 80.48783523 181.2499
## 77 130.8689 94.806651 166.9311 75.71646393 186.0213
## 78 130.8689 91.936025 169.8017 71.32622034 190.4115
## 79 130.8689 89.262990 172.4748 67.23816701 194.4996
## 80 130.8689 86.751617 174.9861 63.39735305 198.3404
## 81 130.8689 84.375701 177.3620 59.76370257 201.9740
## 82 130.8689 82.115434 179.6223 56.30692211 205.4308
## 83 130.8689 79.955411 181.7823 53.00345206 208.7343
## 84 130.8689 77.883371 183.8544 49.83454055 211.9032
## 85 130.8689 75.889365 185.8484 46.78497268 214.9528
## 86 130.8689 73.965191 187.7726 43.84220151 217.8955
## 87 130.8689 72.103987 189.6338 40.99573571 220.7420
## 88 130.8689 70.299948 191.4378 38.23669682 223.5010
## 89 130.8689 68.548111 193.1896 35.55749215 226.1803
## 90 130.8689 66.844188 194.8936 32.95156821 228.7862
## 91 130.8689 65.184453 196.5533 30.41322192 231.3245
## 92 130.8689 63.565635 198.1721 27.93745365 233.8003
## 93 130.8689 61.984850 199.7529 25.51985143 236.2179
## 94 130.8689 60.439537 201.2982 23.15649858 238.5812
## 95 130.8689 58.927409 202.8103 20.84389921 240.8938
## 96 130.8689 57.446417 204.2913 18.57891746 243.1588
## 97 130.8689 55.994713 205.7430 16.35872773 245.3790
## 98 130.8689 54.570625 207.1671 14.18077324 247.5570
## 99 130.8689 53.172635 208.5651 12.04273159 249.6950
## 100 130.8689 51.799358 209.9384 9.94248573 251.7953
## 101 130.8689 50.449528 211.2882 7.87809939 253.8596
## 102 130.8689 49.121985 212.6158 5.84779618 255.8899
## 103 130.8689 47.815658 213.9221 3.84994171 257.8878
## 104 130.8689 46.529562 215.2082 1.88302819 259.8547
## 105 130.8689 45.262786 216.4750 -0.05433891 261.7921
## 106 130.8689 44.014484 217.7233 -1.96345240 263.7012
## 107 130.8689 42.783870 218.9539 -3.84551349 265.5833
## 108 130.8689 41.570214 220.1675 -5.70164059 267.4394
## 109 130.8689 40.372833 221.3649 -7.53287713 269.2706
## 110 130.8689 39.191089 222.5467 -9.34019837 271.0779
## 111 130.8689 38.024385 223.7134 -11.12451751 272.8623
## 112 130.8689 36.872162 224.8656 -12.88669108 274.6244
## 113 130.8689 35.733892 226.0039 -14.62752372 276.3653
## 114 130.8689 34.609082 227.1287 -16.34777251 278.0855
## 115 130.8689 33.497265 228.2405 -18.04815077 279.7859
## 116 130.8689 32.398000 229.3397 -19.72933158 281.4671
## 117 130.8689 31.310871 230.4269 -21.39195085 283.1297
## 118 130.8689 30.235486 231.5023 -23.03661012 284.7744
## 119 130.8689 29.171472 232.5663 -24.66387914 286.4016
## 120 130.8689 28.118476 233.6193 -26.27429817 288.0120
## 121 130.8689 27.076162 234.6616 -27.86838003 289.6061
## 122 130.8689 26.044211 235.6935 -29.44661207 291.1844
## 123 130.8689 25.022321 236.7154 -31.00945788 292.7472
## 124 130.8689 24.010203 237.7275 -32.55735887 294.2951
## 125 130.8689 23.007582 238.7302 -34.09073575 295.8285
## 126 130.8689 22.014195 239.7235 -35.60998984 297.3477
## 127 130.8689 21.029792 240.7080 -37.11550433 298.8532
## 128 130.8689 20.054134 241.6836 -38.60764538 300.3454
## 129 130.8689 19.086991 242.6508 -40.08676317 301.8245
## 130 130.8689 18.128144 243.6096 -41.55319285 303.2909
## 131 130.8689 17.177383 244.5604 -43.00725546 304.7450
## 132 130.8689 16.234508 245.5032 -44.44925870 306.1870
## 133 130.8689 15.299325 246.4384 -45.87949773 307.6172
## 134 130.8689 14.371649 247.3661 -47.29825588 309.0360
## 135 130.8689 13.451302 248.2864 -48.70580524 310.4435
## 136 130.8689 12.538113 249.1996 -50.10240738 311.8402
## 137 130.8689 11.631917 250.1058 -51.48831379 313.2261
## 138 130.8689 10.732557 251.0052 -52.86376653 314.6015
## 139 130.8689 9.839880 251.8979 -54.22899864 315.9667
## 140 130.8689 8.953739 252.7840 -55.58423461 317.3220
## 141 130.8689 8.073992 253.6638 -56.92969088 318.6674
## 142 130.8689 7.200504 254.5372 -58.26557613 320.0033
## 143 130.8689 6.333142 255.4046 -59.59209177 321.3298
## 144 130.8689 5.471779 256.2660 -60.90943223 322.6472Untuk mendapatkan gambar hasil pemulusan pada data latih dengan
fungsi ses() , perlu digunakan fungsi
autoplot() dan autolayer() dari library
packages ggplot2 .
autoplot(ses.1) +
autolayer(fitted(ses.1), series="Fitted") +
ylab("Power Consumed") + xlab("Periode")
Pada fungsi ses() , terdapat beberapa argumen yang umum
digunakan, yaitu nilia y , gamma ,
beta , alpha , dan h .
Nilai y adalah nilai data deret waktu,
gamma adalah parameter pemulusan untuk komponen musiman,
beta adalah parameter pemulusan untuk tren, dan
alpha adalah parameter pemulusan untuk stasioner, serta
h adalah banyaknya periode yang akan diramalkan.
Kasus di atas merupakan contoh inisialisasi nilai parameter \(\lambda\) dengan nilai alpha
0,2 dan 0,7 dan banyak periode data yang akan diramalkan adalah sebanyak
72 periode. Selanjutnya akan digunakan fungsi HoltWinters()
dengan nilai inisialisasi parameter dan panjang periode peramalan yang
sama dengan fungsi ses() .
#Cara 2 (fungsi Holtwinter)
ses.1<- HoltWinters(train.ts, gamma = FALSE, beta = FALSE, alpha = 0.2)
plot(ses.1)
#ramalan
ramalan.1<- forecast(ses.1, h=72)
ramalan.1## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 73 96.97275 67.96219 125.9833 52.60493 141.3406
## 74 96.97275 67.38767 126.5578 51.72627 142.2192
## 75 96.97275 66.82409 127.1214 50.86436 143.0811
## 76 96.97275 66.27086 127.6746 50.01826 143.9272
## 77 96.97275 65.72742 128.2181 49.18714 144.7583
## 78 96.97275 65.19327 128.7522 48.37024 145.5753
## 79 96.97275 64.66796 129.2775 47.56684 146.3787
## 80 96.97275 64.15105 129.7944 46.77629 147.1692
## 81 96.97275 63.64215 130.3033 45.99800 147.9475
## 82 96.97275 63.14091 130.8046 45.23142 148.7141
## 83 96.97275 62.64699 131.2985 44.47604 149.4695
## 84 96.97275 62.16008 131.7854 43.73137 150.2141
## 85 96.97275 61.67988 132.2656 42.99697 150.9485
## 86 96.97275 61.20613 132.7394 42.27243 151.6731
## 87 96.97275 60.73857 133.2069 41.55736 152.3881
## 88 96.97275 60.27697 133.6685 40.85140 153.0941
## 89 96.97275 59.82111 134.1244 40.15422 153.7913
## 90 96.97275 59.37077 134.5747 39.46548 154.4800
## 91 96.97275 58.92576 135.0197 38.78490 155.1606
## 92 96.97275 58.48589 135.4596 38.11219 155.8333
## 93 96.97275 58.05100 135.8945 37.44707 156.4984
## 94 96.97275 57.62091 136.3246 36.78931 157.1562
## 95 96.97275 57.19548 136.7500 36.13866 157.8068
## 96 96.97275 56.77454 137.1710 35.49490 158.4506
## 97 96.97275 56.35797 137.5875 34.85780 159.0877
## 98 96.97275 55.94562 137.9999 34.22718 159.7183
## 99 96.97275 55.53738 138.4081 33.60283 160.3427
## 100 96.97275 55.13313 138.8124 32.98457 160.9609
## 101 96.97275 54.73274 139.2128 32.37223 161.5733
## 102 96.97275 54.33611 139.6094 31.76564 162.1799
## 103 96.97275 53.94314 140.0024 31.16464 162.7809
## 104 96.97275 53.55372 140.3918 30.56908 163.3764
## 105 96.97275 53.16777 140.7777 29.97881 163.9667
## 106 96.97275 52.78518 141.1603 29.39370 164.5518
## 107 96.97275 52.40588 141.5396 28.81361 165.1319
## 108 96.97275 52.02979 141.9157 28.23842 165.7071
## 109 96.97275 51.65681 142.2887 27.66800 166.2775
## 110 96.97275 51.28688 142.6586 27.10224 166.8433
## 111 96.97275 50.91992 143.0256 26.54102 167.4045
## 112 96.97275 50.55586 143.3896 25.98424 167.9613
## 113 96.97275 50.19463 143.7509 25.43179 168.5137
## 114 96.97275 49.83617 144.1093 24.88358 169.0619
## 115 96.97275 49.48042 144.4651 24.33950 169.6060
## 116 96.97275 49.12731 144.8182 23.79947 170.1460
## 117 96.97275 48.77679 145.1687 23.26339 170.6821
## 118 96.97275 48.42880 145.5167 22.73119 171.2143
## 119 96.97275 48.08329 145.8622 22.20277 171.7427
## 120 96.97275 47.74020 146.2053 21.67806 172.2674
## 121 96.97275 47.39949 146.5460 21.15699 172.7885
## 122 96.97275 47.06110 146.8844 20.63947 173.3060
## 123 96.97275 46.72499 147.2205 20.12543 173.8201
## 124 96.97275 46.39111 147.5544 19.61481 174.3307
## 125 96.97275 46.05943 147.8861 19.10754 174.8379
## 126 96.97275 45.72989 148.2156 18.60356 175.3419
## 127 96.97275 45.40245 148.5430 18.10279 175.8427
## 128 96.97275 45.07709 148.8684 17.60518 176.3403
## 129 96.97275 44.75374 149.1917 17.11067 176.8348
## 130 96.97275 44.43239 149.5131 16.61921 177.3263
## 131 96.97275 44.11300 149.8325 16.13074 177.8148
## 132 96.97275 43.79552 150.1500 15.64519 178.3003
## 133 96.97275 43.47992 150.4656 15.16253 178.7830
## 134 96.97275 43.16618 150.7793 14.68270 179.2628
## 135 96.97275 42.85425 151.0912 14.20566 179.7398
## 136 96.97275 42.54412 151.4014 13.73134 180.2141
## 137 96.97275 42.23574 151.7098 13.25972 180.6858
## 138 96.97275 41.92909 152.0164 12.79073 181.1548
## 139 96.97275 41.62413 152.3214 12.32435 181.6211
## 140 96.97275 41.32085 152.6246 11.86052 182.0850
## 141 96.97275 41.01921 152.9263 11.39920 182.5463
## 142 96.97275 40.71919 153.2263 10.94036 183.0051
## 143 96.97275 40.42076 153.5247 10.48395 183.4615
## 144 96.97275 40.12390 153.8216 10.02994 183.9156ses.2<- HoltWinters(train.ts, gamma = FALSE, beta = FALSE, alpha = 0.7)
plot(ses.2)
#ramalan
ramalan.2<- forecast(ses.2, h=72)
ramalan.2## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 73 130.8689 109.958545 151.7792 98.8892857 162.8485
## 74 130.8689 105.344564 156.3932 91.8328121 169.9049
## 75 130.8689 101.445433 160.2923 85.8696053 175.8681
## 76 130.8689 98.005713 163.7320 80.6090069 181.1287
## 77 130.8689 94.893384 166.8444 75.8491112 185.8886
## 78 130.8689 92.029662 169.7081 71.4694266 190.2683
## 79 130.8689 89.363057 172.3747 67.3912055 194.3465
## 80 130.8689 86.857724 174.8800 63.5596291 198.1781
## 81 130.8689 84.487522 177.2502 59.9347179 201.8030
## 82 130.8689 82.232691 179.5051 56.4862514 205.2515
## 83 130.8689 80.077863 181.6599 53.1907265 208.5470
## 84 130.8689 78.010806 183.7269 50.0294366 211.7083
## 85 130.8689 76.021597 185.7161 46.9872033 214.7505
## 86 130.8689 74.102050 187.6357 44.0515098 217.6862
## 87 130.8689 72.245323 189.4924 41.2118900 220.5259
## 88 130.8689 70.445623 191.2921 38.4594869 223.2783
## 89 130.8689 68.697998 193.0397 35.7867260 225.9510
## 90 130.8689 66.998175 194.7396 33.1870696 228.5507
## 91 130.8689 65.342431 196.3953 30.6548283 231.0829
## 92 130.8689 63.727507 198.0102 28.1850145 233.5527
## 93 130.8689 62.150523 199.5872 25.7732268 235.9645
## 94 130.8689 60.608927 201.1288 23.4155581 238.3222
## 95 130.8689 59.100436 202.6373 21.1085208 240.6292
## 96 130.8689 57.623006 204.1147 18.8489865 242.8888
## 97 130.8689 56.174793 205.5630 16.6341366 245.1036
## 98 130.8689 54.754131 206.9836 14.4614203 247.2763
## 99 130.8689 53.359503 208.3782 12.3285209 249.4092
## 100 130.8689 51.989529 209.7482 10.2333263 251.5044
## 101 130.8689 50.642945 211.0948 8.1739051 253.5638
## 102 130.8689 49.318594 212.4192 6.1484849 255.5893
## 103 130.8689 48.015409 213.7223 4.1554355 257.5823
## 104 130.8689 46.732407 215.0053 2.1932526 259.5445
## 105 130.8689 45.468677 216.2691 0.2605451 261.4772
## 106 130.8689 44.223377 217.5144 -1.6439768 263.3817
## 107 130.8689 42.995724 218.7420 -3.5215113 265.2593
## 108 130.8689 41.784986 219.9528 -5.3731742 267.1109
## 109 130.8689 40.590485 221.1473 -7.2000064 268.9378
## 110 130.8689 39.411583 222.3262 -9.0029809 270.7407
## 111 130.8689 38.247686 223.4901 -10.7830086 272.5208
## 112 130.8689 37.098234 224.6395 -12.5409439 274.2787
## 113 130.8689 35.962702 225.7750 -14.2775897 276.0153
## 114 130.8689 34.840597 226.8971 -15.9937011 277.7314
## 115 130.8689 33.731454 228.0063 -17.6899898 279.4277
## 116 130.8689 32.634832 229.1029 -19.3671272 281.1049
## 117 130.8689 31.550319 230.1874 -21.0257477 282.7635
## 118 130.8689 30.477520 231.2602 -22.6664513 284.4042
## 119 130.8689 29.416065 232.3217 -24.2898066 286.0276
## 120 130.8689 28.365601 233.3721 -25.8963524 287.6341
## 121 130.8689 27.325794 234.4120 -27.4866003 289.2243
## 122 130.8689 26.296326 235.4414 -29.0610366 290.7988
## 123 130.8689 25.276893 236.4609 -30.6201236 292.3579
## 124 130.8689 24.267210 237.4705 -32.1643017 293.9020
## 125 130.8689 23.267000 238.4707 -33.6939906 295.4317
## 126 130.8689 22.276002 239.4617 -35.2095908 296.9473
## 127 130.8689 21.293967 240.4438 -36.7114843 298.4492
## 128 130.8689 20.320655 241.4171 -38.2000366 299.9378
## 129 130.8689 19.355838 242.3819 -39.6755970 301.4133
## 130 130.8689 18.399297 243.3384 -41.1384998 302.8762
## 131 130.8689 17.450823 244.2869 -42.5890652 304.3268
## 132 130.8689 16.510216 245.2275 -44.0276003 305.7653
## 133 130.8689 15.577282 246.1605 -45.4543994 307.1921
## 134 130.8689 14.651837 247.0859 -46.8697453 308.6075
## 135 130.8689 13.733703 248.0040 -48.2739094 310.0117
## 136 130.8689 12.822711 248.9150 -49.6671525 311.4049
## 137 130.8689 11.918695 249.8190 -51.0497257 312.7875
## 138 130.8689 11.021498 250.7162 -52.4218703 314.1596
## 139 130.8689 10.130967 251.6068 -53.7838189 315.5216
## 140 130.8689 9.246957 252.4908 -55.1357954 316.8735
## 141 130.8689 8.369327 253.3684 -56.4780157 318.2158
## 142 130.8689 7.497939 254.2398 -57.8106880 319.5484
## 143 130.8689 6.632663 255.1051 -59.1340132 320.8718
## 144 130.8689 5.773372 255.9644 -60.4481854 322.1859Fungsi HoltWinters memiliki argumen yang sama dengan
fungsi ses() . Argumen-argumen kedua fungsi dapat dilihat
lebih lanjut dengan ?ses() atau ?HoltWinters
.
Nilai parameter \(\alpha\) dari
kedua fungsi dapat dioptimalkan menyesuaikan dari error-nya
paling minimumnya. Caranya adalah dengan membuat parameter \(\alpha =\) NULL .
#SES
ses.opt <- ses(train.ts, h = 72, alpha = NULL)
plot(ses.opt)
ses.opt## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 73 134.8992 115.0370872 154.7613 104.5227203 165.2757
## 74 134.8992 106.8113374 162.9871 91.9425217 177.8559
## 75 134.8992 100.4993087 169.2991 82.2891068 187.5093
## 76 134.8992 95.1779587 174.6204 74.1508042 195.6476
## 77 134.8992 90.4897246 179.3087 66.9807690 202.8176
## 78 134.8992 86.2512196 183.5472 60.4985350 209.2999
## 79 134.8992 82.3535010 187.4449 54.5374887 215.2609
## 80 134.8992 78.7255854 191.0728 48.9890707 220.8093
## 81 134.8992 75.3181673 194.4802 43.7778743 226.0205
## 82 134.8992 72.0953470 197.7031 38.8489960 230.9494
## 83 134.8992 69.0300233 200.7684 34.1609880 235.6374
## 84 134.8992 66.1011410 203.6973 29.6816490 240.1167
## 85 134.8992 63.2919558 206.5064 25.3853711 244.4130
## 86 134.8992 60.5888918 209.2095 21.2513914 248.5470
## 87 134.8992 57.9807601 211.8176 17.2625982 252.5358
## 88 134.8992 55.4582101 214.3402 13.4046908 256.3937
## 89 134.8992 53.0133321 216.7851 9.6655726 260.1328
## 90 134.8992 50.6393647 219.1590 6.0349027 263.7635
## 91 134.8992 48.3304739 221.4679 2.5037590 267.2946
## 92 134.8992 46.0815845 223.7168 -0.9356205 270.7340
## 93 134.8992 43.8882484 225.9101 -4.2900386 274.0884
## 94 134.8992 41.7465414 228.0519 -7.5654967 277.3639
## 95 134.8992 39.6529807 230.1454 -10.7673215 280.5657
## 96 134.8992 37.6044583 232.1939 -13.9002663 283.6987
## 97 134.8992 35.5981866 234.2002 -16.9685940 286.7670
## 98 134.8992 33.6316546 236.1667 -19.9761451 289.7745
## 99 134.8992 31.7025904 238.0958 -22.9263942 292.7248
## 100 134.8992 29.8089306 239.9895 -25.8224970 295.6209
## 101 134.8992 27.9487947 241.8496 -28.6673294 298.4657
## 102 134.8992 26.1204627 243.6779 -31.4635219 301.2619
## 103 134.8992 24.3223572 245.4760 -34.2134870 304.0119
## 104 134.8992 22.5530267 247.2454 -36.9194444 306.7178
## 105 134.8992 20.8111325 248.9873 -39.5834417 309.3818
## 106 134.8992 19.0954366 250.7030 -42.2073722 312.0058
## 107 134.8992 17.4047911 252.3936 -44.7929913 314.5914
## 108 134.8992 15.7381300 254.0603 -47.3419295 317.1403
## 109 134.8992 14.0944605 255.7039 -49.8557051 319.6541
## 110 134.8992 12.4728566 257.3255 -52.3357343 322.1341
## 111 134.8992 10.8724527 258.9259 -54.7833409 324.5817
## 112 134.8992 9.2924385 260.5060 -57.1997640 326.9982
## 113 134.8992 7.7320540 262.0663 -59.5861662 329.3846
## 114 134.8992 6.1905853 263.6078 -61.9436392 331.7420
## 115 134.8992 4.6673606 265.1310 -64.2732102 334.0716
## 116 134.8992 3.1617472 266.6367 -66.5758473 336.3742
## 117 134.8992 1.6731479 268.1253 -68.8524634 338.6509
## 118 134.8992 0.2009986 269.5974 -71.1039214 340.9023
## 119 134.8992 -1.2552341 271.0536 -73.3310372 343.1294
## 120 134.8992 -2.6960558 272.4945 -75.5345838 345.3330
## 121 134.8992 -4.1219455 273.9203 -77.7152940 347.5137
## 122 134.8992 -5.5333582 275.3318 -79.8738633 349.6723
## 123 134.8992 -6.9307259 276.7291 -82.0109528 351.8094
## 124 134.8992 -8.3144598 278.1129 -84.1271913 353.9256
## 125 134.8992 -9.6849514 279.4833 -86.2231773 356.0216
## 126 134.8992 -11.0425738 280.8410 -88.2994815 358.0979
## 127 134.8992 -12.3876827 282.1861 -90.3566481 360.1550
## 128 134.8992 -13.7206180 283.5190 -92.3951967 362.1936
## 129 134.8992 -15.0417043 284.8401 -94.4156239 364.2140
## 130 134.8992 -16.3512521 286.1497 -96.4184044 366.2168
## 131 134.8992 -17.6495586 287.4480 -98.4039928 368.2024
## 132 134.8992 -18.9369084 288.7353 -100.3728244 370.1712
## 133 134.8992 -20.2135742 290.0120 -102.3253163 372.1237
## 134 134.8992 -21.4798178 291.2782 -104.2618688 374.0603
## 135 134.8992 -22.7358903 292.5343 -106.1828659 375.9813
## 136 134.8992 -23.9820329 293.7804 -108.0886766 377.8871
## 137 134.8992 -25.2184775 295.0169 -109.9796554 379.7781
## 138 134.8992 -26.4454471 296.2438 -111.8561434 381.6545
## 139 134.8992 -27.6631561 297.4616 -113.7184687 383.5169
## 140 134.8992 -28.8718112 298.6702 -115.5669471 385.3653
## 141 134.8992 -30.0716113 299.8700 -117.4018831 387.2003
## 142 134.8992 -31.2627484 301.0611 -119.2235699 389.0220
## 143 134.8992 -32.4454072 302.2438 -121.0322906 390.8307
## 144 134.8992 -33.6197664 303.4182 -122.8283180 392.6267#Lamda Optimum Holt Winter
sesopt<- HoltWinters(train.ts, gamma = FALSE, beta = FALSE,alpha = NULL)
sesopt## Holt-Winters exponential smoothing without trend and without seasonal component.
##
## Call:
## HoltWinters(x = train.ts, alpha = NULL, beta = FALSE, gamma = FALSE)
##
## Smoothing parameters:
## alpha: 0.9999472
## beta : FALSE
## gamma: FALSE
##
## Coefficients:
## [,1]
## a 134.8996plot(sesopt)
#ramalan
ramalanopt<- forecast(sesopt, h=72)
ramalanopt## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 73 134.8996 115.0674726 154.7317 104.5689903 165.2302
## 74 134.8996 106.8534855 162.9457 92.0067810 177.7924
## 75 134.8996 100.5505721 169.2486 82.3673068 187.4318
## 76 134.8996 95.2369368 174.5622 74.2408029 195.5584
## 77 134.8996 90.5555141 179.2436 67.0811847 202.7180
## 78 134.8996 86.3231752 183.4760 60.6083810 209.1908
## 79 134.8996 82.4311322 187.3680 54.6560148 215.1431
## 80 134.8996 78.8085029 190.9907 49.1156814 220.6835
## 81 134.8996 75.4060523 194.3931 43.9120822 225.8871
## 82 134.8996 72.1879323 197.6112 38.9903924 230.8088
## 83 134.8996 69.1270807 200.6721 34.3092238 235.4899
## 84 134.8996 66.2024725 203.5967 29.8364216 239.9627
## 85 134.8996 63.3973878 206.4018 25.5464147 244.2527
## 86 134.8996 60.6982700 209.1009 21.4184703 248.3807
## 87 134.8996 58.0939467 211.7052 17.4355014 252.3637
## 88 134.8996 55.5750805 214.2241 13.5832281 256.2159
## 89 134.8996 53.1337734 216.6654 9.8495710 259.9496
## 90 134.8996 50.7632737 219.0359 6.2242046 263.5750
## 91 134.8996 48.4577559 221.3414 2.6982195 267.1009
## 92 134.8996 46.2121521 223.5870 -0.7361351 270.5353
## 93 134.8996 44.0220208 225.7771 -4.0856520 273.8848
## 94 134.8996 41.8834433 227.9157 -7.3563240 277.1555
## 95 134.8996 39.7929420 230.0062 -10.5534698 280.3526
## 96 134.8996 37.7474133 232.0517 -13.6818361 283.4810
## 97 134.8996 35.7440738 234.0551 -16.7456794 286.5448
## 98 134.8996 33.7804161 236.0187 -19.7488347 289.5480
## 99 134.8996 31.8541715 237.9450 -22.6947717 292.4939
## 100 134.8996 29.9632797 239.8359 -25.5866411 295.3858
## 101 134.8996 28.1058628 241.6933 -28.4273151 298.2265
## 102 134.8996 26.2802035 243.5190 -31.2194200 301.0186
## 103 134.8996 24.4847266 245.3144 -33.9653650 303.7645
## 104 134.8996 22.7179828 247.0812 -36.6673665 306.4665
## 105 134.8996 20.9786352 248.8205 -39.3274690 309.1266
## 106 134.8996 19.2654476 250.5337 -41.9475633 311.7467
## 107 134.8996 17.5772740 252.2219 -44.5294021 314.3286
## 108 134.8996 15.9130497 253.8861 -47.0746135 316.8738
## 109 134.8996 14.2717835 255.5274 -49.5847136 319.3839
## 110 134.8996 12.6525506 257.1466 -52.0611166 321.8603
## 111 134.8996 11.0544868 258.7447 -54.5051442 324.3043
## 112 134.8996 9.4767830 260.3224 -56.9180340 326.7172
## 113 134.8996 7.9186802 261.8805 -59.3009466 329.1001
## 114 134.8996 6.3794655 263.4197 -61.6549723 331.4541
## 115 134.8996 4.8584683 264.9407 -63.9811368 333.7803
## 116 134.8996 3.3550566 266.4441 -66.2804066 336.0796
## 117 134.8996 1.8686342 267.9305 -68.5536935 338.3528
## 118 134.8996 0.3986378 269.4005 -70.8018590 340.6010
## 119 134.8996 -1.0554653 270.8546 -73.0257178 342.8249
## 120 134.8996 -2.4941799 272.2933 -75.2260419 345.0252
## 121 134.8996 -3.9179843 273.7171 -77.4035628 347.2027
## 122 134.8996 -5.3273328 275.1265 -79.5589753 349.3581
## 123 134.8996 -6.7226569 276.5218 -81.6929393 351.4921
## 124 134.8996 -8.1043671 277.9035 -83.8060827 353.6052
## 125 134.8996 -9.4728543 279.2720 -85.8990033 355.6982
## 126 134.8996 -10.8284910 280.6276 -87.9722708 357.7714
## 127 134.8996 -12.1716327 281.9708 -90.0264287 359.8256
## 128 134.8996 -13.5026184 283.3018 -92.0619958 361.8612
## 129 134.8996 -14.8217725 284.6209 -94.0794679 363.8786
## 130 134.8996 -16.1294050 285.9286 -96.0793191 365.8785
## 131 134.8996 -17.4258125 287.2250 -98.0620034 367.8612
## 132 134.8996 -18.7112794 288.5104 -100.0279553 369.8271
## 133 134.8996 -19.9860779 289.7852 -101.9775914 371.7767
## 134 134.8996 -21.2504694 291.0496 -103.9113113 373.7105
## 135 134.8996 -22.5047047 292.3039 -105.8294986 375.6287
## 136 134.8996 -23.7490246 293.5482 -107.7325217 377.5317
## 137 134.8996 -24.9836607 294.7828 -109.6207346 379.4199
## 138 134.8996 -26.2088355 296.0080 -111.4944779 381.2936
## 139 134.8996 -27.4247634 297.2239 -113.3540791 383.1532
## 140 134.8996 -28.6316505 298.4308 -115.1998537 384.9990
## 141 134.8996 -29.8296957 299.6289 -117.0321056 386.8313
## 142 134.8996 -31.0190903 300.8182 -118.8511278 388.6503
## 143 134.8996 -32.2000193 301.9992 -120.6572027 390.4564
## 144 134.8996 -33.3726607 303.1718 -122.4506030 392.2498Setelah dilakukan peramalan, akan dilakukan perhitungan keakuratan hasil peramalan. Perhitungan akurasi ini dilakukan baik pada data latih dan data uji.
Akurasi Data Latih
Perhitungan akurasi data dapat dilakukan dengan cara langsung maupun manual. Secara langsung, nilai akurasi dapat diambil dari objek yang tersimpan pada hasil SES, yaitu sum of squared errors (SSE). Nilai akurasi lain dapat dihitung pula dari nilai SSE tersebut.
#Keakuratan Metode
#Pada data training
SSE1<-ses.1$SSE
MSE1<-ses.1$SSE/length(train.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 36042.09733
## MSE 500.58469
## RMSE 22.37375SSE2<-ses.2$SSE
MSE2<-ses.2$SSE/length(train.ts)
RMSE2<-sqrt(MSE2)
akurasi2 <- matrix(c(SSE2,MSE2,RMSE2))
row.names(akurasi2)<- c("SSE", "MSE", "RMSE")
colnames(akurasi2) <- c("Akurasi lamda=0.7")
akurasi2## Akurasi lamda=0.7
## SSE 18725.81939
## MSE 260.08082
## RMSE 16.12702#Cara Manual
fitted1<-ramalan.1$fitted
sisaan1<-ramalan.1$residuals
head(sisaan1)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA 0.5000 1.4000 2.0200 -2.3840 -3.5072resid1<- ramalan.1$fitted
head(resid1)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA 74.9000 75.0000 75.2800 75.6840 75.2072#Cara Manual
SSE.1=sum(sisaan1[2:length(train.ts)]^2)
SSE.1## [1] 36042.1MSE.1 = SSE.1/length(train.ts)
MSE.1## [1] 500.5847MAPE.1 = sum(abs(sisaan1[2:length(train.ts)]/train.ts[2:length(train.ts)])*
100)/length(train.ts)
MAPE.1## [1] 16.25704akurasi.1 <- matrix(c(SSE.1,MSE.1,MAPE.1))
row.names(akurasi.1)<- c("SSE", "MSE", "MAPE")
colnames(akurasi.1) <- c("Akurasi lamda=0.2")
akurasi.1## Akurasi lamda=0.2
## SSE 36042.09733
## MSE 500.58469
## MAPE 16.25704fitted2<-ramalan.2$fitted
sisaan2<-ramalan.2$residuals
head(sisaan2)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA 0.50000 1.15000 1.24500 -3.62650 -2.68795resid2<-ramalan.2$fitted
head(resid2)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA 74.90000 75.25000 76.05500 76.92650 74.38795SSE.2=sum(sisaan2[2:length(train.ts)]^2)
SSE.2## [1] 18725.82MSE.2 = SSE.2/length(train.ts)
MSE.2## [1] 260.0808MAPE.2 = sum(abs(sisaan2[2:length(train.ts)]/train.ts[2:length(train.ts)])*
100)/length(train.ts)
MAPE.2## [1] 8.354585akurasi.2 <- matrix(c(SSE.2,MSE.2,MAPE.2))
row.names(akurasi.2)<- c("SSE", "MSE", "MAPE")
colnames(akurasi.2) <- c("Akurasi lamda=0.7")
akurasi.2## Akurasi lamda=0.7
## SSE 18725.819390
## MSE 260.080825
## MAPE 8.354585Berdasarkan nilai SSE, MSE, RMSE, dan MAPE di antara kedua parameter, nilai parameter $,7 menghasilkan akurasi yang lebih baik dibanding \(\lambda=0,2\) Hal ini dilihat dari nilai masing-masing ukuran akurasi yang lebih kecil. Berdasarkan nilai MAPE-nya, hasil ini dapat dikategorikan sebagai peramalan sangat baik.
Akurasi Data Uji
Akurasi data uji dapat dihitung dengan cara yang hampir sama dengan perhitungan akurasi data latih.
selisih1<-ramalan.1$mean-testing$PowerConsumed
SSEtesting1<-sum(selisih1^2)
MSEtesting1<-SSEtesting1/length(testing)
selisih2<-ramalan.2$mean-testing$PowerConsumed
SSEtesting2<-sum(selisih2^2)
MSEtesting2<-SSEtesting2/length(testing)
selisihopt<-ramalanopt$mean-testing$PowerConsumed
SSEtestingopt<-sum(selisihopt^2)
MSEtestingopt<-SSEtestingopt/length(testing)
akurasitesting1 <- matrix(c(SSEtesting1,SSEtesting2,SSEtestingopt))
row.names(akurasitesting1)<- c("SSE1", "SSE2", "SSEopt")
akurasitesting1## [,1]
## SSE1 70036.07
## SSE2 242119.80
## SSEopt 273589.65akurasitesting2 <- matrix(c(MSEtesting1,MSEtesting2,MSEtestingopt))
row.names(akurasitesting2)<- c("MSE1", "MSE2", "MSEopt")
akurasitesting2## [,1]
## MSE1 35018.03
## MSE2 121059.90
## MSEopt 136794.83Selain dengan cara di atas, perhitungan nilai akurasi dapat
menggunakan fungsi accuracy() dari package
forecast . Penggunaannya yaitu dengan menuliskan
accuracy(hasil ramalan, kondisi aktual) . Contohnya adalah
sebagai berikut.
#cara lain
accuracy(ramalanopt,testing$PowerConsumed)## ME RMSE MAE MPE MAPE MASE
## Training set 0.8451091 15.38893 6.470484 -0.5405664 7.376627 1.000009
## Test set -56.2343002 61.64297 56.442692 -85.1190438 85.270191 8.723185
## ACF1
## Training set 0.03294473
## Test set NAPemulusan Data Musiman
Pertama impor kembali data baru untuk latihan data musiman.
#Import data
library(rio)
data2 <- import("https://raw.githubusercontent.com/DindaKhamila/mpdw/main/Data/DataTugas.csv")
data2.ts <- ts(data2$PowerConsumed)Selanjutnya melakukan pembagian data dan mengubahnya menjadi data deret waktu.
#membagi data menjadi training dan testing
training<-data2[1:287,2]
testing<-data2[288:359,2]
training.ts<-ts(training, frequency = 13)
testing.ts<-ts(testing, frequency = 13)Kemudian akan dilakukan eskplorasi dengan plot data deret waktu sebagai berikut.
#Membuat plot time series
plot(data2.ts, col="red",main="Plot semua data")
points(data2.ts)
plot(training.ts, col="blue",main="Plot data latih")
points(training.ts)
plot(testing.ts, col="green",main="Plot data uji")
points(testing.ts)
Metode Holt-Winter untuk peramalan data musiman menggunakan tiga persamaan pemulusan yang terdiri atas persamaan untuk level \((L_t)\), trend \((B_t)\), dan komponen seasonal / musiman \((S_t)\) dengan parameter pemulusan berupa \(\alpha\), \(\beta\), dan \(\gamma\). Metode Holt-Winter musiman terbagi menjadi dua, yaitu metode aditif dan metode multiplikatif. Perbedaan persamaan dan contoh datanya adalah sebagai berikut.
Pemulusan data musiman dengan metode Winter dilakukan menggunakan
fungsi HoltWinters() dengan memasukkan argumen tambahan,
yaitu gamma() dan seasonal() . Arguman
seasonal() diinisialisasi menyesuaikan jenis musiman,
aditif atau multiplikatif.
Winter Multiplikatif
Model multiplikatif digunakan cocok digunakan jika plot data asli menunjukkan fluktuasi musiman yang bervariasi.
Pemulusan
#Pemulusan dengan winter multiplikatif
winter2 <- HoltWinters(training.ts,alpha=0.2,beta=0.1,gamma=0.3,seasonal = "multiplicative")
winter2$fitted## Time Series:
## Start = c(2, 1)
## End = c(23, 1)
## Frequency = 13
## xhat level trend season
## 2.000000 61.72342 78.63702 2.40539307 0.7616187
## 2.076923 95.04317 85.26410 2.82756166 1.0789121
## 2.153846 103.94384 91.19791 3.13818628 1.1018459
## 2.230769 109.50594 96.45185 3.34976143 1.0972362
## 2.307692 117.08772 101.33165 3.50276505 1.1168825
## 2.384615 119.85488 105.69615 3.58893847 1.0967177
## 2.461538 102.69950 109.62156 3.62258647 0.9068857
## 2.538462 127.06870 115.33934 3.83210563 1.0662680
## 2.615385 128.91028 115.59473 3.47443378 1.0826504
## 2.692308 106.82898 115.44652 3.11216943 0.9010641
## 2.769231 124.71472 119.68425 3.22472568 1.0146917
## 2.846154 116.79127 120.83648 3.01747612 0.9429757
## 2.923077 104.79450 122.98622 2.93070241 0.8322511
## 3.000000 104.00722 125.96631 2.93564079 0.8068708
## 3.076923 146.98104 128.03261 2.84870688 1.1230101
## 3.153846 140.02305 121.87320 1.94789509 1.1308498
## 3.230769 119.15204 106.44955 0.21074031 1.1171172
## 3.307692 103.63857 93.04452 -1.15083644 1.1278096
## 3.384615 86.84388 81.12261 -2.22794334 1.1007573
## 3.461538 63.27542 71.27376 -2.99003470 0.9266545
## 3.538462 62.28847 64.08034 -3.41037298 1.0266772
## 3.615385 55.46311 57.00991 -3.77637838 1.0418829
## 3.692308 42.88058 51.05227 -3.99450479 0.9112329
## 3.769231 46.97615 50.88103 -3.61217845 0.9938078
## 3.846154 44.17664 50.53384 -3.28567977 0.9349918
## 3.923077 41.35082 52.42967 -2.76752853 0.8326427
## 4.000000 43.08007 55.96717 -2.13702555 0.8002965
## 4.076923 60.19498 60.30773 -1.48926744 1.0234029
## 4.153846 53.03525 59.71840 -1.39927312 0.9093971
## 4.230769 54.23928 60.11477 -1.21970903 0.9209478
## 4.307692 58.66022 62.70868 -0.83834704 0.9481154
## 4.384615 61.46465 64.62101 -0.56327962 0.9595197
## 4.461538 56.40526 66.39960 -0.32909269 0.8537133
## 4.538462 66.00575 69.63018 0.02687543 0.9475816
## 4.615385 70.09506 70.77448 0.13861781 0.9884642
## 4.692308 70.38476 70.73200 0.12050761 0.9933983
## 4.769231 75.19943 70.17106 0.05236251 1.0708596
## 4.846154 81.36400 77.05916 0.73593620 1.0458758
## 4.923077 80.89569 84.20809 1.37723608 0.9452052
## 5.000000 87.12541 94.19813 2.23851594 0.9034471
## 5.076923 113.20658 105.50736 3.14558822 1.0419098
## 5.153846 108.97203 112.18367 3.49865952 0.9419938
## 5.230769 123.13005 120.61399 3.99182561 0.9881566
## 5.307692 130.27655 126.54274 4.18551854 0.9965447
## 5.384615 121.40193 118.43046 2.95573821 1.0001296
## 5.461538 102.83798 111.52709 1.96982739 0.9060862
## 5.538462 104.21078 106.64591 1.28472733 0.9655347
## 5.615385 100.18935 101.07210 0.59887363 0.9854272
## 5.692308 94.45099 96.15269 0.04704503 0.9818217
## 5.769231 107.01560 90.81159 -0.49176947 1.1848518
## 5.846154 94.11736 83.61593 -1.16215883 1.1414561
## 5.923077 88.82235 85.53451 -0.85408494 1.0489125
## 6.000000 90.39758 90.93026 -0.22910144 0.9966530
## 6.076923 106.79859 98.24690 0.52547260 1.0812598
## 6.153846 103.33539 103.56334 1.00456953 0.9882132
## 6.230769 112.79440 110.49064 1.59684269 1.0063069
## 6.307692 102.39870 115.44741 1.93283555 0.8723674
## 6.384615 109.26316 120.01705 2.19651570 0.8940347
## 6.461538 93.44637 110.70100 1.04525915 0.8362371
## 6.538462 90.17871 101.64234 0.03486705 0.8869117
## 6.615385 86.09419 94.51106 -0.68174779 0.9175618
## 6.692308 79.89330 88.79549 -1.18512939 0.9119161
## 6.769231 88.98568 84.58524 -1.48764189 1.0708574
## 6.846154 92.43789 79.47701 -1.84970086 1.1907910
## 6.923077 80.97638 73.57321 -2.25511029 1.1354253
## 7.000000 71.27885 68.06357 -2.58056324 1.0885091
## 7.076923 69.99525 64.05374 -2.72348994 1.1412843
## 7.153846 60.14204 60.03430 -2.85308517 1.0517798
## 7.230769 57.07198 57.61057 -2.81014923 1.0414514
## 7.307692 47.76616 56.03486 -2.68670567 0.8953667
## 7.384615 42.06964 56.17020 -2.40450090 0.7824624
## 7.461538 40.95979 57.63307 -2.01776385 0.7364841
## 7.538462 48.20590 61.24753 -1.45454166 0.8062134
## 7.615385 53.64323 63.78550 -1.05529014 0.8551419
## 7.692308 56.58070 65.59682 -0.76862968 0.8727794
## 7.769231 67.60942 67.30746 -0.52070225 1.0123177
## 7.846154 74.70404 67.61468 -0.43791041 1.1120518
## 7.923077 71.25872 67.03216 -0.45237096 1.0702755
## 8.000000 69.58286 66.17640 -0.49271042 1.0593629
## 8.076923 70.58492 64.13882 -0.64719685 1.1117202
## 8.153846 65.32781 62.32498 -0.76386145 1.0611862
## 8.230769 65.16236 61.70665 -0.74930805 1.0689829
## 8.307692 57.34155 61.13277 -0.73176536 0.9493477
## 8.384615 52.02739 62.09868 -0.56199729 0.8454694
## 8.461538 52.19721 64.13231 -0.30243468 0.8177552
## 8.538462 56.92977 65.78714 -0.10670893 0.8667692
## 8.615385 74.15359 80.97175 1.42242322 0.8999859
## 8.692308 87.95954 93.93800 2.57680591 0.9113580
## 8.769231 113.47519 106.85991 3.61131614 1.0271923
## 8.846154 131.69819 114.70116 4.03431023 1.1091730
## 8.923077 130.81603 119.06037 4.06679957 1.0624465
## 9.000000 132.10339 124.23479 4.17756220 1.0287436
## 9.076923 144.99744 129.16990 4.25331696 1.0867482
## 9.153846 129.04285 118.49843 2.76083798 1.0641895
## 9.230769 118.51983 108.96017 1.53092841 1.0726640
## 9.307692 98.83279 100.28850 0.51066808 0.9804921
## 9.384615 82.58717 93.38803 -0.23044522 0.8865318
## 9.461538 74.75604 88.91924 -0.65428035 0.8469504
## 9.538462 89.15481 84.85129 -0.99564715 1.0631939
## 9.615385 78.89087 77.97622 -1.58358896 1.0327026
## 9.692308 75.08164 75.48417 -1.67443543 1.0172322
## 9.769231 77.79770 74.16725 -1.63868432 1.0726491
## 9.846154 78.68173 72.36118 -1.65542229 1.1128051
## 9.923077 74.25720 70.79891 -1.64610760 1.0738133
## 10.000000 71.57923 70.59491 -1.50189625 1.0359836
## 10.076923 64.08066 70.79589 -1.33160839 0.9224980
## 10.153846 65.73906 72.48203 -1.02983352 0.9200425
## 10.230769 73.69492 78.57381 -0.31767218 0.9417142
## 10.307692 74.44729 83.69411 0.22612509 0.8871197
## 10.384615 76.12554 90.22214 0.85631527 0.8358238
## 10.461538 79.72209 97.41339 1.48980907 0.8060618
## 10.538462 102.66900 104.15787 2.01527517 0.9669960
## 10.615385 108.24446 104.50426 1.84838726 1.0177881
## 10.692308 105.49535 101.72606 1.38572796 1.0231163
## 10.769231 114.33222 105.28253 1.60280301 1.0696717
## 10.846154 124.27909 109.62782 1.87705117 1.1145620
## 10.923077 126.06475 112.60322 1.98688648 1.1001364
## 11.000000 121.94198 112.61495 1.78937012 1.0658862
## 11.076923 110.01637 112.03221 1.55215936 0.9685872
## 11.153846 115.29321 111.66067 1.35978914 1.0201093
## 11.230769 112.52290 109.80644 1.03838804 1.0151389
## 11.307692 103.27590 106.78176 0.63208100 0.9614767
## 11.384615 96.53501 106.58680 0.54937688 0.9010496
## 11.461538 94.17771 109.39243 0.77500236 0.8548598
## 11.538462 109.42880 114.19670 1.17792897 0.9484650
## 11.615385 112.21208 115.43182 1.18364762 0.9622402
## 11.692308 121.34390 114.74232 0.99633301 1.0484303
## 11.769231 123.38143 111.41907 0.56437476 1.1017828
## 11.846154 109.50938 97.95501 -0.83846856 1.1276079
## 11.923077 90.91231 86.33099 -1.91702399 1.0769819
## 12.000000 76.16771 76.07356 -2.75106420 1.0388040
## 12.076923 60.90119 67.53359 -3.32995502 0.9485629
## 12.153846 56.08126 60.66118 -3.68420007 0.9842792
## 12.230769 49.09995 54.60342 -3.92155669 0.9687874
## 12.307692 43.09108 49.29870 -4.05987287 0.9525242
## 12.384615 45.55268 52.65258 -3.31849696 0.9233510
## 12.461538 47.44530 55.90739 -2.66116677 0.8910548
## 12.538462 54.27567 59.25140 -2.06064932 0.9490289
## 12.615385 56.73827 61.74790 -1.60493449 0.9433901
## 12.692308 63.00812 64.22647 -1.19658325 0.9996546
## 12.769231 57.64217 64.24869 -1.07470359 0.9124352
## 12.846154 60.25560 63.86616 -1.00548594 0.9585580
## 12.923077 59.49353 64.45565 -0.84598802 0.9352907
## 13.000000 60.29157 65.36452 -0.67050308 0.9319498
## 13.076923 58.66271 66.94916 -0.44498820 0.8820907
## 13.153846 64.36005 69.16542 -0.17886387 0.9329362
## 13.230769 66.21270 70.73157 -0.00436219 0.9361702
## 13.307692 76.75569 69.10086 -0.16699718 1.1134687
## 13.384615 69.73669 66.58881 -0.40150206 1.0536264
## 13.461538 72.64777 72.46341 0.22610766 0.9994257
## 13.538462 84.00362 80.32434 0.98959076 1.0330777
## 13.615385 90.05434 87.12112 1.57030958 1.0153669
## 13.692308 97.69993 93.50657 2.05182338 1.0224107
## 13.769231 91.77266 97.08421 2.20440533 0.9243019
## 13.846154 104.27001 103.05954 2.58149725 0.9870218
## 13.923077 103.54011 104.75554 2.49294791 0.9654225
## 14.000000 100.69801 101.89537 1.95763599 0.9696205
## 14.076923 92.45178 98.73801 1.44613676 0.9228184
## 14.153846 93.99158 96.74864 1.10258536 0.9605560
## 14.230769 86.06417 93.89693 0.70715655 0.9097299
## 14.307692 99.04572 92.39153 0.48590039 1.0664132
## 14.384615 101.96025 87.69263 -0.03258003 1.1631326
## 14.461538 88.79266 80.49659 -0.74892580 1.1134202
## 14.538462 91.44819 82.44338 -0.47935392 1.1157113
## 14.615385 91.98467 85.45092 -0.13066505 1.0781107
## 14.692308 94.22894 90.10924 0.34823435 1.0416931
## 14.769231 91.99249 94.57982 0.76046830 0.9648858
## 14.846154 99.46217 100.52380 1.27881990 0.9770099
## 14.923077 95.41011 103.98025 1.49658285 0.9045598
## 15.000000 98.75527 106.95598 1.64449766 0.9093446
## 15.076923 88.64692 99.59284 0.74373323 0.8834956
## 15.153846 85.65815 93.82903 0.09297916 0.9120136
## 15.230769 76.91949 87.59356 -0.53986556 0.8835868
## 15.307692 81.19461 82.90708 -0.95452758 0.9907515
## 15.384615 79.23810 77.65387 -1.38439543 1.0389228
## 15.461538 81.81376 72.46975 -1.76436778 1.1571079
## 15.538462 76.32033 67.31525 -2.10338125 1.1703443
## 15.615385 69.18204 62.67922 -2.35664577 1.1468681
## 15.692308 62.15686 59.17475 -2.47142857 1.0961768
## 15.769231 55.86227 56.96662 -2.44509822 1.0245911
## 15.846154 53.77887 55.99289 -2.29796187 1.0015634
## 15.923077 49.32774 55.73596 -2.09385843 0.9195714
## 16.000000 43.93496 56.05024 -1.85304498 0.8106502
## 16.076923 45.48865 57.66726 -1.50603861 0.8099655
## 16.153846 49.16978 60.13950 -1.10821045 0.8329444
## 16.230769 50.85707 62.03995 -0.80734472 0.8305554
## 16.307692 58.15411 63.45832 -0.58477232 0.9249376
## 16.384615 57.85029 60.26708 -0.84541934 0.9735556
## 16.461538 62.83519 58.71286 -0.91629962 1.0871787
## 16.538462 62.22956 56.88867 -1.00708856 1.1135969
## 16.615385 60.57718 55.15788 -1.07945868 1.1201728
## 16.692308 59.20274 54.72526 -1.01477536 1.1022567
## 16.769231 56.91700 54.76237 -0.90958641 1.0568998
## 16.846154 57.18062 55.43912 -0.75095254 1.0455758
## 16.923077 53.74724 56.18388 -0.60138182 0.9669814
## 17.000000 50.13271 58.03399 -0.35623208 0.8691861
## 17.076923 52.54089 60.20134 -0.10387437 0.8742614
## 17.153846 54.35638 61.62083 0.04846240 0.8814172
## 17.230769 66.47512 75.38439 1.41997232 0.8655122
## 17.307692 75.91442 84.38944 2.17847997 0.8769348
## 17.384615 92.48582 93.52068 2.87375573 0.9594519
## 17.461538 110.62694 100.46221 3.28053332 1.0663583
## 17.538462 120.03439 106.00710 3.50696873 1.0960637
## 17.615385 128.04888 109.23408 3.47897047 1.1360608
## 17.692308 129.48623 111.47212 3.35487704 1.1276636
## 17.769231 117.72406 105.28759 2.40093602 1.0931904
## 17.846154 110.31040 100.54904 1.68698791 1.0789777
## 17.923077 99.57588 96.85864 1.14924936 1.0159986
## 18.000000 87.10636 94.60712 0.80917251 0.9129086
## 18.076923 86.12157 94.91102 0.75864485 0.9001972
## 18.153846 105.01359 96.90905 0.88258290 1.0738506
## 18.230769 92.68742 95.96389 0.69980896 0.9588648
## 18.307692 86.40491 90.38807 0.07224564 0.9551693
## 18.384615 85.89038 85.76902 -0.39688396 1.0060705
## 18.461538 87.96449 81.23914 -0.81018262 1.0936917
## 18.538462 81.64355 75.97350 -1.25572845 1.0926925
## 18.615385 78.42845 71.54331 -1.57317459 1.1208845
## 18.692308 65.24579 66.80684 -1.88950417 1.0050595
## 18.769231 61.75096 63.75407 -2.00583138 1.0000441
## 18.846154 61.46212 62.91799 -1.88885570 1.0070946
## 18.923077 59.35026 62.76440 -1.71532914 0.9721730
## 19.000000 56.04736 63.28113 -1.49212320 0.9070765
## 19.076923 58.91454 65.57097 -1.11392712 0.9140125
## 19.153846 70.47851 67.93303 -0.76632883 1.0493073
## 19.230769 58.40516 67.20891 -0.76210715 0.8789762
## 19.307692 61.21203 69.08507 -0.49828109 0.8924755
## 19.384615 79.08047 82.79176 0.92221654 0.9446507
## 19.461538 96.94843 93.45716 1.89653510 1.0167244
## 19.538462 105.99041 100.08489 2.36965384 1.0345116
## 19.615385 112.59799 103.98369 2.52256829 1.0571960
## 19.692308 107.34520 106.65798 2.53774069 0.9830532
## 19.769231 114.40398 109.34928 2.55309685 1.0223552
## 19.846154 114.52312 107.91081 2.15394054 1.0405068
## 19.923077 101.86054 99.43087 1.09055252 1.0133217
## 20.000000 89.77698 92.29886 0.26829549 0.9698579
## 20.076923 83.66407 86.57102 -0.33131775 0.9701341
## 20.153846 84.71991 81.48488 -0.80679993 1.0500983
## 20.230769 69.31622 76.61752 -1.21285550 0.9192564
## 20.307692 77.21588 73.18195 -1.43512697 1.0762271
## 20.384615 83.69882 79.41884 -0.66792601 1.0628298
## 20.461538 89.29675 83.32383 -0.21063391 1.0743992
## 20.538462 87.77363 83.54195 -0.16775883 1.0527674
## 20.615385 90.95418 85.81089 0.07591084 1.0590007
## 20.692308 88.25807 89.21934 0.40916502 0.9847099
## 20.769231 92.95036 94.26783 0.87309718 0.9769756
## 20.846154 89.66547 97.73047 1.13205237 0.9069713
## 20.923077 92.14847 100.52400 1.29819933 0.9049939
## 21.000000 91.06223 101.17060 1.23303934 0.8892480
## 21.076923 89.62595 98.49871 0.84254689 0.9022027
## 21.153846 94.86136 95.96597 0.50501845 0.9833149
## 21.230769 82.00039 92.47200 0.10511885 0.8857523
## 21.307692 110.32555 91.83190 0.03059704 1.2009858
## 21.384615 97.63982 86.67916 -0.48773628 1.1328252
## 21.461538 90.16142 84.10111 -0.69676797 1.0810160
## 21.538462 89.11686 82.63443 -0.77375894 1.0886408
## 21.615385 89.53742 81.71060 -0.78876600 1.1064680
## 21.692308 83.22837 80.62586 -0.81836319 1.0428640
## 21.769231 80.29864 80.41575 -0.75753774 1.0080397
## 21.846154 73.06098 79.73785 -0.74957465 0.9249599
## 21.923077 70.73654 79.47240 -0.70116139 0.8979995
## 22.000000 65.73989 78.36222 -0.74206422 0.8469436
## 22.076923 67.88228 79.14566 -0.58951303 0.8641243
## 22.153846 73.73578 79.57862 -0.48726574 0.9322862
## 22.230769 68.62788 78.76189 -0.52021222 0.8771268
## 22.307692 88.11839 79.44381 -0.39999874 1.1148044
## 22.384615 81.67868 75.11158 -0.79322273 1.0990378
## 22.461538 74.93882 71.21042 -1.10401606 1.0689297
## 22.538462 82.90342 76.76001 -0.43865553 1.0862415
## 22.615385 88.74498 80.57392 -0.01339873 1.1015938
## 22.692308 87.69494 83.09413 0.23996187 1.0523297
## 22.769231 87.32300 86.01482 0.50803493 1.0092477
## 22.846154 83.84605 89.21338 0.77708688 0.9317215
## 22.923077 81.95823 90.96800 0.87484029 0.8923747
## 23.000000 82.01817 93.60034 1.05059098 0.8665331xhat2 <- winter2$fitted[,2]
winter2.opt<- HoltWinters(training.ts, alpha= NULL, beta = NULL, gamma = NULL, seasonal = "multiplicative")
winter2.opt$fitted## Time Series:
## Start = c(2, 1)
## End = c(23, 1)
## Frequency = 13
## xhat level trend season
## 2.000000 61.72342 78.63702 2.4053931 0.7616187
## 2.076923 110.41830 99.80044 2.5418082 1.0789121
## 2.153846 116.82914 103.48030 2.5500845 1.1018459
## 2.230769 118.04281 105.03907 2.5428753 1.0972362
## 2.307692 122.86637 107.46628 2.5420342 1.1168825
## 2.384615 122.58657 109.23943 2.5364425 1.0967177
## 2.461538 103.01198 111.05750 2.5312183 0.9068857
## 2.538462 133.48469 122.59199 2.5966934 1.0662680
## 2.615385 115.18472 103.94919 2.4422321 1.0826504
## 2.692308 93.68209 101.56118 2.4071048 0.9010641
## 2.769231 126.30171 121.93522 2.5377669 1.0146917
## 2.846154 109.70126 113.87450 2.4606908 0.9429757
## 2.923077 101.23704 119.16117 2.4812424 0.8322511
## 3.000000 99.91631 125.66039 2.5104625 0.7795557
## 3.076923 141.91204 128.83622 2.5153014 1.0803989
## 3.153846 105.82817 93.91691 2.2430632 1.1005429
## 3.230769 50.82423 44.45940 1.8670779 1.0970883
## 3.307692 46.74646 40.06978 1.8215770 1.1158975
## 3.384615 44.52079 38.82821 1.7993006 1.0958288
## 3.461538 39.11383 40.93502 1.8015370 0.9152311
## 3.538462 51.03548 47.28664 1.8346268 1.0389691
## 3.615385 47.85185 42.67602 1.7877546 1.0761986
## 3.692308 39.58131 41.36575 1.7652247 0.9177004
## 3.769231 65.29105 63.19382 1.9111290 1.0028584
## 3.846154 61.61714 63.25204 1.8976539 0.9457779
## 3.923077 61.38784 71.52286 1.9440019 0.8355855
## 4.000000 64.01608 80.07353 1.9920480 0.7800601
## 4.076923 92.15026 87.74330 2.0333384 1.0264393
## 4.153846 63.89393 66.09785 1.8611377 0.9401837
## 4.230769 72.34142 65.41272 1.8426203 1.0756236
## 4.307692 75.84623 66.80803 1.8393673 1.1048669
## 4.384615 73.62968 65.31256 1.8151152 1.0968603
## 4.461538 63.15662 66.37447 1.8096376 0.9262659
## 4.538462 79.66212 76.28461 1.8685474 1.0193078
## 4.615385 77.48243 70.86291 1.8155301 1.0660993
## 4.692308 64.44707 65.77459 1.7653228 0.9542072
## 4.769231 71.64107 69.91745 1.7826131 0.9991773
## 4.846154 104.67983 107.41671 2.0423575 0.9563376
## 4.923077 102.20794 118.95589 2.1114218 0.8442241
## 5.000000 113.03476 141.47987 2.2598694 0.7863849
## 5.076923 159.94439 160.76416 2.3836771 0.9803648
## 5.153846 130.65804 137.45508 2.1968301 0.9355979
## 5.230769 154.03332 141.11650 2.2074811 1.0747212
## 5.307692 140.25839 125.68417 2.0791981 1.0977981
## 5.384615 78.57741 70.08079 1.6597093 1.0953006
## 5.461538 63.92426 66.48517 1.6214907 0.9385903
## 5.538462 77.71550 75.56336 1.6757186 1.0061681
## 5.615385 76.83271 71.39625 1.6332274 1.0520781
## 5.692308 68.42243 69.79213 1.6096842 0.9582729
## 5.769231 75.58015 71.01008 1.6068354 1.0408064
## 5.846154 64.81475 65.54724 1.5554221 0.9659043
## 5.923077 96.35454 110.23802 1.8691181 0.8594862
## 6.000000 111.76842 138.20925 2.0589421 0.7968194
## 6.076923 153.72170 158.37043 2.1905881 0.9574037
## 6.153846 134.05593 141.04891 2.0486891 0.9368146
## 6.230769 151.77974 141.71653 2.0386454 1.0558211
## 6.307692 125.11511 125.17136 1.9034971 0.9845780
## 6.384615 128.81376 116.95243 1.8298832 1.0844523
## 6.461538 58.90931 60.59032 1.4066899 0.9501959
## 6.538462 55.90835 54.78704 1.3542564 0.9958506
## 6.615385 62.48078 58.36473 1.3704260 1.0459632
## 6.692308 58.94086 60.17629 1.3736341 0.9576105
## 6.769231 71.47702 68.19352 1.4219487 1.0267404
## 6.846154 70.32143 67.99090 1.4101343 1.0132620
## 6.923077 60.73033 67.62820 1.3972416 0.8798254
## 7.000000 58.37300 70.81286 1.4102403 0.8082317
## 7.076923 74.61690 77.86024 1.4512356 0.9408084
## 7.153846 64.86955 67.96078 1.3686893 0.9356707
## 7.230769 70.80800 66.98402 1.3516323 1.0361795
## 7.307692 61.72014 62.06814 1.3060527 0.9739002
## 7.384615 60.54411 62.16961 1.2972925 0.9539478
## 7.461538 57.59151 60.35169 1.2746376 0.9345276
## 7.538462 66.87657 65.53314 1.3030493 1.0006043
## 7.615385 68.92351 64.54790 1.2864080 1.0469240
## 7.692308 62.55440 63.26788 1.2677441 0.9693003
## 7.769231 71.94133 68.97805 1.3000510 1.0236664
## 7.846154 72.16438 70.15541 1.2991588 1.0099338
## 7.923077 65.57074 72.98176 1.3102650 0.8826081
## 8.000000 64.57762 77.84545 1.3361068 0.8155639
## 8.076923 70.95393 75.71917 1.3109271 0.9211195
## 8.153846 66.77518 70.41777 1.2628398 0.9315655
## 8.230769 73.96246 71.03653 1.2581559 1.0230691
## 8.307692 64.77593 65.46525 1.2084898 0.9715358
## 8.384615 64.88223 67.24457 1.2126410 0.9477779
## 8.461538 63.92109 66.69240 1.1998067 0.9415084
## 8.538462 65.30253 64.38003 1.1742649 0.9961595
## 8.615385 123.69362 117.20329 1.5498751 1.0416027
## 8.692308 119.57143 120.80619 1.5648054 0.9771224
## 8.769231 141.39985 136.49356 1.6675098 1.0234421
## 8.846154 136.09720 132.77776 1.6283605 1.0125818
## 8.923077 118.71389 132.12680 1.6117844 0.8876563
## 9.000000 124.46170 151.74485 1.7427325 0.8108911
## 9.076923 152.89730 166.13233 1.8346897 0.9102817
## 9.153846 76.56900 81.08453 1.2028487 0.9305071
## 9.230769 71.70309 69.90176 1.1127760 1.0096960
## 9.307692 63.33476 64.05889 1.0621920 0.9725692
## 9.384615 61.79332 64.35835 1.0566452 0.9446353
## 9.461538 63.93384 67.30275 1.0703736 0.9350726
## 9.538462 69.34005 64.91969 1.0452590 1.0511650
## 9.615385 59.77805 56.29358 0.9749252 1.0438207
## 9.692308 69.88985 69.54655 1.0642157 0.9897903
## 9.769231 79.43779 76.90460 1.1099867 1.0182428
## 9.846154 77.69282 75.79978 1.0938798 1.0103930
## 9.923077 71.45825 78.21924 1.1035199 0.9008543
## 10.000000 74.41367 89.72171 1.1791448 0.8186245
## 10.076923 77.72358 97.39927 1.2264037 0.7880664
## 10.153846 91.13591 98.93737 1.2286705 0.9098484
## 10.230769 108.20048 107.35857 1.2809771 0.9959586
## 10.307692 98.97826 100.69802 1.2232235 0.9711249
## 10.384615 100.76611 105.05239 1.2459943 0.9479553
## 10.461538 101.49994 108.01754 1.2584967 0.9288399
## 10.538462 113.09415 108.70205 1.2543224 1.0285365
## 10.615385 101.47994 93.97751 1.1381183 1.0669113
## 10.692308 82.17086 81.13930 1.0364774 0.9999402
## 10.769231 115.68724 112.77309 1.2589922 1.0145148
## 10.846154 128.62989 125.69322 1.3437962 1.0125386
## 10.923077 118.76215 128.59055 1.3550941 0.9139371
## 11.000000 105.50471 126.48205 1.3299055 0.8254682
## 11.076923 105.05711 131.89775 1.3596189 0.7883775
## 11.153846 118.97041 128.34607 1.3239022 0.9174862
## 11.230769 109.86610 110.23035 1.1825302 0.9861167
## 11.307692 93.85622 95.22251 1.0647879 0.9747518
## 11.384615 97.21776 101.25023 1.1008802 0.9498457
## 11.461538 104.32124 111.22244 1.1653957 0.9282253
## 11.538462 121.17685 119.16480 1.2146803 1.0066238
## 11.615385 116.27684 110.24768 1.1409981 1.0438839
## 11.692308 104.75463 100.25645 1.0600405 1.0339346
## 11.769231 99.69029 96.11264 1.0221962 1.0263083
## 11.846154 52.14079 50.73254 0.6847419 1.0140714
## 11.923077 44.68833 48.40205 0.6628140 0.9108012
## 12.000000 42.27616 50.34463 0.6721209 0.8286722
## 12.076923 43.79568 55.11735 0.7019420 0.7845974
## 12.153846 51.02304 56.16398 0.7044487 0.8972121
## 12.230769 49.18704 50.30858 0.6567431 0.9651079
## 12.307692 44.45419 44.71596 0.6112955 0.9807385
## 12.384615 73.79298 76.08569 0.8349819 0.9593387
## 12.461538 74.52694 78.87244 0.8491759 0.9348398
## 12.538462 79.85905 79.41083 0.8469158 0.9950323
## 12.615385 79.81985 76.72197 0.8212023 1.0293602
## 12.692308 77.06286 74.24548 0.7972203 1.0269201
## 12.769231 62.60772 68.15200 0.7471086 0.9086870
## 12.846154 68.28326 67.13124 0.7342521 1.0061558
## 12.923077 62.36820 67.52699 0.7317903 0.9137022
## 13.000000 62.07230 73.44440 0.7695020 0.8363972
## 13.076923 66.21111 83.48686 0.8369384 0.7852008
## 13.153846 79.37329 89.06457 0.8714150 0.8825532
## 13.230769 79.49418 83.01521 0.8210846 0.9482072
## 13.307692 66.90822 64.25446 0.6786784 1.0304171
## 13.384615 60.45721 62.16631 0.6585570 0.9623134
## 13.461538 96.11921 101.92644 0.9429178 0.9343814
## 13.538462 116.61322 116.83164 1.0444566 0.9892864
## 13.615385 119.31047 115.52871 1.0273856 1.0236314
## 13.692308 114.95405 112.37995 0.9970151 1.0139101
## 13.769231 96.02801 105.09087 0.9367556 0.9056886
## 13.846154 120.64533 118.95183 1.0307451 1.0055238
## 13.923077 94.52535 101.64848 0.8974130 0.9217858
## 14.000000 73.86815 86.32536 0.7794513 0.8480376
## 14.076923 71.16224 89.23396 0.7949353 0.7904378
## 14.153846 84.69741 96.14231 0.8393942 0.8733340
## 14.230769 80.14814 87.11421 0.7676342 0.9119989
## 14.307692 86.66474 83.83990 0.7382397 1.0246707
## 14.384615 72.59860 71.33971 0.6419651 1.0085705
## 14.461538 58.52274 61.14539 0.5631597 0.9483732
## 14.538462 103.61677 104.13455 0.8716970 0.9867677
## 14.615385 114.60671 111.56528 0.9193967 1.0188650
## 14.692308 116.66193 115.26986 0.9396515 1.0038931
## 14.769231 106.75774 115.35801 0.9334591 0.9180187
## 14.846154 125.02343 126.20607 1.0055617 0.9827987
## 14.923077 103.17224 113.71780 0.9074296 0.9000832
## 15.000000 97.36198 113.56661 0.8997309 0.8505730
## 15.076923 58.74524 73.13327 0.5991419 0.7967356
## 15.153846 65.11185 75.02039 0.6085085 0.8609388
## 15.230769 61.27473 67.04950 0.5461160 0.9064897
## 15.307692 65.55593 64.97352 0.5270472 1.0008451
## 15.384615 60.12624 60.47867 0.4905261 0.9861741
## 15.461538 60.69568 60.40488 0.4864222 0.9967873
## 15.538462 62.35454 62.23243 0.4961753 0.9940368
## 15.615385 63.82615 61.96466 0.4906197 1.0219497
## 15.692308 62.05535 61.38906 0.4828657 1.0029646
## 15.769231 59.08433 63.24052 0.4928187 0.9270552
## 15.846154 66.21729 67.87023 0.5229036 0.9681862
## 15.923077 60.11475 66.35800 0.5081034 0.8990319
## 16.000000 53.47285 67.14805 0.5101538 0.7903379
## 16.076923 58.52290 72.74851 0.5471723 0.7984496
## 16.153846 65.47718 76.72040 0.5720781 0.8471353
## 16.230769 66.62689 73.33018 0.5432629 0.9019058
## 16.307692 67.28892 67.44248 0.4964946 0.9904318
## 16.384615 48.54743 48.92751 0.3582363 0.9850197
## 16.461538 54.93373 54.56573 0.3966343 0.9994789
## 16.538462 57.58049 57.59972 0.4158141 0.9925012
## 16.615385 60.15369 58.57022 0.4198480 1.0197257
## 16.692308 63.31966 62.51627 0.4454918 1.0056843
## 16.769231 60.62806 64.44656 0.4562898 0.9341356
## 16.846154 67.35433 69.34730 0.4886115 0.9644655
## 16.923077 61.29180 67.66665 0.4728358 0.8995049
## 17.000000 58.12037 72.39570 0.5037885 0.7972672
## 17.076923 61.62263 76.22064 0.5279412 0.8029155
## 17.153846 62.74798 74.06726 0.5084416 0.8413998
## 17.230769 116.25598 129.55085 0.9082408 0.8911298
## 17.307692 107.72812 113.55028 0.7852738 0.9422102
## 17.384615 113.51327 113.08293 0.7761643 0.9969627
## 17.461538 113.86711 112.51023 0.7663548 1.0052132
## 17.538462 121.13779 121.08523 0.8231421 0.9936790
## 17.615385 123.59686 119.54939 0.8059868 1.0269326
## 17.692308 119.91888 118.10819 0.7896444 1.0085875
## 17.769231 75.74866 79.93726 0.5063090 0.9416372
## 17.846154 80.45472 83.22884 0.5265645 0.9605914
## 17.923077 77.08424 84.53738 0.5322513 0.9061311
## 18.000000 72.75041 90.18477 0.5694504 0.8016201
## 18.076923 83.74677 104.11202 0.6665932 0.7992735
## 18.153846 101.33180 113.62121 0.7308997 0.8861385
## 18.230769 95.22379 108.20292 0.6861806 0.8745025
## 18.307692 71.68038 75.73749 0.4450901 0.9409024
## 18.384615 69.00669 68.92872 0.3923374 0.9954650
## 18.461538 67.08337 65.83356 0.3669750 1.0133358
## 18.538462 62.93322 63.14577 0.3447597 0.9912221
## 18.615385 66.66274 64.71588 0.3536708 1.0244844
## 18.692308 57.02169 59.89739 0.3160571 0.9469926
## 18.769231 59.36153 62.44524 0.3322874 0.9455857
## 18.846154 68.19308 70.51995 0.3885931 0.9617047
## 18.923077 66.76833 72.76301 0.4020795 0.9125709
## 19.000000 62.66264 76.50681 0.4263817 0.8145073
## 19.076923 71.78039 88.42975 0.5099889 0.8070677
## 19.153846 81.64699 92.26459 0.5341684 0.8798284
## 19.230769 67.93801 81.74200 0.4537596 0.8265391
## 19.307692 78.81309 84.41270 0.4698820 0.9284954
## 19.384615 128.05033 128.70465 0.7885720 0.9888574
## 19.461538 128.52911 126.84187 0.7692904 1.0071934
## 19.538462 120.90717 120.96819 0.7209803 0.9935738
## 19.615385 117.65304 115.42197 0.6754029 1.0133997
## 19.692308 107.50476 112.36788 0.6482807 0.9512335
## 19.769231 109.49498 113.57224 0.6523247 0.9585940
## 19.846154 96.87124 99.86016 0.5478616 0.9647759
## 19.923077 60.56365 65.70920 0.2955192 0.9175654
## 20.000000 54.58807 65.65253 0.2929579 0.8277757
## 20.076923 59.05839 72.50689 0.3406748 0.8107119
## 20.153846 64.77389 74.53739 0.3529638 0.8649164
## 20.230769 61.21711 73.47875 0.3426982 0.8292591
## 20.307692 69.58655 71.55271 0.3261991 0.9681080
## 20.384615 115.81791 116.77781 0.6527202 0.9862674
## 20.461538 111.01709 110.38641 0.6014927 1.0002630
## 20.538462 92.97116 93.73742 0.4760410 0.9868139
## 20.615385 102.54274 101.08343 0.5260019 1.0091852
## 20.692308 102.32798 106.94323 0.5647912 0.9518171
## 20.769231 109.49604 115.69791 0.6243510 0.9413163
## 20.846154 102.02398 112.64419 0.5976028 0.9009392
## 20.923077 99.99014 108.48361 0.5629996 0.9169486
## 21.000000 82.94299 98.58946 0.4869514 0.8371618
## 21.076923 72.91161 89.26494 0.4155988 0.8130148
## 21.153846 79.15197 91.30740 0.4274299 0.8628344
## 21.230769 72.73645 87.66461 0.3978298 0.8259645
## 21.307692 96.32297 94.47860 0.4444904 1.0147475
## 21.384615 78.52814 79.92789 0.3354399 0.9783813
## 21.461538 85.26220 86.86826 0.3834734 0.9771977
## 21.538462 87.88869 87.92268 0.3883527 0.9952175
## 21.615385 90.44919 88.67831 0.3910236 1.0154920
## 21.692308 83.74743 86.83855 0.3748006 0.9602594
## 21.769231 84.42882 89.66810 0.3926525 0.9374651
## 21.846154 77.85512 86.52610 0.3669472 0.8959878
## 21.923077 76.64001 84.35886 0.3485176 0.9047620
## 22.000000 63.90262 77.10518 0.2932317 0.8256321
## 22.076923 70.63541 86.32912 0.3581791 0.8148299
## 22.153846 76.23750 88.50270 0.3713813 0.8578148
## 22.230769 70.83139 84.69145 0.3409637 0.8329929
## 22.307692 87.86332 88.30605 0.3647708 0.9908932
## 22.384615 68.61199 69.24277 0.2234829 0.9877025
## 22.461538 64.60938 65.85660 0.1972322 0.9781321
## 22.538462 107.78496 107.74631 0.5004350 0.9957340
## 22.615385 108.45223 106.65374 0.4888502 1.0122233
## 22.692308 98.80731 102.09260 0.4521247 0.9635533
## 22.769231 98.65464 105.30478 0.4721969 0.9326665
## 22.846154 96.76317 107.91636 0.4877553 0.8926152
## 22.923077 89.80998 100.07809 0.4272054 0.8935845
## 23.000000 84.40495 100.49537 0.4271332 0.8363342xhat2.opt <- winter2.opt$fitted[,2]Peramalan
#Forecast
forecast2 <- predict(winter2, n.ahead = 49)
forecast2.opt <- predict(winter2.opt, n.ahead = 49)Plot Deret Waktu
#Plot time series
plot(training.ts,main="Winter 0.2;0.1;0.1",type="l",col="black",
xlim=c(1,25),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 Latih
#Akurasi data training
SSE2<-winter2$SSE
MSE2<-winter2$SSE/length(training.ts)
RMSE2<-sqrt(MSE2)
akurasi1 <- matrix(c(SSE2,MSE2,RMSE2))
row.names(akurasi1)<- c("SSE2", "MSE2", "RMSE2")
colnames(akurasi1) <- c("Akurasi lamda=0.2")
akurasi1## Akurasi lamda=0.2
## SSE2 169898.46357
## MSE2 591.98071
## RMSE2 24.33065SSE2.opt<-winter2.opt$SSE
MSE2.opt<-winter2.opt$SSE/length(training.ts)
RMSE2.opt<-sqrt(MSE2.opt)
akurasi1.opt <- matrix(c(SSE2.opt,MSE2.opt,RMSE2.opt))
row.names(akurasi1.opt)<- c("SSE2.opt", "MSE2.opt", "RMSE2.opt")
colnames(akurasi1.opt) <- c("Akurasi")
akurasi1.opt## Akurasi
## SSE2.opt 74942.44579
## MSE2.opt 261.12350
## RMSE2.opt 16.15932akurasi2.train = data.frame(Model_Winter = c("Winter 1","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 1 169898.46 591.9807 24.33065
## 2 winter2 optimal 74942.45 261.1235 16.15932Akurasi Data Uji
#Akurasi Data Testing
forecast2<-data.frame(forecast2)
testing.ts<-data.frame(testing.ts)
selisih2<-testing.ts
SSEtesting2<-sum(selisih2^2)
MSEtesting2<-SSEtesting2/length(testing.ts)
forecast2.opt<-data.frame(forecast2.opt)
selisih2.opt<-testing.ts
SSEtesting2.opt<-sum(selisih2.opt^2)
MSEtesting2.opt<-SSEtesting2.opt/length(testing.ts)Berdasarkan perhitungan di atas, metode yang paling baik digunakan adalah SES karena menghasilkan SSE, MSE, dan MAPE yang paling kecil jika dibandingkan dengan dua metode lainnya. Maka, pola yang terbentuk dari data ini adalah pola stasioner.