Praktikum Analisis Deret Waktu (ADW) Pertemuan ke-2
Akbar Rizki & Abdul Aziz N
Single Moving Average (SMA)
Pada Praktikum Analisis Deret Waktu (ADW) kali ini kita akan membahas mengenai Rataan Bergerak Sederhana atau Single Moving Average. Data contoh yang digunakan adalah data The sales of mature pharmaceutical product yang diambil dari Buku Montgomery 1 (Appendix B, Table B.2, halaman 587). Data tersebut akan dianalisis menggunakan SMA dengan n=4. Berikut adalah tahapan analisisnya:
Tahap Persiapan
Pada tahap persiapan ini yang perlu dilakukan adalah :
- Melakukan Instalasi Packages (Ada 2 package R yang akan digunakan dalam Praktikum kali ini, yaitu : forecast dan TTR.)
install.packages("forecast")## Installing package into '/home/rstudio-user/R/x86_64-pc-linux-gnu-library/4.0'
## (as 'lib' is unspecified)install.packages("TTR")## Installing package into '/home/rstudio-user/R/x86_64-pc-linux-gnu-library/4.0'
## (as 'lib' is unspecified)- Melakukan Load Packages yang diperlukan.
library("forecast")## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary("TTR")
library("graphics")- Memanggil data yang diperlukan
data1<-read.csv("https://raw.githubusercontent.com/akbarrizki/ADW/master/datap2.csv",header=TRUE)Tahap analisis data
Dalam sub bab ini, kita akan mulai melakukan beberapa hal :
- Membuat Data ke Bentuk Time Series
data.ts<-ts(data1)
data.ts## Time Series:
## Start = 1
## End = 120
## Frequency = 1
## Sales..in.thousands.
## [1,] 10618.1
## [2,] 10537.9
## [3,] 10209.3
## [4,] 10553.0
## [5,] 9934.9
## [6,] 10534.5
## [7,] 10196.5
## [8,] 10511.8
## [9,] 10089.6
## [10,] 10371.2
## [11,] 10239.4
## [12,] 10472.4
## [13,] 10827.2
## [14,] 10640.8
## [15,] 10517.8
## [16,] 10154.2
## [17,] 9969.2
## [18,] 10260.4
## [19,] 10737.0
## [20,] 10430.0
## [21,] 10689.0
## [22,] 10430.4
## [23,] 10002.4
## [24,] 10135.7
## [25,] 10096.2
## [26,] 10288.7
## [27,] 10289.1
## [28,] 10589.9
## [29,] 10551.9
## [30,] 10208.3
## [31,] 10334.5
## [32,] 10480.1
## [33,] 10387.6
## [34,] 10202.6
## [35,] 10219.3
## [36,] 10382.7
## [37,] 10820.5
## [38,] 10358.7
## [39,] 10494.6
## [40,] 10497.6
## [41,] 10431.5
## [42,] 10447.8
## [43,] 10684.4
## [44,] 10176.5
## [45,] 10616.0
## [46,] 10627.7
## [47,] 10684.0
## [48,] 10246.7
## [49,] 10265.0
## [50,] 10090.4
## [51,] 9881.1
## [52,] 10449.7
## [53,] 10276.3
## [54,] 10175.2
## [55,] 10212.5
## [56,] 10395.5
## [57,] 10545.9
## [58,] 10635.7
## [59,] 10265.2
## [60,] 10551.6
## [61,] 10538.2
## [62,] 10286.2
## [63,] 10171.3
## [64,] 10393.1
## [65,] 10162.3
## [66,] 10164.5
## [67,] 10327.0
## [68,] 10365.1
## [69,] 10755.9
## [70,] 10463.6
## [71,] 10080.5
## [72,] 10479.6
## [73,] 9980.9
## [74,] 10039.2
## [75,] 10246.1
## [76,] 10368.0
## [77,] 10446.3
## [78,] 10535.3
## [79,] 10786.9
## [80,] 9975.8
## [81,] 10160.9
## [82,] 10422.1
## [83,] 10757.2
## [84,] 10463.8
## [85,] 10307.0
## [86,] 10134.7
## [87,] 10207.7
## [88,] 10488.0
## [89,] 10262.3
## [90,] 10785.9
## [91,] 10375.4
## [92,] 10123.4
## [93,] 10462.7
## [94,] 10205.5
## [95,] 10522.7
## [96,] 10253.2
## [97,] 10428.7
## [98,] 10615.8
## [99,] 10417.3
## [100,] 10445.4
## [101,] 10690.6
## [102,] 10271.8
## [103,] 10524.8
## [104,] 9815.0
## [105,] 10398.5
## [106,] 10553.1
## [107,] 10655.8
## [108,] 10199.1
## [109,] 10416.6
## [110,] 10391.3
## [111,] 10210.1
## [112,] 10352.5
## [113,] 10423.8
## [114,] 10519.3
## [115,] 10596.7
## [116,] 10650.0
## [117,] 10741.6
## [118,] 10246.0
## [119,] 10354.4
## [120,] 10155.4- Membuat Plot Time Series dari data.ts
ts.plot(data.ts, xlab="Time Period ", ylab="Sales", main= "Time Series Plot Data Sales")
points(data.ts)
- Melakukan Proses Pemulusan SMA dengan n=4
data.sma<-SMA(data.ts, n=4)
data.sma## Time Series:
## Start = 1
## End = 120
## Frequency = 1
## [1] NA NA NA 10479.58 10308.78 10307.93 10304.73 10294.43
## [9] 10333.10 10292.28 10303.00 10293.15 10477.55 10544.95 10614.55 10535.00
## [17] 10320.50 10225.40 10280.20 10349.15 10529.10 10571.60 10387.95 10314.38
## [25] 10166.18 10130.75 10202.43 10315.98 10429.90 10409.80 10421.15 10393.70
## [33] 10352.63 10351.20 10322.40 10298.05 10406.28 10445.30 10514.13 10542.85
## [41] 10445.60 10467.88 10515.33 10435.05 10481.18 10526.15 10526.05 10543.60
## [49] 10455.85 10321.53 10120.80 10171.55 10174.38 10195.58 10278.43 10264.88
## [57] 10332.28 10447.40 10460.58 10499.60 10497.68 10410.30 10386.83 10347.20
## [65] 10253.23 10222.80 10261.73 10254.73 10403.13 10477.90 10416.28 10444.90
## [73] 10251.15 10145.05 10186.45 10158.55 10274.90 10398.93 10534.13 10436.08
## [81] 10364.73 10336.43 10329.00 10451.00 10487.53 10415.68 10278.30 10284.35
## [89] 10273.18 10435.98 10477.90 10386.75 10436.85 10291.75 10328.58 10361.03
## [97] 10352.53 10455.10 10428.75 10476.80 10542.28 10456.28 10483.15 10325.55
## [105] 10252.53 10322.85 10355.60 10451.63 10456.15 10415.70 10304.28 10342.63
## [113] 10344.43 10376.43 10473.08 10547.45 10626.90 10558.58 10498.00 10374.35data.ramal<-c(NA,data.sma)
data.ramal## [1] NA NA NA NA 10479.58 10308.78 10307.93 10304.73
## [9] 10294.43 10333.10 10292.28 10303.00 10293.15 10477.55 10544.95 10614.55
## [17] 10535.00 10320.50 10225.40 10280.20 10349.15 10529.10 10571.60 10387.95
## [25] 10314.38 10166.18 10130.75 10202.43 10315.98 10429.90 10409.80 10421.15
## [33] 10393.70 10352.63 10351.20 10322.40 10298.05 10406.28 10445.30 10514.13
## [41] 10542.85 10445.60 10467.88 10515.33 10435.05 10481.18 10526.15 10526.05
## [49] 10543.60 10455.85 10321.53 10120.80 10171.55 10174.38 10195.58 10278.43
## [57] 10264.88 10332.28 10447.40 10460.58 10499.60 10497.68 10410.30 10386.83
## [65] 10347.20 10253.23 10222.80 10261.73 10254.73 10403.13 10477.90 10416.28
## [73] 10444.90 10251.15 10145.05 10186.45 10158.55 10274.90 10398.93 10534.13
## [81] 10436.08 10364.73 10336.43 10329.00 10451.00 10487.53 10415.68 10278.30
## [89] 10284.35 10273.18 10435.98 10477.90 10386.75 10436.85 10291.75 10328.58
## [97] 10361.03 10352.53 10455.10 10428.75 10476.80 10542.28 10456.28 10483.15
## [105] 10325.55 10252.53 10322.85 10355.60 10451.63 10456.15 10415.70 10304.28
## [113] 10342.63 10344.43 10376.43 10473.08 10547.45 10626.90 10558.58 10498.00
## [121] 10374.35data<-cbind(aktual=c(data.ts,rep(NA,5)),pemulusan=c(data.sma,rep(NA,5)),ramalan=c(data.ramal,rep(data.ramal[length(data.ramal)],4)))
data## aktual pemulusan ramalan
## [1,] 10618.1 NA NA
## [2,] 10537.9 NA NA
## [3,] 10209.3 NA NA
## [4,] 10553.0 10479.58 NA
## [5,] 9934.9 10308.78 10479.58
## [6,] 10534.5 10307.93 10308.78
## [7,] 10196.5 10304.73 10307.93
## [8,] 10511.8 10294.43 10304.73
## [9,] 10089.6 10333.10 10294.43
## [10,] 10371.2 10292.28 10333.10
## [11,] 10239.4 10303.00 10292.28
## [12,] 10472.4 10293.15 10303.00
## [13,] 10827.2 10477.55 10293.15
## [14,] 10640.8 10544.95 10477.55
## [15,] 10517.8 10614.55 10544.95
## [16,] 10154.2 10535.00 10614.55
## [17,] 9969.2 10320.50 10535.00
## [18,] 10260.4 10225.40 10320.50
## [19,] 10737.0 10280.20 10225.40
## [20,] 10430.0 10349.15 10280.20
## [21,] 10689.0 10529.10 10349.15
## [22,] 10430.4 10571.60 10529.10
## [23,] 10002.4 10387.95 10571.60
## [24,] 10135.7 10314.38 10387.95
## [25,] 10096.2 10166.18 10314.38
## [26,] 10288.7 10130.75 10166.18
## [27,] 10289.1 10202.43 10130.75
## [28,] 10589.9 10315.98 10202.43
## [29,] 10551.9 10429.90 10315.98
## [30,] 10208.3 10409.80 10429.90
## [31,] 10334.5 10421.15 10409.80
## [32,] 10480.1 10393.70 10421.15
## [33,] 10387.6 10352.63 10393.70
## [34,] 10202.6 10351.20 10352.63
## [35,] 10219.3 10322.40 10351.20
## [36,] 10382.7 10298.05 10322.40
## [37,] 10820.5 10406.28 10298.05
## [38,] 10358.7 10445.30 10406.28
## [39,] 10494.6 10514.13 10445.30
## [40,] 10497.6 10542.85 10514.13
## [41,] 10431.5 10445.60 10542.85
## [42,] 10447.8 10467.88 10445.60
## [43,] 10684.4 10515.33 10467.88
## [44,] 10176.5 10435.05 10515.33
## [45,] 10616.0 10481.18 10435.05
## [46,] 10627.7 10526.15 10481.18
## [47,] 10684.0 10526.05 10526.15
## [48,] 10246.7 10543.60 10526.05
## [49,] 10265.0 10455.85 10543.60
## [50,] 10090.4 10321.53 10455.85
## [51,] 9881.1 10120.80 10321.53
## [52,] 10449.7 10171.55 10120.80
## [53,] 10276.3 10174.38 10171.55
## [54,] 10175.2 10195.58 10174.38
## [55,] 10212.5 10278.43 10195.58
## [56,] 10395.5 10264.88 10278.43
## [57,] 10545.9 10332.28 10264.88
## [58,] 10635.7 10447.40 10332.28
## [59,] 10265.2 10460.58 10447.40
## [60,] 10551.6 10499.60 10460.58
## [61,] 10538.2 10497.68 10499.60
## [62,] 10286.2 10410.30 10497.68
## [63,] 10171.3 10386.83 10410.30
## [64,] 10393.1 10347.20 10386.83
## [65,] 10162.3 10253.23 10347.20
## [66,] 10164.5 10222.80 10253.23
## [67,] 10327.0 10261.73 10222.80
## [68,] 10365.1 10254.73 10261.73
## [69,] 10755.9 10403.13 10254.73
## [70,] 10463.6 10477.90 10403.13
## [71,] 10080.5 10416.28 10477.90
## [72,] 10479.6 10444.90 10416.28
## [73,] 9980.9 10251.15 10444.90
## [74,] 10039.2 10145.05 10251.15
## [75,] 10246.1 10186.45 10145.05
## [76,] 10368.0 10158.55 10186.45
## [77,] 10446.3 10274.90 10158.55
## [78,] 10535.3 10398.93 10274.90
## [79,] 10786.9 10534.13 10398.93
## [80,] 9975.8 10436.08 10534.13
## [81,] 10160.9 10364.73 10436.08
## [82,] 10422.1 10336.43 10364.73
## [83,] 10757.2 10329.00 10336.43
## [84,] 10463.8 10451.00 10329.00
## [85,] 10307.0 10487.53 10451.00
## [86,] 10134.7 10415.68 10487.53
## [87,] 10207.7 10278.30 10415.68
## [88,] 10488.0 10284.35 10278.30
## [89,] 10262.3 10273.18 10284.35
## [90,] 10785.9 10435.98 10273.18
## [91,] 10375.4 10477.90 10435.98
## [92,] 10123.4 10386.75 10477.90
## [93,] 10462.7 10436.85 10386.75
## [94,] 10205.5 10291.75 10436.85
## [95,] 10522.7 10328.58 10291.75
## [96,] 10253.2 10361.03 10328.58
## [97,] 10428.7 10352.53 10361.03
## [98,] 10615.8 10455.10 10352.53
## [99,] 10417.3 10428.75 10455.10
## [100,] 10445.4 10476.80 10428.75
## [101,] 10690.6 10542.28 10476.80
## [102,] 10271.8 10456.28 10542.28
## [103,] 10524.8 10483.15 10456.28
## [104,] 9815.0 10325.55 10483.15
## [105,] 10398.5 10252.53 10325.55
## [106,] 10553.1 10322.85 10252.53
## [107,] 10655.8 10355.60 10322.85
## [108,] 10199.1 10451.63 10355.60
## [109,] 10416.6 10456.15 10451.63
## [110,] 10391.3 10415.70 10456.15
## [111,] 10210.1 10304.28 10415.70
## [112,] 10352.5 10342.63 10304.28
## [113,] 10423.8 10344.43 10342.63
## [114,] 10519.3 10376.43 10344.43
## [115,] 10596.7 10473.08 10376.43
## [116,] 10650.0 10547.45 10473.08
## [117,] 10741.6 10626.90 10547.45
## [118,] 10246.0 10558.58 10626.90
## [119,] 10354.4 10498.00 10558.58
## [120,] 10155.4 10374.35 10498.00
## [121,] NA NA 10374.35
## [122,] NA NA 10374.35
## [123,] NA NA 10374.35
## [124,] NA NA 10374.35
## [125,] NA NA 10374.35- Plot Time Series
ts.plot(data.ts, xlab="Time Period ", ylab="Sales", main= "SMA N=4 Data Sales")
points(data.ts)
lines(data.sma,col="green",lwd=2)
lines(data.ramal,col="red",lwd=2)
legend("topleft",c("data aktual","data pemulusan","data peramalan"), lty=8, col=c("black","green","red"), cex=0.8)
- Menyimpan Plot
Anda dapat menyimpan Plot dengan memasukkan Alamat Folder di Laptop Masing-masing sebagaimana contoh di bawah ini
setwd("D:/Dropbox/campus/")
dev.copy(png, "sma4.png")
dev.off()
- Menghitung Nilai Keakuratan
Nilai keakuratan yang akan dihitung disini adalah SSE,MSE, dan MAPE.
error=data.ts-data.ramal[1:length(data.ts)]
SSE=sum(error[5:length(data.ts)]^2)
SSE## [1] 7781583MSE=mean(error[5:length(data.ts)]^2)
MSE## [1] 67082.61MAPE=mean(abs((error[5:length(data.ts)]/data.ts[5:length(data.ts)])*100))
MAPE## [1] 2.008453Referensi
Montgomery, D.C., et.al. 2008. Forecasting Time Series Analysis 2nd. John Wiley↩︎