31

PRAKTIKUM 8

Metode Dekomposisi

Tujuan:

Mahasiswa dapat menggunakan RStudio untuk peramalan time series dengan metode dekomposisi

additive dan multiplikatif.

Petunjuk

1. Import Datasets – From TextFile... – pilih data outboard marine sales (Hanke & Wichern, 2005: 173) >outboardmarine<-ts(Tab5.4, frequency=4,start=c(1990,1)) >outboardmarine Qtr1 Qtr2 Qtr3 Qtr4 1990 232.7 309.2 310.7 293.0 1991 205.1 234.4 285.4 258.7 1992 193.2 263.7 292.5 315.2 1993 178.3 274.5 295.4 286.4 1994 190.8 263.5 318.8 305.3 1995 242.6 318.8 329.6 338.2 1996 232.1 285.6 291.0 281.4

2. Menentukan komponen dekomposisi multiplikatif

>komp_outboardmarine<-decompose(outboardmarine, type="multiplicative") >komp_outboardmarine $x Qtr1 Qtr2 Qtr3 Qtr4 1990 232.7 309.2 310.7 293.0 1991 205.1 234.4 285.4 258.7 1992 193.2 263.7 292.5 315.2 1993 178.3 274.5 295.4 286.4 1994 190.8 263.5 318.8 305.3 1995 242.6 318.8 329.6 338.2 1996 232.1 285.6 291.0 281.4 $seasonal Qtr1 Qtr2 Qtr3 Qtr4 1990 0.7631976 1.0106864 1.1239890 1.1021270 1991 0.7631976 1.0106864 1.1239890 1.1021270 1992 0.7631976 1.0106864 1.1239890 1.1021270 1993 0.7631976 1.0106864 1.1239890 1.1021270 1994 0.7631976 1.0106864 1.1239890 1.1021270 1995 0.7631976 1.0106864 1.1239890 1.1021270 1996 0.7631976 1.0106864 1.1239890 1.1021270 $trend Qtr1 Qtr2 Qtr3 Qtr4 1990 NA NA 282.9500 270.1500 1991 257.6375 250.1875 244.4125 246.5875 1992 251.1375 259.0875 264.2875 263.7750 1993 265.4875 262.2500 260.2125 260.4000 1994 261.9500 267.2375 276.0750 289.4625 1995 297.7250 303.1875 305.9875 300.5250 1996 291.5500 279.6250 NA NA $random Qtr1 Qtr2 Qtr3 Qtr4 1990 NA NA 0.9769436 0.9840814 1991 1.0430847 0.9269911 1.0388874 0.9519053 1992 1.0079954 1.0070412 0.9846620 1.0842288 1993 0.8799748 1.0356438 1.0099975 0.9979308 1994 0.9543836 0.9755888 1.0273754 0.9569800 1995 1.0676736 1.0403766 0.9583441 1.0210838 1996 1.0430979 1.0105685 NA NA

32

$figure [1] 0.7631976 1.0106864 1.1239890 1.1021270 $type [1] "multiplicative" attr(,"class") [1] "decomposed.ts"

3. Grafik dari masing-masing komponen

>plot(komp_outboardmarine)

4. Menentukan indeks musiman

>indmusiman<- sindexf(komp_outboardmarine,4) >indmusiman Qtr1 Qtr2 Qtr3 Qtr4 1997 0.7631976 1.0106864 1.1239890 1.1021270

5. Menentukan persamaan garis tren, yaitu persamaan regresi terhadap waktu.

Tentukanvariabeltterlebihdahulu

> t=1:28 >length(t) [1] 28 >length(outboardmarine) [1] 28

Persamaan regresi ditentukan dengan fungsi lm()

>res=lm(outboardmarine~t) >res Call: lm(formula = outboardmarine ~ t)

33

Coefficients: (Intercept) t 253.742 1.284

Sehinggapersamaannyaadalah T = 253,742 + 1,284t

>abline(res)

6. Peramalan data ke-29 menggunakan metode dekomposisi multiplikatif

Ramalan tren data ke-29

> t29=253.742+1.284*29 >t29 [1] 290.978

Dalam langkah 4 diperoleh indeks musiman tahun 2007 kuartal 1 adalah 0,7631976 sehingga

> y29=t29*0.7631976 > y29 [1] 222.0737

Dengan cara yang sama, dapat ditentukan peramalan data ke-30 dan seterusnya.

> t30=253.742+1.284*30 > y30=t30*1.009305 > y30 [1] 294.9815 > y31=(253.742+1.284*31)*1.129605 > y31 [1] 331.591

dst

7. Menentukan komponen tren dan musiman dengan metode dekomposisi additif. Data yang

digunakan adalah data pada Tabel 5-10 (Hanke & Wichern, 2005: 197)

>murphi<- read.table("D:/bahan ajar/bahanmodul/Hanke/excel/Ch5/murphi.csv", header=T, quote="\"") >murphy=ts(murphi,frequency=12,start=c(1996,1)) >murphy Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1996 4946 4968 5601 5454 5721 5690 5804 6040 5843 6087 6469 7002 1997 5416 5393 5907 5768 6107 6016 6131 6499 6249 6472 6946 7615

34

1998 5876 5818 6342 6143 6442 6407 6545 6758 6485 6805 7361 8079 1999 6061 6187 6792 6587 6918 6920 7030 7491 7305 7571 8013 8727 2000 6776 6847 7531 7333 7685 7518 7672 7992 7645 7923 8297 8537 2001 7005 6855 7420 7183 7554 7475 7687 7922 7426 7736 8483 9329 2002 7120 7124 7817 7538 7921 7757 7816 8208 7828

Untuk menentukan komponen dekomposisi additive, caranya sama dengan dekomposisi

multiplikatif. Dalam hal ini default adlah additive, sehingga tanpa menuliskan

type=”additive”, model dekomposisi yang diperoleh adalah dekomposisi additive.

>komponen_murphy=decompose(murphy) >komponen_murphy $x Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1996 4946 4968 5601 5454 5721 5690 5804 6040 5843 6087 6469 7002 1997 5416 5393 5907 5768 6107 6016 6131 6499 6249 6472 6946 7615 1998 5876 5818 6342 6143 6442 6407 6545 6758 6485 6805 7361 8079 1999 6061 6187 6792 6587 6918 6920 7030 7491 7305 7571 8013 8727 2000 6776 6847 7531 7333 7685 7518 7672 7992 7645 7923 8297 8537 2001 7005 6855 7420 7183 7554 7475 7687 7922 7426 7736 8483 9329 2002 7120 7124 7817 7538 7921 7757 7816 8208 7828 $seasonal Jan Feb Mar Apr May Jun Jul 1996 -660.60324 -694.63102 -125.97130 -362.30324 -54.42824 -164.60324 -46.76991 1997 -660.60324 -694.63102 -125.97130 -362.30324 -54.42824 -164.60324 -46.76991 1998 -660.60324 -694.63102 -125.97130 -362.30324 -54.42824 -164.60324 -46.76991 1999 -660.60324 -694.63102 -125.97130 -362.30324 -54.42824 -164.60324 -46.76991 2000 -660.60324 -694.63102 -125.97130 -362.30324 -54.42824 -164.60324 -46.76991 2001 -660.60324 -694.63102 -125.97130 -362.30324 -54.42824 -164.60324 -46.76991 2002 -660.60324 -694.63102 -125.97130 -362.30324 -54.42824 -164.60324 -46.76991 Aug Sep Oct Nov Dec 1996 228.66065 -93.20046 150.43843 616.52176 1206.88981 1997 228.66065 -93.20046 150.43843 616.52176 1206.88981 1998 228.66065 -93.20046 150.43843 616.52176 1206.88981 1999 228.66065 -93.20046 150.43843 616.52176 1206.88981 2000 228.66065 -93.20046 150.43843 616.52176 1206.88981 2001 228.66065 -93.20046 150.43843 616.52176 1206.88981 2002 228.66065 -93.20046 $trend Jan Feb Mar Apr May Jun Jul Aug Sep 1996 NA NANANANANA 5821.667 5858.958 5889.417 1997 6001.292 6034.042 6070.083 6103.042 6138.958 6184.375 6229.083 6265.958 6301.792 1998 6428.917 6456.958 6477.583 6501.292 6532.458 6569.083 6596.125 6619.208 6653.333 1999 6811.708 6862.458 6927.167 6993.250 7052.333 7106.500 7163.292 7220.583 7278.875 2000 7512.333 7559.958 7595.000 7623.833 7650.333 7654.250 7655.875 7665.750 7661.458 2001 7630.458 7628.167 7616.125 7599.208 7599.167 7639.917 7677.708 7693.708 7721.458 2002 7827.042 7844.333 7873.000 NA NANANANANA Oct Nov Dec 1996 5915.250 5944.417 5974.083 1997 6335.542 6365.125 6395.375 1998 6690.583 6728.917 6770.125 1999 7340.750 7403.792 7460.667 2000 7650.583 7638.875 7631.625 2001 7752.792 7782.875 7809.917 2002 $random Jan Feb Mar Apr May Jun 1996 NA NANANANANA 1997 75.3115741 53.5893519 -37.1120370 27.2615741 22.4699074 -3.7717593 1998 107.6865741 55.6726852 -9.6120370 4.0115741 -36.0300926 2.5199074 1999 -90.1050926 19.1726852 -9.1953704 -43.9467593 -79.9050926 -21.8967593 2000 -75.7300926 -18.3273148 61.9712963 71.4699074 89.0949074 28.3532407 2001 35.1449074 -78.5356481 -70.1537037 -53.9050926 9.2615741 -0.3134259 2002 -46.4384259 -25.7023148 69.9712963 NA NANA Jul Aug Sep Oct Nov Dec 1996 29.1032407 -47.6189815 46.7837963 21.3115741 -91.9384259 -178.9731481 1997 -51.3134259 4.3810185 40.4087963 -13.9800926 -35.6467593 12.7351852 1998 -4.3550926 -89.8689815 -75.1328704 -36.0217593 15.5615741 101.9851852 1999 -86.5217593 41.7560185 119.3254630 79.8115741 -7.3134259 59.4435185 2000 62.8949074 97.5893519 76.7421296 121.9782407 41.6032407 -301.5148148 2001 56.0615741 -0.3689815 -202.2578704 -167.2300926 83.6032407 312.1935185 2002 NA NANA $figure [1] -660.60324 -694.63102 -125.97130 -362.30324 -54.42824 -164.60324 -46.76991 [8] 228.66065 -93.20046 150.43843 616.52176 1206.88981

35

$type [1] "additive" attr(,"class") [1] "decomposed.ts"

8. Plot komponen dekomposisi

>plot(komponen_murphy)

9. Menentukan persamaan garis tren.

>i=1:81 >tren=lm(murphy~i) >tren Call: lm(formula = murphy ~ i) Coefficients: (Intercept) i 5604.80 32.45

Diperoleh persamaan tren 𝑇𝑡 = 5604,8 + 32,45𝑡.

10. Menentukan nilai ramalan tren

>ramaltren=5604.80+32.45*i >ramaltren [1] 5637.25 5669.70 5702.15 5734.60 5767.05 5799.50 5831.95 5864.40 5896.85 5929.30 [11] 5961.75 5994.20 6026.65 6059.10 6091.55 6124.00 6156.45 6188.90 6221.35 6253.80 [21] 6286.25 6318.70 6351.15 6383.60 6416.05 6448.50 6480.95 6513.40 6545.85 6578.30 [31] 6610.75 6643.20 6675.65 6708.10 6740.55 6773.00 6805.45 6837.90 6870.35 6902.80 [41] 6935.25 6967.70 7000.15 7032.60 7065.05 7097.50 7129.95 7162.40 7194.85 7227.30 [51] 7259.75 7292.20 7324.65 7357.10 7389.55 7422.00 7454.45 7486.90 7519.35 7551.80 [61] 7584.25 7616.70 7649.15 7681.60 7714.05 7746.50 7778.95 7811.40 7843.85 7876.30 [71] 7908.75 7941.20 7973.65 8006.10 8038.55 8071.00 8103.45 8135.90 8168.35 8200.80 [81] 8233.25

11. Menentukan nilai ramalan menggunakan metode dekomposisi additive

>ramal_murphy=ramaltren+komponen_murphy$seasonal

36

>ramal_murphy Jan Feb Mar Apr May Jun Jul Aug Sep 1996 4976.647 4975.069 5576.179 5372.297 5712.622 5634.897 5785.180 6093.061 5803.650 1997 5366.047 5364.469 5965.579 5761.697 6102.022 6024.297 6174.580 6482.461 6193.050 1998 5755.447 5753.869 6354.979 6151.097 6491.422 6413.697 6563.980 6871.861 6582.450 1999 6144.847 6143.269 6744.379 6540.497 6880.822 6803.097 6953.380 7261.261 6971.850 2000 6534.247 6532.669 7133.779 6929.897 7270.222 7192.497 7342.780 7650.661 7361.250 2001 6923.647 6922.069 7523.179 7319.297 7659.622 7581.897 7732.180 8040.061 7750.650 2002 7313.047 7311.469 7912.579 7708.697 8049.022 7971.297 8121.580 8429.461 8140.050 Oct Nov Dec 1996 6079.738 6578.272 7201.090 1997 6469.138 6967.672 7590.490 1998 6858.538 7357.072 7979.890 1999 7247.938 7746.472 8369.290 2000 7637.338 8135.872 8758.690 2001 8026.738 8525.272 9148.090 2002

12. Menghitung residu dan menggambarkan plot residu, acf dan pacf.

>residu=murphy-ramal_murphy

>tsdisplay(residu,main="residudenganmetodedekomposisi additive")