Peramalan Data Time Series #2
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Transcript of Peramalan Data Time Series #2
LAPORAN UAS
PRAKTIKUM PERAMALAN DATA TIME SERIES
Oleh:
Adhitya Akbar (13065)
Dosen Pengampu:
Herni Utami, M.Sc
Asisten Praktikum:
1. Wirda Ardanti2. Chandra Purwana
LABORATORIUM KOMPUTASI STATISTIKA
FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM
UNIVERSITAS GADJAH MADA
YOGYAKARTA
2011
PERMASALAHAN
Lakukan Forecast untuk data tahun 2009 bulan Januari dari data di bawah ini:
1. Lakukan Forecast untuk data tahun 2009 bulan Januari dari data dibawah ini:
2006 116.873167.916145.031140.214170.839171.674186.047241.416276.384174.249293.389255.136
2007 153.806150.979151.074138.434169.217159.859143.233187.436239.213214.098243.181190.495
2008 208.13206.748
227.59254.272250.891258.038278.823300.585263.094222.012230.544173.849
2. Tentukan Model ARIMA, Overfitting, Diagnostic Checking dan Model yang terbaik. (Tulis keterangan dan penjelasannya)
PEMBAHASAN
Langkah Pengerjaan:
Masukkan data(menggunakan Eviews) dalam table dan plot data tersebut
2006M01 116.87302006M02 167.91602006M03 145.03102006M04 140.21402006M05 170.83902006M06 171.67402006M07 186.04702006M08 241.41602006M09 276.38402006M10 174.24902006M11 293.38902006M12 255.13602007M01 153.80602007M02 150.97902007M03 151.07402007M04 138.43402007M05 169.21702007M06 159.85902007M07 143.23302007M08 187.43602007M09 239.21302007M10 214.09802007M11 243.18102007M12 190.49502008M01 208.13002008M02 206.74802008M03 227.59002008M04 254.27202008M05 250.89102008M06 258.03802008M07 278.82302008M08 300.58502008M09 263.09402008M10 222.01202008M11 230.54402008M12 173.8490
Hasil Plot Data:
80
120
160
200
240
280
320
06M01 06M07 07M01 07M07 08M01 08M07 09M01
DATA
Terlihat data belum stasioner, dapat dilihat dari root testnya:
Null Hypothesis: DATA has a unit rootExogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.096144 0.0361Test critical values: 1% level -3.632900
5% level -2.94840410% level -2.612874
*MacKinnon (1996) one-sided p-values.
Nilai t-statistic lebih besar dari salah satu test critical values (1% level), sehingga data tidak stasioner.
Menstasionerkan Data
o Menyamakan variansinya(dtrans)
2006M01 4.7610882006M02 5.1234642006M03 4.9769482006M04 4.9431702006M05 5.1407222006M06 5.1455972006M07 5.2259992006M08 5.4865222006M09 5.6217912006M10 5.1604852006M11 5.6814992006M12 5.5417972007M01 5.0356922007M02 5.0171412007M03 5.0177702007M04 4.9303942007M05 5.1311822007M06 5.0742922007M07 4.9644732007M08 5.2334372007M09 5.4773542007M10 5.3664342007M11 5.4938062007M12 5.2496262008M01 5.3381632008M02 5.3315012008M03 5.4275462008M04 5.5384052008M05 5.5250192008M06 5.5531072008M07 5.6305772008M08 5.7057312008M09 5.5725112008M10 5.4027312008M11 5.4404422008M12 5.158187
Hasil Plot dtrans:
4.6
4.8
5.0
5.2
5.4
5.6
5.8
06M01 06M07 07M01 07M07 08M01 08M07 09M01
TRANS
Terlihat data belum stasioner, dapat dilihat dari root testnya:
Null Hypothesis: TRANS has a unit rootExogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.221547 0.0271Test critical values: 1% level -3.632900
5% level -2.94840410% level -2.612874
*MacKinnon (1996) one-sided p-values.
Nilai t-statistic lebih besar dari salah satu test critical values (1% level), sehingga data tidak stasioner.
Stasionerkan mean (ddif)
2006M01 NA2006M02 0.3623762006M03 -0.1465162006M04 -0.0337782006M05 0.1975522006M06 0.0048762006M07 0.0804022006M08 0.2605222006M09 0.1352702006M10 -0.4613062006M11 0.5210142006M12 -0.1397032007M01 -0.5061052007M02 -0.0185512007M03 0.0006292007M04 -0.0873762007M05 0.2007882007M06 -0.0568902007M07 -0.1098202007M08 0.2689652007M09 0.2439172007M10 -0.1109212007M11 0.1273722007M12 -0.2441802008M01 0.0885372008M02 -0.0066622008M03 0.0960452008M04 0.1108592008M05 -0.0133862008M06 0.0280882008M07 0.0774702008M08 0.0751532008M09 -0.1332192008M10 -0.1697802008M11 0.0377102008M12 -0.282255
Hasil Plot ddif:
-.6
-.4
-.2
.0
.2
.4
.6
06M01 06M07 07M01 07M07 08M01 08M07 09M01
DIF
Hasil Root test:
Null Hypothesis: DIF has a unit rootExogenous: ConstantLag Length: 0 (Automatic based on SIC, MAXLAG=8)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -7.476707 0.0000Test critical values: 1% level -3.639407
5% level -2.95112510% level -2.614300
*MacKinnon (1996) one-sided p-values.
Nilai t-statistic Fuller test lebih kecil dari semua test critical values, sehingga bias dikatakan data stasioner.
Pengujian ACF dan PACF untuk menentukan model ARIMA
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
**| . | **| . | 1 -0.245 -0.245 2.2844 0.131 .*| . | **| . | 2 -0.168 -0.242 3.3898 0.184 . |** | . |** | 3 0.337 0.256 7.9734 0.047 .*| . | . | . | 4 -0.128 -0.014 8.6561 0.070 **| . | .*| . | 5 -0.211 -0.178 10.587 0.060 . |** | . | . | 6 0.236 0.052 13.073 0.042 .*| . | .*| . | 7 -0.147 -0.111 14.071 0.050 ***| . | **| . | 8 -0.347 -0.343 19.852 0.011 . |** | . | . | 9 0.291 0.023 24.055 0.004 . | . | . |*. | 10 0.023 0.100 24.083 0.007 .*| . | . |*. | 11 -0.167 0.076 25.586 0.007 . |*. | . | . | 12 0.194 0.024 27.716 0.006 .*| . | **| . | 13 -0.176 -0.314 29.530 0.006 . | . | . |*. | 14 0.033 0.090 29.599 0.009 . | . | **| . | 15 -0.010 -0.228 29.606 0.013 . | . | .*| . | 16 -0.047 -0.105 29.757 0.019
o ARIMA (0,1,3) c
Variable Coefficient Std. Error t-Statistic Prob.
C -0.003284 0.037713 -0.087084 0.9312MA(1) -0.515038 0.132016 -3.901334 0.0005MA(2) 0.023941 0.162903 0.146965 0.8841MA(3) 0.723072 0.123777 5.841745 0.0000
R-squared 0.292583 Mean dependent var 0.011346Adjusted R-squared 0.224123 S.D. dependent var 0.209641S.E. of regression 0.184660 Akaike info criterion -0.433390Sum squared resid 1.057079 Schwarz criterion -0.255636Log likelihood 11.58433 Hannan-Quinn criter. -0.372029F-statistic 4.273791 Durbin-Watson stat 1.609941Prob(F-statistic) 0.012302
Inverted MA Roots .63+.75i .63-.75i -.75
ARIMA (0,1,3) c diatas tidak signifikan karena ada satu atau lebih variable yang tidak signifikan yaitu pada variable kontan (C) dan MA(2)
o ARIMA (0,1,3)
Variable Coefficient Std. Error t-Statistic Prob.
MA(1) -0.515102 0.129874 -3.966173 0.0004MA(2) 0.022846 0.160092 0.142708 0.8874MA(3) 0.721979 0.121120 5.960839 0.0000
R-squared 0.292429 Mean dependent var 0.011346Adjusted R-squared 0.248205 S.D. dependent var 0.209641S.E. of regression 0.181772 Akaike info criterion -0.490315Sum squared resid 1.057309 Schwarz criterion -0.357000Log likelihood 11.58052 Hannan-Quinn criter. -0.444295Durbin-Watson stat 1.609457
Inverted MA Roots .63+.75i .63-.75i -.75
o ARIMA (0,1,2) c
Variable Coefficient Std. Error t-Statistic Prob.
C 0.010215 0.006757 1.511886 0.1404MA(1) -0.409837 0.163661 -2.504185 0.0176MA(2) -0.504828 0.164022 -3.077807 0.0043
R-squared 0.171342 Mean dependent var 0.011346Adjusted R-squared 0.119550 S.D. dependent var 0.209641S.E. of regression 0.196711 Akaike info criterion -0.332346Sum squared resid 1.238247 Schwarz criterion -0.199030Log likelihood 8.816051 Hannan-Quinn criter. -0.286325F-statistic 3.308317 Durbin-Watson stat 1.766512Prob(F-statistic) 0.049432
Inverted MA Roots .94 -.53
o ARIMA (0,1,2)
Variable Coefficient Std. Error t-Statistic Prob.
MA(1) -0.406722 0.174328 -2.333079 0.0259MA(2) 0.105046 0.176739 0.594359 0.5563
R-squared 0.095804 Mean dependent var 0.011346Adjusted R-squared 0.068404 S.D. dependent var 0.209641S.E. of regression 0.202344 Akaike info criterion -0.302250Sum squared resid 1.351122 Schwarz criterion -0.213373Log likelihood 7.289377 Hannan-Quinn criter. -0.271570Durbin-Watson stat 1.729426
Inverted MA Roots .20-.25i .20+.25i
o ARIMA (0,1,1) c
Variable Coefficient Std. Error t-Statistic Prob.
C 0.010776 0.021972 0.490461 0.6271MA(1) -0.369844 0.168091 -2.200267 0.0349
R-squared 0.101095 Mean dependent var 0.011346Adjusted R-squared 0.073855 S.D. dependent var 0.209641S.E. of regression 0.201751 Akaike info criterion -0.308119Sum squared resid 1.343215 Schwarz criterion -0.219242Log likelihood 7.392088 Hannan-Quinn criter. -0.277439F-statistic 3.711331 Durbin-Watson stat 1.761946Prob(F-statistic) 0.062693
Inverted MA Roots .37
o ARIMA (0,1,1)
Variable Coefficient Std. Error t-Statistic Prob.
MA(1) -0.359030 0.164103 -2.187833 0.0357
R-squared 0.094611 Mean dependent var 0.011346Adjusted R-squared 0.094611 S.D. dependent var 0.209641S.E. of regression 0.199477 Akaike info criterion -0.358075Sum squared resid 1.352903 Schwarz criterion -0.313637Log likelihood 7.266318 Hannan-Quinn criter. -0.342735Durbin-Watson stat 1.766286
Inverted MA Roots .36
Uji Hipotesis:
MA(1) signifikan karena p-value (0.0357) < α (0.05)
Dari uji hipotesis ini didapat bahwa hanya model ARIMA (0,1,1) sajalah yang signifikan karena semua variable yang diuji di dalam model ini signifikan.
Diagnostic checking:
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
. | . | . | . | 1 0.036 0.036 0.0493 .*| . | .*| . | 2 -0.072 -0.073 0.2523 0.615 . |** | . |** | 3 0.249 0.257 2.7708 0.250 .*| . | .*| . | 4 -0.128 -0.170 3.4546 0.327 **| . | .*| . | 5 -0.220 -0.174 5.5368 0.237 . |*. | . | . | 6 0.088 0.034 5.8815 0.318 **| . | **| . | 7 -0.229 -0.219 8.2966 0.217 **| . | **| . | 8 -0.342 -0.269 13.902 0.053 . |*. | . |*. | 9 0.191 0.148 15.718 0.047 . | . | . |*. | 10 0.066 0.108 15.946 0.068 .*| . | . | . | 11 -0.091 0.004 16.392 0.089 . |*. | .*| . | 12 0.118 -0.102 17.178 0.103 .*| . | **| . | 13 -0.163 -0.323 18.747 0.095 . | . | . |*. | 14 -0.025 0.088 18.785 0.130 . | . | **| . | 15 -0.054 -0.281 18.977 0.166 . | . | . | . | 16 -0.064 -0.004 19.260 0.202
Karena tidak ada data yang keluar, maka tidak ada autokorelasi.
Normalitas Residual
0
1
2
3
4
5
6
7
8
9
-0.6 -0.4 -0.2 -0.0 0.2 0.4
Series: ResidualsSample 2006M02 2008M12Observations 35
Mean 0.020607Median 0.017577Maximum 0.386639Minimum -0.506423Std. Dev. 0.198379Skewness -0.461079Kurtosis 3.250110
Jarque-Bera 1.331358Probability 0.513925
Karena p-value(0.513925) > α (0.05), H0 tidak ditolak, sehingga dapat disimpulkan bahwa Residual berdistribusi normal.
HomoskedastisitasResidual
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
. |*. | . |*. | 1 0.076 0.076 0.2191 . |** | . |*. | 2 0.215 0.210 2.0293 0.154 . |** | . |** | 3 0.264 0.248 4.8580 0.088 . | . | .*| . | 4 -0.059 -0.136 5.0023 0.172 .*| . | **| . | 5 -0.091 -0.217 5.3573 0.253 .*| . | .*| . | 6 -0.130 -0.176 6.1064 0.296 .*| . | . | . | 7 -0.106 0.018 6.6288 0.357 . |*. | . |** | 8 0.123 0.341 7.3599 0.392 .*| . | . | . | 9 -0.088 0.025 7.7437 0.459 . | . | **| . | 10 -0.029 -0.222 7.7872 0.556 . |*. | . | . | 11 0.196 -0.006 9.8566 0.453 . | . | . | . | 12 -0.054 0.018 10.020 0.529 . | . | . | . | 13 -0.023 0.054 10.050 0.612 .*| . | **| . | 14 -0.125 -0.210 11.016 0.610 . | . | .*| . | 15 -0.051 -0.078 11.187 0.671 .*| . | . | . | 16 -0.114 -0.027 12.072 0.674
Hasil Forecast untuk Januari 2009 (menggunakan ARIMA (0,1,1) :
2006M01 NA2006M02 121.72712006M03 149.60082006M04 146.65542006M05 142.49342006M06 160.06572006M07 167.41252006M08 179.12932006M09 216.88822006M10 253.34682006M11 199.30992006M12 255.36262007M01 255.21732007M02 184.47482007M03 162.24062007M04 154.99182007M05 144.16472007M06 159.75742007M07 159.82252007M08 148.98112007M09 172.60362007M10 212.76382007M11 213.61802007M12 232.1236
2008M01 204.50372008M02 206.82072008M03 206.77412008M04 219.88572008M05 241.34772008M06 247.42202008M07 254.17512008M08 269.71012008M09 289.11312008M10 272.15462008M11 238.85192008M12 233.49302009M01 193.2700
Didapat forecast untuk Januari 2009 adalah 193.2700
