Lampiran 1Harga Beras IR-1 periode Januari 2008-Maret 2013 untuk Regional Yogyakarta

BulanTahun

2008 2009 2010 2011 2012 2013jan 4533.33 5200.00 6355.89 6918.11 8150.46 8173.59feb 4535.90 5433.33 6403.95 6588.53 8211.12 8150.75mar 4533.33 5308.33 6109.28 6553.41 8038.20 8065.21apr 4477.78 5141.58 5769.37 6530.76 7827.77  may 4775.00 5300.00 5760.40 6472.32 7732.36  jun 5147.22 5416.67 5990.97 6589.18 7708.77  jul 5115.28 5400.00 6382.74 7353.32 7708.77  aug 5186.11 5545.45 6705.56 7508.50 7789.15  sep 5066.67 5700.00 6724.04 7662.12 7797.4  oct 5066.67 5791.67 6831.71 7604.97 7741.62  nov 5127.78 5700.00 6948.70 7828.52 7715.14  dec 5115.15 6063.64 6975.33 8029.67 7984.85  

Lampiran 2

30

Plot Stasioneritas Data Awal

Index

IR-1

60544842363024181261

8000

7000

6000

5000

4000

Time Series Plot of IR-1

 

Uji Dickey-Fuller Data Awal

Plot PACF Data Awal

31

Lag

Part

ial A

uto

corr

ela

tion

16151413121110987654321

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Partial Autocorrelation Function for IR-1(with 5% significance limits for the partial autocorrelations)

Plot ACF Data Awal

Lag

Auto

corr

ela

tion

16151413121110987654321

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Autocorrelation Function for IR-1(with 5% significance limits for the autocorrelations)

32

Differensiasi pertama Lampiran 3 Plot Stasioneritas Data Differensi Pertama

Index

diff-

1

60544842363024181261

750

500

250

0

-250

-500

Time Series Plot of diff-1

Uji Dickey-Fuller Differensi Pertama

33

Plot PACF Differensi Pertama

Lag

Part

ial A

uto

corr

ela

tion

16151413121110987654321

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Partial Autocorrelation Function for diff-1(with 5% significance limits for the partial autocorrelations)

Plot ACF Differensi Pertama

Lag

Auto

corr

ela

tion

16151413121110987654321

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Autocorrelation Function for diff-1(with 5% significance limits for the autocorrelations)

 

34

Lampiran 4

Model ARIMA (2,1,1)

ARIMA (2,1,1)ARIMA Model: IR-1

Estimates at each iteration

Iteration SSE Parameters 0 2188227 0.100 0.100 0.100 45.653 1 2052631 0.010 0.045 -0.050 53.847 2 2021613 -0.124 0.043 -0.200 61.608 3 2007428 -0.266 0.051 -0.350 69.295 4 1998202 -0.411 0.061 -0.500 76.937 5 1990933 -0.556 0.074 -0.650 84.522 6 1984329 -0.701 0.088 -0.800 91.987 7 1975850 -0.842 0.106 -0.950 98.917 8 1868267 -0.692 0.223 -0.953 82.820 9 1854274 -0.680 0.231 -0.967 81.438 10 1842713 -0.675 0.241 -0.979 80.222 11 1829381 -0.648 0.280 -0.996 73.509 12 1822246 -0.614 0.288 -0.992 72.528 13 1814847 -0.622 0.298 -1.006 71.739 14 1793004 -0.605 0.301 -1.007 67.125 15 1789730 -0.612 0.299 -1.010 71.043 16 1760937 -0.612 0.300 -1.021 71.338

Unable to reduce sum of squares any further

* WARNING * Back forecasts not dying out rapidly

Back forecasts (after differencing)

Lag -97 - -92 54.343 54.361 54.342 54.363 54.340 54.364Lag -91 - -86 54.339 54.366 54.337 54.368 54.335 54.371Lag -85 - -80 54.332 54.373 54.329 54.377 54.326 54.380Lag -79 - -74 54.322 54.384 54.317 54.389 54.312 54.395Lag -73 - -68 54.306 54.401 54.300 54.408 54.292 54.416Lag -67 - -62 54.283 54.426 54.273 54.437 54.261 54.449Lag -61 - -56 54.248 54.464 54.232 54.480 54.215 54.499Lag -55 - -50 54.195 54.521 54.171 54.545 54.145 54.574Lag -49 - -44 54.114 54.607 54.079 54.644 54.039 54.687Lag -43 - -38 53.993 54.737 53.940 54.794 53.879 54.859Lag -37 - -32 53.809 54.934 53.729 55.020 53.637 55.118Lag -31 - -26 53.531 55.231 53.410 55.361 53.271 55.510Lag -25 - -20 53.112 55.680 52.929 55.876 52.719 56.101Lag -19 - -14 52.478 56.360 52.201 56.656 51.884 56.996Lag -13 - -8 51.520 57.386 51.102 57.833 50.622 58.345Lag -7 - -2 50.067 58.921 49.392 59.461 48.244 58.919Lag -1 - 0 43.309 47.032

Back forecast residuals

Lag -97 - -92 -0.001 0.003 -0.005 0.007 -0.009 0.011Lag -91 - -86 -0.013 0.016 -0.019 0.022 -0.025 0.029Lag -85 - -80 -0.033 0.037 -0.042 0.047 -0.052 0.058Lag -79 - -74 -0.064 0.071 -0.078 0.086 -0.094 0.103Lag -73 - -68 -0.113 0.124 -0.135 0.147 -0.160 0.174Lag -67 - -62 -0.189 0.206 -0.223 0.242 -0.262 0.284Lag -61 - -56 -0.307 0.332 -0.359 0.388 -0.418 0.452Lag -55 - -50 -0.487 0.525 -0.566 0.611 -0.658 0.708Lag -49 - -44 -0.763 0.821 -0.884 0.951 -1.023 1.100Lag -43 - -38 -1.183 1.271 -1.366 1.468 -1.578 1.695Lag -37 - -32 -1.821 1.956 -2.100 2.255 -2.421 2.599Lag -31 - -26 -2.790 2.994 -3.213 3.448 -3.700 3.970

35

Lag -25 - -20 -4.259 4.569 -4.901 5.257 -5.638 6.047Lag -19 - -14 -6.485 6.954 -7.457 7.996 -8.573 9.192Lag -13 - -8 -9.855 10.565 -11.326 12.141 -13.016 13.950Lag -7 - -2 -14.959 16.015 -17.223 18.281 -20.150 19.861Lag -1 - 0 -26.686 11.786

Final Estimates of Parameters

Type Coef SE Coef T PAR 1 -0.6123 0.1289 -4.75 0.000AR 2 0.2998 0.1284 2.33 0.023MA 1 -1.0206 0.0026 -397.12 0.000Constant 71.338 6.756 10.56 0.000

Differencing: 1 regular differenceNumber of observations: Original series 63, after differencing 62Residuals: SS = 1756680 (backforecasts excluded) MS = 30288 DF = 58

Modified Box-Pierce (Ljung-Box) Chi-Square statistic

Lag 12 24 36 48Chi-Square 15.8 35.8 55.7 62.0DF 8 20 32 44P-Value 0.045 0.016 0.006 0.038

Plot Normalitas Residual untuk ARIMA(2,1,1)

RESI1

Perc

ent

7505002500-250-500

99.9

99

95

90

80706050403020

10

5

1

0.1

Mean

0.122

1.066StDev 169.7N 62KS 0.100P-Value

Probability Plot of RESI ARIMA(2,1,1)Normal

36

Lampiran 5

Model ARIMA (2,1,0)

ARIMA (2,1,0)ARIMA Model: IR-1

Estimates at each iteration

Iteration SSE Parameters 0 2069027 0.100 0.100 45.653 1 1850350 0.234 -0.050 46.386 2 1744272 0.368 -0.200 47.255 3 1733214 0.424 -0.263 47.803 4 1733184 0.427 -0.267 47.905 5 1733184 0.427 -0.267 47.915

Relative change in each estimate less than 0.0010

Final Estimates of Parameters

Type Coef SE Coef T PAR 1 0.4274 0.1260 3.39 0.001AR 2 -0.2669 0.1262 -2.12 0.039Constant 47.91 21.77 2.20 0.032

Differencing: 1 regular differenceNumber of observations: Original series 63, after differencing 62Residuals: SS = 1732960 (backforecasts excluded) MS = 29372 DF = 59

Modified Box-Pierce (Ljung-Box) Chi-Square statistic

Lag 12 24 36 48Chi-Square 10.3 24.0 38.2 43.2DF 9 21 33 45P-Value 0.329 0.294 0.247 0.548

Plot Normalitas Residual untuk ARIMA (2,1,0)

RESI2

Perc

ent

7505002500-250-500

99.9

99

95

90

80706050403020

10

5

1

0.1

Mean

0.118

-0.04701StDev 168.6N 62KS 0.101P-Value

Probability Plot of RESI ARIMA(2,1,0)Normal

37

Lampiran 6

Model ARIMA (1,1,1)

ARIMA (1,1,1)ARIMA Model: IR-1

Estimates at each iteration

Iteration SSE Parameters 0 2103153 0.100 0.100 51.359 1 1860115 0.243 -0.042 42.569 2 1826275 0.118 -0.192 49.644 3 1805471 0.006 -0.342 55.955 4 1798060 0.050 -0.359 53.150 5 1798035 0.072 -0.340 51.806 6 1798032 0.054 -0.359 52.820 7 1798027 0.072 -0.341 51.823 8 1798024 0.055 -0.358 52.782 9 1798020 0.071 -0.342 51.857 10 1798017 0.055 -0.358 52.748 11 1798013 0.071 -0.342 51.890 12 1798011 0.056 -0.357 52.716 13 1798008 0.070 -0.343 51.920 14 1798006 0.057 -0.356 52.687 15 1798004 0.070 -0.343 51.947 16 1798002 0.057 -0.356 52.660 17 1798000 0.069 -0.344 51.973 18 1797998 0.057 -0.356 52.635 19 1797996 0.069 -0.344 51.997 20 1797995 0.058 -0.355 52.612 21 1797993 0.068 -0.344 52.019 22 1797992 0.058 -0.355 52.590 23 1797991 0.068 -0.345 52.039 24 1797989 0.059 -0.354 52.570 25 1797989 0.068 -0.345 52.058

** Convergence criterion not met after 25 iterations **

Final Estimates of Parameters

Type Coef SE Coef T PAR 1 0.0676 0.3236 0.21 0.835MA 1 -0.3452 0.3040 -1.14 0.261Constant 52.06 29.83 1.75 0.086

Differencing: 1 regular differenceNumber of observations: Original series 63, after differencing 62Residuals: SS = 1797563 (backforecasts excluded) MS = 30467 DF = 59

Modified Box-Pierce (Ljung-Box) Chi-Square statistic

Lag 12 24 36 48Chi-Square 12.3 30.3 47.3 53.1DF 9 21 33 45P-Value 0.195 0.085 0.051 0.191

38

Plot Normalitas Residual untuk ARIMA (1,1,1)

RESI3

Perc

ent

7505002500-250-500

99.9

99

95

90

80706050403020

10

5

1

0.1

Mean

>0.150

0.3557StDev 171.7N 62KS 0.096P-Value

Probability Plot of RESI ARIMA(1,1,1)Normal

39

Lampiran 7

Model ARIMA (1,1,0)

ARIMA (1,1,0)ARIMA Model: IR-1

Estimates at each iteration

Iteration SSE Parameters 0 1983006 0.100 51.359 1 1880743 0.250 42.324 2 1864335 0.334 37.060 3 1864286 0.339 36.630 4 1864286 0.339 36.601

Relative change in each estimate less than 0.0010

Final Estimates of Parameters

Type Coef SE Coef T PAR 1 0.3389 0.1221 2.78 0.007Constant 36.60 22.39 1.63 0.107

Differencing: 1 regular differenceNumber of observations: Original series 63, after differencing 62Residuals: SS = 1864003 (backforecasts excluded) MS = 31067 DF = 60

Modified Box-Pierce (Ljung-Box) Chi-Square statistic

Lag 12 24 36 48Chi-Square 16.1 36.6 57.2 63.6DF 10 22 34 46P-Value 0.096 0.026 0.008 0.044

Plot Normal Residual untuk ARIMA (1,1,0)

RESI4

Perc

ent

7505002500-250-500

99.9

99

95

90

80706050403020

10

5

1

0.1

Mean

0.093

0.3853StDev 174.8N 62KS 0.104P-Value

Probability Plot of RESI ARIMA(1,1,0)Normal

40

Lampiran 8

Model ARIMA (0,1,1)

ARIMA (0,1,1)ARIMA Model: IR-1

Estimates at each iteration

Iteration SSE Parameters 0 2260158 0.100 57.066 1 2036555 -0.050 56.754 2 1882955 -0.200 56.451 3 1805050 -0.350 56.187 4 1800152 -0.403 56.011 5 1799976 -0.393 55.956 6 1799971 -0.395 55.962 7 1799970 -0.395 55.961

Relative change in each estimate less than 0.0010

Final Estimates of Parameters

Type Coef SE Coef T PMA 1 -0.3949 0.1188 -3.32 0.002Constant 55.96 30.66 1.83 0.073

Differencing: 1 regular differenceNumber of observations: Original series 63, after differencing 62Residuals: SS = 1799521 (backforecasts excluded) MS = 29992 DF = 60

Modified Box-Pierce (Ljung-Box) Chi-Square statistic

Lag 12 24 36 48Chi-Square 12.9 31.1 47.9 53.7DF 10 22 34 46P-Value 0.232 0.094 0.057 0.204

Plot Normalitas Residual untuk ARIMA (0,1,1)

RESI5

Perc

ent

7505002500-250-500

99.9

99

95

90

80706050403020

10

5

1

0.1

Mean

0.120

0.3423StDev 171.8N 62KS 0.101P-Value

Probability Plot of RESI ARIMA(0,1,1)Normal

41

Lampiran 9

Peramalan Harga Beras IR-1 untuk 12 Bulan Kedepan

Forecasts from period 63

95 Percent LimitsPeriod Forecast Lower Upper Actual 64 8082.7 7746.7 8418.6 65 8160.9 7575.3 8746.4 66 8237.6 7498.3 8976.8 67 8297.4 7456.4 9138.3 68 8350.4 7424.7 9276.0 69 8405.0 7398.8 9411.1 70 8462.1 7378.9 9545.3 71 8519.8 7364.4 9675.3 72 8577.2 7354.2 9800.2 73 8634.2 7347.5 9920.9 74 8691.2 7343.7 10038.6 75 8748.2 7342.6 10153.8

Plot Hasil Peramalan

Time

IR-1

757065605550454035302520151051

10000

9000

8000

7000

6000

5000

4000

Time Series Plot for forcast IR-1(with forecasts and their 95% confidence limits)

42