Appendix Perbandingan Metode Pemulusan (Smoothing) Eksponensial Ganda Dua Parameter Dari Holt Dan Metode BoxJenkins Dalam Meramalkan Hasil Produksi Kernel Kelapa Sawit PT. Eka Dura Indonesia.

Lampiran 1. Tabel Perhitungan Pemulusan (Smoothing) Eksponensial Ganda (Linier Dua Perameter dari Holt) dengan α= 0,1 dan Berbagai Nilai γ

Data

Ramalan

Periode Aktual

untuk α = 0,1

Periode Aktual

untuk α = 0,1

Periode Aktual

untuk α = 0,1

13.161.560.38 14.011.321.18 SSE 8.444,600

2.838,800 2.255,800 MS

E 31,803

Periode Aktual

untuk α = 0,2

Periode Aktual

untuk α = 0,2

Periode Aktual

untuk α = 0,2

13.948.672.289. 15.451.877.535. SSE 22,660

153,400 801,301 MS

E 1,425

Periode Aktual

untuk α = 0,3

Periode Aktual

untuk α = 0,3

Periode Aktual

untuk α = 0,3

6.179.910.679.6 6.647.674.855.5 7.394.945.502.5 8.240.736.181.7 9.100.225.985.2 9.845.914.002.7 10.311.672.028. 10.376.469.493. 10.041.010.098. SSE 68,990

177.787.448.769 178.904.646.441 173.120.863.774 MSE 2,224

Periode Aktual

untuk α = 0,4

Periode Aktual

untuk α = 0,4

Periode Aktual

untuk α = 0,4

219079,3589 -202184,0700

35340,3160 -434239,4500

-148398,7270 -666294,8300 -148398,7270 -666294,8300

-332137,7700 -898350,2000

-515876,8130 -1130405,600

5.329.817.556.4 5.802.538.904.3 6.367.095.150.2 6.857.305.044.1 7.153.294.467.3 7.180.174.240.2 6.956.426.967.5 6.579.609.783.1 6.163.064.406.4 SSE 36,770

113.441.547.98 106.259.731.14 MSE 462

Periode Aktual

untuk α = 0,5

Periode Aktual

untuk α = 0,5

Periode Aktual

untuk α = 0,5

215691,7822 -15946,0610

-5854,1137 -271830,0600

-227400,0100 -527714,0580

-448945,9060 -783598,0570

-670491,8020 -1039482,060 -670491,8020 -1039482,060

-892037,6980 -1295366,050

-1113583,590 -1551250,050

4.678.125.387.7 5.043.045.865.2 5.381.369.774.3 5.571.238.574.9 5.573.690.075.6 5.425.345.643.6 5.207.129.293.8 4.993.820.668.6 4.828.663.520.8 SSE 38,430

MSE 352

Periode Aktual

untuk α = 0,6

Periode Aktual

untuk α = 0,6

Periode Aktual

untuk α = 0,6

77560,2472 -93231,7570

-152870,2770 -348941,7430

-383300,8010 -604651,7300

-613731,3250 -860361,7170

-844161,8490 -1116071,700 -844161,8490 -1116071,700

-1074592,370 -1371781,690

-1305022,900 -1627491,680

4.187.221.478.7 4.451.052.601.5 4.645.033.138.7 4.708.681.256.0 4.661.483.861.0 4.561.826.590.4 4.465.578.097.7 4.404.547.228.8 4.388.099.927.8 SSE 25,220

MSE 124

Periode Aktual

untuk α = 0,7

Periode Aktual

untuk α = 0,7

Periode Aktual

untuk α = 0,7

76114,5174 -35667,2100

-146305,3180 -274410,0960

-368725,1540 -513152,9810

-591144,9900 -751895,8670

-813564,8250 -990638,7530 -813564,8250 -990638,7530

-1035984,6600 -1229381,6400

-1258404,5000 -1468124,5200

3.841.126.456.2 4.042.755.585.6 4.174.350.323.4 4.217.117.641.0 4.207.496.673.0 4.191.443.924.0 4.199.657.319.0 4.244.395.532.9 4.326.759.041.6 SSE 14,100

MSE 588

Periode Aktual

untuk α = 0,8

Periode Aktual

untuk α = 0,8

Periode Aktual

untuk α = 0,8

-25699,0451 -82442,1496

-227427,1700 -290998,1960

-429155,2940 -499554,2420

-630883,4190 -708110,2890 -630883,4190 -708110,2890

-832611,5440 -916666,3350

-1034339,670 -1125222,380

3.620.504.647.3 2.958.007.360.4 3.918.949.627.3 3.989.259.350.0 4.043.176.952.8 4.112.902.774.7 4.216.268.254.5 4.359.888.076.7 4.545.446.062.2 SSE 80,570

MSE 355

Periode Aktual

untuk α = 0,9

Periode Aktual

untuk α = 0,9

Periode Aktual

untuk α = 0,9

-158635,8300 -136167,6560

-329776,9330 -304328,3060

Periode Aktual

0,9

γ = 0,1

γ = 0,2

γ = 0,3

γ = 0,4

γ = 0,5

γ = 0,6

γ = 0,7

γ = 0,8

γ = 0,9 71

1309751,7890

1122516,9380

788636,4655

392913,1379

26580,2549

-254887,7780

-430929,1450

-500918,0370 -472488,9560

72

-672059,1410 -640649,6050 3.508.030.123.681, 3.688.049.285.323 3.063.519.124.930

1300952,2010

1096695,9280

732645,4161

301283,9668

-97928,2318

-404532,0590

-596131,2730

3.958.146.223.679

4.090.700.459.382,

4.466.305.643.821,0

SSE

4.729.367.226.228,250 5.049.847.978.042,540 790

4.255.692.968.219,140

80

,790

,400

,310

440

60.483.277.994,51

63.587.056.643,51 52.819.295.257,42

68.243.900.408,26

MSE

70.529.318.265,215

73.374.016.693,434

77.005.269.721,053

81.540.814.245,315 87.066.344.449,009

ARIMA Model (1,3,1)(0,3,0) 12 Type Coef SECoef T P

AR 1 0.4627 0.1653 2.80 0.008 MA 1 0.9171 0.0734 12.49 0.000

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 2771632000648 (backforecasts excluded)

MS = 61591822237 DF = 45

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

Lag 12 24 36 48 Chi-Square 15.8 34.1 45.7 * DF 10 22 34 * P-Value 0.106 0.048 0.087 *

Forecasts from period 60

95% Limits Period Forecast Lower Upper Actual

ARIMA Model (1,3,1)(1,3,0) 12 Type Coef SECoef T P

AR 1 0.3052 0.2329 1.31 0.197 SAR 12 -0.6861 0.1245 -5.51 0.000 MA 1 0.7745 0.1541 5.03 0.000

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1964110857598 (backforecasts excluded)

MS = 44638883127 DF = 44

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

Lag 12 24 36 48 Chi-Square 11.0 29.1 36.4 * DF 9 21 33 * P-Value 0.276 0.111 0.313 *

Forecasts from period 60

95% Limits Period Forecast Lower Upper Actual

ARIMA Model (1,3,1) (0,3,1) 12 Final Estimates of Parameters

Type Coef SECoef T P AR 1 0.2465 0.2743 0.90 0.374 MA 1 0.6775 0.2113 3.21 0.003 SMA 12 0.7169 0.1607 4.46 0.000

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1677911672756 (backforecasts excluded)

MS = 38134356199 DF = 44

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

Lag 12 24 36 48 Chi-Square 7.4 27.0 33.7 * DF 9 21 33 * P-Value 0.598 0.171 0.434 *

Forecasts from period 60

95% Limits Period Forecast Lower Upper Actual

ARIMA Model (1,3,1) (1,3,1) 12 Type Coef SECoef T P

AR 1 0.3136 0.2723 1.15 0.256 SAR 12 -0.2353 0.2080 -1.13 0.264 MA 1 0.7143 0.2055 3.48 0.001 SMA 12 0.6918 0.2371 2.92 0.006

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1595297165269 (backforecasts excluded)

MS = 37099934076 DF = 43

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

Lag 12 24 36 48 Chi-Square 8.6 30.7 38.8 * DF 8 20 32 * P-Value 0.378 0.059 0.190 *

Forecasts from period 60

95% Limits Period Forecast Lower Upper Actual

ARIMA Model (1,3,2) (0,3,0) 12

Final Estimates of Parameters

Type Coef SECoef T P AR 1 -0.3416 1.0479 -0.33 0.746 MA 1 0.1209 1.0164 0.12 0.906 MA 2 0.2957 0.5099 0.58 0.565

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 2856188181601 (backforecasts excluded)

MS = 64913367764 DF = 44

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

Lag 12 24 36 48 Chi-Square 12.9 28.1 38.3 * DF 9 21 33 * P-Value 0.168 0.137 0.240 *

Forecasts from period 60

95% Limits Period Forecast Lower Upper Actual

ARIMA Model (1,3,2) (1,3,0) 12 Type Coef SECoef T P

AR 1 0.7975 0.1285 6.21 0.000 SAR 12 -0.6105 0.1304 -4.68 0.000 MA 1 1.3341 0.0508 26.26 0.000 MA 2 -0.3887 0.0591 -6.58 0.000

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1968101351473 (backforecasts excluded)

MS = 45769798871 DF = 43

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

Lag 12 24 36 48 Chi-Square 9.5 27.7 34.6 * DF 8 20 32 * P-Value 0.300 0.118 0.345 *

Forecasts from period 60

95% Limits Period Forecast Lower Upper Actual

ARIMA Model (1,3,2) (0,3,1) 12 Type Coef SECoef T P

AR 1 0.3732 0.5395 0.69 0.493 MA 1 0.8276 0.5681 1.46 0.152 MA 2 -0.0048 0.3952 -0.01 0.990 SMA 12 0.7421 0.1649 4.50 0.000

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1663020806117 (backforecasts excluded)

MS = 38674902468 DF = 43

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

Lag 12 24 36 48 Chi-Square 6.2 23.1 29.1 * DF 8 20 32 * P-Value 0.621 0.284 0.614 *

Forecasts from period 60

95% Limits Period Forecast Lower Upper Actual

ARIMA Model (1,3,2) (1,3,1) 12 Final Estimates of Parameters

Type Coef SECoef T P AR 1 0.3806 0.5379 0.71 0.483 SAR 12 -0.2442 0.2032 -1.20 0.236 MA 1 0.8023 0.5675 1.41 0.165 MA 2 0.0124 0.3843 0.03 0.974 SMA 12 0.7355 0.2234 3.29 0.002

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1574245348383 (backforecasts excluded)

MS = 37482032104 DF = 42

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

Lag 12 24 36 48 Chi-Square 7.2 25.7 33.1 * DF 7 19 31 * P-Value 0.412 0.140 0.367 *

Forecasts from period 60

ARIMA Model (2,3,1)(0,3,0) 12 Final Estimates of Parameters

Type Coef SECoef T P AR 1 -0.3296 0.4990 -0.66 0.512 AR 2 -0.2503 0.2298 -1.09 0.282 MA 1 0.1200 0.5146 0.23 0.817

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 2857760265239 (backforecasts excluded)

MS = 64949096937 DF = 44

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

Lag 12 24 36 48 Chi-Square 10.4 22.9 33.8 * DF 9 21 33 * P-Value 0.321 0.348 0.428 *

Forecasts from period 60

95% Limits Period Forecast Lower Upper Actual

ARIMA Model (2,3,1)(1,3,0) 12

Final Estimates of Parameters

Type Coef SECoef T P AR 1 0.3409 0.2473 1.38 0.175 AR 2 0.1676 0.2017 0.83 0.410 SAR 12 -0.7108 0.1255 -5.66 0.000 MA 1 0.8484 0.1792 4.74 0.000

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1919992324264 (backforecasts excluded)

MS = 44650984285 DF = 43

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

Lag 12 24 36 48 Chi-Square 10.6 30.3 36.3 * DF 8 20 32 * P-Value 0.227 0.064 0.275 *

Forecasts from period 60

95% Limits

ARIMA Model (2,3,1)(0,3,1) 12 Final Estimates of Parameters

Type Coef SECoef T P AR 1 0.2744 0.3216 0.85 0.398 AR 2 0.0385 0.2261 0.17 0.866 MA 1 0.7146 0.2967 2.41 0.020 SMA 12 0.7122 0.1638 4.35 0.000

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1674474318669 (backforecasts excluded)

MS = 38941263225 DF = 43

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

Lag 12 24 36 48 Chi-Square 7.4 27.4 33.9 * DF 8 20 32 * P-Value 0.498 0.123 0.375 *

Forecasts from period 60

95% Limits

ARIMA Model (2,3,1)(1,3,1) 12 Final Estimates of Parameters

Type Coef SECoef T P AR 1 0.3807 0.2267 1.68 0.101 AR 2 0.0669 0.1986 0.34 0.738 SAR 12 -0.2407 0.2070 -1.16 0.252 MA 1 0.8352 0.1668 5.01 0.000 SMA 12 0.7283 0.2312 3.15 0.003

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1573035572290 (backforecasts excluded)

MS = 37453227912 DF = 42

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

Lag 12 24 36 48 Chi-Square 7.5 26.5 33.8 * DF 7 19 31 * P-Value 0.382 0.116 0.335 *

Forecasts from period 60

ARIMA Model (2,3,2)(0,3,0) 12 Final Estimates of Parameters

Type Coef SECoef T P AR 1 -0.3456 1.2071 -0.29 0.776 AR 2 -0.1296 0.3750 -0.35 0.731 MA 1 0.1138 1.2101 0.09 0.926 MA 2 0.1495 0.8102 0.18 0.854

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 2856460974935 (backforecasts excluded)

MS = 66429324998 DF = 43

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

Lag 12 24 36 48 Chi-Square 11.4 25.2 35.6 * DF 8 20 32 * P-Value 0.180 0.195 0.304 *

Forecasts from period 60

95% Limits

ARIMA Model (2,3,2)(1,3,0) 12

Final Estimates of Parameters

Type Coef SECoef T P AR 1 0.3420 0.9740 0.35 0.727 AR 2 0.1740 0.4060 0.43 0.670 SAR 12 -0.7084 0.1283 -5.52 0.000 MA 1 0.8494 0.9644 0.88 0.384 MA 2 0.0042 0.7866 0.01 0.996

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1919526150101 (backforecasts excluded)

MS = 45703003574 DF = 42

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

Lag 12 24 36 48 Chi-Square 10.5 30.4 36.4 * DF 7 19 31 * P-Value 0.162 0.047 0.230 *

Forecasts from period 60

95% Limits

ARIMA Model (2,3,2)(0,3,1) 12 Final Estimates of Parameters

Type Coef SECoef T P AR 1 0.1977 1.8192 0.11 0.914 AR 2 0.1786 0.7933 0.23 0.823 MA 1 0.6598 1.8296 0.36 0.720 MA 2 0.1903 1.5725 0.12 0.904 SMA 12 0.7480 0.1687 4.43 0.000

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1612786624359 (backforecasts excluded)

MS = 38399681532 DF = 42

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

Lag 12 24 36 48 Chi-Square 6.5 25.4 31.0 * DF 7 19 31 * P-Value 0.488 0.149 0.469 *

Forecasts from period 60

95% Limits

ARIMA Model (2,3,2)(1,3,1) 12 Final Estimates of Parameters

Type Coef SECoef T P AR 1 0.1218 1.6570 0.07 0.942 AR 2 0.2590 0.7746 0.33 0.740 SAR 12 -0.2660 0.1931 -1.38 0.176 MA 1 0.5455 1.6782 0.33 0.747 MA 2 0.2980 1.4335 0.21 0.836 SMA 12 0.7431 0.2133 3.48 0.001

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 60, after differencing 47 Residuals: SS = 1503324301931 (backforecasts excluded)

MS = 36666446389 DF = 41

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

Lag 12 24 36 48 Chi-Square 7.3 28.6 35.0 * DF 6 18 30 * P-Value 0.292 0.054 0.244 *

Forecasts from period 60

Data Differencing II

Data Differencing III

Autokorelasi

Box-Ljung Statistic

Lag Autocorrelation

Std. Error a

Value

df Sig. b

1 -.069

3 -.086

5 -.268

7 -.121

9 -.070

11 -.159

13 -.025

15 -.211

17 -.212

19 -.112

21 -.020

22 -.013

24 -.040

Box-Ljung Statistic

Lag Autocorrelation

Std. Error a

Value

df Sig. b

31 -.080

32 -.059

34 -.069

36 -.065

38 -.061

40 -.071

42 -.107

44 -.071

47 -.074

Partial Autokorelasi

Partial Autocorrelations

Series:Produksi_Kernel Partial

Lag

Std. Error

Autocorrelation

1 -.069

3 -.432

4 -.060

5 -.185

6 -.109

7 -.034

8 -.014

9 -.114

10 -.040

11 -.071

12 -.093

13 -.066

Partial Lag

Std. Error

Autocorrelation

29 -.165

32 -.016

34 -.084

37 -.087

38 -.059

39 -.064

40 -.029

41 -.043

45 -.017

Tabel Distribusi t

df 0.005

0.01 0.025

0.05 0.1

38 2.9803

2.7116 2.3337 2.0244 1.6860

39 2.9756

2.7079 2.3313 2.0227 1.6849

40 2.9712

2.7045 2.3289 2.0211 1.6839

41 2.9670

2.7012 2.3267 2.0195 1.6829

42 2.9630

2.6981 2.3246 2.0181 1.6820

43 2.9592

2.6951 2.3226 2.0167 1.6811

44 2.9555

2.6923 2.3207 2.0154 1.6802

45 2.9521

2.6896 2.3189 2.0141 1.6794

46 2.9488

2.6870 2.3172 2.0129 1.6787

47 2.9456

2.6846 2.3155 2.0117 1.6779

48 2.9426

2.6822 2.3139 2.0106 1.6772

49 2.9397

2.6800 2.3124 2.0096 1.6766

50 2.9370

2.6778 2.3109 2.0086 1.6759

51 2.9343

2.6757 2.3095 2.0076 1.6753

52 2.9318

2.6737 2.3082 2.0066 1.6747

53 2.9293

2.6718 2.3069 2.0057 1.6741

54 2.9270

2.6700 2.3056 2.0049 1.6736

55 2.9247

2.6682 2.3044 2.0040 1.6730

56 2.9225

2.6665 2.3033 2.0032 1.6725

57 2.9204

2.6649 2.3022 2.0025 1.6720

58 2.9184

2.6633 2.3011 2.0017 1.6716

59 2.9164

2.6618 2.3000 2.0010 1.6711

60 2.9146

2.6603 2.2990 2.0003 1.6706