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