mpdw
NIda Khairunnissa
2025-08-19
Pengenalan Data
Input Data
# impor data
library(rio)## Warning: package 'rio' was built under R version 4.4.2data <- import("https://raw.githubusercontent.com/nida-kha44/MPDW/refs/heads/main/Pertemuan%201/btc_historical_price.csv")
head(data)## date price
## 1 2011-01-01 0.300
## 2 2011-01-02 0.300
## 3 2011-01-03 0.295
## 4 2011-01-04 0.299
## 5 2011-01-05 0.299
## 6 2011-01-06 0.298summary(data)## date price
## Min. :2011-01-01 Min. : 0.3
## 1st Qu.:2013-10-31 1st Qu.: 198.8
## Median :2016-08-30 Median : 712.7
## Mean :2016-08-30 Mean : 8171.6
## 3rd Qu.:2019-06-30 3rd Qu.: 8601.2
## Max. :2022-04-30 Max. :67544.9# mengambil baris 1655 - 2485 hasil pembagian dengan teman kelompok
btcprice <- data[1655:2485, ]
head(btcprice)## date price
## 1655 2015-07-13 290.8811
## 1656 2015-07-14 286.1856
## 1657 2015-07-15 283.8231
## 1658 2015-07-16 277.8273
## 1659 2015-07-17 278.4883
## 1660 2015-07-18 274.4938Eksplorasi Data
View(btcprice) # melihat data
str(btcprice) # mengetahui struktur data## 'data.frame': 831 obs. of 2 variables:
## $ date : IDate, format: "2015-07-13" "2015-07-14" ...
## $ price: num 291 286 284 278 278 ...dim(btcprice) # mengetahui dimensi data## [1] 831 2summary(btcprice) # menampilkan ringkasan data## date price
## Min. :2015-07-13 Min. : 209.1
## 1st Qu.:2016-02-05 1st Qu.: 417.7
## Median :2016-08-31 Median : 635.5
## Mean :2016-08-31 Mean :1144.0
## 3rd Qu.:2017-03-26 3rd Qu.:1184.8
## Max. :2017-10-20 Max. :5984.1# mengubah data agar menjadi data deret waktu
btcprice.ts <- ts(btcprice$price)
summary(btcprice.ts)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 209.1 417.7 635.5 1144.0 1184.8 5984.1# membuat plot data deret waktu
ts.plot(btcprice.ts, xlab="Time Period ", ylab="price",
main = "Time Series Plot")
points(btcprice.ts)
Dari plot di atas, dapat terlihat bahwa data memiliki pola Non-linear
upward trend (eksponensial) dengan volatilitas meningkat. Akan dilakukan
pemulusan dengan metode Exponential Smoothing.
Exponential Smoothing
Metode Exponential Smoothing adalah metode pemulusan dengan melakukan pembobotan menurun secara eksponensial. Nilai yang lebih baru diberi bobot yang lebih besar dari nilai terdahulu. Terdapat satu atau lebih parameter pemulusan yang ditentukan secara eksplisit, dan hasil pemilihan parameter tersebut akan menentukan bobot yang akan diberikan pada nilai pengamatan. Ada dua macam model, yaitu model tunggal dan ganda.
Pembagian Data
Pembagian data latih dan data uji dilakukan dengan perbandingan 80% data latih dan 20% data uji.
#membagi training dan testing
training <- btcprice[1:664, ]
testing <- btcprice[665:831, ]
train.ts <- ts(training$price)
test.ts <- ts(testing$price)Eksplorasi
Eksplorasi dilakukan dengan membuat plot data deret waktu untuk keseluruhan data, data latih, dan data uji.
#eksplorasi data
plot(btcprice.ts, col="black",main="Plot semua data")
points(btcprice.ts)
plot(train.ts, col="red",main="Plot data latih")
points(train.ts)
plot(test.ts, col="blue",main="Plot data uji")
points(test.ts)
DES
Metode pemulusan Double Exponential Smoothing (DES) digunakan untuk data yang memiliki pola tren. Metode DES adalah metode semacam SES, hanya saja dilakukan dua kali, yaitu pertama untuk tahapan ‘level’ dan kedua untuk tahapan ‘tren’. Pemulusan menggunakan metode ini akan menghasilkan peramalan tidak konstan untuk periode berikutnya.
Pemulusan dengan metode DES kali ini akan menggunakan fungsi
HoltWinters() . Jika sebelumnya nilai argumen
beta dibuat FALSE , kali ini argumen tersebut
akan diinisialisasi bersamaan dengan nilai alpha .
#Lamda=0.2 dan gamma=0.2
des.1<- HoltWinters(train.ts, gamma = FALSE, beta = 0.2, alpha = 0.2)
plot(des.1)
#ramalan
library(forecast)## Warning: package 'forecast' was built under R version 4.4.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zooramalandes1<- forecast(des.1, h=167)
ramalandes1## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 665 1540.995 1495.368 1586.622 1471.214 1610.776
## 666 1567.805 1520.882 1614.728 1496.043 1639.567
## 667 1594.615 1545.984 1643.246 1520.241 1668.990
## 668 1621.425 1570.650 1672.201 1543.771 1699.080
## 669 1648.236 1594.869 1701.602 1566.619 1729.852
## 670 1675.046 1618.645 1731.446 1588.788 1761.303
## 671 1701.856 1641.989 1761.723 1610.297 1793.415
## 672 1728.666 1664.918 1792.414 1631.173 1826.160
## 673 1755.476 1687.456 1823.496 1651.449 1859.503
## 674 1782.286 1709.626 1854.947 1671.162 1893.411
## 675 1809.097 1731.450 1886.743 1690.346 1927.847
## 676 1835.907 1752.951 1918.863 1709.036 1962.777
## 677 1862.717 1774.148 1951.285 1727.263 1998.171
## 678 1889.527 1795.062 1983.992 1745.056 2033.999
## 679 1916.337 1815.709 2016.966 1762.439 2070.235
## 680 1943.147 1836.103 2050.192 1779.438 2106.857
## 681 1969.958 1856.259 2083.656 1796.070 2143.845
## 682 1996.768 1876.188 2117.348 1812.356 2181.179
## 683 2023.578 1895.900 2151.256 1828.311 2218.844
## 684 2050.388 1915.406 2185.371 1843.950 2256.826
## 685 2077.198 1934.713 2219.684 1859.286 2295.111
## 686 2104.008 1953.829 2254.188 1874.329 2333.688
## 687 2130.819 1972.761 2288.876 1889.091 2372.546
## 688 2157.629 1991.516 2323.742 1903.581 2411.677
## 689 2184.439 2010.098 2358.780 1917.807 2451.071
## 690 2211.249 2028.512 2393.986 1931.777 2490.721
## 691 2238.059 2046.764 2429.354 1945.499 2530.620
## 692 2264.870 2064.858 2464.881 1958.978 2570.761
## 693 2291.680 2082.797 2500.563 1972.221 2611.138
## 694 2318.490 2100.585 2536.395 1985.233 2651.747
## 695 2345.300 2118.225 2572.375 1998.019 2692.581
## 696 2372.110 2135.721 2608.500 2010.584 2733.636
## 697 2398.920 2153.075 2644.766 2022.932 2774.909
## 698 2425.731 2170.290 2681.171 2035.068 2816.393
## 699 2452.541 2187.369 2717.713 2046.995 2858.086
## 700 2479.351 2204.313 2754.389 2058.717 2899.985
## 701 2506.161 2221.126 2791.196 2070.237 2942.085
## 702 2532.971 2237.809 2828.134 2081.559 2984.383
## 703 2559.781 2254.364 2865.199 2092.686 3026.877
## 704 2586.592 2270.793 2902.390 2103.620 3069.563
## 705 2613.402 2287.099 2939.705 2114.364 3112.439
## 706 2640.212 2303.282 2977.142 2124.922 3155.502
## 707 2667.022 2319.344 3014.700 2135.295 3198.750
## 708 2693.832 2335.287 3052.377 2145.485 3242.179
## 709 2720.642 2351.113 3090.172 2155.496 3285.789
## 710 2747.453 2366.822 3128.083 2165.329 3329.576
## 711 2774.263 2382.417 3166.109 2174.986 3373.539
## 712 2801.073 2397.898 3204.248 2184.470 3417.676
## 713 2827.883 2413.267 3242.499 2193.782 3461.984
## 714 2854.693 2428.525 3280.862 2202.925 3506.462
## 715 2881.504 2443.673 3319.334 2211.899 3551.108
## 716 2908.314 2458.712 3357.915 2220.707 3595.920
## 717 2935.124 2473.644 3396.604 2229.351 3640.897
## 718 2961.934 2488.469 3435.399 2237.832 3686.036
## 719 2988.744 2503.189 3474.300 2246.151 3731.337
## 720 3015.554 2517.804 3513.305 2254.311 3776.798
## 721 3042.365 2532.315 3552.414 2262.312 3822.417
## 722 3069.175 2546.725 3591.625 2270.156 3868.193
## 723 3095.985 2561.032 3630.938 2277.845 3914.125
## 724 3122.795 2575.238 3670.352 2285.379 3960.211
## 725 3149.605 2589.345 3709.865 2292.761 4006.449
## 726 3176.415 2603.352 3749.478 2299.991 4052.840
## 727 3203.226 2617.262 3789.190 2307.071 4099.380
## 728 3230.036 2631.073 3828.998 2314.002 4146.070
## 729 3256.846 2644.788 3868.904 2320.784 4192.907
## 730 3283.656 2658.407 3908.905 2327.420 4239.892
## 731 3310.466 2671.931 3949.002 2333.911 4287.022
## 732 3337.276 2685.360 3989.193 2340.256 4334.297
## 733 3364.087 2698.695 4029.478 2346.458 4381.715
## 734 3390.897 2711.937 4069.856 2352.518 4429.276
## 735 3417.707 2725.087 4110.327 2358.436 4476.978
## 736 3444.517 2738.145 4150.890 2364.214 4524.821
## 737 3471.327 2751.111 4191.543 2369.852 4572.803
## 738 3498.137 2763.987 4232.288 2375.351 4620.924
## 739 3524.948 2776.773 4273.122 2380.713 4669.182
## 740 3551.758 2789.470 4314.046 2385.939 4717.577
## 741 3578.568 2802.077 4355.059 2391.028 4766.108
## 742 3605.378 2814.597 4396.159 2395.983 4814.774
## 743 3632.188 2827.029 4437.348 2400.803 4863.573
## 744 3658.999 2839.374 4478.623 2405.491 4912.507
## 745 3685.809 2851.632 4519.985 2410.045 4961.572
## 746 3712.619 2863.804 4561.434 2414.469 5010.769
## 747 3739.429 2875.891 4602.967 2418.761 5060.097
## 748 3766.239 2887.892 4644.586 2422.924 5109.555
## 749 3793.049 2899.809 4686.289 2426.957 5159.142
## 750 3819.860 2911.642 4728.077 2430.861 5208.858
## 751 3846.670 2923.392 4769.948 2434.638 5258.701
## 752 3873.480 2935.058 4811.901 2438.288 5308.672
## 753 3900.290 2946.642 4853.938 2441.811 5358.769
## 754 3927.100 2958.144 4896.057 2445.209 5408.991
## 755 3953.910 2969.564 4938.257 2448.482 5459.339
## 756 3980.721 2980.902 4980.539 2451.631 5509.811
## 757 4007.531 2992.160 5022.901 2454.656 5560.406
## 758 4034.341 3003.338 5065.344 2457.558 5611.124
## 759 4061.151 3014.435 5107.867 2460.337 5661.965
## 760 4087.961 3025.453 5150.469 2462.995 5712.927
## 761 4114.771 3036.392 5193.151 2465.532 5764.011
## 762 4141.582 3047.252 5235.911 2467.949 5815.215
## 763 4168.392 3058.033 5278.750 2470.245 5866.538
## 764 4195.202 3068.737 5321.667 2472.423 5917.981
## 765 4222.012 3079.363 5364.661 2474.481 5969.543
## 766 4248.822 3089.912 5407.733 2476.422 6021.223
## 767 4275.633 3100.384 5450.881 2478.245 6073.020
## 768 4302.443 3110.779 5494.106 2479.951 6124.934
## 769 4329.253 3121.099 5537.407 2481.541 6176.965
## 770 4356.063 3131.342 5580.784 2483.014 6229.112
## 771 4382.873 3141.511 5624.236 2484.373 6281.374
## 772 4409.683 3151.604 5667.763 2485.616 6333.750
## 773 4436.494 3161.622 5711.365 2486.746 6386.241
## 774 4463.304 3171.566 5755.042 2487.761 6438.846
## 775 4490.114 3181.436 5798.792 2488.664 6491.564
## 776 4516.924 3191.232 5842.616 2489.453 6544.395
## 777 4543.734 3200.955 5886.514 2490.130 6597.338
## 778 4570.544 3210.604 5930.484 2490.696 6650.393
## 779 4597.355 3220.181 5974.528 2491.150 6703.559
## 780 4624.165 3229.686 6018.644 2491.493 6756.837
## 781 4650.975 3239.118 6062.832 2491.726 6810.224
## 782 4677.785 3248.478 6107.092 2491.849 6863.721
## 783 4704.595 3257.767 6151.424 2491.863 6917.328
## 784 4731.405 3266.985 6195.826 2491.767 6971.044
## 785 4758.216 3276.131 6240.300 2491.563 7024.868
## 786 4785.026 3285.207 6284.845 2491.251 7078.801
## 787 4811.836 3294.212 6329.460 2490.831 7132.841
## 788 4838.646 3303.148 6374.145 2490.304 7186.988
## 789 4865.456 3312.013 6418.900 2489.670 7241.243
## 790 4892.267 3320.809 6463.724 2488.930 7295.603
## 791 4919.077 3329.536 6508.618 2488.083 7350.070
## 792 4945.887 3338.193 6553.581 2487.131 7404.642
## 793 4972.697 3346.782 6598.612 2486.074 7459.320
## 794 4999.507 3355.302 6643.712 2484.912 7514.102
## 795 5026.317 3363.754 6688.881 2483.646 7568.989
## 796 5053.128 3372.138 6734.117 2482.276 7623.980
## 797 5079.938 3380.454 6779.422 2480.802 7679.074
## 798 5106.748 3388.703 6824.793 2479.224 7734.271
## 799 5133.558 3396.884 6870.232 2477.544 7789.572
## 800 5160.368 3404.998 6915.738 2475.762 7844.975
## 801 5187.178 3413.046 6961.311 2473.877 7900.480
## 802 5213.989 3421.027 7006.950 2471.891 7956.087
## 803 5240.799 3428.942 7052.656 2469.803 8011.795
## 804 5267.609 3436.791 7098.427 2467.614 8067.604
## 805 5294.419 3444.574 7144.265 2465.324 8123.514
## 806 5321.229 3452.291 7190.168 2462.934 8179.524
## 807 5348.039 3459.943 7236.136 2460.445 8235.634
## 808 5374.850 3467.529 7282.170 2457.855 8291.844
## 809 5401.660 3475.051 7328.269 2455.166 8348.154
## 810 5428.470 3482.508 7374.432 2452.378 8404.562
## 811 5455.280 3489.901 7420.660 2449.492 8461.069
## 812 5482.090 3497.229 7466.952 2446.507 8517.674
## 813 5508.901 3504.493 7513.308 2443.424 8574.377
## 814 5535.711 3511.694 7559.728 2440.244 8631.178
## 815 5562.521 3518.830 7606.211 2436.966 8688.076
## 816 5589.331 3525.904 7652.758 2433.591 8745.071
## 817 5616.141 3532.914 7699.369 2430.120 8802.163
## 818 5642.951 3539.861 7746.042 2426.552 8859.351
## 819 5669.762 3546.745 7792.778 2422.888 8916.636
## 820 5696.572 3553.566 7839.577 2419.128 8974.016
## 821 5723.382 3560.325 7886.439 2415.272 9031.492
## 822 5750.192 3567.022 7933.362 2411.322 9089.063
## 823 5777.002 3573.657 7980.348 2407.276 9146.728
## 824 5803.812 3580.230 8027.395 2403.136 9204.489
## 825 5830.623 3586.741 8074.504 2398.902 9262.344
## 826 5857.433 3593.191 8121.675 2394.573 9320.292
## 827 5884.243 3599.579 8168.907 2390.151 9378.335
## 828 5911.053 3605.906 8216.200 2385.635 9436.471
## 829 5937.863 3612.173 8263.554 2381.026 9494.700
## 830 5964.673 3618.378 8310.969 2376.325 9553.022
## 831 5991.484 3624.523 8358.444 2371.530 9611.437#Lamda=0.6 dan gamma=0.3
des.2<- HoltWinters(train.ts, gamma = FALSE, beta = 0.3, alpha = 0.6)
plot(des.2)
#ramalan
ramalandes2<- forecast(des.2, h=167)
ramalandes2## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 665 1578.010 1547.40963 1608.611 1531.210699 1624.810
## 666 1604.990 1566.18148 1643.798 1545.637564 1664.342
## 667 1631.970 1583.29653 1680.643 1557.530560 1706.409
## 668 1658.949 1599.06612 1718.833 1567.365845 1750.533
## 669 1685.929 1613.69635 1758.162 1575.458644 1796.400
## 670 1712.909 1627.32584 1798.492 1582.020943 1843.797
## 671 1739.889 1640.05212 1839.725 1587.201893 1892.575
## 672 1766.868 1651.94723 1881.789 1591.111687 1942.625
## 673 1793.848 1663.06679 1924.629 1593.835374 1993.861
## 674 1820.828 1673.45532 1968.200 1595.441044 2046.215
## 675 1847.808 1683.14954 2012.466 1595.984855 2099.630
## 676 1874.787 1692.18046 2057.394 1595.514255 2154.060
## 677 1901.767 1700.57483 2102.959 1594.070111 2209.464
## 678 1928.747 1708.35600 2149.138 1591.688183 2265.805
## 679 1955.727 1715.54472 2195.908 1588.400165 2323.053
## 680 1982.706 1722.15954 2243.253 1584.234449 2381.178
## 681 2009.686 1728.21725 2291.155 1579.216698 2440.155
## 682 2036.666 1733.73312 2339.598 1573.370279 2499.961
## 683 2063.645 1738.72115 2388.570 1566.716611 2560.574
## 684 2090.625 1743.19427 2438.056 1559.275436 2621.975
## 685 2117.605 1747.16441 2488.045 1551.065036 2684.145
## 686 2144.585 1750.64271 2538.527 1542.102417 2747.067
## 687 2171.564 1753.63953 2589.489 1532.403454 2810.725
## 688 2198.544 1756.16461 2640.924 1521.983021 2875.105
## 689 2225.524 1758.22709 2692.821 1510.855091 2940.193
## 690 2252.504 1759.83556 2745.172 1499.032831 3005.974
## 691 2279.483 1760.99818 2797.969 1486.528680 3072.438
## 692 2306.463 1761.72262 2851.204 1473.354411 3139.572
## 693 2333.443 1762.01620 2904.870 1459.521193 3207.365
## 694 2360.423 1761.88586 2958.959 1445.039645 3275.806
## 695 2387.402 1761.33821 3013.467 1429.919875 3344.885
## 696 2414.382 1760.37956 3068.385 1414.171527 3414.593
## 697 2441.362 1759.01592 3123.708 1397.803810 3484.920
## 698 2468.342 1757.25306 3179.430 1380.825535 3555.858
## 699 2495.321 1755.09650 3235.546 1363.245143 3627.398
## 700 2522.301 1752.55152 3292.051 1345.070728 3699.531
## 701 2549.281 1749.62322 3348.938 1326.310063 3772.252
## 702 2576.261 1746.31647 3406.205 1306.970620 3845.550
## 703 2603.240 1742.63599 3463.845 1287.059588 3919.421
## 704 2630.220 1738.58629 3521.854 1266.583894 3993.856
## 705 2657.200 1734.17174 3580.228 1245.550216 4068.849
## 706 2684.180 1729.39656 3638.962 1223.964997 4144.394
## 707 2711.159 1724.26482 3698.054 1201.834463 4220.484
## 708 2738.139 1718.78045 3757.498 1179.164630 4297.113
## 709 2765.119 1712.94726 3817.290 1155.961318 4374.276
## 710 2792.098 1706.76892 3877.428 1132.230162 4451.967
## 711 2819.078 1700.24902 3937.907 1107.976620 4530.180
## 712 2846.058 1693.39101 3998.725 1083.205985 4608.910
## 713 2873.038 1686.19825 4059.877 1057.923389 4688.152
## 714 2900.017 1678.67399 4121.361 1032.133815 4767.901
## 715 2926.997 1670.82140 4183.173 1005.842101 4848.152
## 716 2953.977 1662.64355 4245.310 979.052952 4928.901
## 717 2980.957 1654.14343 4307.770 951.770938 5010.142
## 718 3007.936 1645.32396 4370.549 924.000507 5091.872
## 719 3034.916 1636.18796 4433.644 895.745989 5174.086
## 720 3061.896 1626.73819 4497.054 867.011598 5256.780
## 721 3088.876 1616.97733 4560.774 837.801443 5339.950
## 722 3115.855 1606.90801 4624.803 808.119525 5423.591
## 723 3142.835 1596.53277 4689.137 777.969749 5507.700
## 724 3169.815 1585.85410 4753.776 747.355920 5592.274
## 725 3196.795 1574.87443 4818.715 716.281756 5677.307
## 726 3223.774 1563.59614 4883.953 684.750884 5762.798
## 727 3250.754 1552.02153 4949.487 652.766847 5848.741
## 728 3277.734 1540.15289 5015.315 620.333107 5935.135
## 729 3304.714 1527.99241 5081.435 587.453046 6021.974
## 730 3331.693 1515.54226 5147.844 554.129973 6109.257
## 731 3358.673 1502.80455 5214.542 520.367124 6196.979
## 732 3385.653 1489.78137 5281.524 486.167662 6285.138
## 733 3412.633 1476.47472 5348.790 451.534687 6373.730
## 734 3439.612 1462.88659 5416.338 416.471229 6462.753
## 735 3466.592 1449.01893 5484.165 380.980261 6552.204
## 736 3493.572 1434.87364 5552.270 345.064689 6642.079
## 737 3520.551 1420.45257 5620.650 308.727365 6732.376
## 738 3547.531 1405.75757 5689.305 271.971081 6823.091
## 739 3574.511 1390.79041 5758.232 234.798577 6914.223
## 740 3601.491 1375.55286 5827.429 197.212539 7005.769
## 741 3628.470 1360.04663 5896.894 159.215600 7097.725
## 742 3655.450 1344.27342 5966.627 120.810344 7190.090
## 743 3682.430 1328.23489 6036.625 81.999308 7282.861
## 744 3709.410 1311.93265 6106.887 42.784981 7376.034
## 745 3736.389 1295.36832 6177.411 3.169808 7469.609
## 746 3763.369 1278.54346 6248.195 -36.843812 7563.582
## 747 3790.349 1261.45961 6319.238 -77.253521 7657.951
## 748 3817.329 1244.11828 6390.539 -118.057003 7752.714
## 749 3844.308 1226.52097 6462.096 -159.251982 7847.869
## 750 3871.288 1208.66913 6533.907 -200.836221 7943.412
## 751 3898.268 1190.56421 6605.972 -242.807522 8039.343
## 752 3925.248 1172.20761 6678.288 -285.163722 8135.659
## 753 3952.227 1153.60074 6750.854 -327.902696 8232.357
## 754 3979.207 1134.74495 6823.669 -371.022352 8329.437
## 755 4006.187 1115.64159 6896.732 -414.520633 8426.894
## 756 4033.167 1096.29198 6970.041 -458.395514 8524.729
## 757 4060.146 1076.69743 7043.595 -502.645004 8622.938
## 758 4087.126 1056.85922 7117.393 -547.267141 8721.519
## 759 4114.106 1036.77861 7191.433 -592.259996 8820.472
## 760 4141.086 1016.45684 7265.714 -637.621667 8919.793
## 761 4168.065 995.89515 7340.235 -683.350284 9019.481
## 762 4195.045 975.09472 7414.995 -729.444002 9119.534
## 763 4222.025 954.05675 7489.993 -775.901006 9219.951
## 764 4249.004 932.78242 7565.227 -822.719506 9320.728
## 765 4275.984 911.27287 7640.696 -869.897741 9421.866
## 766 4302.964 889.52923 7716.399 -917.433972 9523.362
## 767 4329.944 867.55264 7792.335 -965.326487 9625.214
## 768 4356.923 845.34418 7868.503 -1013.573599 9727.421
## 769 4383.903 822.90496 7944.901 -1062.173643 9829.980
## 770 4410.883 800.23604 8021.530 -1111.124977 9932.891
## 771 4437.863 777.33848 8098.387 -1160.425985 10036.151
## 772 4464.842 754.21332 8175.472 -1210.075069 10139.760
## 773 4491.822 730.86160 8252.783 -1260.070655 10243.715
## 774 4518.802 707.28433 8330.319 -1310.411191 10348.015
## 775 4545.782 683.48251 8408.081 -1361.095142 10452.658
## 776 4572.761 659.45714 8486.066 -1412.120998 10557.644
## 777 4599.741 635.20918 8564.273 -1463.487265 10662.970
## 778 4626.721 610.73960 8642.702 -1515.192471 10768.634
## 779 4653.701 586.04935 8721.352 -1567.235161 10874.636
## 780 4680.680 561.13937 8800.221 -1619.613900 10980.975
## 781 4707.660 536.01058 8879.310 -1672.327271 11087.647
## 782 4734.640 510.66391 8958.616 -1725.373873 11194.654
## 783 4761.620 485.10025 9038.139 -1778.752325 11301.991
## 784 4788.599 459.32051 9117.878 -1832.461261 11409.660
## 785 4815.579 433.32555 9197.833 -1886.499334 11517.657
## 786 4842.559 407.11625 9278.001 -1940.865211 11625.983
## 787 4869.539 380.69347 9358.384 -1995.557576 11734.635
## 788 4896.518 354.05806 9438.979 -2050.575129 11843.612
## 789 4923.498 327.21086 9519.785 -2105.916585 11952.913
## 790 4950.478 300.15271 9600.803 -2161.580674 12062.536
## 791 4977.458 272.88442 9682.031 -2217.566142 12172.481
## 792 5004.437 245.40679 9763.468 -2273.871748 12282.746
## 793 5031.417 217.72065 9845.113 -2330.496266 12393.330
## 794 5058.397 189.82677 9926.967 -2387.438484 12504.232
## 795 5085.376 161.72594 10009.027 -2444.697204 12615.450
## 796 5112.356 133.41894 10091.293 -2502.271240 12726.984
## 797 5139.336 104.90653 10173.765 -2560.159422 12838.831
## 798 5166.316 76.18947 10256.442 -2618.360589 12950.992
## 799 5193.295 47.26851 10339.322 -2676.873597 13063.464
## 800 5220.275 18.14438 10422.406 -2735.697311 13176.248
## 801 5247.255 -11.18217 10505.692 -2794.830611 13289.340
## 802 5274.235 -40.71042 10589.180 -2854.272387 13402.742
## 803 5301.214 -70.43965 10672.868 -2914.021542 13516.450
## 804 5328.194 -100.36916 10756.757 -2974.076990 13630.465
## 805 5355.174 -130.49825 10840.846 -3034.437657 13744.785
## 806 5382.154 -160.82621 10925.133 -3095.102480 13859.410
## 807 5409.133 -191.35235 11009.619 -3156.070407 13974.337
## 808 5436.113 -222.07601 11094.302 -3217.340397 14089.567
## 809 5463.093 -252.99650 11179.182 -3278.911418 14205.097
## 810 5490.073 -284.11316 11264.258 -3340.782452 14320.928
## 811 5517.052 -315.42532 11349.530 -3402.952488 14437.057
## 812 5544.032 -346.93234 11434.996 -3465.420527 14553.485
## 813 5571.012 -378.63357 11520.657 -3528.185579 14670.209
## 814 5597.992 -410.52836 11606.511 -3591.246664 14787.230
## 815 5624.971 -442.61608 11692.559 -3654.602813 14904.545
## 816 5651.951 -474.89611 11778.798 -3718.253063 15022.155
## 817 5678.931 -507.36781 11865.229 -3782.196465 15140.058
## 818 5705.911 -540.03058 11951.852 -3846.432075 15258.253
## 819 5732.890 -572.88381 12038.664 -3910.958960 15376.739
## 820 5759.870 -605.92689 12125.667 -3975.776197 15495.516
## 821 5786.850 -639.15921 12212.859 -4040.882870 15614.582
## 822 5813.829 -672.58020 12300.239 -4106.278070 15733.937
## 823 5840.809 -706.18926 12387.808 -4171.960902 15853.579
## 824 5867.789 -739.98581 12475.564 -4237.930473 15973.508
## 825 5894.769 -773.96927 12563.507 -4304.185902 16093.723
## 826 5921.748 -808.13907 12651.636 -4370.726315 16214.223
## 827 5948.728 -842.49464 12739.951 -4437.550846 16335.007
## 828 5975.708 -877.03543 12828.451 -4504.658638 16456.074
## 829 6002.688 -911.76088 12917.136 -4572.048840 16577.424
## 830 6029.667 -946.67044 13006.005 -4639.720609 16699.055
## 831 6056.647 -981.76355 13095.058 -4707.673110 16820.967Selanjutnya ingin dibandingkan plot data latih dan data uji adalah sebagai berikut.
#Visually evaluate the prediction
plot(btcprice.ts)
lines(des.1$fitted[,1], lty=2, col="blue")
lines(ramalandes1$mean, col="red")
Untuk mendapatkan nilai parameter optimum dari DES, argumen
alpha dan beta dapat dibuat NULL
seperti berikut.
#Lamda dan gamma optimum
des.opt<- HoltWinters(train.ts, gamma = FALSE)
des.opt## Holt-Winters exponential smoothing with trend and without seasonal component.
##
## Call:
## HoltWinters(x = train.ts, gamma = FALSE)
##
## Smoothing parameters:
## alpha: 1
## beta : 0.01120346
## gamma: FALSE
##
## Coefficients:
## [,1]
## a 1548.286300
## b 5.759443plot(des.opt)
#ramalan
ramalandesopt<- forecast(des.opt, h=167)
ramalandesopt## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 665 1554.046 1527.222 1580.869 1513.023 1595.069
## 666 1559.805 1521.658 1597.952 1501.464 1618.146
## 667 1565.565 1518.583 1612.547 1493.712 1637.417
## 668 1571.324 1516.771 1625.877 1487.893 1654.755
## 669 1577.084 1515.753 1638.414 1483.287 1670.880
## 670 1582.843 1515.287 1650.399 1479.525 1686.161
## 671 1588.602 1515.232 1661.973 1476.392 1700.813
## 672 1594.362 1515.495 1673.229 1473.745 1714.979
## 673 1600.121 1516.013 1684.230 1471.488 1728.755
## 674 1605.881 1516.739 1695.022 1469.551 1742.211
## 675 1611.640 1517.641 1705.640 1467.880 1755.400
## 676 1617.400 1518.689 1716.110 1466.435 1768.364
## 677 1623.159 1519.865 1726.453 1465.184 1781.134
## 678 1628.919 1521.150 1736.687 1464.101 1793.736
## 679 1634.678 1522.531 1746.825 1463.164 1806.192
## 680 1640.437 1523.996 1756.879 1462.356 1818.519
## 681 1646.197 1525.536 1766.858 1461.662 1830.732
## 682 1651.956 1527.141 1776.771 1461.068 1842.844
## 683 1657.716 1528.806 1786.626 1460.565 1854.866
## 684 1663.475 1530.524 1796.427 1460.143 1866.807
## 685 1669.235 1532.289 1806.181 1459.794 1878.675
## 686 1674.994 1534.097 1815.891 1459.510 1890.478
## 687 1680.753 1535.943 1825.564 1459.286 1902.221
## 688 1686.513 1537.825 1835.201 1459.115 1913.911
## 689 1692.272 1539.739 1844.806 1458.993 1925.552
## 690 1698.032 1541.681 1854.382 1458.914 1937.149
## 691 1703.791 1543.650 1863.932 1458.877 1948.706
## 692 1709.551 1545.643 1873.459 1458.875 1960.226
## 693 1715.310 1547.657 1882.963 1458.907 1971.713
## 694 1721.070 1549.691 1892.448 1458.969 1983.170
## 695 1726.829 1551.744 1901.914 1459.059 1994.599
## 696 1732.588 1553.812 1911.365 1459.174 2006.003
## 697 1738.348 1555.896 1920.800 1459.311 2017.385
## 698 1744.107 1557.993 1930.222 1459.469 2028.745
## 699 1749.867 1560.102 1939.632 1459.646 2040.087
## 700 1755.626 1562.222 1949.030 1459.840 2051.412
## 701 1761.386 1564.353 1958.419 1460.050 2062.722
## 702 1767.145 1566.492 1967.798 1460.273 2074.018
## 703 1772.905 1568.640 1977.170 1460.508 2085.301
## 704 1778.664 1570.794 1986.534 1460.755 2096.573
## 705 1784.423 1572.956 1995.891 1461.011 2107.836
## 706 1790.183 1575.123 2005.243 1461.276 2119.089
## 707 1795.942 1577.295 2014.590 1461.549 2130.335
## 708 1801.702 1579.471 2023.933 1461.829 2141.575
## 709 1807.461 1581.651 2033.272 1462.114 2152.808
## 710 1813.221 1583.834 2042.607 1462.404 2164.037
## 711 1818.980 1586.020 2051.940 1462.699 2175.262
## 712 1824.740 1588.208 2061.271 1462.996 2186.483
## 713 1830.499 1590.398 2070.600 1463.296 2197.702
## 714 1836.258 1592.589 2079.928 1463.598 2208.919
## 715 1842.018 1594.781 2089.255 1463.902 2220.134
## 716 1847.777 1596.973 2098.581 1464.206 2231.349
## 717 1853.537 1599.166 2107.908 1464.510 2242.564
## 718 1859.296 1601.358 2117.235 1464.813 2253.779
## 719 1865.056 1603.549 2126.562 1465.116 2264.996
## 720 1870.815 1605.739 2135.891 1465.417 2276.214
## 721 1876.575 1607.929 2145.221 1465.716 2287.433
## 722 1882.334 1610.116 2154.552 1466.013 2298.655
## 723 1888.093 1612.302 2163.885 1466.307 2309.880
## 724 1893.853 1614.486 2173.220 1466.598 2321.108
## 725 1899.612 1616.667 2182.557 1466.885 2332.339
## 726 1905.372 1618.846 2191.897 1467.169 2343.575
## 727 1911.131 1621.023 2201.240 1467.448 2354.814
## 728 1916.891 1623.196 2210.585 1467.723 2366.058
## 729 1922.650 1625.366 2219.934 1467.993 2377.307
## 730 1928.410 1627.533 2229.286 1468.258 2388.561
## 731 1934.169 1629.696 2238.642 1468.518 2399.820
## 732 1939.928 1631.856 2248.001 1468.772 2411.085
## 733 1945.688 1634.012 2257.364 1469.020 2422.356
## 734 1951.447 1636.163 2266.731 1469.262 2433.633
## 735 1957.207 1638.311 2276.103 1469.498 2444.916
## 736 1962.966 1640.454 2285.478 1469.727 2456.206
## 737 1968.726 1642.593 2294.858 1469.949 2467.502
## 738 1974.485 1644.728 2304.243 1470.165 2478.806
## 739 1980.245 1646.857 2313.632 1470.373 2490.116
## 740 1986.004 1648.982 2323.026 1470.574 2501.434
## 741 1991.763 1651.102 2332.425 1470.767 2512.760
## 742 1997.523 1653.217 2341.828 1470.953 2524.093
## 743 2003.282 1655.327 2351.237 1471.131 2535.434
## 744 2009.042 1657.432 2360.652 1471.301 2546.783
## 745 2014.801 1659.531 2370.071 1471.463 2558.140
## 746 2020.561 1661.625 2379.496 1471.616 2569.505
## 747 2026.320 1663.714 2388.926 1471.762 2580.879
## 748 2032.080 1665.797 2398.362 1471.898 2592.261
## 749 2037.839 1667.874 2407.804 1472.027 2603.651
## 750 2043.598 1669.946 2417.251 1472.146 2615.051
## 751 2049.358 1672.012 2426.704 1472.257 2626.459
## 752 2055.117 1674.072 2436.163 1472.358 2637.876
## 753 2060.877 1676.126 2445.628 1472.451 2649.303
## 754 2066.636 1678.174 2455.099 1472.534 2660.738
## 755 2072.396 1680.216 2464.576 1472.608 2672.183
## 756 2078.155 1682.252 2474.058 1472.673 2683.637
## 757 2083.915 1684.282 2483.548 1472.729 2695.101
## 758 2089.674 1686.305 2493.043 1472.774 2706.573
## 759 2095.433 1688.322 2502.544 1472.811 2718.056
## 760 2101.193 1690.333 2512.052 1472.838 2729.548
## 761 2106.952 1692.338 2521.567 1472.855 2741.050
## 762 2112.712 1694.336 2531.087 1472.862 2752.562
## 763 2118.471 1696.328 2540.614 1472.859 2764.083
## 764 2124.231 1698.313 2550.148 1472.847 2775.615
## 765 2129.990 1700.292 2559.688 1472.824 2787.156
## 766 2135.750 1702.265 2569.235 1472.791 2798.708
## 767 2141.509 1704.230 2578.788 1472.749 2810.269
## 768 2147.268 1706.189 2588.348 1472.696 2821.841
## 769 2153.028 1708.142 2597.914 1472.633 2833.423
## 770 2158.787 1710.087 2607.487 1472.560 2845.015
## 771 2164.547 1712.026 2617.067 1472.476 2856.617
## 772 2170.306 1713.958 2626.654 1472.382 2868.230
## 773 2176.066 1715.884 2636.247 1472.278 2879.853
## 774 2181.825 1717.802 2645.848 1472.164 2891.487
## 775 2187.585 1719.714 2655.455 1472.039 2903.131
## 776 2193.344 1721.619 2665.069 1471.903 2914.785
## 777 2199.103 1723.517 2674.690 1471.757 2926.450
## 778 2204.863 1725.408 2684.318 1471.600 2938.126
## 779 2210.622 1727.292 2693.952 1471.433 2949.812
## 780 2216.382 1729.170 2703.594 1471.255 2961.508
## 781 2222.141 1731.040 2713.242 1471.067 2973.216
## 782 2227.901 1732.903 2722.898 1470.867 2984.934
## 783 2233.660 1734.759 2732.561 1470.657 2996.663
## 784 2239.420 1736.609 2742.230 1470.437 3008.402
## 785 2245.179 1738.451 2751.907 1470.205 3020.153
## 786 2250.938 1740.286 2761.591 1469.963 3031.914
## 787 2256.698 1742.114 2771.281 1469.710 3043.685
## 788 2262.457 1743.935 2780.979 1469.446 3055.468
## 789 2268.217 1745.749 2790.684 1469.172 3067.262
## 790 2273.976 1747.556 2800.396 1468.886 3079.066
## 791 2279.736 1749.356 2810.115 1468.590 3090.881
## 792 2285.495 1751.149 2819.841 1468.283 3102.707
## 793 2291.255 1752.934 2829.575 1467.965 3114.544
## 794 2297.014 1754.713 2839.315 1467.635 3126.392
## 795 2302.773 1756.484 2849.063 1467.295 3138.251
## 796 2308.533 1758.248 2858.818 1466.944 3150.121
## 797 2314.292 1760.005 2868.580 1466.583 3162.002
## 798 2320.052 1761.754 2878.349 1466.210 3173.894
## 799 2325.811 1763.497 2888.125 1465.826 3185.797
## 800 2331.571 1765.232 2897.909 1465.431 3197.710
## 801 2337.330 1766.960 2907.700 1465.025 3209.635
## 802 2343.089 1768.681 2917.498 1464.608 3221.571
## 803 2348.849 1770.395 2927.303 1464.180 3233.518
## 804 2354.608 1772.102 2937.115 1463.741 3245.476
## 805 2360.368 1773.801 2946.935 1463.291 3257.445
## 806 2366.127 1775.493 2956.762 1462.830 3269.425
## 807 2371.887 1777.178 2966.596 1462.358 3281.416
## 808 2377.646 1778.855 2976.437 1461.875 3293.418
## 809 2383.406 1780.526 2986.285 1461.381 3305.431
## 810 2389.165 1782.189 2996.141 1460.875 3317.455
## 811 2394.924 1783.845 3006.004 1460.359 3329.490
## 812 2400.684 1785.494 3015.874 1459.832 3341.536
## 813 2406.443 1787.135 3025.752 1459.293 3353.594
## 814 2412.203 1788.769 3035.636 1458.743 3365.662
## 815 2417.962 1790.396 3045.528 1458.183 3377.742
## 816 2423.722 1792.016 3055.427 1457.611 3389.832
## 817 2429.481 1793.628 3065.334 1457.028 3401.934
## 818 2435.241 1795.234 3075.247 1456.435 3414.047
## 819 2441.000 1796.832 3085.168 1455.830 3426.170
## 820 2446.759 1798.422 3095.097 1455.214 3438.305
## 821 2452.519 1800.006 3105.032 1454.586 3450.451
## 822 2458.278 1801.582 3114.974 1453.948 3462.608
## 823 2464.038 1803.151 3124.924 1453.299 3474.777
## 824 2469.797 1804.713 3134.881 1452.639 3486.956
## 825 2475.557 1806.268 3144.846 1451.967 3499.146
## 826 2481.316 1807.815 3154.817 1451.285 3511.347
## 827 2487.076 1809.355 3164.796 1450.591 3523.560
## 828 2492.835 1810.888 3174.782 1449.887 3535.783
## 829 2498.594 1812.413 3184.775 1449.171 3548.018
## 830 2504.354 1813.932 3194.776 1448.444 3560.263
## 831 2510.113 1815.443 3204.784 1447.707 3572.520Selanjutnya akan dilakukan perhitungan akurasi pada data latih maupun data uji dengan ukuran akurasi SSE, MSE dan MAPE.
Akurasi Data Latih
#Akurasi Data Training
ssedes.train1<-des.1$SSE
msedes.train1<-ssedes.train1/length(train.ts)
sisaandes1<-ramalandes1$residuals
head(sisaandes1)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA NA 2.333000 0.472780 5.622493 4.861863mapedes.train1 <- sum(abs(sisaandes1[3:length(train.ts)]/train.ts[3:length(train.ts)])
*100)/length(train.ts)
akurasides.1 <- matrix(c(ssedes.train1,msedes.train1,mapedes.train1))
row.names(akurasides.1)<- c("SSE", "MSE", "MAPE")
colnames(akurasides.1) <- c("Akurasi lamda=0.2 dan gamma=0.2")
akurasides.1## Akurasi lamda=0.2 dan gamma=0.2
## SSE 8.388072e+05
## MSE 1.263264e+03
## MAPE 3.291585e+00ssedes.train2<-des.2$SSE
msedes.train2<-ssedes.train2/length(train.ts)
sisaandes2<-ramalandes2$residuals
head(sisaandes2)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA NA 2.333000 -0.787040 4.763411 1.470678mapedes.train2 <- sum(abs(sisaandes2[3:length(train.ts)]/train.ts[3:length(train.ts)])
*100)/length(train.ts)
akurasides.2 <- matrix(c(ssedes.train2,msedes.train2,mapedes.train2))
row.names(akurasides.2)<- c("SSE", "MSE", "MAPE")
colnames(akurasides.2) <- c("Akurasi lamda=0.6 dan gamma=0.3")
akurasides.2## Akurasi lamda=0.6 dan gamma=0.3
## SSE 3.769123e+05
## MSE 5.676390e+02
## MAPE 2.094042e+00Hasil pemulusan time series menunjukkan bahwa model dengan parameter λ = 0.6 dan γ = 0.3 memiliki performa yang lebih baik dibandingkan dengan model λ = 0.2 dan γ = 0.2. Hal ini terlihat dari nilai SSE, MSE, dan MAPE yang lebih kecil, yaitu masing-masing sebesar 376,912; 567; dan 2.09%. Sementara itu, model pertama menghasilkan nilai kesalahan yang lebih besar, yaitu SSE = 838,807; MSE = 1,263; dan MAPE = 3.29%. Dengan demikian, dapat disimpulkan bahwa model dengan λ = 0.6 dan γ = 0.3 lebih sesuai digunakan untuk meramalkan data karena memberikan tingkat akurasi yang lebih tinggi.
Akurasi Data Uji
# Akurasi Data Uji
# Cek dan sesuaikan panjang dulu
common_length <- min(length(ramalandes1$mean), length(testing$price))
# Akurasi Data Testing - FIXED
selisihdes1 <- ramalandes1$mean[1:common_length] - testing$price[1:common_length]
SSEtestingdes1 <- sum(selisihdes1^2)
MSEtestingdes1 <- SSEtestingdes1/common_length
MAPEtestingdes1 <- sum(abs(selisihdes1/testing$price[1:common_length])*100)/common_length
selisihdes2 <- ramalandes2$mean[1:common_length] - testing$price[1:common_length]
SSEtestingdes2 <- sum(selisihdes2^2)
MSEtestingdes2 <- SSEtestingdes2/common_length
MAPEtestingdes2 <- sum(abs(selisihdes2/testing$price[1:common_length])*100)/common_length
selisihdesopt <- ramalandesopt$mean[1:common_length] - testing$price[1:common_length]
SSEtestingdesopt <- sum(selisihdesopt^2)
MSEtestingdesopt <- SSEtestingdesopt/common_length
MAPEtestingdesopt <- sum(abs(selisihdesopt/testing$price[1:common_length])*100)/common_length
# Buat matrix akurasi
akurasitestingdes <- matrix(
c(SSEtestingdes1, MSEtestingdes1, MAPEtestingdes1,
SSEtestingdes2, MSEtestingdes2, MAPEtestingdes2,
SSEtestingdesopt, MSEtestingdesopt, MAPEtestingdesopt),
nrow = 3, ncol = 3, byrow = FALSE
)
row.names(akurasitestingdes) <- c("SSE", "MSE", "MAPE")
colnames(akurasitestingdes) <- c("des ske1", "des ske2", "des opt")
print(akurasitestingdes)## des ske1 des ske2 des opt
## SSE 9.023515e+07 9.939989e+07 3.873175e+08
## MSE 5.403302e+05 5.952089e+05 2.319266e+06
## MAPE 1.783127e+01 1.864297e+01 3.447167e+01Kesimpulan: model des.ske1 memberikan hasil ramalan terbaik dibandingkan dengan model des.ske2 dan des.opt. Nilai SSE (9.02×10⁷), MSE (5.43×10⁵), dan MAPE (17.94%) dari des.ske1 semuanya lebih kecil daripada dua model lainnya. Hal ini menunjukkan bahwa kesalahan prediksi model des.ske1 relatif paling rendah, sehingga model tersebut lebih sesuai digunakan untuk meramalkan data. Sebaliknya, model des.opt memiliki error yang paling besar pada semua ukuran (SSE, MSE, maupun MAPE), sehingga performanya paling buruk di antara ketiga model.
Peramalan
#Forecast
forecast1 <- predict(des.1, n.ahead = 167)
forecast2 <- predict(des.2, n.ahead = 167)
forecast.opt <- predict(des.opt, n.ahead = 167)Plot Deret Waktu
library(forecast)
# Misalnya meramalkan 10 periode ke depan
horizon <- 200
# Forecast dengan horizon baru (future forecasting)
forecast_des1 <- forecast(ramalandes1$model, h = horizon)
forecast_des2 <- forecast(ramalandes2$model, h = horizon)
forecast_desopt <- forecast(ramalandesopt$model, h = horizon)
# Lihat hasil peramalan
forecast_des1## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 665 1540.995 1495.368 1586.622 1471.214 1610.776
## 666 1567.805 1520.882 1614.728 1496.043 1639.567
## 667 1594.615 1545.984 1643.246 1520.241 1668.990
## 668 1621.425 1570.650 1672.201 1543.771 1699.080
## 669 1648.236 1594.869 1701.602 1566.619 1729.852
## 670 1675.046 1618.645 1731.446 1588.788 1761.303
## 671 1701.856 1641.989 1761.723 1610.297 1793.415
## 672 1728.666 1664.918 1792.414 1631.173 1826.160
## 673 1755.476 1687.456 1823.496 1651.449 1859.503
## 674 1782.286 1709.626 1854.947 1671.162 1893.411
## 675 1809.097 1731.450 1886.743 1690.346 1927.847
## 676 1835.907 1752.951 1918.863 1709.036 1962.777
## 677 1862.717 1774.148 1951.285 1727.263 1998.171
## 678 1889.527 1795.062 1983.992 1745.056 2033.999
## 679 1916.337 1815.709 2016.966 1762.439 2070.235
## 680 1943.147 1836.103 2050.192 1779.438 2106.857
## 681 1969.958 1856.259 2083.656 1796.070 2143.845
## 682 1996.768 1876.188 2117.348 1812.356 2181.179
## 683 2023.578 1895.900 2151.256 1828.311 2218.844
## 684 2050.388 1915.406 2185.371 1843.950 2256.826
## 685 2077.198 1934.713 2219.684 1859.286 2295.111
## 686 2104.008 1953.829 2254.188 1874.329 2333.688
## 687 2130.819 1972.761 2288.876 1889.091 2372.546
## 688 2157.629 1991.516 2323.742 1903.581 2411.677
## 689 2184.439 2010.098 2358.780 1917.807 2451.071
## 690 2211.249 2028.512 2393.986 1931.777 2490.721
## 691 2238.059 2046.764 2429.354 1945.499 2530.620
## 692 2264.870 2064.858 2464.881 1958.978 2570.761
## 693 2291.680 2082.797 2500.563 1972.221 2611.138
## 694 2318.490 2100.585 2536.395 1985.233 2651.747
## 695 2345.300 2118.225 2572.375 1998.019 2692.581
## 696 2372.110 2135.721 2608.500 2010.584 2733.636
## 697 2398.920 2153.075 2644.766 2022.932 2774.909
## 698 2425.731 2170.290 2681.171 2035.068 2816.393
## 699 2452.541 2187.369 2717.713 2046.995 2858.086
## 700 2479.351 2204.313 2754.389 2058.717 2899.985
## 701 2506.161 2221.126 2791.196 2070.237 2942.085
## 702 2532.971 2237.809 2828.134 2081.559 2984.383
## 703 2559.781 2254.364 2865.199 2092.686 3026.877
## 704 2586.592 2270.793 2902.390 2103.620 3069.563
## 705 2613.402 2287.099 2939.705 2114.364 3112.439
## 706 2640.212 2303.282 2977.142 2124.922 3155.502
## 707 2667.022 2319.344 3014.700 2135.295 3198.750
## 708 2693.832 2335.287 3052.377 2145.485 3242.179
## 709 2720.642 2351.113 3090.172 2155.496 3285.789
## 710 2747.453 2366.822 3128.083 2165.329 3329.576
## 711 2774.263 2382.417 3166.109 2174.986 3373.539
## 712 2801.073 2397.898 3204.248 2184.470 3417.676
## 713 2827.883 2413.267 3242.499 2193.782 3461.984
## 714 2854.693 2428.525 3280.862 2202.925 3506.462
## 715 2881.504 2443.673 3319.334 2211.899 3551.108
## 716 2908.314 2458.712 3357.915 2220.707 3595.920
## 717 2935.124 2473.644 3396.604 2229.351 3640.897
## 718 2961.934 2488.469 3435.399 2237.832 3686.036
## 719 2988.744 2503.189 3474.300 2246.151 3731.337
## 720 3015.554 2517.804 3513.305 2254.311 3776.798
## 721 3042.365 2532.315 3552.414 2262.312 3822.417
## 722 3069.175 2546.725 3591.625 2270.156 3868.193
## 723 3095.985 2561.032 3630.938 2277.845 3914.125
## 724 3122.795 2575.238 3670.352 2285.379 3960.211
## 725 3149.605 2589.345 3709.865 2292.761 4006.449
## 726 3176.415 2603.352 3749.478 2299.991 4052.840
## 727 3203.226 2617.262 3789.190 2307.071 4099.380
## 728 3230.036 2631.073 3828.998 2314.002 4146.070
## 729 3256.846 2644.788 3868.904 2320.784 4192.907
## 730 3283.656 2658.407 3908.905 2327.420 4239.892
## 731 3310.466 2671.931 3949.002 2333.911 4287.022
## 732 3337.276 2685.360 3989.193 2340.256 4334.297
## 733 3364.087 2698.695 4029.478 2346.458 4381.715
## 734 3390.897 2711.937 4069.856 2352.518 4429.276
## 735 3417.707 2725.087 4110.327 2358.436 4476.978
## 736 3444.517 2738.145 4150.890 2364.214 4524.821
## 737 3471.327 2751.111 4191.543 2369.852 4572.803
## 738 3498.137 2763.987 4232.288 2375.351 4620.924
## 739 3524.948 2776.773 4273.122 2380.713 4669.182
## 740 3551.758 2789.470 4314.046 2385.939 4717.577
## 741 3578.568 2802.077 4355.059 2391.028 4766.108
## 742 3605.378 2814.597 4396.159 2395.983 4814.774
## 743 3632.188 2827.029 4437.348 2400.803 4863.573
## 744 3658.999 2839.374 4478.623 2405.491 4912.507
## 745 3685.809 2851.632 4519.985 2410.045 4961.572
## 746 3712.619 2863.804 4561.434 2414.469 5010.769
## 747 3739.429 2875.891 4602.967 2418.761 5060.097
## 748 3766.239 2887.892 4644.586 2422.924 5109.555
## 749 3793.049 2899.809 4686.289 2426.957 5159.142
## 750 3819.860 2911.642 4728.077 2430.861 5208.858
## 751 3846.670 2923.392 4769.948 2434.638 5258.701
## 752 3873.480 2935.058 4811.901 2438.288 5308.672
## 753 3900.290 2946.642 4853.938 2441.811 5358.769
## 754 3927.100 2958.144 4896.057 2445.209 5408.991
## 755 3953.910 2969.564 4938.257 2448.482 5459.339
## 756 3980.721 2980.902 4980.539 2451.631 5509.811
## 757 4007.531 2992.160 5022.901 2454.656 5560.406
## 758 4034.341 3003.338 5065.344 2457.558 5611.124
## 759 4061.151 3014.435 5107.867 2460.337 5661.965
## 760 4087.961 3025.453 5150.469 2462.995 5712.927
## 761 4114.771 3036.392 5193.151 2465.532 5764.011
## 762 4141.582 3047.252 5235.911 2467.949 5815.215
## 763 4168.392 3058.033 5278.750 2470.245 5866.538
## 764 4195.202 3068.737 5321.667 2472.423 5917.981
## 765 4222.012 3079.363 5364.661 2474.481 5969.543
## 766 4248.822 3089.912 5407.733 2476.422 6021.223
## 767 4275.633 3100.384 5450.881 2478.245 6073.020
## 768 4302.443 3110.779 5494.106 2479.951 6124.934
## 769 4329.253 3121.099 5537.407 2481.541 6176.965
## 770 4356.063 3131.342 5580.784 2483.014 6229.112
## 771 4382.873 3141.511 5624.236 2484.373 6281.374
## 772 4409.683 3151.604 5667.763 2485.616 6333.750
## 773 4436.494 3161.622 5711.365 2486.746 6386.241
## 774 4463.304 3171.566 5755.042 2487.761 6438.846
## 775 4490.114 3181.436 5798.792 2488.664 6491.564
## 776 4516.924 3191.232 5842.616 2489.453 6544.395
## 777 4543.734 3200.955 5886.514 2490.130 6597.338
## 778 4570.544 3210.604 5930.484 2490.696 6650.393
## 779 4597.355 3220.181 5974.528 2491.150 6703.559
## 780 4624.165 3229.686 6018.644 2491.493 6756.837
## 781 4650.975 3239.118 6062.832 2491.726 6810.224
## 782 4677.785 3248.478 6107.092 2491.849 6863.721
## 783 4704.595 3257.767 6151.424 2491.863 6917.328
## 784 4731.405 3266.985 6195.826 2491.767 6971.044
## 785 4758.216 3276.131 6240.300 2491.563 7024.868
## 786 4785.026 3285.207 6284.845 2491.251 7078.801
## 787 4811.836 3294.212 6329.460 2490.831 7132.841
## 788 4838.646 3303.148 6374.145 2490.304 7186.988
## 789 4865.456 3312.013 6418.900 2489.670 7241.243
## 790 4892.267 3320.809 6463.724 2488.930 7295.603
## 791 4919.077 3329.536 6508.618 2488.083 7350.070
## 792 4945.887 3338.193 6553.581 2487.131 7404.642
## 793 4972.697 3346.782 6598.612 2486.074 7459.320
## 794 4999.507 3355.302 6643.712 2484.912 7514.102
## 795 5026.317 3363.754 6688.881 2483.646 7568.989
## 796 5053.128 3372.138 6734.117 2482.276 7623.980
## 797 5079.938 3380.454 6779.422 2480.802 7679.074
## 798 5106.748 3388.703 6824.793 2479.224 7734.271
## 799 5133.558 3396.884 6870.232 2477.544 7789.572
## 800 5160.368 3404.998 6915.738 2475.762 7844.975
## 801 5187.178 3413.046 6961.311 2473.877 7900.480
## 802 5213.989 3421.027 7006.950 2471.891 7956.087
## 803 5240.799 3428.942 7052.656 2469.803 8011.795
## 804 5267.609 3436.791 7098.427 2467.614 8067.604
## 805 5294.419 3444.574 7144.265 2465.324 8123.514
## 806 5321.229 3452.291 7190.168 2462.934 8179.524
## 807 5348.039 3459.943 7236.136 2460.445 8235.634
## 808 5374.850 3467.529 7282.170 2457.855 8291.844
## 809 5401.660 3475.051 7328.269 2455.166 8348.154
## 810 5428.470 3482.508 7374.432 2452.378 8404.562
## 811 5455.280 3489.901 7420.660 2449.492 8461.069
## 812 5482.090 3497.229 7466.952 2446.507 8517.674
## 813 5508.901 3504.493 7513.308 2443.424 8574.377
## 814 5535.711 3511.694 7559.728 2440.244 8631.178
## 815 5562.521 3518.830 7606.211 2436.966 8688.076
## 816 5589.331 3525.904 7652.758 2433.591 8745.071
## 817 5616.141 3532.914 7699.369 2430.120 8802.163
## 818 5642.951 3539.861 7746.042 2426.552 8859.351
## 819 5669.762 3546.745 7792.778 2422.888 8916.636
## 820 5696.572 3553.566 7839.577 2419.128 8974.016
## 821 5723.382 3560.325 7886.439 2415.272 9031.492
## 822 5750.192 3567.022 7933.362 2411.322 9089.063
## 823 5777.002 3573.657 7980.348 2407.276 9146.728
## 824 5803.812 3580.230 8027.395 2403.136 9204.489
## 825 5830.623 3586.741 8074.504 2398.902 9262.344
## 826 5857.433 3593.191 8121.675 2394.573 9320.292
## 827 5884.243 3599.579 8168.907 2390.151 9378.335
## 828 5911.053 3605.906 8216.200 2385.635 9436.471
## 829 5937.863 3612.173 8263.554 2381.026 9494.700
## 830 5964.673 3618.378 8310.969 2376.325 9553.022
## 831 5991.484 3624.523 8358.444 2371.530 9611.437
## 832 6018.294 3630.608 8405.980 2366.643 9669.944
## 833 6045.104 3636.632 8453.576 2361.664 9728.544
## 834 6071.914 3642.597 8501.232 2356.594 9787.235
## 835 6098.724 3648.501 8548.948 2351.431 9846.017
## 836 6125.535 3654.346 8596.723 2346.178 9904.891
## 837 6152.345 3660.131 8644.558 2340.833 9963.856
## 838 6179.155 3665.857 8692.453 2335.398 10022.912
## 839 6205.965 3671.524 8740.406 2329.872 10082.059
## 840 6232.775 3677.131 8788.419 2324.255 10141.295
## 841 6259.585 3682.680 8836.491 2318.549 10200.622
## 842 6286.396 3688.170 8884.621 2312.753 10260.038
## 843 6313.206 3693.602 8932.810 2306.867 10319.544
## 844 6340.016 3698.975 8981.057 2300.892 10379.139
## 845 6366.826 3704.290 9029.362 2294.829 10438.824
## 846 6393.636 3709.547 9077.726 2288.676 10498.597
## 847 6420.446 3714.746 9126.147 2282.434 10558.458
## 848 6447.257 3719.887 9174.626 2276.105 10618.408
## 849 6474.067 3724.971 9223.163 2269.687 10678.446
## 850 6500.877 3729.997 9271.757 2263.182 10738.572
## 851 6527.687 3734.966 9320.408 2256.588 10798.786
## 852 6554.497 3739.878 9369.117 2249.908 10859.087
## 853 6581.307 3744.732 9417.883 2243.140 10919.475
## 854 6608.118 3749.530 9466.705 2236.285 10979.950
## 855 6634.928 3754.271 9515.584 2229.344 11040.512
## 856 6661.738 3758.956 9564.520 2222.316 11101.160
## 857 6688.548 3763.584 9613.512 2215.202 11161.894
## 858 6715.358 3768.156 9662.560 2208.002 11222.715
## 859 6742.169 3772.672 9711.665 2200.716 11283.621
## 860 6768.979 3777.132 9760.825 2193.344 11344.613
## 861 6795.789 3781.536 9810.042 2185.887 11405.691
## 862 6822.599 3785.884 9859.314 2178.345 11466.853
## 863 6849.409 3790.177 9908.641 2170.718 11528.101
## 864 6876.219 3794.415 9958.024 2163.006 11589.433forecast_des2## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 665 1578.010 1547.40963 1608.611 1531.210699 1624.810
## 666 1604.990 1566.18148 1643.798 1545.637564 1664.342
## 667 1631.970 1583.29653 1680.643 1557.530560 1706.409
## 668 1658.949 1599.06612 1718.833 1567.365845 1750.533
## 669 1685.929 1613.69635 1758.162 1575.458644 1796.400
## 670 1712.909 1627.32584 1798.492 1582.020943 1843.797
## 671 1739.889 1640.05212 1839.725 1587.201893 1892.575
## 672 1766.868 1651.94723 1881.789 1591.111687 1942.625
## 673 1793.848 1663.06679 1924.629 1593.835374 1993.861
## 674 1820.828 1673.45532 1968.200 1595.441044 2046.215
## 675 1847.808 1683.14954 2012.466 1595.984855 2099.630
## 676 1874.787 1692.18046 2057.394 1595.514255 2154.060
## 677 1901.767 1700.57483 2102.959 1594.070111 2209.464
## 678 1928.747 1708.35600 2149.138 1591.688183 2265.805
## 679 1955.727 1715.54472 2195.908 1588.400165 2323.053
## 680 1982.706 1722.15954 2243.253 1584.234449 2381.178
## 681 2009.686 1728.21725 2291.155 1579.216698 2440.155
## 682 2036.666 1733.73312 2339.598 1573.370279 2499.961
## 683 2063.645 1738.72115 2388.570 1566.716611 2560.574
## 684 2090.625 1743.19427 2438.056 1559.275436 2621.975
## 685 2117.605 1747.16441 2488.045 1551.065036 2684.145
## 686 2144.585 1750.64271 2538.527 1542.102417 2747.067
## 687 2171.564 1753.63953 2589.489 1532.403454 2810.725
## 688 2198.544 1756.16461 2640.924 1521.983021 2875.105
## 689 2225.524 1758.22709 2692.821 1510.855091 2940.193
## 690 2252.504 1759.83556 2745.172 1499.032831 3005.974
## 691 2279.483 1760.99818 2797.969 1486.528680 3072.438
## 692 2306.463 1761.72262 2851.204 1473.354411 3139.572
## 693 2333.443 1762.01620 2904.870 1459.521193 3207.365
## 694 2360.423 1761.88586 2958.959 1445.039645 3275.806
## 695 2387.402 1761.33821 3013.467 1429.919875 3344.885
## 696 2414.382 1760.37956 3068.385 1414.171527 3414.593
## 697 2441.362 1759.01592 3123.708 1397.803810 3484.920
## 698 2468.342 1757.25306 3179.430 1380.825535 3555.858
## 699 2495.321 1755.09650 3235.546 1363.245143 3627.398
## 700 2522.301 1752.55152 3292.051 1345.070728 3699.531
## 701 2549.281 1749.62322 3348.938 1326.310063 3772.252
## 702 2576.261 1746.31647 3406.205 1306.970620 3845.550
## 703 2603.240 1742.63599 3463.845 1287.059588 3919.421
## 704 2630.220 1738.58629 3521.854 1266.583894 3993.856
## 705 2657.200 1734.17174 3580.228 1245.550216 4068.849
## 706 2684.180 1729.39656 3638.962 1223.964997 4144.394
## 707 2711.159 1724.26482 3698.054 1201.834463 4220.484
## 708 2738.139 1718.78045 3757.498 1179.164630 4297.113
## 709 2765.119 1712.94726 3817.290 1155.961318 4374.276
## 710 2792.098 1706.76892 3877.428 1132.230162 4451.967
## 711 2819.078 1700.24902 3937.907 1107.976620 4530.180
## 712 2846.058 1693.39101 3998.725 1083.205985 4608.910
## 713 2873.038 1686.19825 4059.877 1057.923389 4688.152
## 714 2900.017 1678.67399 4121.361 1032.133815 4767.901
## 715 2926.997 1670.82140 4183.173 1005.842101 4848.152
## 716 2953.977 1662.64355 4245.310 979.052952 4928.901
## 717 2980.957 1654.14343 4307.770 951.770938 5010.142
## 718 3007.936 1645.32396 4370.549 924.000507 5091.872
## 719 3034.916 1636.18796 4433.644 895.745989 5174.086
## 720 3061.896 1626.73819 4497.054 867.011598 5256.780
## 721 3088.876 1616.97733 4560.774 837.801443 5339.950
## 722 3115.855 1606.90801 4624.803 808.119525 5423.591
## 723 3142.835 1596.53277 4689.137 777.969749 5507.700
## 724 3169.815 1585.85410 4753.776 747.355920 5592.274
## 725 3196.795 1574.87443 4818.715 716.281756 5677.307
## 726 3223.774 1563.59614 4883.953 684.750884 5762.798
## 727 3250.754 1552.02153 4949.487 652.766847 5848.741
## 728 3277.734 1540.15289 5015.315 620.333107 5935.135
## 729 3304.714 1527.99241 5081.435 587.453046 6021.974
## 730 3331.693 1515.54226 5147.844 554.129973 6109.257
## 731 3358.673 1502.80455 5214.542 520.367124 6196.979
## 732 3385.653 1489.78137 5281.524 486.167662 6285.138
## 733 3412.633 1476.47472 5348.790 451.534687 6373.730
## 734 3439.612 1462.88659 5416.338 416.471229 6462.753
## 735 3466.592 1449.01893 5484.165 380.980261 6552.204
## 736 3493.572 1434.87364 5552.270 345.064689 6642.079
## 737 3520.551 1420.45257 5620.650 308.727365 6732.376
## 738 3547.531 1405.75757 5689.305 271.971081 6823.091
## 739 3574.511 1390.79041 5758.232 234.798577 6914.223
## 740 3601.491 1375.55286 5827.429 197.212539 7005.769
## 741 3628.470 1360.04663 5896.894 159.215600 7097.725
## 742 3655.450 1344.27342 5966.627 120.810344 7190.090
## 743 3682.430 1328.23489 6036.625 81.999308 7282.861
## 744 3709.410 1311.93265 6106.887 42.784981 7376.034
## 745 3736.389 1295.36832 6177.411 3.169808 7469.609
## 746 3763.369 1278.54346 6248.195 -36.843812 7563.582
## 747 3790.349 1261.45961 6319.238 -77.253521 7657.951
## 748 3817.329 1244.11828 6390.539 -118.057003 7752.714
## 749 3844.308 1226.52097 6462.096 -159.251982 7847.869
## 750 3871.288 1208.66913 6533.907 -200.836221 7943.412
## 751 3898.268 1190.56421 6605.972 -242.807522 8039.343
## 752 3925.248 1172.20761 6678.288 -285.163722 8135.659
## 753 3952.227 1153.60074 6750.854 -327.902696 8232.357
## 754 3979.207 1134.74495 6823.669 -371.022352 8329.437
## 755 4006.187 1115.64159 6896.732 -414.520633 8426.894
## 756 4033.167 1096.29198 6970.041 -458.395514 8524.729
## 757 4060.146 1076.69743 7043.595 -502.645004 8622.938
## 758 4087.126 1056.85922 7117.393 -547.267141 8721.519
## 759 4114.106 1036.77861 7191.433 -592.259996 8820.472
## 760 4141.086 1016.45684 7265.714 -637.621667 8919.793
## 761 4168.065 995.89515 7340.235 -683.350284 9019.481
## 762 4195.045 975.09472 7414.995 -729.444002 9119.534
## 763 4222.025 954.05675 7489.993 -775.901006 9219.951
## 764 4249.004 932.78242 7565.227 -822.719506 9320.728
## 765 4275.984 911.27287 7640.696 -869.897741 9421.866
## 766 4302.964 889.52923 7716.399 -917.433972 9523.362
## 767 4329.944 867.55264 7792.335 -965.326487 9625.214
## 768 4356.923 845.34418 7868.503 -1013.573599 9727.421
## 769 4383.903 822.90496 7944.901 -1062.173643 9829.980
## 770 4410.883 800.23604 8021.530 -1111.124977 9932.891
## 771 4437.863 777.33848 8098.387 -1160.425985 10036.151
## 772 4464.842 754.21332 8175.472 -1210.075069 10139.760
## 773 4491.822 730.86160 8252.783 -1260.070655 10243.715
## 774 4518.802 707.28433 8330.319 -1310.411191 10348.015
## 775 4545.782 683.48251 8408.081 -1361.095142 10452.658
## 776 4572.761 659.45714 8486.066 -1412.120998 10557.644
## 777 4599.741 635.20918 8564.273 -1463.487265 10662.970
## 778 4626.721 610.73960 8642.702 -1515.192471 10768.634
## 779 4653.701 586.04935 8721.352 -1567.235161 10874.636
## 780 4680.680 561.13937 8800.221 -1619.613900 10980.975
## 781 4707.660 536.01058 8879.310 -1672.327271 11087.647
## 782 4734.640 510.66391 8958.616 -1725.373873 11194.654
## 783 4761.620 485.10025 9038.139 -1778.752325 11301.991
## 784 4788.599 459.32051 9117.878 -1832.461261 11409.660
## 785 4815.579 433.32555 9197.833 -1886.499334 11517.657
## 786 4842.559 407.11625 9278.001 -1940.865211 11625.983
## 787 4869.539 380.69347 9358.384 -1995.557576 11734.635
## 788 4896.518 354.05806 9438.979 -2050.575129 11843.612
## 789 4923.498 327.21086 9519.785 -2105.916585 11952.913
## 790 4950.478 300.15271 9600.803 -2161.580674 12062.536
## 791 4977.458 272.88442 9682.031 -2217.566142 12172.481
## 792 5004.437 245.40679 9763.468 -2273.871748 12282.746
## 793 5031.417 217.72065 9845.113 -2330.496266 12393.330
## 794 5058.397 189.82677 9926.967 -2387.438484 12504.232
## 795 5085.376 161.72594 10009.027 -2444.697204 12615.450
## 796 5112.356 133.41894 10091.293 -2502.271240 12726.984
## 797 5139.336 104.90653 10173.765 -2560.159422 12838.831
## 798 5166.316 76.18947 10256.442 -2618.360589 12950.992
## 799 5193.295 47.26851 10339.322 -2676.873597 13063.464
## 800 5220.275 18.14438 10422.406 -2735.697311 13176.248
## 801 5247.255 -11.18217 10505.692 -2794.830611 13289.340
## 802 5274.235 -40.71042 10589.180 -2854.272387 13402.742
## 803 5301.214 -70.43965 10672.868 -2914.021542 13516.450
## 804 5328.194 -100.36916 10756.757 -2974.076990 13630.465
## 805 5355.174 -130.49825 10840.846 -3034.437657 13744.785
## 806 5382.154 -160.82621 10925.133 -3095.102480 13859.410
## 807 5409.133 -191.35235 11009.619 -3156.070407 13974.337
## 808 5436.113 -222.07601 11094.302 -3217.340397 14089.567
## 809 5463.093 -252.99650 11179.182 -3278.911418 14205.097
## 810 5490.073 -284.11316 11264.258 -3340.782452 14320.928
## 811 5517.052 -315.42532 11349.530 -3402.952488 14437.057
## 812 5544.032 -346.93234 11434.996 -3465.420527 14553.485
## 813 5571.012 -378.63357 11520.657 -3528.185579 14670.209
## 814 5597.992 -410.52836 11606.511 -3591.246664 14787.230
## 815 5624.971 -442.61608 11692.559 -3654.602813 14904.545
## 816 5651.951 -474.89611 11778.798 -3718.253063 15022.155
## 817 5678.931 -507.36781 11865.229 -3782.196465 15140.058
## 818 5705.911 -540.03058 11951.852 -3846.432075 15258.253
## 819 5732.890 -572.88381 12038.664 -3910.958960 15376.739
## 820 5759.870 -605.92689 12125.667 -3975.776197 15495.516
## 821 5786.850 -639.15921 12212.859 -4040.882870 15614.582
## 822 5813.829 -672.58020 12300.239 -4106.278070 15733.937
## 823 5840.809 -706.18926 12387.808 -4171.960902 15853.579
## 824 5867.789 -739.98581 12475.564 -4237.930473 15973.508
## 825 5894.769 -773.96927 12563.507 -4304.185902 16093.723
## 826 5921.748 -808.13907 12651.636 -4370.726315 16214.223
## 827 5948.728 -842.49464 12739.951 -4437.550846 16335.007
## 828 5975.708 -877.03543 12828.451 -4504.658638 16456.074
## 829 6002.688 -911.76088 12917.136 -4572.048840 16577.424
## 830 6029.667 -946.67044 13006.005 -4639.720609 16699.055
## 831 6056.647 -981.76355 13095.058 -4707.673110 16820.967
## 832 6083.627 -1017.03969 13184.293 -4775.905515 16943.159
## 833 6110.607 -1052.49830 13273.712 -4844.417004 17065.630
## 834 6137.586 -1088.13887 13363.312 -4913.206764 17188.380
## 835 6164.566 -1123.96087 13453.093 -4982.273988 17311.406
## 836 6191.546 -1159.96376 13543.055 -5051.617876 17434.710
## 837 6218.526 -1196.14704 13633.198 -5121.237637 17558.289
## 838 6245.505 -1232.51019 13723.521 -5191.132485 17682.143
## 839 6272.485 -1269.05270 13814.023 -5261.301640 17806.272
## 840 6299.465 -1305.77406 13904.704 -5331.744331 17930.674
## 841 6326.445 -1342.67378 13995.563 -5402.459791 18055.349
## 842 6353.424 -1379.75135 14086.600 -5473.447261 18180.296
## 843 6380.404 -1417.00629 14177.814 -5544.705988 18305.514
## 844 6407.384 -1454.43811 14269.206 -5616.235225 18431.003
## 845 6434.364 -1492.04632 14360.773 -5688.034230 18556.761
## 846 6461.343 -1529.83044 14452.517 -5760.102270 18682.789
## 847 6488.323 -1567.79000 14544.436 -5832.438614 18809.085
## 848 6515.303 -1605.92452 14636.530 -5905.042541 18935.648
## 849 6542.282 -1644.23353 14728.799 -5977.913333 19062.478
## 850 6569.262 -1682.71657 14821.241 -6051.050280 19189.575
## 851 6596.242 -1721.37318 14913.857 -6124.452674 19316.937
## 852 6623.222 -1760.20290 15006.646 -6198.119816 19444.563
## 853 6650.201 -1799.20527 15099.608 -6272.051011 19572.454
## 854 6677.181 -1838.37985 15192.742 -6346.245571 19700.608
## 855 6704.161 -1877.72619 15286.048 -6420.702811 19829.025
## 856 6731.141 -1917.24384 15379.525 -6495.422052 19957.703
## 857 6758.120 -1956.93236 15473.173 -6570.402623 20086.643
## 858 6785.100 -1996.79132 15566.992 -6645.643853 20215.844
## 859 6812.080 -2036.82028 15660.980 -6721.145081 20345.305
## 860 6839.060 -2077.01882 15755.138 -6796.905649 20475.025
## 861 6866.039 -2117.38650 15849.465 -6872.924903 20605.004
## 862 6893.019 -2157.92291 15943.961 -6949.202195 20735.240
## 863 6919.999 -2198.62761 16038.625 -7025.736882 20865.735
## 864 6946.979 -2239.50020 16133.457 -7102.528325 20996.486forecast_desopt## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 665 1554.046 1527.222 1580.869 1513.023 1595.069
## 666 1559.805 1521.658 1597.952 1501.464 1618.146
## 667 1565.565 1518.583 1612.547 1493.712 1637.417
## 668 1571.324 1516.771 1625.877 1487.893 1654.755
## 669 1577.084 1515.753 1638.414 1483.287 1670.880
## 670 1582.843 1515.287 1650.399 1479.525 1686.161
## 671 1588.602 1515.232 1661.973 1476.392 1700.813
## 672 1594.362 1515.495 1673.229 1473.745 1714.979
## 673 1600.121 1516.013 1684.230 1471.488 1728.755
## 674 1605.881 1516.739 1695.022 1469.551 1742.211
## 675 1611.640 1517.641 1705.640 1467.880 1755.400
## 676 1617.400 1518.689 1716.110 1466.435 1768.364
## 677 1623.159 1519.865 1726.453 1465.184 1781.134
## 678 1628.919 1521.150 1736.687 1464.101 1793.736
## 679 1634.678 1522.531 1746.825 1463.164 1806.192
## 680 1640.437 1523.996 1756.879 1462.356 1818.519
## 681 1646.197 1525.536 1766.858 1461.662 1830.732
## 682 1651.956 1527.141 1776.771 1461.068 1842.844
## 683 1657.716 1528.806 1786.626 1460.565 1854.866
## 684 1663.475 1530.524 1796.427 1460.143 1866.807
## 685 1669.235 1532.289 1806.181 1459.794 1878.675
## 686 1674.994 1534.097 1815.891 1459.510 1890.478
## 687 1680.753 1535.943 1825.564 1459.286 1902.221
## 688 1686.513 1537.825 1835.201 1459.115 1913.911
## 689 1692.272 1539.739 1844.806 1458.993 1925.552
## 690 1698.032 1541.681 1854.382 1458.914 1937.149
## 691 1703.791 1543.650 1863.932 1458.877 1948.706
## 692 1709.551 1545.643 1873.459 1458.875 1960.226
## 693 1715.310 1547.657 1882.963 1458.907 1971.713
## 694 1721.070 1549.691 1892.448 1458.969 1983.170
## 695 1726.829 1551.744 1901.914 1459.059 1994.599
## 696 1732.588 1553.812 1911.365 1459.174 2006.003
## 697 1738.348 1555.896 1920.800 1459.311 2017.385
## 698 1744.107 1557.993 1930.222 1459.469 2028.745
## 699 1749.867 1560.102 1939.632 1459.646 2040.087
## 700 1755.626 1562.222 1949.030 1459.840 2051.412
## 701 1761.386 1564.353 1958.419 1460.050 2062.722
## 702 1767.145 1566.492 1967.798 1460.273 2074.018
## 703 1772.905 1568.640 1977.170 1460.508 2085.301
## 704 1778.664 1570.794 1986.534 1460.755 2096.573
## 705 1784.423 1572.956 1995.891 1461.011 2107.836
## 706 1790.183 1575.123 2005.243 1461.276 2119.089
## 707 1795.942 1577.295 2014.590 1461.549 2130.335
## 708 1801.702 1579.471 2023.933 1461.829 2141.575
## 709 1807.461 1581.651 2033.272 1462.114 2152.808
## 710 1813.221 1583.834 2042.607 1462.404 2164.037
## 711 1818.980 1586.020 2051.940 1462.699 2175.262
## 712 1824.740 1588.208 2061.271 1462.996 2186.483
## 713 1830.499 1590.398 2070.600 1463.296 2197.702
## 714 1836.258 1592.589 2079.928 1463.598 2208.919
## 715 1842.018 1594.781 2089.255 1463.902 2220.134
## 716 1847.777 1596.973 2098.581 1464.206 2231.349
## 717 1853.537 1599.166 2107.908 1464.510 2242.564
## 718 1859.296 1601.358 2117.235 1464.813 2253.779
## 719 1865.056 1603.549 2126.562 1465.116 2264.996
## 720 1870.815 1605.739 2135.891 1465.417 2276.214
## 721 1876.575 1607.929 2145.221 1465.716 2287.433
## 722 1882.334 1610.116 2154.552 1466.013 2298.655
## 723 1888.093 1612.302 2163.885 1466.307 2309.880
## 724 1893.853 1614.486 2173.220 1466.598 2321.108
## 725 1899.612 1616.667 2182.557 1466.885 2332.339
## 726 1905.372 1618.846 2191.897 1467.169 2343.575
## 727 1911.131 1621.023 2201.240 1467.448 2354.814
## 728 1916.891 1623.196 2210.585 1467.723 2366.058
## 729 1922.650 1625.366 2219.934 1467.993 2377.307
## 730 1928.410 1627.533 2229.286 1468.258 2388.561
## 731 1934.169 1629.696 2238.642 1468.518 2399.820
## 732 1939.928 1631.856 2248.001 1468.772 2411.085
## 733 1945.688 1634.012 2257.364 1469.020 2422.356
## 734 1951.447 1636.163 2266.731 1469.262 2433.633
## 735 1957.207 1638.311 2276.103 1469.498 2444.916
## 736 1962.966 1640.454 2285.478 1469.727 2456.206
## 737 1968.726 1642.593 2294.858 1469.949 2467.502
## 738 1974.485 1644.728 2304.243 1470.165 2478.806
## 739 1980.245 1646.857 2313.632 1470.373 2490.116
## 740 1986.004 1648.982 2323.026 1470.574 2501.434
## 741 1991.763 1651.102 2332.425 1470.767 2512.760
## 742 1997.523 1653.217 2341.828 1470.953 2524.093
## 743 2003.282 1655.327 2351.237 1471.131 2535.434
## 744 2009.042 1657.432 2360.652 1471.301 2546.783
## 745 2014.801 1659.531 2370.071 1471.463 2558.140
## 746 2020.561 1661.625 2379.496 1471.616 2569.505
## 747 2026.320 1663.714 2388.926 1471.762 2580.879
## 748 2032.080 1665.797 2398.362 1471.898 2592.261
## 749 2037.839 1667.874 2407.804 1472.027 2603.651
## 750 2043.598 1669.946 2417.251 1472.146 2615.051
## 751 2049.358 1672.012 2426.704 1472.257 2626.459
## 752 2055.117 1674.072 2436.163 1472.358 2637.876
## 753 2060.877 1676.126 2445.628 1472.451 2649.303
## 754 2066.636 1678.174 2455.099 1472.534 2660.738
## 755 2072.396 1680.216 2464.576 1472.608 2672.183
## 756 2078.155 1682.252 2474.058 1472.673 2683.637
## 757 2083.915 1684.282 2483.548 1472.729 2695.101
## 758 2089.674 1686.305 2493.043 1472.774 2706.573
## 759 2095.433 1688.322 2502.544 1472.811 2718.056
## 760 2101.193 1690.333 2512.052 1472.838 2729.548
## 761 2106.952 1692.338 2521.567 1472.855 2741.050
## 762 2112.712 1694.336 2531.087 1472.862 2752.562
## 763 2118.471 1696.328 2540.614 1472.859 2764.083
## 764 2124.231 1698.313 2550.148 1472.847 2775.615
## 765 2129.990 1700.292 2559.688 1472.824 2787.156
## 766 2135.750 1702.265 2569.235 1472.791 2798.708
## 767 2141.509 1704.230 2578.788 1472.749 2810.269
## 768 2147.268 1706.189 2588.348 1472.696 2821.841
## 769 2153.028 1708.142 2597.914 1472.633 2833.423
## 770 2158.787 1710.087 2607.487 1472.560 2845.015
## 771 2164.547 1712.026 2617.067 1472.476 2856.617
## 772 2170.306 1713.958 2626.654 1472.382 2868.230
## 773 2176.066 1715.884 2636.247 1472.278 2879.853
## 774 2181.825 1717.802 2645.848 1472.164 2891.487
## 775 2187.585 1719.714 2655.455 1472.039 2903.131
## 776 2193.344 1721.619 2665.069 1471.903 2914.785
## 777 2199.103 1723.517 2674.690 1471.757 2926.450
## 778 2204.863 1725.408 2684.318 1471.600 2938.126
## 779 2210.622 1727.292 2693.952 1471.433 2949.812
## 780 2216.382 1729.170 2703.594 1471.255 2961.508
## 781 2222.141 1731.040 2713.242 1471.067 2973.216
## 782 2227.901 1732.903 2722.898 1470.867 2984.934
## 783 2233.660 1734.759 2732.561 1470.657 2996.663
## 784 2239.420 1736.609 2742.230 1470.437 3008.402
## 785 2245.179 1738.451 2751.907 1470.205 3020.153
## 786 2250.938 1740.286 2761.591 1469.963 3031.914
## 787 2256.698 1742.114 2771.281 1469.710 3043.685
## 788 2262.457 1743.935 2780.979 1469.446 3055.468
## 789 2268.217 1745.749 2790.684 1469.172 3067.262
## 790 2273.976 1747.556 2800.396 1468.886 3079.066
## 791 2279.736 1749.356 2810.115 1468.590 3090.881
## 792 2285.495 1751.149 2819.841 1468.283 3102.707
## 793 2291.255 1752.934 2829.575 1467.965 3114.544
## 794 2297.014 1754.713 2839.315 1467.635 3126.392
## 795 2302.773 1756.484 2849.063 1467.295 3138.251
## 796 2308.533 1758.248 2858.818 1466.944 3150.121
## 797 2314.292 1760.005 2868.580 1466.583 3162.002
## 798 2320.052 1761.754 2878.349 1466.210 3173.894
## 799 2325.811 1763.497 2888.125 1465.826 3185.797
## 800 2331.571 1765.232 2897.909 1465.431 3197.710
## 801 2337.330 1766.960 2907.700 1465.025 3209.635
## 802 2343.089 1768.681 2917.498 1464.608 3221.571
## 803 2348.849 1770.395 2927.303 1464.180 3233.518
## 804 2354.608 1772.102 2937.115 1463.741 3245.476
## 805 2360.368 1773.801 2946.935 1463.291 3257.445
## 806 2366.127 1775.493 2956.762 1462.830 3269.425
## 807 2371.887 1777.178 2966.596 1462.358 3281.416
## 808 2377.646 1778.855 2976.437 1461.875 3293.418
## 809 2383.406 1780.526 2986.285 1461.381 3305.431
## 810 2389.165 1782.189 2996.141 1460.875 3317.455
## 811 2394.924 1783.845 3006.004 1460.359 3329.490
## 812 2400.684 1785.494 3015.874 1459.832 3341.536
## 813 2406.443 1787.135 3025.752 1459.293 3353.594
## 814 2412.203 1788.769 3035.636 1458.743 3365.662
## 815 2417.962 1790.396 3045.528 1458.183 3377.742
## 816 2423.722 1792.016 3055.427 1457.611 3389.832
## 817 2429.481 1793.628 3065.334 1457.028 3401.934
## 818 2435.241 1795.234 3075.247 1456.435 3414.047
## 819 2441.000 1796.832 3085.168 1455.830 3426.170
## 820 2446.759 1798.422 3095.097 1455.214 3438.305
## 821 2452.519 1800.006 3105.032 1454.586 3450.451
## 822 2458.278 1801.582 3114.974 1453.948 3462.608
## 823 2464.038 1803.151 3124.924 1453.299 3474.777
## 824 2469.797 1804.713 3134.881 1452.639 3486.956
## 825 2475.557 1806.268 3144.846 1451.967 3499.146
## 826 2481.316 1807.815 3154.817 1451.285 3511.347
## 827 2487.076 1809.355 3164.796 1450.591 3523.560
## 828 2492.835 1810.888 3174.782 1449.887 3535.783
## 829 2498.594 1812.413 3184.775 1449.171 3548.018
## 830 2504.354 1813.932 3194.776 1448.444 3560.263
## 831 2510.113 1815.443 3204.784 1447.707 3572.520
## 832 2515.873 1816.947 3214.799 1446.958 3584.788
## 833 2521.632 1818.444 3224.821 1446.198 3597.066
## 834 2527.392 1819.933 3234.850 1445.427 3609.356
## 835 2533.151 1821.415 3244.887 1444.645 3621.657
## 836 2538.911 1822.890 3254.931 1443.852 3633.969
## 837 2544.670 1824.358 3264.982 1443.048 3646.292
## 838 2550.429 1825.819 3275.040 1442.233 3658.626
## 839 2556.189 1827.272 3285.105 1441.407 3670.971
## 840 2561.948 1828.719 3295.178 1440.570 3683.326
## 841 2567.708 1830.158 3305.258 1439.722 3695.693
## 842 2573.467 1831.590 3315.345 1438.863 3708.071
## 843 2579.227 1833.014 3325.439 1437.993 3720.460
## 844 2584.986 1834.432 3335.541 1437.112 3732.860
## 845 2590.746 1835.842 3345.649 1436.220 3745.271
## 846 2596.505 1837.245 3355.765 1435.317 3757.693
## 847 2602.264 1838.641 3365.888 1434.403 3770.126
## 848 2608.024 1840.030 3376.018 1433.478 3782.569
## 849 2613.783 1841.412 3386.155 1432.543 3795.024
## 850 2619.543 1842.786 3396.300 1431.596 3807.490
## 851 2625.302 1844.153 3406.451 1430.638 3819.966
## 852 2631.062 1845.514 3416.610 1429.670 3832.454
## 853 2636.821 1846.867 3426.776 1428.690 3844.952
## 854 2642.581 1848.213 3436.949 1427.700 3857.462
## 855 2648.340 1849.551 3447.129 1426.698 3869.982
## 856 2654.099 1850.883 3457.316 1425.686 3882.513
## 857 2659.859 1852.208 3467.510 1424.663 3895.055
## 858 2665.618 1853.525 3477.712 1423.629 3907.608
## 859 2671.378 1854.835 3487.920 1422.584 3920.172
## 860 2677.137 1856.138 3498.136 1421.528 3932.746
## 861 2682.897 1857.435 3508.359 1420.461 3945.332
## 862 2688.656 1858.724 3518.589 1419.384 3957.928
## 863 2694.416 1860.006 3528.826 1418.296 3970.535
## 864 2700.175 1861.280 3539.070 1417.196 3983.153# Plot hasil peramalan
plot(forecast_des1, main = "Peramalan DES1 (200 periode ke depan)")
plot(forecast_des2, main = "Peramalan DES2 (200 periode ke depan)")
plot(forecast_desopt, main = "Peramalan DES Optimal (200 periode ke depan)")
# Plot data aktual (training)
plot(train.ts, main="Forecasting dengan Double Exponential Smoothing",
type="l", col="black", xlim=c(1, length(train.ts) + horizon),
xlab="Time", ylab="Value")
# Tambahkan hasil ramalan
lines(forecast_des1$mean, col="red", lty=1)
lines(forecast_des2$mean, col="blue", lty=1)
lines(forecast_desopt$mean, col="green", lty=1)
# (Opsional) Tambahkan interval prediksi model terbaik
lines(forecast_desopt$lower[,2], col="green", lty=2)
lines(forecast_desopt$upper[,2], col="green", lty=2)
# Tambahkan legend
legend("topleft",
legend=c("Data Aktual", "DES1", "DES2", "DES Optimal"),
col=c("black", "red", "blue", "green"),
lty=1, cex=0.7)
Akurasi Data Latih
# --- Akurasi untuk model des.1 ---
SSE1 <- des.1$SSE
MSE1 <- des.1$SSE / length(train.ts)
RMSE1 <- sqrt(MSE1)
# --- Akurasi untuk model des.2 ---
SSE2 <- des.2$SSE
MSE2 <- des.2$SSE / length(train.ts)
RMSE2 <- sqrt(MSE2)
# --- Akurasi untuk model des.opt ---
SSE.opt <- des.opt$SSE
MSE.opt <- des.opt$SSE / length(train.ts)
RMSE.opt <- sqrt(MSE.opt)
# --- Gabungkan ke dalam 1 data frame ---
akurasi.train <- data.frame(
Model = c("des.1 (α=0.2, β=0.2)", "des.2 (α=0.6, β=0.3)", "des.opt (optimal)"),
SSE = c(SSE1, SSE2, SSE.opt),
MSE = c(MSE1, MSE2, MSE.opt),
RMSE = c(RMSE1, RMSE2, RMSE.opt)
)
akurasi.train## Model SSE MSE RMSE
## 1 des.1 (α=0.2, β=0.2) 838807.2 1263.2638 35.54242
## 2 des.2 (α=0.6, β=0.3) 376912.3 567.6390 23.82518
## 3 des.opt (optimal) 290888.8 438.0856 20.93049Akurasi Data Uji
# --- Akurasi Data Testing untuk des.1 ---
forecast1 <- data.frame(ramalandes1$mean) # ambil nilai ramalan
testing.df <- data.frame(test.ts) # ubah test.ts ke data frame
selisih1 <- forecast1 - testing.df## Warning in .cbind.ts(list(e1, e2), c(deparse(substitute(e1))[1L],
## deparse(substitute(e2))[1L]), : non-intersecting seriesSSEtest1 <- sum(selisih1^2)
MSEtest1 <- SSEtest1 / length(test.ts)
RMSEtest1 <- sqrt(MSEtest1)
# --- Akurasi Data Testing untuk des.2 ---
forecast2 <- data.frame(ramalandes2$mean)
selisih2 <- forecast2 - testing.df## Warning in .cbind.ts(list(e1, e2), c(deparse(substitute(e1))[1L],
## deparse(substitute(e2))[1L]), : non-intersecting seriesSSEtest2 <- sum(selisih2^2)
MSEtest2 <- SSEtest2 / length(test.ts)
RMSEtest2 <- sqrt(MSEtest2)
# --- Akurasi Data Testing untuk des.opt ---
forecast.opt <- data.frame(ramalandesopt$mean)
selisih.opt <- forecast.opt - testing.df## Warning in .cbind.ts(list(e1, e2), c(deparse(substitute(e1))[1L],
## deparse(substitute(e2))[1L]), : non-intersecting seriesSSEtest.opt <- sum(selisih.opt^2)
MSEtest.opt <- SSEtest.opt / length(test.ts)
RMSEtest.opt <- sqrt(MSEtest.opt)
# --- Gabungkan hasil ke dalam tabel ---
akurasi.test <- data.frame(
Model = c("des.1 (α=0.2, β=0.2)",
"des.2 (α=0.6, β=0.3)",
"des.opt (optimal)"),
SSE_Test = c(SSEtest1, SSEtest2, SSEtest.opt),
MSE_Test = c(MSEtest1, MSEtest2, MSEtest.opt),
RMSE_Test = c(RMSEtest1, RMSEtest2, RMSEtest.opt)
)
akurasi.test## Model SSE_Test MSE_Test RMSE_Test
## 1 des.1 (α=0.2, β=0.2) 0 0 0
## 2 des.2 (α=0.6, β=0.3) 0 0 0
## 3 des.opt (optimal) 0 0 0length(test.ts) # panjang data uji## [1] 167length(ramalandesopt$mean) # panjang hasil ramalan## [1] 167# ambil vektor forecast dan testing dengan panjang yang sama
n <- min(length(test.ts), length(ramalandes1$mean))
forecast1 <- as.numeric(ramalandes1$mean[1:n])
testing.vec <- as.numeric(test.ts[1:n])
# cek beberapa nilai dulu
head(forecast1)## [1] 1540.995 1567.805 1594.615 1621.425 1648.236 1675.046head(testing.vec)## [1] 1555.471 1639.322 1706.931 1756.803 1807.372 1676.994# selisih
selisih1 <- forecast1 - testing.vec
head(selisih1)## [1] -14.476491 -71.517517 -112.316143 -135.377169 -159.136995 -1.948122# hitung error
SSEtest1 <- sum(selisih1^2)
MSEtest1 <- mean(selisih1^2)
RMSEtest1 <- sqrt(MSEtest1)
SSEtest1; MSEtest1; RMSEtest1## [1] 90235151## [1] 540330.2## [1] 735.0716head(test.ts)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] 1555.471 1639.322 1706.931 1756.803 1807.372 1676.994tail(test.ts)## Time Series:
## Start = 162
## End = 167
## Frequency = 1
## [1] 5697.392 5754.221 5595.235 5572.199 5699.584 5984.086head(ramalandes1$mean)## Time Series:
## Start = 665
## End = 670
## Frequency = 1
## [1] 1540.995 1567.805 1594.615 1621.425 1648.236 1675.046tail(ramalandes1$mean)## Time Series:
## Start = 826
## End = 831
## Frequency = 1
## [1] 5857.433 5884.243 5911.053 5937.863 5964.673 5991.484# fungsi untuk hitung SSE, MSE, RMSE antara ramalan & testing
hitung_error <- function(ramalan, testing){
n <- min(length(testing), length(ramalan$mean)) # samakan panjang
forecast.vec <- as.numeric(ramalan$mean[1:n]) # vektor forecast
testing.vec <- as.numeric(testing[1:n]) # vektor testing
selisih <- forecast.vec - testing.vec
SSE <- sum(selisih^2)
MSE <- mean(selisih^2)
RMSE <- sqrt(MSE)
return(c(SSE=SSE, MSE=MSE, RMSE=RMSE))
}
# hitung untuk semua model
err1 <- hitung_error(ramalandes1, test.ts)
err2 <- hitung_error(ramalandes2, test.ts)
errop <- hitung_error(ramalandesopt, test.ts)
# gabungkan jadi tabel
akurasi.test <- data.frame(
Model = c("des.1 (α=0.2, β=0.2)",
"des.2 (α=0.6, β=0.3)",
"des.opt (optimal)"),
SSE_Test = c(err1["SSE"], err2["SSE"], errop["SSE"]),
MSE_Test = c(err1["MSE"], err2["MSE"], errop["MSE"]),
RMSE_Test = c(err1["RMSE"], err2["RMSE"], errop["RMSE"])
)
akurasi.test## Model SSE_Test MSE_Test RMSE_Test
## 1 des.1 (α=0.2, β=0.2) 90235151 540330.2 735.0716
## 2 des.2 (α=0.6, β=0.3) 99399886 595208.9 771.4978
## 3 des.opt (optimal) 387317450 2319266.2 1522.9137Kesimpulan: hasil evaluasi menggunakan data testing, model des.1 (α=0.2, β=0.2) menghasilkan nilai SSE sebesar 90,235,151 dan MSE sebesar 540,330, lebih rendah dibandingkan model des.2 (α=0.6, β=0.3) yang memiliki SSE 99,399,886 dan MSE 595,208. Sementara itu, model des.opt (parameter optimal dari fungsi HoltWinters) justru menunjukkan error yang jauh lebih besar, yaitu SSE 387,317,450 dan MSE 2,319,266. Hal ini menunjukkan bahwa pada data BTC yang digunakan, model dengan parameter α=0.2 dan β=0.2 (des.1) lebih baik dalam memprediksi harga dibandingkan dua model lainnya.