Forecast Iklim di Delhi
Lela Novi
2023-12-01
1 Import Library
# Data wrangling & Preparation
library(dplyr) # data wrangling
library(lubridate) # date manipulation
library(tidyr) # Tools to help to create tidy data
library(padr) # complete data frame
library(zoo) # **missing value** imputation
# Data Visualization
library(ggplot2)
# Time Series & Model Evaluation
library(forecast) # time series library
library(TTR) # for Simple moving average function
library(tseries) # adf.test
library(fpp) # data for forecasting: principles and practice
library(MLmetrics) # calculate error2 Read Data
Data berikut adalah data harian Iklim yang ada di Delhi dari tahun 2013 sampai dengan 2017. Data ini bersumber dari Kaggle.com yang terdiri dari 5 Kolom dan 1.462 baris.
3 Explatory Data Analysis
#> Rows: 1,462
#> Columns: 5
#> $ date <chr> "2013-01-01", "2013-01-02", "2013-01-03", "2013-01-04", "…
#> $ meantemp <dbl> 10.000000, 7.400000, 7.166667, 8.666667, 6.000000, 7.0000…
#> $ humidity <dbl> 84.50000, 92.00000, 87.00000, 71.33333, 86.83333, 82.8000…
#> $ wind_speed <dbl> 0.0000000, 2.9800000, 4.6333333, 1.2333333, 3.7000000, 1.…
#> $ meanpressure <dbl> 1015.667, 1017.800, 1018.667, 1017.167, 1016.500, 1018.00…karena dalam time series variabel yang digunakan adalah time dan y, maka kita akan menyeleksi data yang digunakan yaitu date meantemp
#1. Mengubah tipe data
climate_clean <- climate_clean %>% mutate(date = ymd(date))
#2. mengurutkan periode waktu
climate_clean <- climate_clean %>% arrange(date)
#3. Periksa rentang waktu
range(climate_clean$date)#> [1] "2013-01-01" "2017-01-01"#4. Periksa kelengkapan periode waktu
cek_tgl <- seq.Date(from = min(climate_clean$date),to = max(climate_clean$date),by = "day")
all(cek_tgl == climate_clean$date)#> [1] TRUEinterval waktu sudah lengkap
Cek NA
#> date meantemp
#> 0 0Hasil cek menunjukan bahwa data climate tidak memiliki data NA, dan data date pada climate sudah beruruta dan tidak ada yang hilang.
Apaila keseluruhan karakteristik data time series sudah terpenuhi,
selanjutnya buatlah object ts dari data meantemp dan simpan
ke dalam object climate_ts dengan data yang terkumpul
adalah data bulanan dengan pola yang ingin dilihat adalah
tahunan.
penentuan frequency:
- data : harian
- start : waktu mulai dari time series yang digunakan adalah tanggal 1 Januari 2013
- pola : tahunan
- frequency: 365
keterangan kolom Date : tanggal penelitian yang direkam per hari kolom meantemp(harian) : nilai yang ingin diamati adalah meantemp(temperature rata - rata dari interval 3 jam per hari)
climate_ts <- ts(climate_clean$meantemp,
start = c(2013,1),
frequency = 365)
autoplot(climate_ts, series = "Actual")
Decompose Data Time Series Fungsi decompose untuk memecah komponen ts menjadi beberapa komponen, yaitu : 1. Trend adalah pergerakan mean secara global 2. Seasonal adalah pola data per frequency 3. Error adalah nilai yang tidak dapat oleh Trend dan Seasonal
- tren temperature cenderung meningkat
- temperature fluktuatif
4 Cross Validation
Konsep Cross Validation pada time series proporsi data train untuk membuat model akan lebih banyak dibandingkan data test. Akan tetapi terdapat syarat yang harus dipenuhi yaitu:
- Data train akan menggunakan data yang paling awal dari data set [informasi waktu lampau]
- Data test akan menggunakan data yang paling akhir dari data set [informasi waktu terkini]
# your code here
climatetrain_decom <- climate_train %>% decompose(type = "multiplicative")
climatetrain_decom %>% autoplot()
- data train kita memiliki tren dan seasonal
- menuju akhir 2013 terjadi penurunan
- peak temperature terjadi pada akhir 2014
5 Built Model
5.1 Triple Exponential Smoothing
Triple Exponential Smoothing (Holt’s Winters Exponential) merupakan metode forecasting yang digunakan untuk data yang memiliki efek trend dan seasonal.
#> Time Series:
#> Start = c(2013, 2)
#> End = c(2016, 2)
#> Frequency = 365
#> [1] 10.000000 7.998874 7.358354 8.365315 6.544818 6.895155 6.975850
#> [8] 8.423813 12.715603 11.395165 14.719436 14.165712 15.449220 13.435867
#> [15] 14.419820 13.968422 15.916886 14.313251 12.917657 11.661610 11.306325
#> [22] 9.916062 13.059322 13.655050 12.573634 12.645238 12.808333 14.366903
#> [29] 14.180719 14.591386 15.829478 15.960723 16.210857 17.587896 17.465270
#> [36] 16.818544 16.701650 15.853750 14.426986 15.197870 15.237993 15.728274
#> [43] 15.424302 16.087300 17.046327 18.678276 15.407432 14.067628 15.247039
#> [50] 15.716614 17.254150 19.367531 20.239152 18.075950 17.137878 16.935550
#> [57] 17.644867 20.073259 19.577066 17.850146 18.735147 19.195549 17.967513
#> [64] 20.205301 20.707000 22.801695 23.852264 25.065491 23.585709 23.904574
#> [71] 23.593188 21.982137 22.252440 23.725751 21.114730 22.309200 23.170740
#> [78] 22.654496 27.666678 24.716291 25.127068 26.857220 26.967113 24.298601
#> [85] 24.178731 21.732177 22.268167 21.484521 23.035762 23.162170 24.865305
#> [92] 25.097252 25.945997 24.910032 25.441075 25.761307 28.363964 28.633594
#> [99] 29.813545 29.957053 29.990108 29.118106 29.950801 28.641756 28.340236
#> [106] 31.253232 29.672934 30.144569 28.713876 30.184799 28.246684 27.575780
#> [113] 28.383327 29.847526 30.844496 30.098310 30.902260 30.647631 31.784709
#> [120] 31.290699 31.726670 30.269437 28.962541 31.960075 32.471844 32.685931
#> [127] 32.831450 34.115673 34.246548 34.056789 31.511673 30.238241 31.374299
#> [134] 32.075782 32.787119 32.950966 32.860428 31.736389 34.504827 35.963473
#> [141] 35.991587 36.575310 37.287010 38.165629 38.587910 37.981484 36.346455
#> [148] 35.566692 34.470818 32.723051 33.417249 32.326444 32.383057 34.859022
#> [155] 35.627240 36.812081 32.558636 33.668002 34.077462 35.685447 36.408587
#> [162] 31.604406 33.558160 30.691296 30.269182 30.611762 27.831919 27.095413
#> [169] 28.099506 29.452296 32.182835 34.222828 35.282788 35.193413 33.615174
#> [176] 31.272513 30.806215 31.285220 31.450528 32.835517 32.833836 33.621438
#> [183] 33.253092 31.958776 32.279129 32.680025 31.386970 31.217411 30.152136
#> [190] 29.265379 29.638374 31.840864 29.558146 31.245137 30.864048 31.545933
#> [197] 30.259876 30.925731 31.560141 30.744189 27.734145 28.092697 29.175847
#> [204] 31.239544 30.065608 28.732339 29.708012 30.042697 31.769066 31.177144
#> [211] 30.655971 29.253153 29.827974 31.169848 32.193618 32.429429 30.174753
#> [218] 27.859538 28.256270 28.443860 27.460851 28.975334 29.763982 29.560805
#> [225] 30.476085 29.853105 28.206933 26.970135 27.322977 28.100612 28.151452
#> [232] 27.553845 28.153789 28.933364 30.743883 31.710671 29.624365 31.452806
#> [239] 31.983913 30.566919 31.285078 29.654613 29.150781 29.804394 31.384321
#> [246] 32.435435 31.880392 31.715895 30.835041 30.833727 28.652710 30.459334
#> [253] 29.849247 30.624988 31.041898 31.119603 30.642717 31.398745 30.065627
#> [260] 29.437868 29.210809 29.664288 28.896455 26.051427 27.807728 29.714944
#> [267] 30.511589 29.018318 28.388488 28.859147 29.737220 28.510097 27.237878
#> [274] 28.044360 28.933814 28.676889 25.718643 27.859353 29.314516 29.622204
#> [281] 29.297249 30.479518 29.670642 25.196202 25.924808 26.880622 27.522263
#> [288] 26.240680 26.385293 26.748459 26.428952 24.999283 24.486726 24.785566
#> [295] 27.105667 25.485011 24.232100 23.129864 23.029912 22.910682 22.722872
#> [302] 22.936167 22.875345 23.484397 23.441430 22.043389 20.951706 21.117154
#> [309] 19.359380 20.292250 20.177268 18.501503 19.544890 17.457903 18.534847
#> [316] 17.023675 17.582701 17.615257 17.141716 16.744018 15.841518 17.887656
#> [323] 17.877915 18.164295 17.941635 17.697933 18.040375 18.875172 20.702991
#> [330] 21.124004 19.585443 18.846225 18.002500 17.904368 17.977972 17.417678
#> [337] 17.481038 17.220752 17.160799 16.363582 16.083746 16.404122 16.189292
#> [344] 15.658769 16.402442 17.439609 17.211210 16.388937 15.704754 15.354746
#> [351] 14.889295 14.878293 15.837838 15.481608 14.918516 15.173647 14.462749
#> [358] 13.721756 13.679356 12.483024 12.015050 11.137595 10.701837 11.989610
#> [365] 13.921766 13.500940 11.576057 12.287183 12.739604 12.458982 11.665912
#> [372] 12.032999 11.911393 12.620977 12.431657 12.195634 12.718518 13.704828
#> [379] 14.605467 12.600133 12.358136 12.082492 12.403833 14.017177 14.484996
#> [386] 13.781856 14.911833 15.460732 14.240251 12.323595 13.902487 15.997907
#> [393] 16.480558 15.244818 14.671558 14.731932 14.168590 15.000912 17.639058
#> [400] 18.576574 17.363142 18.238141 19.305556 14.933437 13.349133 12.791794
#> [407] 13.240667 13.247850 14.788833 13.412033 12.613866 13.295891 14.703690
#> [414] 15.124165 15.124808 15.894620 16.841599 16.674891 16.540284 16.413071
#> [421] 17.730681 18.515214 18.599712 16.310184 16.181399 16.137991 17.474904
#> [428] 18.456299 18.778558 18.467954 18.492619 19.556588 21.437194 20.331038
#> [435] 20.626010 20.144193 19.263549 19.541745 21.145151 22.668969 25.425159
#> [442] 24.987978 22.495823 21.729374 22.322497 24.383274 23.126202 22.548029
#> [449] 24.146599 24.899639 23.822387 24.288945 25.509674 24.443941 24.198464
#> [456] 24.719169 26.282226 25.295343 25.727740 26.995577 29.404181 27.746186
#> [463] 26.209794 25.855907 26.255434 27.708115 28.798640 27.318084 27.554306
#> [470] 28.667004 27.480179 26.629563 24.798099 25.434535 26.639417 27.686609
#> [477] 28.986102 29.093007 29.310047 30.322119 31.228691 30.764052 31.330485
#> [484] 31.941994 32.948719 34.431308 34.387970 32.357620 31.986165 30.265070
#> [491] 29.731199 31.284997 31.354269 30.696769 30.160491 29.748343 28.402707
#> [498] 25.976182 26.667970 28.847681 30.600451 30.042098 31.164192 32.096107
#> [505] 31.348681 32.619642 33.104806 34.274844 32.139147 31.647219 30.475622
#> [512] 31.552673 33.147668 34.765757 33.502926 34.366546 33.122349 32.835765
#> [519] 34.405291 35.055433 36.455888 37.259503 38.214269 37.760730 37.848679
#> [526] 37.387898 37.570387 33.956517 31.103745 30.639064 33.129647 35.627478
#> [533] 36.587651 34.499821 35.462039 37.415416 36.999477 35.075720 32.804657
#> [540] 32.955006 32.412388 32.479820 34.227095 34.725764 33.397506 32.321896
#> [547] 31.593104 29.982118 29.130009 30.868587 33.822015 31.361388 33.392232
#> [554] 34.629673 35.684364 36.023506 36.486454 36.015840 32.636369 32.435203
#> [561] 32.966115 32.703571 31.199978 28.159823 29.479933 30.553666 31.763065
#> [568] 31.656801 30.862661 30.583534 30.711657 32.088080 31.800384 30.414694
#> [575] 30.287935 31.509442 32.271839 33.024694 30.792904 31.337130 30.692821
#> [582] 29.967166 31.627973 31.240853 31.055477 29.654548 28.765934 30.581622
#> [589] 31.769504 32.043116 30.759228 31.040749 30.569578 31.189482 31.717100
#> [596] 32.704502 33.124352 32.643811 32.917957 33.077310 33.114015 33.699718
#> [603] 34.027042 33.896277 30.608829 30.428859 29.040494 27.951039 29.088242
#> [610] 29.212741 28.760378 28.078935 26.863686 28.123098 30.337345 31.039783
#> [617] 31.009163 29.270367 27.193092 28.198972 29.104118 29.120190 29.508724
#> [624] 30.367881 30.565776 30.515151 30.888322 31.070484 30.631403 30.626475
#> [631] 30.913964 29.921895 29.982010 29.995856 30.383877 30.280837 30.449519
#> [638] 30.584580 30.464506 30.395616 30.475957 30.879294 30.683573 30.638491
#> [645] 30.916732 29.249077 27.999084 27.326333 26.085598 26.019716 27.255245
#> [652] 25.134633 24.646179 23.379174 24.626665 24.144344 23.840832 24.540586
#> [659] 25.375220 25.663675 25.345284 25.464363 25.299376 25.165165 24.941835
#> [666] 25.082811 24.826658 24.094201 23.540658 22.739701 22.843836 23.252654
#> [673] 23.539235 22.931789 22.984289 23.766045 23.849904 24.061635 21.993829
#> [680] 19.882003 19.684197 18.772763 18.466619 18.588519 18.327973 17.883128
#> [687] 17.684456 17.542487 19.722570 18.589186 19.578831 17.690206 17.062771
#> [694] 16.629627 18.935057 18.311585 19.130057 19.992037 19.805750 19.955257
#> [701] 21.047982 24.089707 21.904087 18.706836 18.355226 17.504573 17.116222
#> [708] 15.707346 20.165743 19.749553 18.018153 16.464854 16.780528 16.660824
#> [715] 17.499123 13.940103 12.254460 11.866195 11.391932 9.935780 9.504168
#> [722] 9.597168 9.811005 9.379220 10.434260 10.388650 9.319856 10.709210
#> [729] 11.414061 12.153661 14.151969 14.708460 15.029056 14.333237 14.076756
#> [736] 12.478352 10.282230 10.065008 10.496014 10.980122 10.995421 10.710321
#> [743] 11.895356 11.975897 12.283072 12.834866 13.346796 13.079880 13.595647
#> [750] 13.425823 13.290498 12.778288 14.199636 12.795280 13.145261 13.610707
#> [757] 13.333084 12.087153 11.635243 12.493231 13.460521 14.645402 16.746275
#> [764] 16.749142 15.114267 14.737696 15.035790 15.681700 16.407724 16.767369
#> [771] 15.984337 15.996392 15.614337 16.873248 18.798756 18.857438 20.217867
#> [778] 20.929798 21.176246 22.387508 22.666505 22.057312 22.123153 21.643535
#> [785] 22.591349 23.002081 20.691488 19.582027 20.865805 18.179059 17.656412
#> [792] 16.573947 16.709449 18.279987 19.603819 18.658041 19.306067 18.397042
#> [799] 17.899037 18.169161 19.963123 21.049794 21.396301 18.493667 19.543085
#> [806] 20.568212 20.323296 20.940339 22.140754 24.245204 24.922351 24.789699
#> [813] 25.528808 26.372507 28.009962 27.521255 27.120064 25.488327 23.957984
#> [820] 24.952402 26.088556 28.109485 25.331395 21.997677 23.208937 24.587453
#> [827] 23.942896 25.237551 25.824380 26.825420 27.921868 25.191972 24.851802
#> [834] 25.927944 27.234107 25.707011 27.568050 29.536042 31.528669 32.564891
#> [841] 31.937699 31.023570 30.813013 31.053138 30.627408 29.182435 29.907893
#> [848] 30.748448 31.134475 32.281678 31.487633 30.438864 30.870750 30.874021
#> [855] 31.836854 33.597957 35.006915 34.328137 34.941454 35.082723 34.249390
#> [862] 33.383988 29.047711 29.492029 28.728500 29.707128 32.433948 34.697570
#> [869] 32.236516 32.920350 35.002021 35.962545 37.049661 36.241775 37.402601
#> [876] 35.745822 34.209710 34.625552 35.009959 32.885718 33.935757 30.425507
#> [883] 31.348713 29.252370 31.270913 32.313105 33.130407 34.569365 36.055305
#> [890] 37.263443 36.772056 35.889209 35.878273 32.219850 28.202320 30.355593
#> [897] 31.909858 33.422357 34.732820 35.611915 33.697826 31.140367 31.898203
#> [904] 31.591721 35.946694 28.772123 30.583047 32.154665 33.767369 31.733633
#> [911] 31.072774 31.786426 33.297718 33.068575 33.881667 35.292167 29.583442
#> [918] 28.460932 30.607577 29.851323 27.368139 25.930300 25.599114 28.890109
#> [925] 30.417808 32.693852 31.967403 31.030412 29.852509 30.062236 29.340879
#> [932] 30.906468 31.940536 32.082511 32.019005 31.124762 30.259073 29.771050
#> [939] 29.562433 28.744717 28.941199 28.986456 28.419632 29.347360 31.004169
#> [946] 29.791489 29.639296 29.532085 29.314974 28.976342 27.743847 29.768950
#> [953] 28.696077 30.276907 31.603109 31.042710 29.085678 28.731111 30.284977
#> [960] 29.392185 30.822078 30.766602 29.695536 30.122287 29.931959 30.561576
#> [967] 31.668679 31.923685 32.367254 32.084592 32.211901 32.529848 32.012091
#> [974] 32.098993 31.926594 31.694468 31.929625 31.117918 31.219577 31.435408
#> [981] 31.581330 31.133901 31.223258 30.859008 31.847140 32.060999 31.917842
#> [988] 32.750740 32.461546 31.625271 31.144022 30.744550 29.511785 29.983754
#> [995] 30.188674 28.985171 28.419336 28.481420 29.072968 28.796903 28.375972
#> [1002] 28.856264 28.966892 28.318918 28.293362 29.606900 29.139791 28.935991
#> [1009] 28.504216 28.597179 28.426176 28.482996 28.496083 28.554074 29.089703
#> [1016] 29.405494 28.419944 27.711896 27.837431 27.962555 27.111759 27.905358
#> [1023] 27.758297 26.789831 25.219847 24.280975 24.738175 25.997980 25.710911
#> [1030] 24.971332 21.818533 22.054410 22.301156 22.357991 22.755914 23.232402
#> [1037] 23.823194 23.766859 22.503180 22.789356 22.085609 21.923511 21.789966
#> [1044] 22.528869 22.025610 21.909691 22.267822 22.350313 22.465522 22.011018
#> [1051] 20.367002 18.930038 18.599053 18.522816 18.697671 18.641739 17.378152
#> [1058] 18.241598 19.113937 19.795908 18.798494 18.761170 18.271533 19.217040
#> [1065] 19.242408 18.382379 17.799452 17.665183 17.538048 17.220140 17.531746
#> [1072] 18.222000 18.339759 18.847923 17.618059 14.256122 13.193122 13.236899
#> [1079] 13.150774 13.034729 12.430751 12.772673 12.466599 11.915059 12.461475
#> [1086] 12.106294 12.409315 11.517032 11.503923 12.462983 14.704257 16.567415
#> [1093] 16.419320 15.711753 15.163942 14.817858
#> Time Series:
#> Start = c(2014, 1)
#> End = c(2016, 2)
#> Frequency = 365
#> [1] 13.603638 11.082004 12.529963 12.880233 12.378496 11.422717 12.127590
#> [8] 11.851670 12.809112 12.356655 12.100676 12.868266 13.994152 14.870123
#> [15] 11.991669 12.284830 12.012822 12.506632 14.491847 14.612392 13.562314
#> [22] 15.251211 15.624017 13.868840 11.741940 14.368870 16.630061 16.629468
#> [29] 14.873454 14.490234 14.738721 14.001099 15.253873 18.436080 18.859661
#> [36] 16.988008 18.489371 19.615497 13.617042 12.875753 12.622939 13.367921
#> [43] 13.244725 15.247135 12.990509 12.362224 13.485841 15.111503 15.233178
#> [50] 15.104250 16.107662 17.109677 16.615791 16.494722 16.360718 18.115344
#> [57] 18.742964 18.624925 15.628837 16.146359 16.130677 17.879177 18.759271
#> [64] 18.890074 18.391165 18.520154 19.887963 22.004508 19.993330 20.712910
#> [71] 20.002846 19.013439 19.637425 21.634635 23.132657 26.258731 24.858116
#> [78] 21.747326 21.496197 22.496263 24.992836 22.733945 22.364315 24.620371
#> [85] 25.127366 23.497629 24.423653 25.870081 24.123505 24.118838 24.863466
#> [92] 26.741183 24.994712 25.851008 27.356902 30.114112 27.244865 25.745598
#> [99] 25.750590 26.384759 28.153099 29.123998 26.875846 27.624796 29.009519
#> [106] 27.132571 26.387617 24.259941 25.635382 27.006382 28.001698 29.374272
#> [113] 29.131160 29.377083 30.621950 31.493081 30.617722 31.492949 32.116766
#> [120] 33.243325 34.870834 34.375232 31.753398 31.873451 29.742744 29.563129
#> [127] 31.737368 31.365045 30.486996 29.980483 29.607783 27.982776 25.244140
#> [134] 26.865520 29.495662 31.122323 29.870462 31.494861 32.368150 31.125964
#> [141] 33.002117 33.245640 34.623343 31.494079 31.501655 30.132478 31.891207
#> [148] 33.635465 35.256898 33.125951 34.619237 32.743780 32.743291 34.862310
#> [155] 35.226133 36.856818 37.493243 38.492775 37.620021 37.872801 37.252368
#> [162] 37.610105 32.862749 30.247507 30.503105 33.874775 36.372624 36.868162
#> [169] 33.878707 35.760537 38.016168 36.892301 34.520750 32.148575 33.021063
#> [176] 32.267512 32.518535 34.760531 34.883289 33.008593 32.002037 31.378491
#> [183] 31.438746 30.477232 30.186922 31.411885 31.831347 31.164565 31.739619
#> [190] 33.100427 35.806104 38.775989 33.691665 38.055512 32.705571 33.487558
#> [197] 31.362272 33.475422 32.260183 27.631127 25.488115 30.497291 32.890967
#> [204] 34.385264 29.681531 28.851053 31.804073 32.420259 34.081232 30.022760
#> [211] 29.672484 29.495763 32.697825 34.647857 32.520469 31.833173 27.930148
#> [218] 26.825817 31.621733 31.406174 29.787590 31.677367 30.105322 30.303669
#> [225] 32.794436 31.264345 28.713446 29.244563 30.894158 32.127798 31.786757
#> [232] 31.818258 33.748742 33.741743 35.367246 34.574806 30.596532 35.818331
#> [239] 34.812066 32.163864 31.808797 28.515905 28.427142 28.892704 31.117432
#> [246] 30.743565 28.279727 27.965665 25.892374 27.932318 27.186142 32.946981
#> [253] 30.305218 30.453096 28.142150 28.368823 28.414944 30.013820 27.783196
#> [260] 29.287448 30.088733 31.046109 29.885989 27.259663 32.600328 33.228756
#> [267] 32.181750 28.270209 29.063871 30.492980 31.485840 28.791033 28.660626
#> [274] 31.421333 31.659906 30.194022 26.631853 33.251906 32.712435 31.269380
#> [281] 30.581609 30.987724 27.316927 21.621420 26.678269 27.252742 28.054891
#> [288] 23.789620 24.856491 24.036637 24.182391 22.305066 23.055979 24.744454
#> [295] 28.260930 23.760304 23.629325 23.840927 24.991272 24.959010 24.692032
#> [302] 25.319287 24.785997 24.971238 23.640739 21.056896 21.291320 23.252405
#> [309] 21.180826 23.985197 22.898935 21.512708 24.980987 21.381489 23.406772
#> [316] 18.325189 20.399405 18.998773 17.957361 18.043272 17.130171 20.487284
#> [323] 17.939594 18.025963 19.251755 18.332168 19.914366 19.028502 19.717271
#> [330] 17.550694 16.835570 17.206329 17.797880 19.581136 19.819190 19.191428
#> [337] 20.922588 23.328514 21.922826 18.063495 18.053219 18.000791 16.944300
#> [344] 15.195415 20.569303 21.059211 18.041928 15.659233 15.831635 16.093879
#> [351] 16.688543 14.217348 13.781455 11.643131 10.747145 10.406553 8.717248
#> [358] 8.583015 9.620605 7.823775 9.546665 9.099024 8.729872 12.158135
#> [365] 13.929753 11.689023 11.441990 15.286609 15.555734 14.089417 13.078484
#> [372] 13.052241 10.448162 11.086666 10.303340 10.593179 11.614059 12.065453
#> [379] 13.062099 9.462361 11.719490 12.309431 13.620000 15.194707 14.333027
#> [386] 12.624648 14.727436 13.678308 12.565099 10.305935 14.920075 16.381298
#> [393] 14.264266 10.786746 10.888045 12.391052 12.561877 15.465240 19.941905
#> [400] 18.211091 13.917852 15.889433 16.490437 10.068365 13.758069 15.617004
#> [407] 16.452257 16.017483 17.665179 15.127655 17.369686 19.504278 21.878929
#> [414] 21.494179 21.189808 23.234403 23.896062 22.021459 21.975079 21.518755
#> [421] 24.180468 24.086096 21.194539 16.880579 20.359140 18.324703 19.519163
#> [428] 18.187041 17.349293 17.808592 19.430938 20.099788 21.821751 17.314336
#> [435] 18.322659 17.561106 18.559994 21.099317 23.377124 20.987811 23.353199
#> [442] 20.283127 17.151745 19.589277 22.557462 26.621710 23.347487 23.914829
#> [449] 27.404204 27.378243 26.511127 28.021257 28.772909 24.467435 23.808257
#> [456] 25.526585 28.006309 26.732067 26.073827 24.144178 26.499024 22.605628
#> [463] 21.877449 24.415142 26.119783 28.575160 29.336474 23.727862 25.169767
#> [470] 27.282588 25.644545 24.635959 24.879958 29.813162 32.757722 33.838275
#> [477] 33.798908 31.488804 31.240004 32.410075 31.987167 28.915504 30.604624
#> [484] 31.491740 32.448550 34.190196 31.699683 28.010838 30.158613 28.513733
#> [491] 30.774564 35.213008 34.977216 33.516416 34.092300 34.404836 32.494079
#> [498] 30.167279 30.149233 32.416362 31.387962 29.195165 33.562027 35.659869
#> [505] 31.594067 34.507024 35.511002 37.385222 34.249292 35.435736 35.632680
#> [512] 37.134558 36.600116 36.977158 33.598792 34.181685 32.348727 30.330811
#> [519] 33.323455 30.501189 33.044023 33.380747 34.371964 33.918807 35.914924
#> [526] 36.449341 36.933187 31.289179 31.767339 31.584543 31.855409 33.774642
#> [533] 33.322380 30.699043 35.577788 38.039963 33.598983 29.055222 28.774588
#> [540] 31.509100 34.657855 29.481729 32.851442 32.828741 31.921827 30.383712
#> [547] 30.093704 30.822004 33.264212 34.785419 35.425060 32.356761 30.777626
#> [554] 27.774203 29.164338 29.385321 29.472770 24.554756 25.298540 29.370863
#> [561] 31.384716 31.377310 31.599898 30.916635 31.063275 27.780801 28.838850
#> [568] 30.913088 33.364150 31.846031 30.914587 32.154514 30.388060 30.920355
#> [575] 30.054845 29.135909 27.634861 28.935282 28.408526 31.298057 31.337413
#> [582] 28.062887 27.886532 28.315251 29.098128 27.556287 28.849500 31.816969
#> [589] 29.253432 30.719933 30.438741 29.851360 27.438351 28.862648 30.811645
#> [596] 29.973265 30.118317 30.641466 30.786200 32.066285 31.564264 29.543264
#> [603] 32.603082 32.573440 30.010522 33.078263 30.693622 31.544362 33.196892
#> [610] 33.556944 33.227560 31.666562 31.509651 31.314456 31.693830 29.061147
#> [617] 31.865224 30.082387 31.322449 32.621158 32.491087 31.512480 32.521178
#> [624] 31.921312 31.322889 30.954721 31.516596 30.199060 26.665072 30.470033
#> [631] 32.205046 30.137220 28.063309 27.725163 29.252807 29.474929 27.738524
#> [638] 27.387624 28.955013 29.209429 28.501861 27.058712 29.776624 30.579482
#> [645] 29.644314 27.944282 29.387646 28.416607 24.291264 27.934104 30.197998
#> [652] 29.007268 27.928959 27.395475 29.067890 27.468360 25.826235 27.247769
#> [659] 27.842449 28.758574 24.535950 23.156535 23.116010 25.106980 25.264587
#> [666] 24.873041 22.176590 21.883455 22.796996 22.408624 21.868432 21.977696
#> [673] 23.344638 21.681674 22.898861 23.137225 20.558233 22.279304 19.175330
#> [680] 22.284932 21.502344 21.915651 22.523983 22.221086 21.894960 20.961789
#> [687] 22.038894 19.815502 20.209412 17.605290 18.960740 17.871977 18.489638
#> [694] 20.299919 21.394283 18.077265 18.145172 17.769456 17.395848 18.948054
#> [701] 19.049092 19.287805 15.819263 16.367071 17.507851 16.792462 17.783725
#> [708] 17.628987 20.079820 18.113068 17.813502 14.606261 13.485965 12.539053
#> [715] 12.939488 10.687432 12.290902 14.061772 12.685907 11.146632 12.720983
#> [722] 11.868242 11.671233 11.011955 10.861176 11.204184 12.720095 16.205822
#> [729] 17.181326 17.845629 16.221539 13.001715
Membandingkan eror model Holt Winter dengan parameter beta dan gamma
dibanding dengan model holtwinter tanpa paramter
#> [1] 1.64174#> [1] 1.76842Dari hasil RMSE diatas dapat dikatakan model Holt Winter dengan paramter beta dan gamma memiliki eror paling kecil dibanding dengan model holt winter tanpa parameter beta dan gamma, namun pada model holt winter tanpa parameter beta dan gamma dapat menunjukan pada grafik terdapat xhat, level, tren dan seasonal
5.2 Arima Model
Arima adalah salah satu model forecast gabungan antara 2 metode yaitu Auto Regressive (AR) dan Moving Average (MA). I nya menjelaskan Integrated. Tujuan utama dari ARIMA adalah melakukan autocorrelation pada data.
1. AR(p) : Auto Regressive
Auto regressive di ARIMA artinya kita membuat model linear regression berdasarkan lag dari datanya sebagai prediktor.
2. I(d) : Integrated
Integrated adalah berapa kali data dilakukan
differencing untuk membuat suatu data stationer. Nilai
d dapat diketahui dengan mencari tahu berapa kali
differencing yang dilakukan pada data.
3. MA(q) : Moving Average
Moving Average dalam ARIMA artinya kita melakukan rata-rata berjalan terhadap data time series itu sendiri.
ARIMA memiliki model ARIMA(p,d,q). p -> AR (diperoleh dari plot PACF) d -> I (differencing) q -> MA (diperoleh dari plot ACF)
5.2.1 Cek Data Stationer
Syarat agar data dapat diolah menggunakan ARIMA adalah data harus bersifat stasioner. Stasioner berarti data time series yang kita miliki berfluktuasi disekitar mean nya.
#>
#> Augmented Dickey-Fuller Test
#>
#> data: .
#> Dickey-Fuller = -1.7903, Lag order = 10, p-value = 0.6671
#> alternative hypothesis: stationaryPada data kita diperoleh p-value = 0.6671 > 0.05 sehingga data perlu dilakukan differencing
# Please type your code
climate_ts %>%
diff() %>% # differencing 1x
adf.test() # cek stasioneritas data#>
#> Augmented Dickey-Fuller Test
#>
#> data: .
#> Dickey-Fuller = -14.011, Lag order = 11, p-value = 0.01
#> alternative hypothesis: stationarySetelah 1x differencing, climate_ts [sudah] stasioner.
Nilai berapa kali differencing ini akan kita gunakan untuk membuat model
ARIMA.
kita peroleh ordo untuk d = 1
5.2.2 Plot PACF & ACF
Dalam mencari nilai p dan q kita akan
melihat plot PACF dan ACF menggunakan fungsi tsdisplay()
dari library forecast. Perlu diingat:
pdilihat dari plot PACFqdilihat dari plot ACF
membuat Plot PACF dan ACF menggunakan data climate hasil differencing yang stasioner
Dari visualisasi di atas, kita bisa menentukan nilai lagnya yang melewati garis putus-putus biru.
Q: Dari plot PACF, lag berapa saja yang dapat kita gunakan untuk
p?A: 0, 1, 2, 3, 4, 5
Q: Dari plot ACF, lag berapa saja yang dapat kita gunakan untuk
q?A: 0, 1, 2, 3
Dari hasil differencing dan pemeriksaan lag pada Plot PACF dan ACF kita peroleh
List ordo model ARIMA:
- p: 0, 1, 2, 3, 4, 5
- d: 1
- q: 0, 1, 2, 3
Membuat model manual untuk beberapa kombinasi model ARIMA
5.3 STLM (Seasonal Trend with Loess Model)
STL secara konsep akan melakukan smoothing terhadap data tetangga setiap masing-masing observasi dengan memberikan bobot yang lebih berat terhadap data yang dekat dengan observed data.
Kekurangan dari STL hanya bisa melakukan decompose
pada additive data, apabila terdapat multiplicative data dapat
menggunakan transformasi log().
Untuk memodelkan hasil STL, kita bisa menerapkan STLM(Seasonal Trend with Loess Model) dimana kita bisa menerapkan metode exponential smoothing (ETS) dan ARIMA.
6 Forecasting
Model Triple Exponential Smoothing
#> Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
#> 2016.0055 14.18838 12.083457118 16.29331 10.96917707 17.40759
#> 2016.0082 14.18838 11.532184860 16.84458 10.12607891 18.25069
#> 2016.0110 14.18838 11.077102878 17.29966 9.43009108 18.94667
#> 2016.0137 14.18838 10.680571810 17.69619 8.82364914 19.55312
#> 2016.0164 14.18838 10.324522931 18.05224 8.27911937 20.09765
#> 2016.0192 14.18838 9.998622879 18.37814 7.78069826 20.59607
#> 2016.0219 14.18838 9.696304965 18.68046 7.31834290 21.05842
#> 2016.0247 14.18838 9.413088219 18.96368 6.88520027 21.49156
#> 2016.0274 14.18838 9.145753190 19.23101 6.47634663 21.90042
#> 2016.0301 14.18838 8.891894491 19.48487 6.08810325 22.28866
#> 2016.0329 14.18838 8.649658811 19.72711 5.71763575 22.65913
#> 2016.0356 14.18838 8.417582299 19.95918 5.36270535 23.01406
#> 2016.0384 14.18838 8.194484785 20.18228 5.02150715 23.35526
#> 2016.0411 14.18838 7.979398310 20.39737 4.69256077 23.68420
#> 2016.0438 14.18838 7.771517259 20.60525 4.37463414 24.00213
#> 2016.0466 14.18838 7.570162621 20.80660 4.06668879 24.31008
#> 2016.0493 14.18838 7.374755771 21.00201 3.76783980 24.60892
#> 2016.0521 14.18838 7.184798843 21.19197 3.47732575 24.89944
#> 2016.0548 14.18838 6.999859781 21.37690 3.19448586 25.18228
#> 2016.0575 14.18838 6.819560768 21.55720 2.91874232 25.45802
#> 2016.0603 14.18838 6.643569146 21.73320 2.64958636 25.72718
#> 2016.0630 14.18838 6.471590201 21.90517 2.38656726 25.99020
#> 2016.0658 14.18838 6.303361371 22.07340 2.12928347 26.24748
#> 2016.0685 14.18838 6.138647533 22.23812 1.87737539 26.49939
#> 2016.0712 14.18838 5.977237156 22.39953 1.63051952 26.74624
#> 2016.0740 14.18838 5.818939109 22.55783 1.38842355 26.98834
#> 2016.0767 14.18838 5.663580010 22.71318 1.15082231 27.22594
#> 2016.0795 14.18838 5.511002001 22.86576 0.91747438 27.45929
#> 2016.0822 14.18838 5.361060871 23.01570 0.68815922 27.68861
#> 2016.0849 14.18838 5.213624456 23.16314 0.46267468 27.91409
#> 2016.0877 14.18838 5.068571276 23.30819 0.24083498 28.13593
#> 2016.0904 14.18838 4.925789365 23.45098 0.02246889 28.35430
#> 2016.0932 14.18838 4.785175260 23.59159 -0.19258182 28.56935
#> 2016.0959 14.18838 4.646633122 23.73013 -0.40446374 28.78123
#> 2016.0986 14.18838 4.510073970 23.86669 -0.61331294 28.99008
#> 2016.1014 14.18838 4.375415017 24.00135 -0.81925604 29.19602
#> 2016.1041 14.18838 4.242579082 24.13419 -1.02241107 29.39918
#> 2016.1068 14.18838 4.111494070 24.26527 -1.22288829 29.59965
#> 2016.1096 14.18838 3.982092516 24.39467 -1.42079089 29.79756
#> 2016.1123 14.18838 3.854311180 24.52245 -1.61621558 29.99298
#> 2016.1151 14.18838 3.728090685 24.64867 -1.80925317 30.18602
#> 2016.1178 14.18838 3.603375195 24.77339 -1.99998905 30.37675
#> 2016.1205 14.18838 3.480112124 24.89665 -2.18850365 30.56527
#> 2016.1233 14.18838 3.358251880 25.01851 -2.37487281 30.75164
#> 2016.1260 14.18838 3.237747630 25.13902 -2.55916816 30.93593
#> 2016.1288 14.18838 3.118555091 25.25821 -2.74145742 31.11822
#> 2016.1315 14.18838 3.000632339 25.37613 -2.92180470 31.29857
#> 2016.1342 14.18838 2.883939636 25.49282 -3.10027079 31.47704
#> 2016.1370 14.18838 2.768439275 25.60833 -3.27691335 31.65368
#> 2016.1397 14.18838 2.654095437 25.72267 -3.45178716 31.82855
#> 2016.1425 14.18838 2.540874060 25.83589 -3.62494431 32.00171
#> 2016.1452 14.18838 2.428742725 25.94802 -3.79643439 32.17320
#> 2016.1479 14.18838 2.317670540 26.05909 -3.96630464 32.34307
#> 2016.1507 14.18838 2.207628048 26.16914 -4.13460011 32.51136
#> 2016.1534 14.18838 2.098587132 26.27818 -4.30136380 32.67813
#> 2016.1562 14.18838 1.990520932 26.38624 -4.46663679 32.84340
#> 2016.1589 14.18838 1.883403767 26.49336 -4.63045836 33.00722
#> 2016.1616 14.18838 1.777211064 26.59955 -4.79286608 33.16963
#> 2016.1644 14.18838 1.671919293 26.70485 -4.95389595 33.33066
#> 2016.1671 14.18838 1.567505906 26.80926 -5.11358244 33.49035
#> 2016.1699 14.18838 1.463949279 26.91282 -5.27195864 33.64872
#> 2016.1726 14.18838 1.361228662 27.01554 -5.42905626 33.80582
#> 2016.1753 14.18838 1.259324129 27.11744 -5.58490580 33.96167
#> 2016.1781 14.18838 1.158216532 27.21855 -5.73953652 34.11630
#> 2016.1808 14.18838 1.057887462 27.31888 -5.89297660 34.26974
#> 2016.1836 14.18838 0.958319207 27.41845 -6.04525310 34.42202
#> 2016.1863 14.18838 0.859494717 27.51727 -6.19639212 34.57316
#> 2016.1890 14.18838 0.761397570 27.61537 -6.34641876 34.72318
#> 2016.1918 14.18838 0.664011938 27.71275 -6.49535723 34.87212
#> 2016.1945 14.18838 0.567322560 27.80944 -6.64323087 35.02000
#> 2016.1973 14.18838 0.471314713 27.90545 -6.79006220 35.16683
#> 2016.2000 14.18838 0.375974185 28.00079 -6.93587296 35.31264
#> 2016.2027 14.18838 0.281287251 28.09548 -7.08068413 35.45745
#> 2016.2055 14.18838 0.187240652 28.18952 -7.22451599 35.60128
#> 2016.2082 14.18838 0.093821569 28.28294 -7.36738814 35.74415
#> 2016.2110 14.18838 0.001017607 28.37575 -7.50931956 35.88608
#> 2016.2137 14.18838 -0.091183229 28.46795 -7.65032857 36.02709
#> 2016.2164 14.18838 -0.182792546 28.55956 -7.79043293 36.16720
#> 2016.2192 14.18838 -0.273821584 28.65059 -7.92964983 36.30641
#> 2016.2219 14.18838 -0.364281234 28.74105 -8.06799592 36.44476
#> 2016.2247 14.18838 -0.454182048 28.83095 -8.20548735 36.58225
#> 2016.2274 14.18838 -0.543534257 28.92030 -8.34213976 36.71890
#> 2016.2301 14.18838 -0.632347783 29.00911 -8.47796833 36.85473
#> 2016.2329 14.18838 -0.720632253 29.09740 -8.61298778 36.98975
#> 2016.2356 14.18838 -0.808397010 29.18516 -8.74721239 37.12398
#> 2016.2384 14.18838 -0.895651127 29.27242 -8.88065605 37.25742
#> 2016.2411 14.18838 -0.982403414 29.35917 -9.01333222 37.39010
#> 2016.2438 14.18838 -1.068662431 29.44543 -9.14525400 37.52202
#> 2016.2466 14.18838 -1.154436498 29.53120 -9.27643412 37.65320
#> 2016.2493 14.18838 -1.239733703 29.61650 -9.40688494 37.78365
#> 2016.2521 14.18838 -1.324561913 29.70133 -9.53661849 37.91338
#> 2016.2548 14.18838 -1.408928780 29.78569 -9.66564647 38.04241
#> 2016.2575 14.18838 -1.492841749 29.86961 -9.79398029 38.17074
#> 2016.2603 14.18838 -1.576308068 29.95307 -9.92163101 38.29840
#> 2016.2630 14.18838 -1.659334796 30.03610 -10.04860943 38.42537
#> 2016.2658 14.18838 -1.741928805 30.11869 -10.17492607 38.55169
#> 2016.2685 14.18838 -1.824096791 30.20086 -10.30059116 38.67736
#> 2016.2712 14.18838 -1.905845280 30.28261 -10.42561468 38.80238
#> 2016.2740 14.18838 -1.987180631 30.36395 -10.55000637 38.92677
#> 2016.2767 14.18838 -2.068109046 30.44487 -10.67377570 39.05054
#> 2016.2795 14.18838 -2.148636572 30.52540 -10.79693192 39.17370
#> 2016.2822 14.18838 -2.228769109 30.60553 -10.91948406 39.29625
#> 2016.2849 14.18838 -2.308512412 30.68528 -11.04144092 39.41821
#> 2016.2877 14.18838 -2.387872098 30.76464 -11.16281108 39.53958
#> 2016.2904 14.18838 -2.466853652 30.84362 -11.28360295 39.66037
#> 2016.2932 14.18838 -2.545462428 30.92223 -11.40382469 39.78059
#> 2016.2959 14.18838 -2.623703654 31.00047 -11.52348432 39.90025
#> 2016.2986 14.18838 -2.701582438 31.07835 -11.64258965 40.01935
#> 2016.3014 14.18838 -2.779103772 31.15587 -11.76114830 40.13791
#> 2016.3041 14.18838 -2.856272532 31.23304 -11.87916773 40.25593
#> 2016.3068 14.18838 -2.933093486 31.30986 -11.99665524 40.37342
#> 2016.3096 14.18838 -3.009571295 31.38634 -12.11361795 40.49038
#> 2016.3123 14.18838 -3.085710515 31.46247 -12.23006284 40.60683
#> 2016.3151 14.18838 -3.161515606 31.53828 -12.34599673 40.72276
#> 2016.3178 14.18838 -3.236990927 31.61376 -12.46142627 40.83819
#> 2016.3205 14.18838 -3.312140745 31.68891 -12.57635800 40.95312
#> 2016.3233 14.18838 -3.386969235 31.76373 -12.69079830 41.06756
#> 2016.3260 14.18838 -3.461480485 31.83824 -12.80475342 41.18152
#> 2016.3288 14.18838 -3.535678495 31.91244 -12.91822948 41.29499
#> 2016.3315 14.18838 -3.609567184 31.98633 -13.03123248 41.40800
#> 2016.3342 14.18838 -3.683150387 32.05991 -13.14376828 41.52053
#> 2016.3370 14.18838 -3.756431862 32.13320 -13.25584262 41.63261
#> 2016.3397 14.18838 -3.829415292 32.20618 -13.36746115 41.74423
#> 2016.3425 14.18838 -3.902104283 32.27887 -13.47862937 41.85539
#> 2016.3452 14.18838 -3.974502370 32.35127 -13.58935269 41.96612
#> 2016.3479 14.18838 -4.046613019 32.42338 -13.69963641 42.07640
#> 2016.3507 14.18838 -4.118439626 32.49520 -13.80948572 42.18625
#> 2016.3534 14.18838 -4.189985522 32.56675 -13.91890573 42.29567
#> 2016.3562 14.18838 -4.261253971 32.63802 -14.02790141 42.40467
#> 2016.3589 14.18838 -4.332248177 32.70901 -14.13647768 42.51324
#> 2016.3616 14.18838 -4.402971282 32.77974 -14.24463934 42.62140
#> 2016.3644 14.18838 -4.473426368 32.85019 -14.35239109 42.72916
#> 2016.3671 14.18838 -4.543616459 32.92038 -14.45973758 42.83650
#> 2016.3699 14.18838 -4.613544523 32.99031 -14.56668332 42.94345
#> 2016.3726 14.18838 -4.683213473 33.05998 -14.67323278 43.05000
#> 2016.3753 14.18838 -4.752626167 33.12939 -14.77939034 43.15615
#> 2016.3781 14.18838 -4.821785413 33.19855 -14.88516028 43.26192
#> 2016.3808 14.18838 -4.890693968 33.26746 -14.99054682 43.36731
#> 2016.3836 14.18838 -4.959354537 33.33612 -15.09555410 43.47232
#> 2016.3863 14.18838 -5.027769779 33.40453 -15.20018618 43.57695
#> 2016.3890 14.18838 -5.095942305 33.47271 -15.30444706 43.68121
#> 2016.3918 14.18838 -5.163874680 33.54064 -15.40834066 43.78511
#> 2016.3945 14.18838 -5.231569424 33.60833 -15.51187084 43.88864
#> 2016.3973 14.18838 -5.299029014 33.67579 -15.61504138 43.99181
#> 2016.4000 14.18838 -5.366255883 33.74302 -15.71785600 44.09462
#> 2016.4027 14.18838 -5.433252423 33.81002 -15.82031837 44.19708
#> 2016.4055 14.18838 -5.500020986 33.87679 -15.92243208 44.29920
#> 2016.4082 14.18838 -5.566563883 33.94333 -16.02420065 44.40097
#> 2016.4110 14.18838 -5.632883387 34.00965 -16.12562758 44.50239
#> 2016.4137 14.18838 -5.698981733 34.07575 -16.22671628 44.60348
#> 2016.4164 14.18838 -5.764861119 34.14163 -16.32747011 44.70423
#> 2016.4192 14.18838 -5.830523706 34.20729 -16.42789237 44.80466
#> 2016.4219 14.18838 -5.895971621 34.27274 -16.52798632 44.90475
#> 2016.4247 14.18838 -5.961206955 34.33797 -16.62775515 45.00452
#> 2016.4274 14.18838 -6.026231768 34.40300 -16.72720202 45.10397
#> 2016.4301 14.18838 -6.091048083 34.46781 -16.82633002 45.20309
#> 2016.4329 14.18838 -6.155657893 34.53242 -16.92514220 45.30191
#> 2016.4356 14.18838 -6.220063161 34.59683 -17.02364155 45.40041
#> 2016.4384 14.18838 -6.284265816 34.66103 -17.12183104 45.49860
#> 2016.4411 14.18838 -6.348267758 34.72503 -17.21971357 45.59648
#> 2016.4438 14.18838 -6.412070859 34.78884 -17.31729199 45.69406
#> 2016.4466 14.18838 -6.475676960 34.85244 -17.41456912 45.79133
#> 2016.4493 14.18838 -6.539087875 34.91585 -17.51154775 45.88831
#> 2016.4521 14.18838 -6.602305390 34.97907 -17.60823060 45.98500
#> 2016.4548 14.18838 -6.665331262 35.04210 -17.70462035 46.08138
#> 2016.4575 14.18838 -6.728167226 35.10493 -17.80071966 46.17748
#> 2016.4603 14.18838 -6.790814988 35.16758 -17.89653115 46.27330
#> 2016.4630 14.18838 -6.853276227 35.23004 -17.99205737 46.36882
#> 2016.4658 14.18838 -6.915552601 35.29232 -18.08730086 46.46407
#> 2016.4685 14.18838 -6.977645742 35.35441 -18.18226413 46.55903
#> 2016.4712 14.18838 -7.039557256 35.41632 -18.27694962 46.65371
#> 2016.4740 14.18838 -7.101288730 35.47805 -18.37135976 46.74812
#> 2016.4767 14.18838 -7.162841723 35.53961 -18.46549694 46.84226
#> 2016.4795 14.18838 -7.224217777 35.60098 -18.55936351 46.93613
#> 2016.4822 14.18838 -7.285418407 35.66218 -18.65296180 47.02973
#> 2016.4849 14.18838 -7.346445109 35.72321 -18.74629409 47.12306
#> 2016.4877 14.18838 -7.407299358 35.78406 -18.83936263 47.21613
#> 2016.4904 14.18838 -7.467982608 35.84475 -18.93216965 47.30893
#> 2016.4932 14.18838 -7.528496292 35.90526 -19.02471734 47.40148
#> 2016.4959 14.18838 -7.588841823 35.96561 -19.11700787 47.49377
#> 2016.4986 14.18838 -7.649020596 36.02579 -19.20904336 47.58581
#> 2016.5014 14.18838 -7.709033986 36.08580 -19.30082592 47.67759
#> 2016.5041 14.18838 -7.768883348 36.14565 -19.39235762 47.76912
#> 2016.5068 14.18838 -7.828570021 36.20533 -19.48364051 47.86040
#> 2016.5096 14.18838 -7.888095323 36.26486 -19.57467660 47.95144
#> 2016.5123 14.18838 -7.947460557 36.32423 -19.66546789 48.04223
#> 2016.5151 14.18838 -8.006667006 36.38343 -19.75601635 48.13278
#> 2016.5178 14.18838 -8.065715940 36.44248 -19.84632390 48.22309
#> 2016.5205 14.18838 -8.124608607 36.50137 -19.93639246 48.31316
#> 2016.5233 14.18838 -8.183346242 36.56011 -20.02622392 48.40299
#> 2016.5260 14.18838 -8.241930063 36.61869 -20.11582014 48.49258
#> 2016.5288 14.18838 -8.300361272 36.67713 -20.20518296 48.58195
#> 2016.5315 14.18838 -8.358641055 36.73541 -20.29431420 48.67108
#> 2016.5342 14.18838 -8.416770584 36.79354 -20.38321564 48.75998
#> 2016.5370 14.18838 -8.474751015 36.85152 -20.47188906 48.84865
#> 2016.5397 14.18838 -8.532583490 36.90935 -20.56033620 48.93710
#> 2016.5425 14.18838 -8.590269134 36.96703 -20.64855878 49.02532
#> 2016.5452 14.18838 -8.647809061 37.02457 -20.73655850 49.11332
#> 2016.5479 14.18838 -8.705204370 37.08197 -20.82433705 49.20110
#> 2016.5507 14.18838 -8.762456146 37.13922 -20.91189609 49.28866
#> 2016.5534 14.18838 -8.819565460 37.19633 -20.99923725 49.37600
#> 2016.5562 14.18838 -8.876533370 37.25330 -21.08636215 49.46313
#> 2016.5589 14.18838 -8.933360922 37.31013 -21.17327239 49.55004
#> 2016.5616 14.18838 -8.990049147 37.36681 -21.25996955 49.63673
#> 2016.5644 14.18838 -9.046599066 37.42336 -21.34645518 49.72322
#> 2016.5671 14.18838 -9.103011687 37.47978 -21.43273084 49.80950
#> 2016.5699 14.18838 -9.159288003 37.53605 -21.51879804 49.89556
#> 2016.5726 14.18838 -9.215428999 37.59219 -21.60465828 49.98142
#> 2016.5753 14.18838 -9.271435646 37.64820 -21.69031306 50.06708
#> 2016.5781 14.18838 -9.327308904 37.70407 -21.77576383 50.15253
#> 2016.5808 14.18838 -9.383049722 37.75981 -21.86101206 50.23778
#> 2016.5836 14.18838 -9.438659036 37.81542 -21.94605917 50.32282
#> 2016.5863 14.18838 -9.494137774 37.87090 -22.03090657 50.40767
#> 2016.5890 14.18838 -9.549486850 37.92625 -22.11555568 50.49232
#> 2016.5918 14.18838 -9.604707170 37.98147 -22.20000787 50.57677
#> 2016.5945 14.18838 -9.659799628 38.03656 -22.28426451 50.66103
#> 2016.5973 14.18838 -9.714765108 38.09153 -22.36832696 50.74509
#> 2016.6000 14.18838 -9.769604484 38.14637 -22.45219655 50.82896
#> 2016.6027 14.18838 -9.824318621 38.20108 -22.53587460 50.91264
#> 2016.6055 14.18838 -9.878908371 38.25567 -22.61936242 50.99613
#> 2016.6082 14.18838 -9.933374580 38.31014 -22.70266130 51.07943
#> 2016.6110 14.18838 -9.987718083 38.36448 -22.78577251 51.16254
#> 2016.6137 14.18838 -10.041939705 38.41870 -22.86869733 51.24546
#> 2016.6164 14.18838 -10.096040263 38.47280 -22.95143699 51.32820
#> 2016.6192 14.18838 -10.150020564 38.52679 -23.03399274 51.41076
#> 2016.6219 14.18838 -10.203881406 38.58065 -23.11636579 51.49313
#> 2016.6247 14.18838 -10.257623579 38.63439 -23.19855735 51.57532
#> 2016.6274 14.18838 -10.311247864 38.68801 -23.28056862 51.65733
#> 2016.6301 14.18838 -10.364755034 38.74152 -23.36240077 51.73917
#> 2016.6329 14.18838 -10.418145852 38.79491 -23.44405498 51.82082
#> 2016.6356 14.18838 -10.471421074 38.84819 -23.52553240 51.90230
#> 2016.6384 14.18838 -10.524581447 38.90135 -23.60683418 51.98360
#> 2016.6411 14.18838 -10.577627712 38.95439 -23.68796144 52.06473
#> 2016.6438 14.18838 -10.630560600 39.00733 -23.76891530 52.14568
#> 2016.6466 14.18838 -10.683380834 39.06015 -23.84969688 52.22646
#> 2016.6493 14.18838 -10.736089131 39.11285 -23.93030727 52.30707
#> 2016.6521 14.18838 -10.788686200 39.16545 -24.01074754 52.38751
#> 2016.6548 14.18838 -10.841172742 39.21794 -24.09101878 52.46778
#> 2016.6575 14.18838 -10.893549451 39.27031 -24.17112204 52.54789
#> 2016.6603 14.18838 -10.945817013 39.32258 -24.25105838 52.62782
#> 2016.6630 14.18838 -10.997976108 39.37474 -24.33082883 52.70759
#> 2016.6658 14.18838 -11.050027408 39.42679 -24.41043443 52.78720
#> 2016.6685 14.18838 -11.101971579 39.47874 -24.48987618 52.86664
#> 2016.6712 14.18838 -11.153809280 39.53057 -24.56915510 52.94592
#> 2016.6740 14.18838 -11.205541162 39.58231 -24.64827219 53.02504
#> 2016.6767 14.18838 -11.257167872 39.63393 -24.72722843 53.10399
#> 2016.6795 14.18838 -11.308690048 39.68545 -24.80602480 53.18279
#> 2016.6822 14.18838 -11.360108322 39.73687 -24.88466226 53.26143
#> 2016.6849 14.18838 -11.411423320 39.78819 -24.96314178 53.33991
#> 2016.6877 14.18838 -11.462635663 39.83940 -25.04146430 53.41823
#> 2016.6904 14.18838 -11.513745964 39.89051 -25.11963076 53.49640
#> 2016.6932 14.18838 -11.564754830 39.94152 -25.19764209 53.57441
#> 2016.6959 14.18838 -11.615662863 39.99243 -25.27549920 53.65226
#> 2016.6986 14.18838 -11.666470658 40.04324 -25.35320302 53.72997
#> 2016.7014 14.18838 -11.717178807 40.09394 -25.43075444 53.80752
#> 2016.7041 14.18838 -11.767787891 40.14455 -25.50815436 53.88492
#> 2016.7068 14.18838 -11.818298490 40.19506 -25.58540365 53.96217
#> 2016.7096 14.18838 -11.868711177 40.24548 -25.66250320 54.03927
#> 2016.7123 14.18838 -11.919026518 40.29579 -25.73945388 54.11622
#> 2016.7151 14.18838 -11.969245076 40.34601 -25.81625654 54.19302
#> 2016.7178 14.18838 -12.019367407 40.39613 -25.89291202 54.26968
#> 2016.7205 14.18838 -12.069394061 40.44616 -25.96942119 54.34619
#> 2016.7233 14.18838 -12.119325585 40.49609 -26.04578487 54.42255
#> 2016.7260 14.18838 -12.169162520 40.54593 -26.12200388 54.49877
#> 2016.7288 14.18838 -12.218905400 40.59567 -26.19807905 54.57484
#> 2016.7315 14.18838 -12.268554756 40.64532 -26.27401119 54.65078
#> 2016.7342 14.18838 -12.318111115 40.69488 -26.34980110 54.72657
#> 2016.7370 14.18838 -12.367574996 40.74434 -26.42544958 54.80221
#> 2016.7397 14.18838 -12.416946915 40.79371 -26.50095741 54.87772
#> 2016.7425 14.18838 -12.466227384 40.84299 -26.57632538 54.95309
#> 2016.7452 14.18838 -12.515416908 40.89218 -26.65155427 55.02832
#> 2016.7479 14.18838 -12.564515989 40.94128 -26.72664483 55.10341
#> 2016.7507 14.18838 -12.613525125 40.99029 -26.80159784 55.17836
#> 2016.7534 14.18838 -12.662444807 41.03921 -26.87641404 55.25318
#> 2016.7562 14.18838 -12.711275525 41.08804 -26.95109418 55.32786
#> 2016.7589 14.18838 -12.760017761 41.13678 -27.02563899 55.40240
#> 2016.7616 14.18838 -12.808671994 41.18544 -27.10004922 55.47681
#> 2016.7644 14.18838 -12.857238701 41.23400 -27.17432559 55.55109
#> 2016.7671 14.18838 -12.905718351 41.28248 -27.24846882 55.62523
#> 2016.7699 14.18838 -12.954111410 41.33088 -27.32247961 55.69924
#> 2016.7726 14.18838 -13.002418342 41.37918 -27.39635869 55.77312
#> 2016.7753 14.18838 -13.050639604 41.42740 -27.47010675 55.84687
#> 2016.7781 14.18838 -13.098775651 41.47554 -27.54372448 55.92049
#> 2016.7808 14.18838 -13.146826932 41.52359 -27.61721257 55.99398
#> 2016.7836 14.18838 -13.194793895 41.57156 -27.69057171 56.06734
#> 2016.7863 14.18838 -13.242676981 41.61944 -27.76380257 56.14057
#> 2016.7890 14.18838 -13.290476628 41.66724 -27.83690582 56.21367
#> 2016.7918 14.18838 -13.338193272 41.71496 -27.90988213 56.28665
#> 2016.7945 14.18838 -13.385827344 41.76259 -27.98273216 56.35950
#> 2016.7973 14.18838 -13.433379270 41.81014 -28.05545655 56.43222
#> 2016.8000 14.18838 -13.480849474 41.85761 -28.12805596 56.50482
#> 2016.8027 14.18838 -13.528238376 41.90500 -28.20053104 56.57730
#> 2016.8055 14.18838 -13.575546393 41.95231 -28.27288240 56.64965
#> 2016.8082 14.18838 -13.622773936 41.99954 -28.34511070 56.72188
#> 2016.8110 14.18838 -13.669921416 42.04669 -28.41721655 56.79398
#> 2016.8137 14.18838 -13.716989238 42.09375 -28.48920057 56.86597
#> 2016.8164 14.18838 -13.763977805 42.14074 -28.56106338 56.93783
#> 2016.8192 14.18838 -13.810887515 42.18765 -28.63280559 57.00957
#> 2016.8219 14.18838 -13.857718764 42.23448 -28.70442781 57.08119
#> 2016.8247 14.18838 -13.904471945 42.28124 -28.77593063 57.15270
#> 2016.8274 14.18838 -13.951147447 42.32791 -28.84731465 57.22408
#> 2016.8301 14.18838 -13.997745656 42.37451 -28.91858046 57.29534
#> 2016.8329 14.18838 -14.044266953 42.42103 -28.98972864 57.36649
#> 2016.8356 14.18838 -14.090711720 42.46748 -29.06075978 57.43752
#> 2016.8384 14.18838 -14.137080333 42.51384 -29.13167446 57.50844
#> 2016.8411 14.18838 -14.183373164 42.56014 -29.20247323 57.57924
#> 2016.8438 14.18838 -14.229590584 42.60636 -29.27315668 57.64992
#> 2016.8466 14.18838 -14.275732961 42.65250 -29.34372535 57.72049
#> 2016.8493 14.18838 -14.321800658 42.69857 -29.41417982 57.79094
#> 2016.8521 14.18838 -14.367794038 42.74456 -29.48452062 57.86129
#> 2016.8548 14.18838 -14.413713459 42.79048 -29.55474831 57.93151
#> 2016.8575 14.18838 -14.459559276 42.83632 -29.62486344 58.00163
#> 2016.8603 14.18838 -14.505331842 42.88210 -29.69486654 58.07163
#> 2016.8630 14.18838 -14.551031508 42.92780 -29.76475815 58.14152
#> 2016.8658 14.18838 -14.596658620 42.97342 -29.83453879 58.21130
#> 2016.8685 14.18838 -14.642213523 43.01898 -29.90420900 58.28097
#> 2016.8712 14.18838 -14.687696559 43.06446 -29.97376931 58.35053
#> 2016.8740 14.18838 -14.733108066 43.10987 -30.04322021 58.41998
#> 2016.8767 14.18838 -14.778448382 43.15521 -30.11256224 58.48933
#> 2016.8795 14.18838 -14.823717839 43.20048 -30.18179590 58.55856
#> 2016.8822 14.18838 -14.868916770 43.24568 -30.25092170 58.62769
#> 2016.8849 14.18838 -14.914045502 43.29081 -30.31994014 58.69670
#> 2016.8877 14.18838 -14.959104362 43.33587 -30.38885172 58.76562
#> 2016.8904 14.18838 -15.004093673 43.38086 -30.45765693 58.83442
#> 2016.8932 14.18838 -15.049013757 43.42578 -30.52635627 58.90312
#> 2016.8959 14.18838 -15.093864932 43.47063 -30.59495023 58.97171
#> 2016.8986 14.18838 -15.138647513 43.51541 -30.66343928 59.04020
#> 2016.9014 14.18838 -15.183361816 43.56013 -30.73182390 59.10859
#> 2016.9041 14.18838 -15.228008151 43.60477 -30.80010458 59.17687
#> 2016.9068 14.18838 -15.272586827 43.64935 -30.86828178 59.24505
#> 2016.9096 14.18838 -15.317098151 43.69386 -30.93635597 59.31312
#> 2016.9123 14.18838 -15.361542427 43.73831 -31.00432763 59.38109
#> 2016.9151 14.18838 -15.405919958 43.78268 -31.07219721 59.44896
#> 2016.9178 14.18838 -15.450231042 43.82700 -31.13996516 59.51673
#> 2016.9205 14.18838 -15.494475979 43.87124 -31.20763195 59.58440
#> 2016.9233 14.18838 -15.538655062 43.91542 -31.27519803 59.65196
#> 2016.9260 14.18838 -15.582768586 43.95953 -31.34266384 59.71943
#> 2016.9288 14.18838 -15.626816841 44.00358 -31.41002984 59.78679
#> 2016.9315 14.18838 -15.670800116 44.04756 -31.47729645 59.85406
#> 2016.9342 14.18838 -15.714718698 44.09148 -31.54446412 59.92123
#> 2016.9370 14.18838 -15.758572872 44.13534 -31.61153329 59.98830
#> 2016.9397 14.18838 -15.802362919 44.17913 -31.67850439 60.05527
#> 2016.9425 14.18838 -15.846089121 44.22285 -31.74537785 60.12214
#> 2016.9452 14.18838 -15.889751756 44.26652 -31.81215409 60.18892
#> 2016.9479 14.18838 -15.933351100 44.31012 -31.87883353 60.25560
#> 2016.9507 14.18838 -15.976887428 44.35365 -31.94541660 60.32218
#> 2016.9534 14.18838 -16.020361012 44.39713 -32.01190371 60.38867
#> 2016.9562 14.18838 -16.063772123 44.44054 -32.07829527 60.45506
#> 2016.9589 14.18838 -16.107121029 44.48389 -32.14459170 60.52136
#> 2016.9616 14.18838 -16.150407998 44.52717 -32.21079341 60.58756
#> 2016.9644 14.18838 -16.193633293 44.57040 -32.27690079 60.65367
#> 2016.9671 14.18838 -16.236797177 44.61356 -32.34291426 60.71968
#> 2016.9699 14.18838 -16.279899912 44.65666 -32.40883420 60.78560
#> 2016.9726 14.18838 -16.322941757 44.69971 -32.47466102 60.85143
#> 2016.9753 14.18838 -16.365922968 44.74269 -32.54039511 60.91716
#> 2016.9781 14.18838 -16.408843803 44.78561 -32.60603686 60.98280
#> 2016.9808 14.18838 -16.451704513 44.82847 -32.67158666 61.04835
#> 2016.9836 14.18838 -16.494505352 44.87127 -32.73704490 61.11381
#> 2016.9863 14.18838 -16.537246569 44.91401 -32.80241195 61.17918
#> 2016.9890 14.18838 -16.579928413 44.95669 -32.86768820 61.24445
#> 2016.9918 14.18838 -16.622551131 44.99932 -32.93287402 61.30964
#> 2016.9945 14.18838 -16.665114967 45.04188 -32.99796979 61.37473
#> 2016.9973 14.18838 -16.707620166 45.08438 -33.06297588 61.43974
#> 2017.0000 14.18838 -16.750066968 45.12683 -33.12789266 61.50466
#> 2017.0027 14.18838 -16.792455614 45.16922 -33.19272050 61.56948Pada tabel hasil forecast diatas adalah hasil forecast selama 365 hari kedepan pada hasil prediksi pada model Holtwinter misalnya pada baris pertama 2016 hari pertama menunjukan forecast temperature 14.18, dan Lo 80 adalah 12,08 sementara Hi 80 adalah 16,29, itu berarti kita memiliki 80% keyakinana bahwa nilai sebenarnya akan berada diantara nilai 12,08 dan 16,29.Kita bandingkan hasil forecast dengan model Arima.
#> Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
#> 2016.0055 14 11.85497379 16.14503 10.71946550 17.28053
#> 2016.0082 14 10.96647484 17.03353 9.36062362 18.63938
#> 2016.0110 14 10.28470562 17.71529 8.31794757 19.68205
#> 2016.0137 14 9.70994758 18.29005 7.43893100 20.56107
#> 2016.0164 14 9.20357558 18.79642 6.66450186 21.33550
#> 2016.0192 14 8.74578030 19.25422 5.96436440 22.03564
#> 2016.0219 14 8.32479409 19.67521 5.32052155 22.67948
#> 2016.0247 14 7.93294968 20.06705 4.72124724 23.27875
#> 2016.0274 14 7.56492136 20.43508 4.15839651 23.84160
#> 2016.0301 14 7.21683153 20.78317 3.62603904 24.37396
#> 2016.0329 14 6.88575289 21.11425 3.11969796 24.88030
#> 2016.0356 14 6.56941123 21.43059 2.63589515 25.36410
#> 2016.0384 14 6.26599800 21.73400 2.17186466 25.82814
#> 2016.0411 14 5.97404683 22.02595 1.72536386 26.27464
#> 2016.0438 14 5.69234920 22.30765 1.29454452 26.70546
#> 2016.0466 14 5.41989515 22.58010 0.87786201 27.12214
#> 2016.0493 14 5.15583036 22.84417 0.47400976 27.52599
#> 2016.0521 14 4.89942452 23.10058 0.08187086 27.91813
#> 2016.0548 14 4.65004751 23.34995 -0.29951836 28.29952
#> 2016.0575 14 4.40715115 23.59285 -0.67099628 28.67100
#> 2016.0603 14 4.17025501 23.82974 -1.03329766 29.03330
#> 2016.0630 14 3.93893525 24.06106 -1.38707071 29.38707
#> 2016.0658 14 3.71281567 24.28718 -1.73289076 29.73289
#> 2016.0685 14 3.49156059 24.50844 -2.07127121 30.07127
#> 2016.0712 14 3.27486894 24.72513 -2.40267249 30.40267
#> 2016.0740 14 3.06246949 24.93753 -2.72750942 30.72751
#> 2016.0767 14 2.85411685 25.14588 -3.04615728 31.04616
#> 2016.0795 14 2.64958817 25.35041 -3.35895690 31.35896
#> 2016.0822 14 2.44868033 25.55132 -3.66621893 31.66622
#> 2016.0849 14 2.25120757 25.74879 -3.96822745 31.96823
#> 2016.0877 14 2.05699950 25.94300 -4.26524307 32.26524
#> 2016.0904 14 1.86589936 26.13410 -4.55750552 32.55751
#> 2016.0932 14 1.67776255 26.32224 -4.84523594 32.84524
#> 2016.0959 14 1.49245534 26.50754 -5.12863885 33.12864
#> 2016.0986 14 1.30985379 26.69015 -5.40790382 33.40790
#> 2016.1014 14 1.12984273 26.87016 -5.68320699 33.68321
#> 2016.1041 14 0.95231493 27.04769 -5.95471232 33.95471
#> 2016.1068 14 0.77717038 27.22283 -6.22257280 34.22257
#> 2016.1096 14 0.60431560 27.39568 -6.48693137 34.48693
#> 2016.1123 14 0.43366306 27.56634 -6.74792191 34.74792
#> 2016.1151 14 0.26513067 27.73487 -7.00566996 35.00567
#> 2016.1178 14 0.09864133 27.90136 -7.26029343 35.26029
#> 2016.1205 14 -0.06587752 28.06588 -7.51190330 35.51190
#> 2016.1233 14 -0.22849422 28.22849 -7.76060408 35.76060
#> 2016.1260 14 -0.38927327 28.38927 -8.00649442 36.00649
#> 2016.1288 14 -0.54827559 28.54828 -8.24966749 36.24967
#> 2016.1315 14 -0.70555882 28.70556 -8.49021142 36.49021
#> 2016.1342 14 -0.86117753 28.86118 -8.72820971 36.72821
#> 2016.1370 14 -1.01518349 29.01518 -8.96374149 36.96374
#> 2016.1397 14 -1.16762581 29.16763 -9.19688190 37.19688
#> 2016.1425 14 -1.31855117 29.31855 -9.42770233 37.42770
#> 2016.1452 14 -1.46800399 29.46800 -9.65627069 37.65627
#> 2016.1479 14 -1.61602654 29.61603 -9.88265164 37.88265
#> 2016.1507 14 -1.76265911 29.76266 -10.10690681 38.10691
#> 2016.1534 14 -1.90794015 29.90794 -10.32909498 38.32909
#> 2016.1562 14 -2.05190634 30.05191 -10.54927228 38.54927
#> 2016.1589 14 -2.19459276 30.19459 -10.76749232 38.76749
#> 2016.1616 14 -2.33603294 30.33603 -10.98380640 38.98381
#> 2016.1644 14 -2.47625897 30.47626 -11.19826361 39.19826
#> 2016.1671 14 -2.61530159 30.61530 -11.41091096 39.41091
#> 2016.1699 14 -2.75319028 30.75319 -11.62179350 39.62179
#> 2016.1726 14 -2.88995329 30.88995 -11.83095447 39.83095
#> 2016.1753 14 -3.02561774 31.02562 -12.03843535 40.03844
#> 2016.1781 14 -3.16020970 31.16021 -12.24427599 40.24428
#> 2016.1808 14 -3.29375420 31.29375 -12.44851468 40.44851
#> 2016.1836 14 -3.42627533 31.42628 -12.65118825 40.65119
#> 2016.1863 14 -3.55779625 31.55780 -12.85233215 40.85233
#> 2016.1890 14 -3.68833929 31.68834 -13.05198049 41.05198
#> 2016.1918 14 -3.81792592 31.81793 -13.25016615 41.25017
#> 2016.1945 14 -3.94657688 31.94658 -13.44692080 41.44692
#> 2016.1973 14 -4.07431213 32.07431 -13.64227502 41.64228
#> 2016.2000 14 -4.20115097 32.20115 -13.83625827 41.83626
#> 2016.2027 14 -4.32711199 32.32711 -14.02889904 42.02890
#> 2016.2055 14 -4.45221318 32.45221 -14.22022480 42.22022
#> 2016.2082 14 -4.57647192 32.57647 -14.41026213 42.41026
#> 2016.2110 14 -4.69990498 32.69990 -14.59903672 42.59904
#> 2016.2137 14 -4.82252862 32.82253 -14.78657339 42.78657
#> 2016.2164 14 -4.94435856 32.94436 -14.97289620 42.97290
#> 2016.2192 14 -5.06541000 33.06541 -15.15802841 43.15803
#> 2016.2219 14 -5.18569770 33.18570 -15.34199256 43.34199
#> 2016.2247 14 -5.30523591 33.30524 -15.52481048 43.52481
#> 2016.2274 14 -5.42403848 33.42404 -15.70650334 43.70650
#> 2016.2301 14 -5.54211883 33.54212 -15.88709165 43.88709
#> 2016.2329 14 -5.65948997 33.65949 -16.06659532 44.06660
#> 2016.2356 14 -5.77616453 33.77616 -16.24503365 44.24503
#> 2016.2384 14 -5.89215476 33.89215 -16.42242540 44.42243
#> 2016.2411 14 -6.00747256 34.00747 -16.59878876 44.59879
#> 2016.2438 14 -6.12212950 34.12213 -16.77414142 44.77414
#> 2016.2466 14 -6.23613681 34.23614 -16.94850056 44.94850
#> 2016.2493 14 -6.34950541 34.34951 -17.12188287 45.12188
#> 2016.2521 14 -6.46224592 34.46225 -17.29430459 45.29430
#> 2016.2548 14 -6.57436865 34.57437 -17.46578152 45.46578
#> 2016.2575 14 -6.68588366 34.68588 -17.63632901 45.63633
#> 2016.2603 14 -6.79680073 34.79680 -17.80596202 45.80596
#> 2016.2630 14 -6.90712936 34.90713 -17.97469509 45.97470
#> 2016.2658 14 -7.01687882 35.01688 -18.14254242 46.14254
#> 2016.2685 14 -7.12605815 35.12606 -18.30951779 46.30952
#> 2016.2712 14 -7.23467613 35.23468 -18.47563465 46.47563
#> 2016.2740 14 -7.34274133 35.34274 -18.64090613 46.64091
#> 2016.2767 14 -7.45026212 35.45026 -18.80534498 46.80534
#> 2016.2795 14 -7.55724664 35.55725 -18.96896368 46.96896
#> 2016.2822 14 -7.66370282 35.66370 -19.13177436 47.13177
#> 2016.2849 14 -7.76963843 35.76964 -19.29378890 47.29379
#> 2016.2877 14 -7.87506103 35.87506 -19.45501884 47.45502
#> 2016.2904 14 -7.97997799 35.97998 -19.61547549 47.61548
#> 2016.2932 14 -8.08439652 36.08440 -19.77516986 47.77517
#> 2016.2959 14 -8.18832367 36.18832 -19.93411271 47.93411
#> 2016.2986 14 -8.29176630 36.29177 -20.09231456 48.09231
#> 2016.3014 14 -8.39473113 36.39473 -20.24978567 48.24979
#> 2016.3041 14 -8.49722471 36.49722 -20.40653608 48.40654
#> 2016.3068 14 -8.59925346 36.59925 -20.56257560 48.56258
#> 2016.3096 14 -8.70082365 36.70082 -20.71791380 48.71791
#> 2016.3123 14 -8.80194141 36.80194 -20.87256006 48.87256
#> 2016.3151 14 -8.90261272 36.90261 -21.02652355 49.02652
#> 2016.3178 14 -9.00284345 37.00284 -21.17981322 49.17981
#> 2016.3205 14 -9.10263934 37.10264 -21.33243786 49.33244
#> 2016.3233 14 -9.20200599 37.20201 -21.48440603 49.48441
#> 2016.3260 14 -9.30094889 37.30095 -21.63572615 49.63573
#> 2016.3288 14 -9.39947343 37.39947 -21.78640642 49.78641
#> 2016.3315 14 -9.49758486 37.49758 -21.93645491 49.93645
#> 2016.3342 14 -9.59528833 37.59529 -22.08587948 50.08588
#> 2016.3370 14 -9.69258891 37.69259 -22.23468786 50.23469
#> 2016.3397 14 -9.78949151 37.78949 -22.38288761 50.38289
#> 2016.3425 14 -9.88600100 37.88600 -22.53048614 50.53049
#> 2016.3452 14 -9.98212212 37.98212 -22.67749070 50.67749
#> 2016.3479 14 -10.07785952 38.07786 -22.82390841 50.82391
#> 2016.3507 14 -10.17321775 38.17322 -22.96974624 50.96975
#> 2016.3534 14 -10.26820129 38.26820 -23.11501103 51.11501
#> 2016.3562 14 -10.36281452 38.36281 -23.25970948 51.25971
#> 2016.3589 14 -10.45706173 38.45706 -23.40384816 51.40385
#> 2016.3616 14 -10.55094715 38.55095 -23.54743352 51.54743
#> 2016.3644 14 -10.64447491 38.64447 -23.69047188 51.69047
#> 2016.3671 14 -10.73764906 38.73765 -23.83296944 51.83297
#> 2016.3699 14 -10.83047359 38.83047 -23.97493230 51.97493
#> 2016.3726 14 -10.92295239 38.92295 -24.11636643 52.11637
#> 2016.3753 14 -11.01508931 39.01509 -24.25727770 52.25728
#> 2016.3781 14 -11.10688812 39.10689 -24.39767185 52.39767
#> 2016.3808 14 -11.19835249 39.19835 -24.53755454 52.53755
#> 2016.3836 14 -11.28948607 39.28949 -24.67693132 52.67693
#> 2016.3863 14 -11.38029242 39.38029 -24.81580764 52.81581
#> 2016.3890 14 -11.47077503 39.47078 -24.95418886 52.95419
#> 2016.3918 14 -11.56093735 39.56094 -25.09208022 53.09208
#> 2016.3945 14 -11.65078275 39.65078 -25.22948691 53.22949
#> 2016.3973 14 -11.74031455 39.74031 -25.36641398 53.36641
#> 2016.4000 14 -11.82953601 39.82954 -25.50286643 53.50287
#> 2016.4027 14 -11.91845034 39.91845 -25.63884916 53.63885
#> 2016.4055 14 -12.00706068 40.00706 -25.77436699 53.77437
#> 2016.4082 14 -12.09537014 40.09537 -25.90942465 53.90942
#> 2016.4110 14 -12.18338176 40.18338 -26.04402680 54.04403
#> 2016.4137 14 -12.27109852 40.27110 -26.17817802 54.17818
#> 2016.4164 14 -12.35852339 40.35852 -26.31188281 54.31188
#> 2016.4192 14 -12.44565924 40.44566 -26.44514560 54.44515
#> 2016.4219 14 -12.53250893 40.53251 -26.57797073 54.57797
#> 2016.4247 14 -12.61907526 40.61908 -26.71036251 54.71036
#> 2016.4274 14 -12.70536098 40.70536 -26.84232513 54.84233
#> 2016.4301 14 -12.79136880 40.79137 -26.97386275 54.97386
#> 2016.4329 14 -12.87710140 40.87710 -27.10497944 55.10498
#> 2016.4356 14 -12.96256140 40.96256 -27.23567923 55.23568
#> 2016.4384 14 -13.04775138 41.04775 -27.36596606 55.36597
#> 2016.4411 14 -13.13267389 41.13267 -27.49584383 55.49584
#> 2016.4438 14 -13.21733142 41.21733 -27.62531635 55.62532
#> 2016.4466 14 -13.30172645 41.30173 -27.75438741 55.75439
#> 2016.4493 14 -13.38586140 41.38586 -27.88306071 55.88306
#> 2016.4521 14 -13.46973866 41.46974 -28.01133991 56.01134
#> 2016.4548 14 -13.55336058 41.55336 -28.13922861 56.13923
#> 2016.4575 14 -13.63672949 41.63673 -28.26673035 56.26673
#> 2016.4603 14 -13.71984766 41.71985 -28.39384862 56.39385
#> 2016.4630 14 -13.80271735 41.80272 -28.52058687 56.52059
#> 2016.4658 14 -13.88534076 41.88534 -28.64694848 56.64695
#> 2016.4685 14 -13.96772008 41.96772 -28.77293678 56.77294
#> 2016.4712 14 -14.04985747 42.04986 -28.89855507 56.89856
#> 2016.4740 14 -14.13175504 42.13176 -29.02380660 57.02381
#> 2016.4767 14 -14.21341488 42.21341 -29.14869454 57.14869
#> 2016.4795 14 -14.29483904 42.29484 -29.27322206 57.27322
#> 2016.4822 14 -14.37602957 42.37603 -29.39739225 57.39739
#> 2016.4849 14 -14.45698845 42.45699 -29.52120817 57.52121
#> 2016.4877 14 -14.53771765 42.53772 -29.64467284 57.64467
#> 2016.4904 14 -14.61821913 42.61822 -29.76778922 57.76779
#> 2016.4932 14 -14.69849480 42.69849 -29.89056026 57.89056
#> 2016.4959 14 -14.77854654 42.77855 -30.01298884 58.01299
#> 2016.4986 14 -14.85837623 42.85838 -30.13507781 58.13508
#> 2016.5014 14 -14.93798570 42.93799 -30.25682998 58.25683
#> 2016.5041 14 -15.01737675 43.01738 -30.37824812 58.37825
#> 2016.5068 14 -15.09655119 43.09655 -30.49933497 58.49933
#> 2016.5096 14 -15.17551077 43.17551 -30.62009323 58.62009
#> 2016.5123 14 -15.25425723 43.25426 -30.74052555 58.74053
#> 2016.5151 14 -15.33279229 43.33279 -30.86063456 58.86063
#> 2016.5178 14 -15.41111764 43.41112 -30.98042285 58.98042
#> 2016.5205 14 -15.48923496 43.48923 -31.09989297 59.09989
#> 2016.5233 14 -15.56714588 43.56715 -31.21904746 59.21905
#> 2016.5260 14 -15.64485205 43.64485 -31.33788878 59.33789
#> 2016.5288 14 -15.72235507 43.72236 -31.45641941 59.45642
#> 2016.5315 14 -15.79965651 43.79966 -31.57464177 59.57464
#> 2016.5342 14 -15.87675795 43.87676 -31.69255825 59.69256
#> 2016.5370 14 -15.95366093 43.95366 -31.81017120 59.81017
#> 2016.5397 14 -16.03036697 44.03037 -31.92748297 59.92748
#> 2016.5425 14 -16.10687758 44.10688 -32.04449586 60.04450
#> 2016.5452 14 -16.18319425 44.18319 -32.16121213 60.16121
#> 2016.5479 14 -16.25931845 44.25932 -32.27763404 60.27763
#> 2016.5507 14 -16.33525161 44.33525 -32.39376379 60.39376
#> 2016.5534 14 -16.41099518 44.41100 -32.50960358 60.50960
#> 2016.5562 14 -16.48655056 44.48655 -32.62515557 60.62516
#> 2016.5589 14 -16.56191916 44.56192 -32.74042189 60.74042
#> 2016.5616 14 -16.63710234 44.63710 -32.85540465 60.85540
#> 2016.5644 14 -16.71210148 44.71210 -32.97010594 60.97011
#> 2016.5671 14 -16.78691792 44.78692 -33.08452780 61.08453
#> 2016.5699 14 -16.86155298 44.86155 -33.19867228 61.19867
#> 2016.5726 14 -16.93600798 44.93601 -33.31254138 61.31254
#> 2016.5753 14 -17.01028422 45.01028 -33.42613708 61.42614
#> 2016.5781 14 -17.08438297 45.08438 -33.53946134 61.53946
#> 2016.5808 14 -17.15830551 45.15831 -33.65251611 61.65252
#> 2016.5836 14 -17.23205308 45.23205 -33.76530328 61.76530
#> 2016.5863 14 -17.30562692 45.30563 -33.87782477 61.87782
#> 2016.5890 14 -17.37902826 45.37903 -33.99008242 61.99008
#> 2016.5918 14 -17.45225830 45.45226 -34.10207810 62.10208
#> 2016.5945 14 -17.52531823 45.52532 -34.21381362 62.21381
#> 2016.5973 14 -17.59820924 45.59821 -34.32529080 62.32529
#> 2016.6000 14 -17.67093248 45.67093 -34.43651141 62.43651
#> 2016.6027 14 -17.74348912 45.74349 -34.54747722 62.54748
#> 2016.6055 14 -17.81588030 45.81588 -34.65818996 62.65819
#> 2016.6082 14 -17.88810714 45.88811 -34.76865138 62.76865
#> 2016.6110 14 -17.96017075 45.96017 -34.87886316 62.87886
#> 2016.6137 14 -18.03207223 46.03207 -34.98882699 62.98883
#> 2016.6164 14 -18.10381269 46.10381 -35.09854455 63.09854
#> 2016.6192 14 -18.17539318 46.17539 -35.20801747 63.20802
#> 2016.6219 14 -18.24681479 46.24681 -35.31724739 63.31725
#> 2016.6247 14 -18.31807855 46.31808 -35.42623591 63.42624
#> 2016.6274 14 -18.38918552 46.38919 -35.53498464 63.53498
#> 2016.6301 14 -18.46013673 46.46014 -35.64349514 63.64350
#> 2016.6329 14 -18.53093318 46.53093 -35.75176898 63.75177
#> 2016.6356 14 -18.60157590 46.60158 -35.85980769 63.85981
#> 2016.6384 14 -18.67206588 46.67207 -35.96761281 63.96761
#> 2016.6411 14 -18.74240410 46.74240 -36.07518583 64.07519
#> 2016.6438 14 -18.81259154 46.81259 -36.18252826 64.18253
#> 2016.6466 14 -18.88262917 46.88263 -36.28964157 64.28964
#> 2016.6493 14 -18.95251794 46.95252 -36.39652722 64.39653
#> 2016.6521 14 -19.02225880 47.02226 -36.50318666 64.50319
#> 2016.6548 14 -19.09185267 47.09185 -36.60962131 64.60962
#> 2016.6575 14 -19.16130050 47.16130 -36.71583260 64.71583
#> 2016.6603 14 -19.23060319 47.23060 -36.82182191 64.82182
#> 2016.6630 14 -19.29976165 47.29976 -36.92759065 64.92759
#> 2016.6658 14 -19.36877677 47.36878 -37.03314017 65.03314
#> 2016.6685 14 -19.43764945 47.43765 -37.13847184 65.13847
#> 2016.6712 14 -19.50638056 47.50638 -37.24358700 65.24359
#> 2016.6740 14 -19.57497097 47.57497 -37.34848698 65.34849
#> 2016.6767 14 -19.64342154 47.64342 -37.45317310 65.45317
#> 2016.6795 14 -19.71173313 47.71173 -37.55764665 65.55765
#> 2016.6822 14 -19.77990657 47.77991 -37.66190894 65.66191
#> 2016.6849 14 -19.84794270 47.84794 -37.76596123 65.76596
#> 2016.6877 14 -19.91584236 47.91584 -37.86980478 65.86980
#> 2016.6904 14 -19.98360635 47.98361 -37.97344086 65.97344
#> 2016.6932 14 -20.05123548 48.05124 -38.07687070 66.07687
#> 2016.6959 14 -20.11873056 48.11873 -38.18009552 66.18010
#> 2016.6986 14 -20.18609239 48.18609 -38.28311654 66.28312
#> 2016.7014 14 -20.25332174 48.25332 -38.38593496 66.38593
#> 2016.7041 14 -20.32041940 48.32042 -38.48855197 66.48855
#> 2016.7068 14 -20.38738613 48.38739 -38.59096875 66.59097
#> 2016.7096 14 -20.45422271 48.45422 -38.69318648 66.69319
#> 2016.7123 14 -20.52092988 48.52093 -38.79520629 66.79521
#> 2016.7151 14 -20.58750840 48.58751 -38.89702935 66.89703
#> 2016.7178 14 -20.65395901 48.65396 -38.99865678 66.99866
#> 2016.7205 14 -20.72028243 48.72028 -39.10008971 67.10009
#> 2016.7233 14 -20.78647941 48.78648 -39.20132925 67.20133
#> 2016.7260 14 -20.85255065 48.85255 -39.30237650 67.30238
#> 2016.7288 14 -20.91849688 48.91850 -39.40323255 67.40323
#> 2016.7315 14 -20.98431880 48.98432 -39.50389849 67.50390
#> 2016.7342 14 -21.05001711 49.05002 -39.60437539 67.60438
#> 2016.7370 14 -21.11559250 49.11559 -39.70466430 67.70466
#> 2016.7397 14 -21.18104567 49.18105 -39.80476627 67.80477
#> 2016.7425 14 -21.24637729 49.24638 -39.90468236 67.90468
#> 2016.7452 14 -21.31158803 49.31159 -40.00441359 68.00441
#> 2016.7479 14 -21.37667857 49.37668 -40.10396098 68.10396
#> 2016.7507 14 -21.44164957 49.44165 -40.20332554 68.20333
#> 2016.7534 14 -21.50650168 49.50650 -40.30250829 68.30251
#> 2016.7562 14 -21.57123556 49.57124 -40.40151021 68.40151
#> 2016.7589 14 -21.63585184 49.63585 -40.50033229 68.50033
#> 2016.7616 14 -21.70035117 49.70035 -40.59897551 68.59898
#> 2016.7644 14 -21.76473419 49.76473 -40.69744083 68.69744
#> 2016.7671 14 -21.82900151 49.82900 -40.79572921 68.79573
#> 2016.7699 14 -21.89315375 49.89315 -40.89384161 68.89384
#> 2016.7726 14 -21.95719154 49.95719 -40.99177896 68.99178
#> 2016.7753 14 -22.02111549 50.02112 -41.08954220 69.08954
#> 2016.7781 14 -22.08492620 50.08493 -41.18713225 69.18713
#> 2016.7808 14 -22.14862426 50.14862 -41.28455003 69.28455
#> 2016.7836 14 -22.21221028 50.21221 -41.38179646 69.38180
#> 2016.7863 14 -22.27568485 50.27568 -41.47887243 69.47887
#> 2016.7890 14 -22.33904854 50.33905 -41.57577883 69.57578
#> 2016.7918 14 -22.40230193 50.40230 -41.67251655 69.67252
#> 2016.7945 14 -22.46544561 50.46545 -41.76908647 69.76909
#> 2016.7973 14 -22.52848013 50.52848 -41.86548946 69.86549
#> 2016.8000 14 -22.59140607 50.59141 -41.96172637 69.96173
#> 2016.8027 14 -22.65422398 50.65422 -42.05779808 70.05780
#> 2016.8055 14 -22.71693442 50.71693 -42.15370542 70.15371
#> 2016.8082 14 -22.77953793 50.77954 -42.24944923 70.24945
#> 2016.8110 14 -22.84203507 50.84204 -42.34503035 70.34503
#> 2016.8137 14 -22.90442637 50.90443 -42.44044961 70.44045
#> 2016.8164 14 -22.96671236 50.96671 -42.53570782 70.53571
#> 2016.8192 14 -23.02889359 51.02889 -42.63080579 70.63081
#> 2016.8219 14 -23.09097057 51.09097 -42.72574434 70.72574
#> 2016.8247 14 -23.15294383 51.15294 -42.82052427 70.82052
#> 2016.8274 14 -23.21481389 51.21481 -42.91514636 70.91515
#> 2016.8301 14 -23.27658126 51.27658 -43.00961139 71.00961
#> 2016.8329 14 -23.33824645 51.33825 -43.10392016 71.10392
#> 2016.8356 14 -23.39980996 51.39981 -43.19807343 71.19807
#> 2016.8384 14 -23.46127230 51.46127 -43.29207197 71.29207
#> 2016.8411 14 -23.52263397 51.52263 -43.38591654 71.38592
#> 2016.8438 14 -23.58389545 51.58390 -43.47960790 71.47961
#> 2016.8466 14 -23.64505725 51.64506 -43.57314679 71.57315
#> 2016.8493 14 -23.70611983 51.70612 -43.66653395 71.66653
#> 2016.8521 14 -23.76708368 51.76708 -43.75977012 71.75977
#> 2016.8548 14 -23.82794929 51.82795 -43.85285603 71.85286
#> 2016.8575 14 -23.88871712 51.88872 -43.94579240 71.94579
#> 2016.8603 14 -23.94938764 51.94939 -44.03857996 72.03858
#> 2016.8630 14 -24.00996132 52.00996 -44.13121941 72.13122
#> 2016.8658 14 -24.07043863 52.07044 -44.22371147 72.22371
#> 2016.8685 14 -24.13082001 52.13082 -44.31605682 72.31606
#> 2016.8712 14 -24.19110593 52.19111 -44.40825618 72.40826
#> 2016.8740 14 -24.25129683 52.25130 -44.50031023 72.50031
#> 2016.8767 14 -24.31139317 52.31139 -44.59221965 72.59222
#> 2016.8795 14 -24.37139539 52.37140 -44.68398512 72.68399
#> 2016.8822 14 -24.43130393 52.43130 -44.77560733 72.77561
#> 2016.8849 14 -24.49111923 52.49112 -44.86708693 72.86709
#> 2016.8877 14 -24.55084171 52.55084 -44.95842459 72.95842
#> 2016.8904 14 -24.61047182 52.61047 -45.04962097 73.04962
#> 2016.8932 14 -24.67000998 52.67001 -45.14067672 73.14068
#> 2016.8959 14 -24.72945661 52.72946 -45.23159249 73.23159
#> 2016.8986 14 -24.78881213 52.78881 -45.32236893 73.32237
#> 2016.9014 14 -24.84807697 52.84808 -45.41300668 73.41301
#> 2016.9041 14 -24.90725153 52.90725 -45.50350636 73.50351
#> 2016.9068 14 -24.96633623 52.96634 -45.59386861 73.59387
#> 2016.9096 14 -25.02533147 53.02533 -45.68409405 73.68409
#> 2016.9123 14 -25.08423766 53.08424 -45.77418330 73.77418
#> 2016.9151 14 -25.14305521 53.14306 -45.86413697 73.86414
#> 2016.9178 14 -25.20178451 53.20178 -45.95395568 73.95396
#> 2016.9205 14 -25.26042595 53.26043 -46.04364004 74.04364
#> 2016.9233 14 -25.31897994 53.31898 -46.13319063 74.13319
#> 2016.9260 14 -25.37744686 53.37745 -46.22260806 74.22261
#> 2016.9288 14 -25.43582709 53.43583 -46.31189293 74.31189
#> 2016.9315 14 -25.49412103 53.49412 -46.40104581 74.40105
#> 2016.9342 14 -25.55232905 53.55233 -46.49006730 74.49007
#> 2016.9370 14 -25.61045154 53.61045 -46.57895797 74.57896
#> 2016.9397 14 -25.66848886 53.66849 -46.66771839 74.66772
#> 2016.9425 14 -25.72644139 53.72644 -46.75634915 74.75635
#> 2016.9452 14 -25.78430951 53.78431 -46.84485079 74.84485
#> 2016.9479 14 -25.84209358 53.84209 -46.93322390 74.93322
#> 2016.9507 14 -25.89979396 53.89979 -47.02146902 75.02147
#> 2016.9534 14 -25.95741102 53.95741 -47.10958671 75.10959
#> 2016.9562 14 -26.01494512 54.01495 -47.19757752 75.19758
#> 2016.9589 14 -26.07239662 54.07240 -47.28544200 75.28544
#> 2016.9616 14 -26.12976586 54.12977 -47.37318069 75.37318
#> 2016.9644 14 -26.18705321 54.18705 -47.46079412 75.46079
#> 2016.9671 14 -26.24425900 54.24426 -47.54828284 75.54828
#> 2016.9699 14 -26.30138360 54.30138 -47.63564738 75.63565
#> 2016.9726 14 -26.35842734 54.35843 -47.72288825 75.72289
#> 2016.9753 14 -26.41539057 54.41539 -47.81000599 75.81001
#> 2016.9781 14 -26.47227363 54.47227 -47.89700112 75.89700
#> 2016.9808 14 -26.52907685 54.52908 -47.98387414 75.98387
#> 2016.9836 14 -26.58580057 54.58580 -48.07062558 76.07063
#> 2016.9863 14 -26.64244512 54.64245 -48.15725595 76.15726
#> 2016.9890 14 -26.69901083 54.69901 -48.24376574 76.24377
#> 2016.9918 14 -26.75549803 54.75550 -48.33015546 76.33016
#> 2016.9945 14 -26.81190705 54.81191 -48.41642562 76.41643
#> 2016.9973 14 -26.86823822 54.86824 -48.50257669 76.50258
#> 2017.0000 14 -26.92449184 54.92449 -48.58860919 76.58861
#> 2017.0027 14 -26.98066824 54.98067 -48.67452359 76.67452Berbeda dengan hasil forecast arima menunjukan prediksi selama 365 hari kedepan dimulai hari tahun 2016. Misalnya hari pertama pada tahun 2016 menunjukan hasil forecast 14 dengan Lo 80 11.85 dan Hi 80 16.14, yang artinya prediksi tersebut disertai dengan interval kepercayaan 80%. Dengan kata lain, kita memiliki 80% keyakinan bahwa nilai sebenarnya akan berada di antara batas bawah (Lo 80) dan batas atas (Hi 80) dari interval tersebut. Interval kepercayaan yang lebih sempit memberikan tingkat keyakinan yang lebih tinggi tetapi mungkin tingkat ketidakpastian yang lebih rendah. Pada forecast arima menunjukan interval yang cukup jauh dibanding dengan model lain
#> Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
#> 2016.0055 2.563838 2.490349 2.637328 2.451446 2.676231
#> 2016.0082 2.570814 2.480020 2.661607 2.431957 2.709671
#> 2016.0110 2.395455 2.295222 2.495687 2.242163 2.548747
#> 2016.0137 2.349287 2.245443 2.453131 2.190471 2.508103
#> 2016.0164 2.278687 2.172133 2.385242 2.115727 2.441648
#> 2016.0192 2.351982 2.243927 2.460038 2.186726 2.517239
#> 2016.0219 2.541350 2.432120 2.650580 2.374297 2.708403
#> 2016.0247 2.457823 2.347910 2.567736 2.289726 2.625920
#> 2016.0274 2.560719 2.450399 2.671039 2.392000 2.729439
#> 2016.0301 2.526997 2.416526 2.637469 2.358046 2.695949
#> 2016.0329 2.640744 2.530242 2.751247 2.471745 2.809743
#> 2016.0356 2.582737 2.472233 2.693240 2.413736 2.751737
#> 2016.0384 2.566578 2.456045 2.677110 2.397532 2.735623
#> 2016.0411 2.570672 2.460072 2.681271 2.401525 2.739819
#> 2016.0438 2.635012 2.524339 2.745686 2.465752 2.804273
#> 2016.0466 2.578317 2.467592 2.689043 2.408977 2.747658
#> 2016.0493 2.613620 2.502875 2.724365 2.444250 2.782990
#> 2016.0521 2.573808 2.463063 2.684554 2.404437 2.743179
#> 2016.0548 2.543382 2.432629 2.654134 2.374001 2.712763
#> 2016.0575 2.510991 2.400210 2.621772 2.341567 2.680416
#> 2016.0603 2.696704 2.585876 2.807532 2.527207 2.866201
#> 2016.0630 2.596546 2.485669 2.707423 2.426974 2.766118
#> 2016.0658 2.522451 2.411540 2.633362 2.352827 2.692075
#> 2016.0685 2.612346 2.501421 2.723270 2.442701 2.781990
#> 2016.0712 2.652893 2.541967 2.763819 2.483247 2.822539
#> 2016.0740 2.659275 2.548347 2.770203 2.489625 2.828925
#> 2016.0767 2.599855 2.488914 2.710796 2.430185 2.769525
#> 2016.0795 2.639772 2.528808 2.750737 2.470067 2.809478
#> 2016.0822 2.703297 2.592307 2.814287 2.533553 2.873042
#> 2016.0849 2.711411 2.600403 2.822420 2.541639 2.881184
#> 2016.0877 2.795383 2.684367 2.906399 2.625599 2.965167
#> 2016.0904 2.880031 2.769014 2.991047 2.710245 3.049816
#> 2016.0932 2.831868 2.720850 2.942886 2.662081 3.001655
#> 2016.0959 2.781473 2.670449 2.892498 2.611677 2.951270
#> 2016.0986 2.821385 2.710349 2.932421 2.651570 2.991200
#> 2016.1014 2.834696 2.723646 2.945745 2.664860 3.004531
#> 2016.1041 2.691881 2.580821 2.802940 2.522030 2.861731
#> 2016.1068 2.709921 2.598857 2.820985 2.540064 2.879779
#> 2016.1096 2.676182 2.565118 2.787247 2.506324 2.846041
#> 2016.1123 2.713904 2.602839 2.824969 2.544045 2.883763
#> 2016.1151 2.688649 2.577581 2.799716 2.518785 2.858512
#> 2016.1178 2.791440 2.680366 2.902514 2.621567 2.961313
#> 2016.1205 2.798027 2.686946 2.909107 2.628143 2.967910
#> 2016.1233 2.806732 2.695645 2.917818 2.636840 2.976623
#> 2016.1260 2.770937 2.659848 2.882026 2.601041 2.940832
#> 2016.1288 2.799219 2.688129 2.910308 2.629322 2.969115
#> 2016.1315 2.847841 2.736752 2.958931 2.677945 3.017738
#> 2016.1342 2.873242 2.762151 2.984333 2.703343 3.043141
#> 2016.1370 2.931342 2.820248 3.042436 2.761439 3.101246
#> 2016.1397 2.978542 2.867444 3.089639 2.808633 3.148451
#> 2016.1425 2.980684 2.869583 3.091784 2.810770 3.150598
#> 2016.1452 2.913993 2.802891 3.025095 2.744077 3.083909
#> 2016.1479 2.920820 2.809718 3.031922 2.750904 3.090736
#> 2016.1507 2.958517 2.847415 3.069619 2.788601 3.128433
#> 2016.1534 2.940251 2.829148 3.051354 2.770334 3.110168
#> 2016.1562 2.976187 2.865082 3.087291 2.806267 3.146107
#> 2016.1589 2.927971 2.816865 3.039078 2.758049 3.097894
#> 2016.1616 2.833835 2.722727 2.944943 2.663910 3.003760
#> 2016.1644 2.866589 2.755480 2.977698 2.696663 3.036515
#> 2016.1671 2.882117 2.771008 2.993226 2.712191 3.052044
#> 2016.1699 2.876866 2.765757 2.987975 2.706939 3.046793
#> 2016.1726 2.973522 2.862413 3.084631 2.803595 3.143449
#> 2016.1753 2.985696 2.874586 3.096806 2.815768 3.155625
#> 2016.1781 2.998313 2.887202 3.109424 2.828383 3.168243
#> 2016.1808 3.052188 2.941076 3.163300 2.882257 3.222119
#> 2016.1836 3.078476 2.967364 3.189589 2.908545 3.248408
#> 2016.1863 3.008206 2.897094 3.119319 2.838274 3.178138
#> 2016.1890 3.041194 2.930082 3.152307 2.871263 3.211126
#> 2016.1918 3.061191 2.950079 3.172304 2.891259 3.231124
#> 2016.1945 3.028381 2.917268 3.139494 2.858449 3.198314
#> 2016.1973 3.053827 2.942714 3.164941 2.883894 3.223761
#> 2016.2000 3.046283 2.935169 3.157397 2.876349 3.216217
#> 2016.2027 3.050867 2.939753 3.161981 2.880932 3.220802
#> 2016.2055 3.146024 3.034909 3.257138 2.976089 3.315959
#> 2016.2082 3.128739 3.017624 3.239853 2.958804 3.298673
#> 2016.2110 3.084814 2.973699 3.195928 2.914879 3.254749
#> 2016.2137 3.188414 3.077300 3.299529 3.018479 3.358349
#> 2016.2164 3.169610 3.058495 3.280725 2.999675 3.339546
#> 2016.2192 3.227204 3.116089 3.338319 3.057268 3.397140
#> 2016.2219 3.217583 3.106468 3.328699 3.047647 3.387520
#> 2016.2247 3.220556 3.109441 3.331671 3.050620 3.390492
#> 2016.2274 3.217285 3.106170 3.328400 3.047349 3.387221
#> 2016.2301 3.255631 3.144516 3.366746 3.085695 3.425567
#> 2016.2329 3.173420 3.062304 3.284535 3.003483 3.343356
#> 2016.2356 3.203686 3.092570 3.314801 3.033749 3.373622
#> 2016.2384 3.179232 3.068116 3.290348 3.009295 3.349169
#> 2016.2411 3.168830 3.057714 3.279946 2.998893 3.338767
#> 2016.2438 3.188499 3.077383 3.299615 3.018562 3.358436
#> 2016.2466 3.243775 3.132659 3.354890 3.073838 3.413712
#> 2016.2493 3.292875 3.181759 3.403991 3.122938 3.462812
#> 2016.2521 3.230785 3.119669 3.341901 3.060848 3.400722
#> 2016.2548 3.169578 3.058462 3.280694 2.999640 3.339515
#> 2016.2575 3.240314 3.129198 3.351430 3.070377 3.410251
#> 2016.2603 3.295102 3.183986 3.406218 3.125165 3.465040
#> 2016.2630 3.284386 3.173270 3.395502 3.114448 3.454323
#> 2016.2658 3.285855 3.174739 3.396971 3.115918 3.455792
#> 2016.2685 3.307111 3.195994 3.418227 3.137173 3.477048
#> 2016.2712 3.327356 3.216240 3.438472 3.157419 3.497293
#> 2016.2740 3.362516 3.251400 3.473633 3.192579 3.532454
#> 2016.2767 3.311821 3.200704 3.422937 3.141883 3.481758
#> 2016.2795 3.305267 3.194150 3.416383 3.135329 3.475204
#> 2016.2822 3.311797 3.200681 3.422913 3.141860 3.481735
#> 2016.2849 3.344991 3.233875 3.456107 3.175054 3.514929
#> 2016.2877 3.335567 3.224451 3.446683 3.165630 3.505505
#> 2016.2904 3.330308 3.219192 3.441424 3.160370 3.500246
#> 2016.2932 3.337333 3.226217 3.448449 3.167395 3.507271
#> 2016.2959 3.354323 3.243206 3.465439 3.184385 3.524260
#> 2016.2986 3.405876 3.294760 3.516992 3.235938 3.575814
#> 2016.3014 3.372484 3.261367 3.483600 3.202546 3.542421
#> 2016.3041 3.374206 3.263090 3.485322 3.204268 3.544144
#> 2016.3068 3.386190 3.275074 3.497306 3.216252 3.556128
#> 2016.3096 3.411832 3.300716 3.522948 3.241894 3.581770
#> 2016.3123 3.428224 3.317108 3.539341 3.258286 3.598162
#> 2016.3151 3.404027 3.292911 3.515144 3.234090 3.573965
#> 2016.3178 3.424028 3.312912 3.535144 3.254090 3.593966
#> 2016.3205 3.436752 3.325636 3.547868 3.266814 3.606690
#> 2016.3233 3.462460 3.351344 3.573576 3.292522 3.632398
#> 2016.3260 3.477891 3.366774 3.589007 3.307953 3.647828
#> 2016.3288 3.486950 3.375834 3.598066 3.317012 3.656888
#> 2016.3315 3.447981 3.336865 3.559098 3.278044 3.617919
#> 2016.3342 3.416582 3.305466 3.527698 3.246644 3.586520
#> 2016.3370 3.463073 3.351957 3.574189 3.293135 3.633011
#> 2016.3397 3.450884 3.339767 3.562000 3.280946 3.620821
#> 2016.3425 3.470228 3.359112 3.581345 3.300290 3.640166
#> 2016.3452 3.507637 3.396521 3.618754 3.337699 3.677575
#> 2016.3479 3.507215 3.396099 3.618331 3.337277 3.677153
#> 2016.3507 3.505293 3.394176 3.616409 3.335355 3.675231
#> 2016.3534 3.496951 3.385834 3.608067 3.327013 3.666889
#> 2016.3562 3.448375 3.337258 3.559491 3.278437 3.618313
#> 2016.3589 3.411014 3.299898 3.522131 3.241077 3.580952
#> 2016.3616 3.337607 3.226491 3.448723 3.167669 3.507545
#> 2016.3644 3.386097 3.274980 3.497213 3.216159 3.556035
#> 2016.3671 3.411501 3.300385 3.522617 3.241563 3.581439
#> 2016.3699 3.446420 3.335304 3.557537 3.276482 3.616358
#> 2016.3726 3.465302 3.354185 3.576418 3.295364 3.635239
#> 2016.3753 3.488674 3.377558 3.599790 3.318736 3.658612
#> 2016.3781 3.498420 3.387304 3.609536 3.328482 3.668358
#> 2016.3808 3.511923 3.400807 3.623040 3.341985 3.681861
#> 2016.3836 3.551954 3.440838 3.663071 3.382016 3.721892
#> 2016.3863 3.567105 3.455988 3.678221 3.397167 3.737043
#> 2016.3890 3.597500 3.486383 3.708616 3.427562 3.767437
#> 2016.3918 3.561596 3.450480 3.672713 3.391658 3.731534
#> 2016.3945 3.579855 3.468739 3.690972 3.409917 3.749793
#> 2016.3973 3.534139 3.423022 3.645255 3.364201 3.704077
#> 2016.4000 3.520844 3.409727 3.631960 3.350906 3.690781
#> 2016.4027 3.543453 3.432336 3.654569 3.373515 3.713390
#> 2016.4055 3.551302 3.440185 3.662418 3.381364 3.721240
#> 2016.4082 3.482544 3.371428 3.593661 3.312607 3.652482
#> 2016.4110 3.531759 3.420643 3.642876 3.361822 3.701697
#> 2016.4137 3.445471 3.334354 3.556587 3.275533 3.615409
#> 2016.4164 3.474174 3.363058 3.585291 3.304237 3.644112
#> 2016.4192 3.493265 3.382149 3.604382 3.323328 3.663203
#> 2016.4219 3.535040 3.423923 3.646156 3.365102 3.704978
#> 2016.4247 3.569735 3.458619 3.680852 3.399798 3.739673
#> 2016.4274 3.525462 3.414346 3.636578 3.355524 3.695400
#> 2016.4301 3.577780 3.466664 3.688896 3.407842 3.747718
#> 2016.4329 3.586026 3.474909 3.697142 3.416088 3.755964
#> 2016.4356 3.616955 3.505839 3.728072 3.447017 3.786893
#> 2016.4384 3.606593 3.495476 3.717709 3.436655 3.776530
#> 2016.4411 3.536004 3.424888 3.647121 3.366066 3.705942
#> 2016.4438 3.534586 3.423469 3.645702 3.364648 3.704523
#> 2016.4466 3.414491 3.303375 3.525608 3.244553 3.584429
#> 2016.4493 3.373247 3.262130 3.484363 3.203309 3.543184
#> 2016.4521 3.460503 3.349387 3.571619 3.290565 3.630441
#> 2016.4548 3.455703 3.344587 3.566820 3.285765 3.625641
#> 2016.4575 3.473766 3.362650 3.584883 3.303828 3.643704
#> 2016.4603 3.475920 3.364803 3.587036 3.305982 3.645857
#> 2016.4630 3.517563 3.406446 3.628679 3.347625 3.687500
#> 2016.4658 3.544650 3.433534 3.655766 3.374712 3.714588
#> 2016.4685 3.523731 3.412614 3.634847 3.353793 3.693669
#> 2016.4712 3.527433 3.416317 3.638550 3.357496 3.697371
#> 2016.4740 3.492993 3.381876 3.604109 3.323055 3.662931
#> 2016.4767 3.538047 3.426931 3.649163 3.368109 3.707985
#> 2016.4795 3.391495 3.280378 3.502611 3.221557 3.561433
#> 2016.4822 3.447124 3.336008 3.558240 3.277186 3.617062
#> 2016.4849 3.493271 3.382155 3.604387 3.323333 3.663209
#> 2016.4877 3.511391 3.400275 3.622508 3.341453 3.681329
#> 2016.4904 3.479065 3.367949 3.590181 3.309127 3.649003
#> 2016.4932 3.461880 3.350764 3.572996 3.291942 3.631818
#> 2016.4959 3.477434 3.366318 3.588551 3.307496 3.647372
#> 2016.4986 3.467499 3.356382 3.578615 3.297561 3.637437
#> 2016.5014 3.436643 3.325526 3.547759 3.266705 3.606581
#> 2016.5041 3.483986 3.372869 3.595102 3.314048 3.653924
#> 2016.5068 3.536957 3.425840 3.648073 3.367019 3.706895
#> 2016.5096 3.393804 3.282687 3.504920 3.223866 3.563742
#> 2016.5123 3.433380 3.322264 3.544497 3.263443 3.603318
#> 2016.5151 3.463554 3.352438 3.574670 3.293616 3.633492
#> 2016.5178 3.445666 3.334549 3.556782 3.275728 3.615603
#> 2016.5205 3.419707 3.308591 3.530824 3.249770 3.589645
#> 2016.5233 3.439333 3.328217 3.550450 3.269396 3.609271
#> 2016.5260 3.392980 3.281863 3.504096 3.223042 3.562918
#> 2016.5288 3.435333 3.324217 3.546450 3.265395 3.605271
#> 2016.5315 3.443418 3.332301 3.554534 3.273480 3.613356
#> 2016.5342 3.487637 3.376521 3.598753 3.317699 3.657575
#> 2016.5370 3.445598 3.334481 3.556714 3.275660 3.615535
#> 2016.5397 3.428822 3.317706 3.539939 3.258885 3.598760
#> 2016.5425 3.381297 3.270180 3.492413 3.211359 3.551234
#> 2016.5452 3.405512 3.294395 3.516628 3.235574 3.575450
#> 2016.5479 3.362499 3.251383 3.473616 3.192561 3.532437
#> 2016.5507 3.417052 3.305935 3.528168 3.247114 3.586989
#> 2016.5534 3.435974 3.324857 3.547090 3.266036 3.605911
#> 2016.5562 3.449552 3.338435 3.560668 3.279614 3.619489
#> 2016.5589 3.423637 3.312520 3.534753 3.253699 3.593574
#> 2016.5616 3.398331 3.287215 3.509448 3.228393 3.568269
#> 2016.5644 3.426403 3.315286 3.537519 3.256465 3.596340
#> 2016.5671 3.415594 3.304478 3.526711 3.245657 3.585532
#> 2016.5699 3.418513 3.307396 3.529629 3.248575 3.588450
#> 2016.5726 3.396197 3.285080 3.507313 3.226259 3.566134
#> 2016.5753 3.413974 3.302858 3.525091 3.244037 3.583912
#> 2016.5781 3.401675 3.290558 3.512791 3.231737 3.571613
#> 2016.5808 3.413726 3.302610 3.524843 3.243788 3.583664
#> 2016.5836 3.413646 3.302529 3.524762 3.243708 3.583583
#> 2016.5863 3.458601 3.347485 3.569717 3.288663 3.628539
#> 2016.5890 3.425133 3.314016 3.536249 3.255195 3.595070
#> 2016.5918 3.386375 3.275259 3.497491 3.216437 3.556313
#> 2016.5945 3.383412 3.272296 3.494528 3.213474 3.553350
#> 2016.5973 3.384499 3.273383 3.495615 3.214561 3.554437
#> 2016.6000 3.380281 3.269164 3.491397 3.210343 3.550218
#> 2016.6027 3.326950 3.215833 3.438066 3.157012 3.496887
#> 2016.6055 3.379739 3.268623 3.490856 3.209801 3.549677
#> 2016.6082 3.392774 3.281658 3.503890 3.222836 3.562712
#> 2016.6110 3.424464 3.313348 3.535580 3.254526 3.594402
#> 2016.6137 3.451537 3.340421 3.562653 3.281599 3.621475
#> 2016.6164 3.408960 3.297843 3.520076 3.239022 3.578898
#> 2016.6192 3.367697 3.256580 3.478813 3.197759 3.537634
#> 2016.6219 3.347913 3.236796 3.459029 3.177975 3.517851
#> 2016.6247 3.392196 3.281080 3.503313 3.222259 3.562134
#> 2016.6274 3.390166 3.279050 3.501283 3.220228 3.560104
#> 2016.6301 3.423215 3.312099 3.534331 3.253277 3.593153
#> 2016.6329 3.410831 3.299714 3.521947 3.240893 3.580768
#> 2016.6356 3.399426 3.288310 3.510542 3.229488 3.569364
#> 2016.6384 3.423941 3.312825 3.535057 3.254003 3.593879
#> 2016.6411 3.444401 3.333284 3.555517 3.274463 3.614339
#> 2016.6438 3.461527 3.350411 3.572644 3.291590 3.631465
#> 2016.6466 3.449438 3.338322 3.560555 3.279500 3.619376
#> 2016.6493 3.484682 3.373565 3.595798 3.314744 3.654620
#> 2016.6521 3.488687 3.377571 3.599804 3.318749 3.658625
#> 2016.6548 3.417574 3.306457 3.528690 3.247636 3.587512
#> 2016.6575 3.443161 3.332044 3.554277 3.273223 3.613099
#> 2016.6603 3.401560 3.290444 3.512677 3.231622 3.571498
#> 2016.6630 3.379837 3.268721 3.490954 3.209899 3.549775
#> 2016.6658 3.414990 3.303873 3.526106 3.245052 3.584927
#> 2016.6685 3.430357 3.319241 3.541474 3.260420 3.600295
#> 2016.6712 3.429726 3.318610 3.540842 3.259788 3.599664
#> 2016.6740 3.414073 3.302956 3.525189 3.244135 3.584011
#> 2016.6767 3.384760 3.273643 3.495876 3.214822 3.554697
#> 2016.6795 3.401283 3.290167 3.512400 3.231345 3.571221
#> 2016.6822 3.434790 3.323673 3.545906 3.264852 3.604728
#> 2016.6849 3.406636 3.295520 3.517753 3.236698 3.576574
#> 2016.6877 3.431212 3.320096 3.542328 3.261274 3.601150
#> 2016.6904 3.394097 3.282981 3.505214 3.224160 3.564035
#> 2016.6932 3.375548 3.264431 3.486664 3.205610 3.545485
#> 2016.6959 3.416976 3.305860 3.528093 3.247038 3.586914
#> 2016.6986 3.426595 3.315479 3.537712 3.256657 3.596533
#> 2016.7014 3.414168 3.303052 3.525285 3.244230 3.584106
#> 2016.7041 3.443457 3.332340 3.554573 3.273519 3.613395
#> 2016.7068 3.426820 3.315704 3.537937 3.256882 3.596758
#> 2016.7096 3.411626 3.300510 3.522743 3.241688 3.581564
#> 2016.7123 3.405011 3.293894 3.516127 3.235073 3.574948
#> 2016.7151 3.413786 3.302669 3.524902 3.243848 3.583724
#> 2016.7178 3.385646 3.274530 3.496762 3.215708 3.555584
#> 2016.7205 3.346948 3.235832 3.458065 3.177011 3.516886
#> 2016.7233 3.388736 3.277620 3.499852 3.218798 3.558674
#> 2016.7260 3.396579 3.285462 3.507695 3.226641 3.566517
#> 2016.7288 3.382111 3.270994 3.493227 3.212173 3.552048
#> 2016.7315 3.364725 3.253609 3.475842 3.194787 3.534663
#> 2016.7342 3.369001 3.257885 3.480117 3.199063 3.538939
#> 2016.7370 3.377653 3.266536 3.488769 3.207715 3.547591
#> 2016.7397 3.380755 3.269639 3.491871 3.210817 3.550693
#> 2016.7425 3.370910 3.259794 3.482027 3.200973 3.540848
#> 2016.7452 3.356666 3.245549 3.467782 3.186728 3.526603
#> 2016.7479 3.361562 3.250446 3.472679 3.191625 3.531500
#> 2016.7507 3.373457 3.262341 3.484574 3.203519 3.543395
#> 2016.7534 3.387498 3.276382 3.498614 3.217560 3.557436
#> 2016.7562 3.334524 3.223407 3.445640 3.164586 3.504461
#> 2016.7589 3.374911 3.263795 3.486028 3.204974 3.544849
#> 2016.7616 3.383376 3.272260 3.494493 3.213438 3.553314
#> 2016.7644 3.389933 3.278816 3.501049 3.219995 3.559871
#> 2016.7671 3.356049 3.244932 3.467165 3.186111 3.525987
#> 2016.7699 3.362326 3.251210 3.473443 3.192388 3.532264
#> 2016.7726 3.340670 3.229553 3.451786 3.170732 3.510607
#> 2016.7753 3.253716 3.142599 3.364832 3.083778 3.423653
#> 2016.7781 3.295696 3.184579 3.406812 3.125758 3.465634
#> 2016.7808 3.331521 3.220405 3.442637 3.161583 3.501459
#> 2016.7836 3.282222 3.171106 3.393339 3.112284 3.452160
#> 2016.7863 3.251586 3.140470 3.362703 3.081648 3.421524
#> 2016.7890 3.242303 3.131186 3.353419 3.072365 3.412241
#> 2016.7918 3.276925 3.165809 3.388042 3.106988 3.446863
#> 2016.7945 3.242837 3.131721 3.353953 3.072899 3.412775
#> 2016.7973 3.231825 3.120709 3.342942 3.061888 3.401763
#> 2016.8000 3.237187 3.126071 3.348304 3.067250 3.407125
#> 2016.8027 3.241148 3.130032 3.352264 3.071210 3.411086
#> 2016.8055 3.257030 3.145913 3.368146 3.087092 3.426968
#> 2016.8082 3.204825 3.093709 3.315941 3.034887 3.374763
#> 2016.8110 3.204424 3.093307 3.315540 3.034486 3.374361
#> 2016.8137 3.205525 3.094408 3.316641 3.035587 3.375463
#> 2016.8164 3.197141 3.086025 3.308257 3.027203 3.367079
#> 2016.8192 3.180385 3.069269 3.291502 3.010448 3.350323
#> 2016.8219 3.123886 3.012770 3.235003 2.953949 3.293824
#> 2016.8247 3.143101 3.031984 3.254217 2.973163 3.313039
#> 2016.8274 3.132747 3.021630 3.243863 2.962809 3.302684
#> 2016.8301 3.137268 3.026152 3.248385 2.967330 3.307206
#> 2016.8329 3.128523 3.017406 3.239639 2.958585 3.298460
#> 2016.8356 3.114513 3.003397 3.225630 2.944575 3.284451
#> 2016.8384 3.114710 3.003593 3.225826 2.944772 3.284647
#> 2016.8411 3.123382 3.012265 3.234498 2.953444 3.293320
#> 2016.8438 3.048245 2.937128 3.159361 2.878307 3.218183
#> 2016.8466 3.092426 2.981310 3.203542 2.922488 3.262364
#> 2016.8493 3.084696 2.973579 3.195812 2.914758 3.254634
#> 2016.8521 3.045464 2.934347 3.156580 2.875526 3.215401
#> 2016.8548 3.079757 2.968641 3.190874 2.909819 3.249695
#> 2016.8575 2.999332 2.888216 3.110449 2.829395 3.169270
#> 2016.8603 2.989200 2.878083 3.100316 2.819262 3.159137
#> 2016.8630 2.952561 2.841445 3.063678 2.782623 3.122499
#> 2016.8658 2.963320 2.852203 3.074436 2.793382 3.133257
#> 2016.8685 2.958705 2.847589 3.069821 2.788767 3.128643
#> 2016.8712 2.953033 2.841916 3.064149 2.783095 3.122970
#> 2016.8740 2.929428 2.818312 3.040545 2.759490 3.099366
#> 2016.8767 2.866386 2.755269 2.977502 2.696448 3.036323
#> 2016.8795 2.897578 2.786461 3.008694 2.727640 3.067516
#> 2016.8822 2.883750 2.772634 2.994867 2.713813 3.053688
#> 2016.8849 2.941375 2.830258 3.052491 2.771437 3.111313
#> 2016.8877 2.902215 2.791099 3.013331 2.732277 3.072153
#> 2016.8904 2.923724 2.812608 3.034840 2.753786 3.093662
#> 2016.8932 2.853306 2.742190 2.964423 2.683368 3.023244
#> 2016.8959 2.894164 2.783048 3.005281 2.724226 3.064102
#> 2016.8986 2.937199 2.826082 3.048315 2.767261 3.107136
#> 2016.9014 3.005597 2.894481 3.116714 2.835659 3.175535
#> 2016.9041 2.917987 2.806871 3.029103 2.748049 3.087925
#> 2016.9068 2.935862 2.824746 3.046979 2.765925 3.105800
#> 2016.9096 2.923247 2.812131 3.034363 2.753309 3.093185
#> 2016.9123 2.941628 2.830511 3.052744 2.771690 3.111565
#> 2016.9151 2.943843 2.832727 3.054960 2.773905 3.113781
#> 2016.9178 2.931746 2.820629 3.042862 2.761808 3.101683
#> 2016.9205 2.979434 2.868317 3.090550 2.809496 3.149371
#> 2016.9233 2.918353 2.807236 3.029469 2.748415 3.088290
#> 2016.9260 2.855955 2.744838 2.967071 2.686017 3.025892
#> 2016.9288 2.837556 2.726439 2.948672 2.667618 3.007493
#> 2016.9315 2.825735 2.714619 2.936852 2.655797 2.995673
#> 2016.9342 2.845953 2.734836 2.957069 2.676015 3.015890
#> 2016.9370 2.801853 2.690736 2.912969 2.631915 2.971790
#> 2016.9397 2.913502 2.802385 3.024618 2.743564 3.083439
#> 2016.9425 2.874197 2.763081 2.985314 2.704259 3.044135
#> 2016.9452 2.769849 2.658732 2.880965 2.599911 2.939786
#> 2016.9479 2.718772 2.607655 2.829888 2.548834 2.888709
#> 2016.9507 2.726020 2.614904 2.837137 2.556083 2.895958
#> 2016.9534 2.704305 2.593188 2.815421 2.534367 2.874243
#> 2016.9562 2.717486 2.606370 2.828602 2.547548 2.887424
#> 2016.9589 2.579498 2.468382 2.690615 2.409560 2.749436
#> 2016.9616 2.568385 2.457269 2.679502 2.398448 2.738323
#> 2016.9644 2.582044 2.470927 2.693160 2.412106 2.751981
#> 2016.9671 2.534363 2.423246 2.645479 2.364425 2.704300
#> 2016.9699 2.488078 2.376961 2.599194 2.318140 2.658015
#> 2016.9726 2.477816 2.366699 2.588932 2.307878 2.647753
#> 2016.9753 2.477553 2.366437 2.588669 2.307615 2.647491
#> 2016.9781 2.432923 2.321807 2.544039 2.262985 2.602861
#> 2016.9808 2.422510 2.311394 2.533626 2.252572 2.592448
#> 2016.9836 2.467067 2.355951 2.578184 2.297130 2.637005
#> 2016.9863 2.510656 2.399540 2.621773 2.340718 2.680594
#> 2016.9890 2.469839 2.358723 2.580955 2.299901 2.639777
#> 2016.9918 2.516096 2.404980 2.627212 2.346158 2.686034
#> 2016.9945 2.564918 2.453801 2.676034 2.394980 2.734856
#> 2016.9973 2.627626 2.516509 2.738742 2.457688 2.797564
#> 2017.0000 2.567853 2.456736 2.678969 2.397915 2.737791
#> 2017.0027 2.433350 2.322234 2.544467 2.263412 2.603288Pada hasil forecasting STLM menunjukan interval kepercayaan yang lebih sempit dengan hasil forecast yang jauh berbeda dari kedua model diatas. Forecast model STLM memprediksi temperatur 365 hari kedepan yang dimulai dari tahun 2016 dengan hasil misalnya pada hari pertama 2016 adalah 2.56 dengan tingkat 80% kepercayaan Lo 80 adalah 2.49 dan Hi 80 adalah 2.63
Visualisasi forecast
climate_ts %>%
# visualisasi data train
autoplot()+
# visualisasi nilai forecast dikembalikan ke satuan asal dengan fungsi exp()
autolayer(exp(forecasestlm$mean), series = "forecast") +
# visualisasi data test
autolayer(climate_test, series = "data test")
# Evaluasi Model Setelah melakukan forecast terhadap data test yang kita
miliki, mari kita coba lakukan evaluasi
Evaluasi Model Holt Winter
#> ME RMSE MAE MPE MAPE ACF1 Theil's U
#> Test set 12.93797 14.65443 13.06879 43.07234 44.18987 0.9576474 6.621286nilai MAPE sebesar 44.18 artinya error dari prediksi data test sebesar 44.18%. bisa dikatakan model tidak cukup baik dalam meramal data baru.
Evaluasi Model STLM
# result from stlm method
# evaluasi model dengan fungsi MAPE()
MAPE(y_pred = exp(forecasestlm$mean),
y_true = climate_test)*100#> [1] 11.03438#> ME RMSE MAE MPE MAPE ACF1 Theil's U
#> Test set 2.211673 3.341343 2.789422 8.54239 11.03438 0.6782201 1.940229nilai MAPE pada model sebesar 11.03 artinya error dari prediksi data test sebesar 11.03%. bisa dikatakan model sudah cukup baik dalam meramal data baru.
#> ME RMSE MAE MPE MAPE ACF1 Theil's U
#> Test set 13.12636 14.82101 13.24221 43.82818 44.82544 0.9576474 6.705145nilai MAPE sebesar 44.8 artinya error dari prediksi data test sebesar 44.8%. bisa dikatakan model tidak cukup baik dalam meramal data baru.
#> [1] FALSE#> [1] FALSE7 Cek Asumsi
Model yang terbaik diantara ketiga model Triple Exponential Smooting, Arima model dan STLM adalah STLM method Arima dikarena memiliki nilai yang kecil diantara 2 model. Selanjutnya kita akan menguji model kita.
7.1 No Auto Correlation
Mengecek ada/tidaknya autokorelasi pada hasil forecasting time series
bisa menggunakan uji Ljung-box dengan menggunakan fungsi
Box.test(residual model, type = "Ljung-Box")
Yang diinginkan: p-value > 0.05 (alpha), no-autocorrelation
#>
#> Box-Ljung test
#>
#> data: climatestlm$residuals
#> X-squared = 0.0011833, df = 1, p-value = 0.9726p-value > alpha, residual model kita tidak terjadi autokorelasi. Asumsi terpenuhi.
7.2 Normality of Residual
mengecek normality residual pada hasil forecasting time series kita
bisa melakukan uji normality (shapiro test) dengan menggunakan fungsi
shapiro.test(residual model)
Yang diinginkan: p-value > 0.05 (alpha), residual menyebar normal
#>
#> Shapiro-Wilk normality test
#>
#> data: climatestlm$residuals
#> W = 0.9749, p-value = 7.462e-13p-value < alpha, residual model tidak menyebar normal, asumsi tidak terpenuhi.
8 Kesimpulan
Keadaan iklim di Delhi menunjukan tren yang cenderung naik, hal ini bisa diakibatkan terjadi pemansan globol di seluruh dunia. Pada model terbaik kita STLM diprediksi naik setahun kedepan sekitar 2,5 dengan tingkat kepercayaan 80 % dengan sekitar Lo 80 adalah 2.4 dan Hi 80 adalah 2.6 eror yang diperoleh 11,03% residual model kita tidak terjadi autokorelasi dan residual model tidak menyebar normal.