Mengaplikasikan Metode Pemulusan SMA, DMA, SES, dan DES pada Data Temperature
Nabil Ibni Nawawi
Library / Packages
library("forecast")## Warning: package 'forecast' was built under R version 4.3.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary("graphics")
library("TTR")## Warning: package 'TTR' was built under R version 4.3.3library("TSA")## Warning: package 'TSA' was built under R version 4.3.3## Registered S3 methods overwritten by 'TSA':
## method from
## fitted.Arima forecast
## plot.Arima forecast##
## Attaching package: 'TSA'## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tarlibrary("readxl")## Warning: package 'readxl' was built under R version 4.3.2Data
url <- "https://raw.githubusercontent.com/raihanadisecha/getfile/main/Merged%20Data.xlsx"
destfile <- "local_filename.xlsx"
download.file(url, destfile, mode = "wb")
data <- read_excel(destfile)
file.remove(destfile)## [1] TRUEdata## # A tibble: 500 × 2
## date temperature
## <dttm> <dbl>
## 1 2022-08-20 12:00:00 29.5
## 2 2022-08-21 12:00:00 29.7
## 3 2022-08-22 12:00:00 30.0
## 4 2022-08-23 12:00:00 30.2
## 5 2022-08-24 12:00:00 30.0
## 6 2022-08-25 12:00:00 29.5
## 7 2022-08-26 12:00:00 29.4
## 8 2022-08-27 12:00:00 29.1
## 9 2022-08-28 12:00:00 29.0
## 10 2022-08-29 12:00:00 28.0
## # ℹ 490 more rowsdata.ts <- ts(data$temperature)ts.plot(data.ts, xlab="Time Period ", ylab="Temperature",
main = "Time Series Plot")
points(data.ts)
Single Moving Average & Double Moving Average
Pembagian Data
Pembagian data latih dan data uji dilakukan dengan perbandingan 63% data latih dan 37% data uji.
#membagi data latih dan data uji
training_ma <- data[1:315,]
testing_ma <- data[316:500,]
train_ma.ts <- ts(training_ma$temperature)
test_ma.ts <- ts(testing_ma$temperature)Eksplorasi Data
Eksplorasi data dilakukan pada keseluruhan data, data latih serta data uji menggunakan plot data deret waktu.
#eksplorasi keseluruhan data
plot(data.ts, col="red",main="Plot semua data")
points(data.ts)
#eksplorasi data latih
plot(train_ma.ts, col="blue",main="Plot data latih")
points(train_ma.ts)
#eksplorasi data uji
plot(test_ma.ts, col="blue",main="Plot data uji")
points(test_ma.ts)
Eksplorasi data juga dapat dilakukan menggunakan package
ggplot2 dengan terlebih dahulu memanggil library
package ggplot2.
#Eksplorasi dengan GGPLOT
library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.3.2ggplot() +
geom_line(data = training_ma, aes(x = date, y = temperature, col = "Data Latih")) +
geom_line(data = testing_ma, aes(x = date, y = temperature, col = "Data Uji")) +
labs(x = "Periode Waktu", y = "Temperature", color = "Legend") +
scale_colour_manual(name="Keterangan:", breaks = c("Data Latih", "Data Uji"),
values = c("blue", "red")) +
theme_bw() + theme(legend.position = "bottom",
plot.caption = element_text(hjust=0.5, size=12))
Single Moving Average (SMA)
Ide dasar dari Single Moving Average (SMA) adalah data suatu periode dipengaruhi oleh data periode sebelumnya. Metode pemulusan ini cocok digunakan untuk pola data stasioner atau konstan. Prinsip dasar metode pemulusan ini adalah data pemulusan pada periode ke-t merupakan rata rata dari m buah data pada periode ke-t hingga periode ke (t-m+1). Data pemulusan pada periode ke-t selanjutnya digunakan sebagai nilai peramalan pada periode ke t+1
Pemulusan menggunakan metode SMA dilakukan dengan fungsi
SMA(). Dalam hal ini akan dilakukan pemulusan dengan
parameter m=4.
data.sma<-SMA(train_ma.ts, n=4)
data.sma## Time Series:
## Start = 1
## End = 315
## Frequency = 1
## [1] NA NA NA 29.85448 29.97195 29.92870 29.79212 29.53335
## [9] 29.28100 28.88482 28.59395 28.45320 28.30070 28.34230 28.38050 28.35225
## [17] 28.46187 28.45560 28.48435 28.32397 28.07392 27.97292 27.85032 28.01642
## [25] 28.28472 28.58972 28.81157 28.90912 28.85895 28.81937 28.80137 28.87067
## [33] 28.98937 29.01857 28.98287 28.93135 28.87432 28.86937 28.91400 28.92090
## [41] 28.88212 28.79592 28.65220 28.52350 28.50042 28.54322 28.61227 28.42257
## [49] 28.14632 27.94220 27.78157 27.83497 27.88770 27.89070 27.90520 27.85405
## [57] 27.74642 27.65742 27.77600 27.89452 28.16575 28.37985 28.28102 28.30362
## [65] 28.34827 28.36640 28.38997 28.38460 28.35257 28.37762 28.48997 28.58927
## [73] 28.66365 28.77867 28.87877 28.90627 28.86515 28.78992 28.68020 28.63257
## [81] 28.60357 28.59865 28.66687 28.79442 29.00152 29.16710 29.28645 29.40217
## [89] 29.41365 29.37840 29.32985 29.24050 29.16777 29.12815 29.10685 29.07545
## [97] 28.97647 29.00732 28.99517 29.00290 29.10362 29.08872 29.10472 29.12167
## [105] 29.10890 29.05072 29.00157 28.90125 28.85790 28.74725 28.65207 28.55205
## [113] 28.49235 28.54427 28.62370 28.77315 28.83998 28.96525 29.02660 29.19613
## [121] 29.39500 29.55140 29.65363 29.63775 29.48793 29.28292 29.19900 29.05925
## [129] 29.02135 29.02303 28.94035 28.85250 28.73115 28.60700 28.51540 28.45437
## [137] 28.39102 28.33062 28.27045 28.23707 28.26000 28.29612 28.37092 28.43442
## [145] 28.53545 28.65590 28.75712 28.83952 28.84687 28.78577 28.72115 28.64582
## [153] 28.59630 28.53185 28.45135 28.40770 28.37867 28.39278 28.39588 28.36280
## [161] 28.30508 28.20550 28.07215 28.04715 27.98627 27.93217 27.92785 27.89632
## [169] 27.97942 28.14520 28.26567 28.38957 28.36322 28.33800 28.27375 28.00882
## [177] 27.92495 27.91520 27.95552 28.15025 28.26972 28.28950 28.39615 28.57550
## [185] 28.71790 28.82930 28.85245 28.69127 28.50322 28.32775 28.17730 28.15148
## [193] 28.16515 28.18938 28.15453 28.14670 28.13355 28.14335 28.30265 28.45000
## [201] 28.53592 28.57377 28.66005 28.63465 28.73318 28.90887 28.86910 28.84860
## [209] 28.78967 28.66595 28.71677 28.88517 29.09935 29.30247 29.50100 29.67927
## [217] 29.79982 29.83210 29.78630 29.71742 29.63302 29.53180 29.42285 29.24725
## [225] 29.12883 29.11855 29.11587 29.15230 29.22520 29.31227 29.41695 29.55952
## [233] 29.57327 29.53842 29.48327 29.38857 29.35042 29.32835 29.30140 29.28317
## [241] 29.28107 29.37357 29.46287 29.50075 29.50460 29.40487 29.34095 29.39390
## [249] 29.44347 29.58502 29.65152 29.69880 29.79202 29.83012 29.93372 29.97085
## [257] 29.94697 29.93635 30.02330 30.17972 30.33577 30.49785 30.54250 30.51850
## [265] 30.58427 30.51050 30.33875 30.15987 29.90177 29.72952 29.56797 29.35107
## [273] 29.22452 29.14142 29.16680 29.27522 29.30422 29.32097 29.28565 29.27012
## [281] 29.28187 29.29462 29.34477 29.36812 29.37302 29.39897 29.41412 29.45692
## [289] 29.51430 29.54860 29.58232 29.53655 29.50260 29.55280 29.58582 29.65565
## [297] 29.65660 29.53322 29.36525 29.13792 28.85530 28.65337 28.47762 28.25427
## [305] 28.25405 28.33835 28.39060 28.45602 28.44825 28.32885 28.30452 28.39205
## [313] 28.37187 28.25687 28.11662Data pemulusan pada periode ke-t selanjutnya digunakan sebagai nilai peramalan pada periode ke t+1 sehingga hasil peramalan 1 periode kedepan adalah sebagai berikut.
data.ramal<-c(NA,data.sma)
data.ramal #forecast 1 periode ke depan## [1] NA NA NA NA 29.85448 29.97195 29.92870 29.79212
## [9] 29.53335 29.28100 28.88482 28.59395 28.45320 28.30070 28.34230 28.38050
## [17] 28.35225 28.46187 28.45560 28.48435 28.32397 28.07392 27.97292 27.85032
## [25] 28.01642 28.28472 28.58972 28.81157 28.90912 28.85895 28.81937 28.80137
## [33] 28.87067 28.98937 29.01857 28.98287 28.93135 28.87432 28.86937 28.91400
## [41] 28.92090 28.88212 28.79592 28.65220 28.52350 28.50042 28.54322 28.61227
## [49] 28.42257 28.14632 27.94220 27.78157 27.83497 27.88770 27.89070 27.90520
## [57] 27.85405 27.74642 27.65742 27.77600 27.89452 28.16575 28.37985 28.28102
## [65] 28.30362 28.34827 28.36640 28.38997 28.38460 28.35257 28.37762 28.48997
## [73] 28.58927 28.66365 28.77867 28.87877 28.90627 28.86515 28.78992 28.68020
## [81] 28.63257 28.60357 28.59865 28.66687 28.79442 29.00152 29.16710 29.28645
## [89] 29.40217 29.41365 29.37840 29.32985 29.24050 29.16777 29.12815 29.10685
## [97] 29.07545 28.97647 29.00732 28.99517 29.00290 29.10362 29.08872 29.10472
## [105] 29.12167 29.10890 29.05072 29.00157 28.90125 28.85790 28.74725 28.65207
## [113] 28.55205 28.49235 28.54427 28.62370 28.77315 28.83998 28.96525 29.02660
## [121] 29.19613 29.39500 29.55140 29.65363 29.63775 29.48793 29.28292 29.19900
## [129] 29.05925 29.02135 29.02303 28.94035 28.85250 28.73115 28.60700 28.51540
## [137] 28.45437 28.39102 28.33062 28.27045 28.23707 28.26000 28.29612 28.37092
## [145] 28.43442 28.53545 28.65590 28.75712 28.83952 28.84687 28.78577 28.72115
## [153] 28.64582 28.59630 28.53185 28.45135 28.40770 28.37867 28.39278 28.39588
## [161] 28.36280 28.30508 28.20550 28.07215 28.04715 27.98627 27.93217 27.92785
## [169] 27.89632 27.97942 28.14520 28.26567 28.38957 28.36322 28.33800 28.27375
## [177] 28.00882 27.92495 27.91520 27.95552 28.15025 28.26972 28.28950 28.39615
## [185] 28.57550 28.71790 28.82930 28.85245 28.69127 28.50322 28.32775 28.17730
## [193] 28.15148 28.16515 28.18938 28.15453 28.14670 28.13355 28.14335 28.30265
## [201] 28.45000 28.53592 28.57377 28.66005 28.63465 28.73318 28.90887 28.86910
## [209] 28.84860 28.78967 28.66595 28.71677 28.88517 29.09935 29.30247 29.50100
## [217] 29.67927 29.79982 29.83210 29.78630 29.71742 29.63302 29.53180 29.42285
## [225] 29.24725 29.12883 29.11855 29.11587 29.15230 29.22520 29.31227 29.41695
## [233] 29.55952 29.57327 29.53842 29.48327 29.38857 29.35042 29.32835 29.30140
## [241] 29.28317 29.28107 29.37357 29.46287 29.50075 29.50460 29.40487 29.34095
## [249] 29.39390 29.44347 29.58502 29.65152 29.69880 29.79202 29.83012 29.93372
## [257] 29.97085 29.94697 29.93635 30.02330 30.17972 30.33577 30.49785 30.54250
## [265] 30.51850 30.58427 30.51050 30.33875 30.15987 29.90177 29.72952 29.56797
## [273] 29.35107 29.22452 29.14142 29.16680 29.27522 29.30422 29.32097 29.28565
## [281] 29.27012 29.28187 29.29462 29.34477 29.36812 29.37302 29.39897 29.41412
## [289] 29.45692 29.51430 29.54860 29.58232 29.53655 29.50260 29.55280 29.58582
## [297] 29.65565 29.65660 29.53322 29.36525 29.13792 28.85530 28.65337 28.47762
## [305] 28.25427 28.25405 28.33835 28.39060 28.45602 28.44825 28.32885 28.30452
## [313] 28.39205 28.37187 28.25687 28.11662Selanjutnya akan dilakukan peramalan sejumlah data uji yaitu 185 periode. Pada metode SMA, hasil peramalan 185 periode ke depan akan bernilai sama dengan hasil peramalan 1 periode kedepan. Dalam hal ini akan dilakukan pengguabungan data aktual train, data hasil pemulusan dan data hasil ramalan 185 periode kedepan.
data.gab<-cbind(aktual=c(train_ma.ts,rep(NA,185)),pemulusan=c(data.sma,rep(NA,185)),ramalan=c(data.ramal,rep(data.ramal[length(data.ramal)],184)))
data.gab #forecast 185 periode ke depan## aktual pemulusan ramalan
## [1,] 29.5199 NA NA
## [2,] 29.7223 NA NA
## [3,] 29.9959 NA NA
## [4,] 30.1798 29.85448 NA
## [5,] 29.9898 29.97195 29.85448
## [6,] 29.5493 29.92870 29.97195
## [7,] 29.4496 29.79212 29.92870
## [8,] 29.1447 29.53335 29.79212
## [9,] 28.9804 29.28100 29.53335
## [10,] 27.9646 28.88482 29.28100
## [11,] 28.2861 28.59395 28.88482
## [12,] 28.5817 28.45320 28.59395
## [13,] 28.3704 28.30070 28.45320
## [14,] 28.1310 28.34230 28.30070
## [15,] 28.4389 28.38050 28.34230
## [16,] 28.4687 28.35225 28.38050
## [17,] 28.8089 28.46187 28.35225
## [18,] 28.1059 28.45560 28.46187
## [19,] 28.5539 28.48435 28.45560
## [20,] 27.8272 28.32397 28.48435
## [21,] 27.8087 28.07392 28.32397
## [22,] 27.7019 27.97292 28.07392
## [23,] 28.0635 27.85032 27.97292
## [24,] 28.4916 28.01642 27.85032
## [25,] 28.8819 28.28472 28.01642
## [26,] 28.9219 28.58972 28.28472
## [27,] 28.9509 28.81157 28.58972
## [28,] 28.8818 28.90912 28.81157
## [29,] 28.6812 28.85895 28.90912
## [30,] 28.7636 28.81937 28.85895
## [31,] 28.8789 28.80137 28.81937
## [32,] 29.1590 28.87067 28.80137
## [33,] 29.1560 28.98937 28.87067
## [34,] 28.8804 29.01857 28.98937
## [35,] 28.7361 28.98287 29.01857
## [36,] 28.9529 28.93135 28.98287
## [37,] 28.9279 28.87432 28.93135
## [38,] 28.8606 28.86937 28.87432
## [39,] 28.9146 28.91400 28.86937
## [40,] 28.9805 28.92090 28.91400
## [41,] 28.7728 28.88212 28.92090
## [42,] 28.5158 28.79592 28.88212
## [43,] 28.3397 28.65220 28.79592
## [44,] 28.4657 28.52350 28.65220
## [45,] 28.6805 28.50042 28.52350
## [46,] 28.6870 28.54322 28.50042
## [47,] 28.6159 28.61227 28.54322
## [48,] 27.7069 28.42257 28.61227
## [49,] 27.5755 28.14632 28.42257
## [50,] 27.8705 27.94220 28.14632
## [51,] 27.9734 27.78157 27.94220
## [52,] 27.9205 27.83497 27.78157
## [53,] 27.7864 27.88770 27.83497
## [54,] 27.8825 27.89070 27.88770
## [55,] 28.0314 27.90520 27.89070
## [56,] 27.7159 27.85405 27.90520
## [57,] 27.3559 27.74642 27.85405
## [58,] 27.5265 27.65742 27.74642
## [59,] 28.5057 27.77600 27.65742
## [60,] 28.1900 27.89452 27.77600
## [61,] 28.4408 28.16575 27.89452
## [62,] 28.3829 28.37985 28.16575
## [63,] 28.1104 28.28102 28.37985
## [64,] 28.2804 28.30362 28.28102
## [65,] 28.6194 28.34827 28.30362
## [66,] 28.4554 28.36640 28.34827
## [67,] 28.2047 28.38997 28.36640
## [68,] 28.2589 28.38460 28.38997
## [69,] 28.4913 28.35257 28.38460
## [70,] 28.5556 28.37762 28.35257
## [71,] 28.6541 28.48997 28.37762
## [72,] 28.6561 28.58927 28.48997
## [73,] 28.7888 28.66365 28.58927
## [74,] 29.0157 28.77867 28.66365
## [75,] 29.0545 28.87877 28.77867
## [76,] 28.7661 28.90627 28.87877
## [77,] 28.6243 28.86515 28.90627
## [78,] 28.7148 28.78992 28.86515
## [79,] 28.6156 28.68020 28.78992
## [80,] 28.5756 28.63257 28.68020
## [81,] 28.5083 28.60357 28.63257
## [82,] 28.6951 28.59865 28.60357
## [83,] 28.8885 28.66687 28.59865
## [84,] 29.0858 28.79442 28.66687
## [85,] 29.3367 29.00152 28.79442
## [86,] 29.3574 29.16710 29.00152
## [87,] 29.3659 29.28645 29.16710
## [88,] 29.5487 29.40217 29.28645
## [89,] 29.3826 29.41365 29.40217
## [90,] 29.2164 29.37840 29.41365
## [91,] 29.1717 29.32985 29.37840
## [92,] 29.1913 29.24050 29.32985
## [93,] 29.0917 29.16777 29.24050
## [94,] 29.0579 29.12815 29.16777
## [95,] 29.0865 29.10685 29.12815
## [96,] 29.0657 29.07545 29.10685
## [97,] 28.6958 28.97647 29.07545
## [98,] 29.1813 29.00732 28.97647
## [99,] 29.0379 28.99517 29.00732
## [100,] 29.0966 29.00290 28.99517
## [101,] 29.0987 29.10362 29.00290
## [102,] 29.1217 29.08872 29.10362
## [103,] 29.1019 29.10472 29.08872
## [104,] 29.1644 29.12167 29.10472
## [105,] 29.0476 29.10890 29.12167
## [106,] 28.8890 29.05072 29.10890
## [107,] 28.9053 29.00157 29.05072
## [108,] 28.7631 28.90125 29.00157
## [109,] 28.8742 28.85790 28.90125
## [110,] 28.4464 28.74725 28.85790
## [111,] 28.5246 28.65207 28.74725
## [112,] 28.3630 28.55205 28.65207
## [113,] 28.6354 28.49235 28.55205
## [114,] 28.6541 28.54427 28.49235
## [115,] 28.8423 28.62370 28.54427
## [116,] 28.9608 28.77315 28.62370
## [117,] 28.9027 28.83998 28.77315
## [118,] 29.1552 28.96525 28.83998
## [119,] 29.0877 29.02660 28.96525
## [120,] 29.6389 29.19613 29.02660
## [121,] 29.6982 29.39500 29.19613
## [122,] 29.7808 29.55140 29.39500
## [123,] 29.4966 29.65363 29.55140
## [124,] 29.5754 29.63775 29.65363
## [125,] 29.0989 29.48793 29.63775
## [126,] 28.9608 29.28292 29.48793
## [127,] 29.1609 29.19900 29.28292
## [128,] 29.0164 29.05925 29.19900
## [129,] 28.9473 29.02135 29.05925
## [130,] 28.9675 29.02303 29.02135
## [131,] 28.8302 28.94035 29.02303
## [132,] 28.6650 28.85250 28.94035
## [133,] 28.4619 28.73115 28.85250
## [134,] 28.4709 28.60700 28.73115
## [135,] 28.4638 28.51540 28.60700
## [136,] 28.4209 28.45437 28.51540
## [137,] 28.2085 28.39102 28.45437
## [138,] 28.2293 28.33062 28.39102
## [139,] 28.2231 28.27045 28.33062
## [140,] 28.2874 28.23707 28.27045
## [141,] 28.3002 28.26000 28.23707
## [142,] 28.3738 28.29612 28.26000
## [143,] 28.5223 28.37092 28.29612
## [144,] 28.5414 28.43442 28.37092
## [145,] 28.7043 28.53545 28.43442
## [146,] 28.8556 28.65590 28.53545
## [147,] 28.9272 28.75712 28.65590
## [148,] 28.8710 28.83952 28.75712
## [149,] 28.7337 28.84687 28.83952
## [150,] 28.6112 28.78577 28.84687
## [151,] 28.6687 28.72115 28.78577
## [152,] 28.5697 28.64582 28.72115
## [153,] 28.5356 28.59630 28.64582
## [154,] 28.3534 28.53185 28.59630
## [155,] 28.3467 28.45135 28.53185
## [156,] 28.3951 28.40770 28.45135
## [157,] 28.4195 28.37867 28.40770
## [158,] 28.4098 28.39278 28.37867
## [159,] 28.3591 28.39588 28.39278
## [160,] 28.2628 28.36280 28.39588
## [161,] 28.1886 28.30508 28.36280
## [162,] 28.0115 28.20550 28.30508
## [163,] 27.8257 28.07215 28.20550
## [164,] 28.1628 28.04715 28.07215
## [165,] 27.9451 27.98627 28.04715
## [166,] 27.7951 27.93217 27.98627
## [167,] 27.8084 27.92785 27.93217
## [168,] 28.0367 27.89632 27.92785
## [169,] 28.2775 27.97942 27.89632
## [170,] 28.4582 28.14520 27.97942
## [171,] 28.2903 28.26567 28.14520
## [172,] 28.5323 28.38957 28.26567
## [173,] 28.1721 28.36322 28.38957
## [174,] 28.3573 28.33800 28.36322
## [175,] 28.0333 28.27375 28.33800
## [176,] 27.4726 28.00882 28.27375
## [177,] 27.8366 27.92495 28.00882
## [178,] 28.3183 27.91520 27.92495
## [179,] 28.1946 27.95552 27.91520
## [180,] 28.2515 28.15025 27.95552
## [181,] 28.3145 28.26972 28.15025
## [182,] 28.3974 28.28950 28.26972
## [183,] 28.6212 28.39615 28.28950
## [184,] 28.9689 28.57550 28.39615
## [185,] 28.8841 28.71790 28.57550
## [186,] 28.8430 28.82930 28.71790
## [187,] 28.7138 28.85245 28.82930
## [188,] 28.3242 28.69127 28.85245
## [189,] 28.1319 28.50322 28.69127
## [190,] 28.1411 28.32775 28.50322
## [191,] 28.1120 28.17730 28.32775
## [192,] 28.2209 28.15148 28.17730
## [193,] 28.1866 28.16515 28.15148
## [194,] 28.2380 28.18938 28.16515
## [195,] 27.9726 28.15453 28.18938
## [196,] 28.1896 28.14670 28.15453
## [197,] 28.1340 28.13355 28.14670
## [198,] 28.2772 28.14335 28.13355
## [199,] 28.6098 28.30265 28.14335
## [200,] 28.7790 28.45000 28.30265
## [201,] 28.4777 28.53592 28.45000
## [202,] 28.4286 28.57377 28.53592
## [203,] 28.9549 28.66005 28.57377
## [204,] 28.6774 28.63465 28.66005
## [205,] 28.8718 28.73318 28.63465
## [206,] 29.1314 28.90887 28.73318
## [207,] 28.7958 28.86910 28.90887
## [208,] 28.5954 28.84860 28.86910
## [209,] 28.6361 28.78967 28.84860
## [210,] 28.6365 28.66595 28.78967
## [211,] 28.9991 28.71677 28.66595
## [212,] 29.2690 28.88517 28.71677
## [213,] 29.4928 29.09935 28.88517
## [214,] 29.4490 29.30247 29.09935
## [215,] 29.7932 29.50100 29.30247
## [216,] 29.9821 29.67927 29.50100
## [217,] 29.9750 29.79982 29.67927
## [218,] 29.5781 29.83210 29.79982
## [219,] 29.6100 29.78630 29.83210
## [220,] 29.7066 29.71742 29.78630
## [221,] 29.6374 29.63302 29.71742
## [222,] 29.1732 29.53180 29.63302
## [223,] 29.1742 29.42285 29.53180
## [224,] 29.0042 29.24725 29.42285
## [225,] 29.1637 29.12883 29.24725
## [226,] 29.1321 29.11855 29.12883
## [227,] 29.1635 29.11587 29.11855
## [228,] 29.1499 29.15230 29.11587
## [229,] 29.4553 29.22520 29.15230
## [230,] 29.4804 29.31227 29.22520
## [231,] 29.5822 29.41695 29.31227
## [232,] 29.7202 29.55952 29.41695
## [233,] 29.5103 29.57327 29.55952
## [234,] 29.3410 29.53842 29.57327
## [235,] 29.3616 29.48327 29.53842
## [236,] 29.3414 29.38857 29.48327
## [237,] 29.3577 29.35042 29.38857
## [238,] 29.2527 29.32835 29.35042
## [239,] 29.2538 29.30140 29.32835
## [240,] 29.2685 29.28317 29.30140
## [241,] 29.3493 29.28107 29.28317
## [242,] 29.6227 29.37357 29.28107
## [243,] 29.6110 29.46287 29.37357
## [244,] 29.4200 29.50075 29.46287
## [245,] 29.3647 29.50460 29.50075
## [246,] 29.2238 29.40487 29.50460
## [247,] 29.3553 29.34095 29.40487
## [248,] 29.6318 29.39390 29.34095
## [249,] 29.5630 29.44347 29.39390
## [250,] 29.7900 29.58502 29.44347
## [251,] 29.6213 29.65152 29.58502
## [252,] 29.8209 29.69880 29.65152
## [253,] 29.9359 29.79202 29.69880
## [254,] 29.9424 29.83012 29.79202
## [255,] 30.0357 29.93372 29.83012
## [256,] 29.9694 29.97085 29.93372
## [257,] 29.8404 29.94697 29.97085
## [258,] 29.8999 29.93635 29.94697
## [259,] 30.3835 30.02330 29.93635
## [260,] 30.5951 30.17972 30.02330
## [261,] 30.4646 30.33577 30.17972
## [262,] 30.5482 30.49785 30.33577
## [263,] 30.5621 30.54250 30.49785
## [264,] 30.4991 30.51850 30.54250
## [265,] 30.7277 30.58427 30.51850
## [266,] 30.2531 30.51050 30.58427
## [267,] 29.8751 30.33875 30.51050
## [268,] 29.7836 30.15987 30.33875
## [269,] 29.6953 29.90177 30.15987
## [270,] 29.5641 29.72952 29.90177
## [271,] 29.2289 29.56797 29.72952
## [272,] 28.9160 29.35107 29.56797
## [273,] 29.1891 29.22452 29.35107
## [274,] 29.2317 29.14142 29.22452
## [275,] 29.3304 29.16680 29.14142
## [276,] 29.3497 29.27522 29.16680
## [277,] 29.3051 29.30422 29.27522
## [278,] 29.2987 29.32097 29.30422
## [279,] 29.1891 29.28565 29.32097
## [280,] 29.2876 29.27012 29.28565
## [281,] 29.3521 29.28187 29.27012
## [282,] 29.3497 29.29462 29.28187
## [283,] 29.3897 29.34477 29.29462
## [284,] 29.3810 29.36812 29.34477
## [285,] 29.3717 29.37302 29.36812
## [286,] 29.4535 29.39897 29.37302
## [287,] 29.4503 29.41412 29.39897
## [288,] 29.5522 29.45692 29.41412
## [289,] 29.6012 29.51430 29.45692
## [290,] 29.5907 29.54860 29.51430
## [291,] 29.5852 29.58232 29.54860
## [292,] 29.3691 29.53655 29.58232
## [293,] 29.4654 29.50260 29.53655
## [294,] 29.7915 29.55280 29.50260
## [295,] 29.7173 29.58582 29.55280
## [296,] 29.6484 29.65565 29.58582
## [297,] 29.4692 29.65660 29.65565
## [298,] 29.2980 29.53322 29.65660
## [299,] 29.0454 29.36525 29.53322
## [300,] 28.7391 29.13792 29.36525
## [301,] 28.3387 28.85530 29.13792
## [302,] 28.4903 28.65337 28.85530
## [303,] 28.3424 28.47762 28.65337
## [304,] 27.8457 28.25427 28.47762
## [305,] 28.3378 28.25405 28.25427
## [306,] 28.8275 28.33835 28.25405
## [307,] 28.5514 28.39060 28.33835
## [308,] 28.1074 28.45602 28.39060
## [309,] 28.3067 28.44825 28.45602
## [310,] 28.3499 28.32885 28.44825
## [311,] 28.4541 28.30452 28.32885
## [312,] 28.4575 28.39205 28.30452
## [313,] 28.2260 28.37187 28.39205
## [314,] 27.8899 28.25687 28.37187
## [315,] 27.8931 28.11662 28.25687
## [316,] NA NA 28.11662
## [317,] NA NA 28.11662
## [318,] NA NA 28.11662
## [319,] NA NA 28.11662
## [320,] NA NA 28.11662
## [321,] NA NA 28.11662
## [322,] NA NA 28.11662
## [323,] NA NA 28.11662
## [324,] NA NA 28.11662
## [325,] NA NA 28.11662
## [326,] NA NA 28.11662
## [327,] NA NA 28.11662
## [328,] NA NA 28.11662
## [329,] NA NA 28.11662
## [330,] NA NA 28.11662
## [331,] NA NA 28.11662
## [332,] NA NA 28.11662
## [333,] NA NA 28.11662
## [334,] NA NA 28.11662
## [335,] NA NA 28.11662
## [336,] NA NA 28.11662
## [337,] NA NA 28.11662
## [338,] NA NA 28.11662
## [339,] NA NA 28.11662
## [340,] NA NA 28.11662
## [341,] NA NA 28.11662
## [342,] NA NA 28.11662
## [343,] NA NA 28.11662
## [344,] NA NA 28.11662
## [345,] NA NA 28.11662
## [346,] NA NA 28.11662
## [347,] NA NA 28.11662
## [348,] NA NA 28.11662
## [349,] NA NA 28.11662
## [350,] NA NA 28.11662
## [351,] NA NA 28.11662
## [352,] NA NA 28.11662
## [353,] NA NA 28.11662
## [354,] NA NA 28.11662
## [355,] NA NA 28.11662
## [356,] NA NA 28.11662
## [357,] NA NA 28.11662
## [358,] NA NA 28.11662
## [359,] NA NA 28.11662
## [360,] NA NA 28.11662
## [361,] NA NA 28.11662
## [362,] NA NA 28.11662
## [363,] NA NA 28.11662
## [364,] NA NA 28.11662
## [365,] NA NA 28.11662
## [366,] NA NA 28.11662
## [367,] NA NA 28.11662
## [368,] NA NA 28.11662
## [369,] NA NA 28.11662
## [370,] NA NA 28.11662
## [371,] NA NA 28.11662
## [372,] NA NA 28.11662
## [373,] NA NA 28.11662
## [374,] NA NA 28.11662
## [375,] NA NA 28.11662
## [376,] NA NA 28.11662
## [377,] NA NA 28.11662
## [378,] NA NA 28.11662
## [379,] NA NA 28.11662
## [380,] NA NA 28.11662
## [381,] NA NA 28.11662
## [382,] NA NA 28.11662
## [383,] NA NA 28.11662
## [384,] NA NA 28.11662
## [385,] NA NA 28.11662
## [386,] NA NA 28.11662
## [387,] NA NA 28.11662
## [388,] NA NA 28.11662
## [389,] NA NA 28.11662
## [390,] NA NA 28.11662
## [391,] NA NA 28.11662
## [392,] NA NA 28.11662
## [393,] NA NA 28.11662
## [394,] NA NA 28.11662
## [395,] NA NA 28.11662
## [396,] NA NA 28.11662
## [397,] NA NA 28.11662
## [398,] NA NA 28.11662
## [399,] NA NA 28.11662
## [400,] NA NA 28.11662
## [401,] NA NA 28.11662
## [402,] NA NA 28.11662
## [403,] NA NA 28.11662
## [404,] NA NA 28.11662
## [405,] NA NA 28.11662
## [406,] NA NA 28.11662
## [407,] NA NA 28.11662
## [408,] NA NA 28.11662
## [409,] NA NA 28.11662
## [410,] NA NA 28.11662
## [411,] NA NA 28.11662
## [412,] NA NA 28.11662
## [413,] NA NA 28.11662
## [414,] NA NA 28.11662
## [415,] NA NA 28.11662
## [416,] NA NA 28.11662
## [417,] NA NA 28.11662
## [418,] NA NA 28.11662
## [419,] NA NA 28.11662
## [420,] NA NA 28.11662
## [421,] NA NA 28.11662
## [422,] NA NA 28.11662
## [423,] NA NA 28.11662
## [424,] NA NA 28.11662
## [425,] NA NA 28.11662
## [426,] NA NA 28.11662
## [427,] NA NA 28.11662
## [428,] NA NA 28.11662
## [429,] NA NA 28.11662
## [430,] NA NA 28.11662
## [431,] NA NA 28.11662
## [432,] NA NA 28.11662
## [433,] NA NA 28.11662
## [434,] NA NA 28.11662
## [435,] NA NA 28.11662
## [436,] NA NA 28.11662
## [437,] NA NA 28.11662
## [438,] NA NA 28.11662
## [439,] NA NA 28.11662
## [440,] NA NA 28.11662
## [441,] NA NA 28.11662
## [442,] NA NA 28.11662
## [443,] NA NA 28.11662
## [444,] NA NA 28.11662
## [445,] NA NA 28.11662
## [446,] NA NA 28.11662
## [447,] NA NA 28.11662
## [448,] NA NA 28.11662
## [449,] NA NA 28.11662
## [450,] NA NA 28.11662
## [451,] NA NA 28.11662
## [452,] NA NA 28.11662
## [453,] NA NA 28.11662
## [454,] NA NA 28.11662
## [455,] NA NA 28.11662
## [456,] NA NA 28.11662
## [457,] NA NA 28.11662
## [458,] NA NA 28.11662
## [459,] NA NA 28.11662
## [460,] NA NA 28.11662
## [461,] NA NA 28.11662
## [462,] NA NA 28.11662
## [463,] NA NA 28.11662
## [464,] NA NA 28.11662
## [465,] NA NA 28.11662
## [466,] NA NA 28.11662
## [467,] NA NA 28.11662
## [468,] NA NA 28.11662
## [469,] NA NA 28.11662
## [470,] NA NA 28.11662
## [471,] NA NA 28.11662
## [472,] NA NA 28.11662
## [473,] NA NA 28.11662
## [474,] NA NA 28.11662
## [475,] NA NA 28.11662
## [476,] NA NA 28.11662
## [477,] NA NA 28.11662
## [478,] NA NA 28.11662
## [479,] NA NA 28.11662
## [480,] NA NA 28.11662
## [481,] NA NA 28.11662
## [482,] NA NA 28.11662
## [483,] NA NA 28.11662
## [484,] NA NA 28.11662
## [485,] NA NA 28.11662
## [486,] NA NA 28.11662
## [487,] NA NA 28.11662
## [488,] NA NA 28.11662
## [489,] NA NA 28.11662
## [490,] NA NA 28.11662
## [491,] NA NA 28.11662
## [492,] NA NA 28.11662
## [493,] NA NA 28.11662
## [494,] NA NA 28.11662
## [495,] NA NA 28.11662
## [496,] NA NA 28.11662
## [497,] NA NA 28.11662
## [498,] NA NA 28.11662
## [499,] NA NA 28.11662
## [500,] NA NA 28.11662Adapun plot data deret waktu dari hasil peramalan yang dilakukan adalah sebagai berikut.
ts.plot(data.ts, xlab="Time Period ", ylab="Temperature", main= "SMA N=4 Data Temperature")
points(data.ts)
lines(data.gab[,2],col="green",lwd=2)
lines(data.gab[,3],col="red",lwd=2)
legend("topleft",c("data aktual","data pemulusan","data peramalan"), lty=8, col=c("black","green","red"), cex=0.5)
Selanjutnya perhitungan akurasi dilakukan dengan ukuran akurasi Sum Squares Error (SSE), Mean Square Error (MSE) dan Mean Absolute Percentage Error (MAPE). Perhitungan akurasi dilakukan baik pada data latih maupun pada data uji.
#Menghitung nilai keakuratan data latih
error_train.sma = train_ma.ts-data.ramal[1:length(train_ma.ts)]
SSE_train.sma = sum(error_train.sma[5:length(train_ma.ts)]^2)
MSE_train.sma = mean(error_train.sma[5:length(train_ma.ts)]^2)
MAPE_train.sma = mean(abs((error_train.sma[5:length(train_ma.ts)]/train_ma.ts[5:length(train_ma.ts)])*100))
akurasi_train.sma <- matrix(c(SSE_train.sma, MSE_train.sma, MAPE_train.sma))
row.names(akurasi_train.sma)<- c("SSE", "MSE", "MAPE")
colnames(akurasi_train.sma) <- c("Akurasi m = 4")
akurasi_train.sma## Akurasi m = 4
## SSE 28.93459764
## MSE 0.09303729
## MAPE 0.81463292Dalam hal ini nilai MAPE data latih pada metode pemulusan SMA kurang dari 2%, nilai ini dapat dikategorikan sebagai nilai akurasi yang sangat baik. Selanjutnya dilakukan perhitungan nilai MAPE data uji pada metode pemulusan SMA.
#Menghitung nilai keakuratan data uji
error_test.sma = test_ma.ts-data.gab[316:500,3]
SSE_test.sma = sum(error_test.sma^2)
MSE_test.sma = mean(error_test.sma^2)
MAPE_test.sma = mean(abs((error_test.sma/test_ma.ts*100)))
akurasi_test.sma <- matrix(c(SSE_test.sma, MSE_test.sma, MAPE_test.sma))
row.names(akurasi_test.sma)<- c("SSE", "MSE", "MAPE")
colnames(akurasi_test.sma) <- c("Akurasi m = 4")
akurasi_test.sma## Akurasi m = 4
## SSE 71.8464262
## MSE 0.3883591
## MAPE 1.8480564Perhitungan akurasi menggunakan data latih menghasilkan nilai MAPE yang kurang dari 2% sehingga nilai akurasi ini dapat dikategorikan sebagai sangat baik.
Double Moving Average (DMA)
Metode pemulusan Double Moving Average (DMA) pada dasarnya mirip dengan SMA. Namun demikian, metode ini lebih cocok digunakan untuk pola data trend. Proses pemulusan dengan rata rata dalam metode ini dilakukan sebanyak 2 kali.
dma <- SMA(data.sma, n = 4)
At <- 2*data.sma - dma
Bt <- 2/(4-1)*(data.sma - dma)
data.dma<- At+Bt
data.ramal2<- c(NA, data.dma)
t = 1:185
f = c()
for (i in t) {
f[i] = At[length(At)] + Bt[length(Bt)]*(i)
}
data.gab2 <- cbind(aktual = c(train_ma.ts,rep(NA,185)), pemulusan1 = c(data.sma,rep(NA,185)),pemulusan2 = c(data.dma, rep(NA,185)),At = c(At, rep(NA,185)), Bt = c(Bt,rep(NA,185)),ramalan = c(data.ramal2, f[-1]))
data.gab2## aktual pemulusan1 pemulusan2 At Bt ramalan
## [1,] 29.5199 NA NA NA NA NA
## [2,] 29.7223 NA NA NA NA NA
## [3,] 29.9959 NA NA NA NA NA
## [4,] 30.1798 29.85448 NA NA NA NA
## [5,] 29.9898 29.97195 NA NA NA NA
## [6,] 29.5493 29.92870 NA NA NA NA
## [7,] 29.4496 29.79212 29.63431 29.69744 -0.0631250000 NA
## [8,] 29.1447 29.53335 29.07805 29.26017 -0.1821208333 29.634312
## [9,] 28.9804 29.28100 28.69301 28.92821 -0.2351958333 29.078048
## [10,] 27.9646 28.88482 28.07149 28.39682 -0.3253333333 28.693010
## [11,] 28.2861 28.59395 27.79506 28.11462 -0.3195541667 28.071492
## [12,] 28.5817 28.45320 27.86979 28.10316 -0.2333625000 27.795065
## [13,] 28.3704 28.30070 27.87159 28.04323 -0.1716458333 27.869794
## [14,] 28.1310 28.34230 28.20857 28.26206 -0.0534916667 27.871585
## [15,] 28.4389 28.38050 28.39937 28.39182 0.0075500000 28.208571
## [16,] 28.4687 28.35225 28.36610 28.36056 0.0055416667 28.399375
## [17,] 28.8089 28.46187 28.59128 28.53952 0.0517625000 28.366104
## [18,] 28.1059 28.45560 28.52734 28.49864 0.0286958333 28.591281
## [19,] 28.5539 28.48435 28.56074 28.53018 0.0305541667 28.527340
## [20,] 27.8272 28.32397 28.14485 28.21650 -0.0716500000 28.560735
## [21,] 27.8087 28.07392 27.63970 27.81339 -0.1736916667 28.144850
## [22,] 27.7019 27.97292 27.57148 27.73206 -0.1605791667 27.639696
## [23,] 28.0635 27.85032 27.50872 27.64536 -0.1366416667 27.571477
## [24,] 28.4916 28.01642 28.07980 28.05445 0.0253500000 27.508721
## [25,] 28.8819 28.28472 28.70743 28.53835 0.1690833333 28.079800
## [26,] 28.9219 28.58972 29.26377 28.99415 0.2696166667 28.707433
## [27,] 28.9509 28.81157 29.45485 29.19754 0.2573083333 29.263767
## [28,] 28.8818 28.90912 29.34302 29.16946 0.1735583333 29.454846
## [29,] 28.6812 28.85895 28.96996 28.92556 0.0444041667 29.343021
## [30,] 28.7636 28.81937 28.76874 28.78899 -0.0202541667 28.969960
## [31,] 28.8789 28.80137 28.72499 28.75554 -0.0305541667 28.768740
## [32,] 29.1590 28.87067 28.92581 28.90376 0.0220541667 28.724990
## [33,] 29.1560 28.98937 29.18800 29.10855 0.0794500000 28.925810
## [34,] 28.8804 29.01857 29.18287 29.11715 0.0657166667 29.188000
## [35,] 28.7361 28.98287 29.01204 29.00037 0.0116666667 29.182867
## [36,] 28.9529 28.93135 28.84936 28.88216 -0.0327958333 29.012042
## [37,] 28.9279 28.87432 28.74523 28.79687 -0.0516375000 28.849360
## [38,] 28.8606 28.86937 28.79420 28.82427 -0.0300708333 28.745231
## [39,] 28.9146 28.91400 28.94190 28.93074 0.0111583333 28.794198
## [40,] 28.9805 28.92090 28.96465 28.94715 0.0175000000 28.941896
## [41,] 28.7728 28.88212 28.85800 28.86765 -0.0096500000 28.964650
## [42,] 28.5158 28.79592 28.65874 28.71361 -0.0548750000 28.858000
## [43,] 28.3397 28.65220 28.38455 28.49161 -0.1070583333 28.658738
## [44,] 28.4657 28.52350 28.20694 28.33356 -0.1266250000 28.384554
## [45,] 28.6805 28.50042 28.30445 28.38284 -0.0783916667 28.206937
## [46,] 28.6870 28.54322 28.52387 28.53161 -0.0077416667 28.304446
## [47,] 28.6159 28.61227 28.72464 28.67969 0.0449458333 28.523871
## [48,] 27.7069 28.42257 28.26083 28.32552 -0.0647000000 28.724640
## [49,] 27.5755 28.14632 27.67170 27.86155 -0.1898500000 28.260825
## [50,] 27.8705 27.94220 27.37779 27.60356 -0.2257625000 27.671700
## [51,] 27.9734 27.78157 27.29559 27.48998 -0.1943958333 27.377794
## [52,] 27.9205 27.83497 27.68282 27.74368 -0.0608625000 27.295585
## [53,] 27.7864 27.88770 27.93118 27.91379 0.0173916667 27.682819
## [54,] 27.8825 27.89070 27.96064 27.93266 0.0279750000 27.931179
## [55,] 28.0314 27.90520 27.94779 27.93076 0.0170375000 27.960638
## [56,] 27.7159 27.85405 27.80345 27.82369 -0.0202416667 27.947794
## [57,] 27.3559 27.74642 27.57531 27.64376 -0.0684458333 27.803446
## [58,] 27.5265 27.65742 27.43517 27.52407 -0.0889000000 27.575310
## [59,] 28.5057 27.77600 27.80521 27.79352 0.0116833333 27.435175
## [60,] 28.1900 27.89452 28.10441 28.02046 0.0839541667 27.805208
## [61,] 28.4408 28.16575 28.65296 28.45807 0.1948833333 28.104410
## [62,] 28.3829 28.37985 28.92288 28.70567 0.2172125000 28.652958
## [63,] 28.1104 28.28102 28.44892 28.38176 0.0671583333 28.922881
## [64,] 28.2804 28.30362 28.33873 28.32469 0.0140416667 28.448921
## [65,] 28.6194 28.34827 28.38174 28.36836 0.0133875000 28.338729
## [66,] 28.4554 28.36640 28.43568 28.40797 0.0277125000 28.381744
## [67,] 28.2047 28.38997 28.45315 28.42788 0.0252708333 28.435681
## [68,] 28.2589 28.38460 28.40508 28.39689 0.0081916667 28.453152
## [69,] 28.4913 28.35257 28.31789 28.33176 -0.0138750000 28.405079
## [70,] 28.5556 28.37762 28.38001 28.37906 0.0009541667 28.317887
## [71,] 28.6541 28.48997 28.63794 28.57876 0.0591875000 28.380010
## [72,] 28.6561 28.58927 28.81746 28.72619 0.0912750000 28.637944
## [73,] 28.7888 28.66365 28.88618 28.79717 0.0890125000 28.817462
## [74,] 29.0157 28.77867 29.02581 28.92696 0.0988541667 28.886181
## [75,] 29.0545 28.87877 29.13074 29.02996 0.1007875000 29.025810
## [76,] 28.7661 28.90627 29.07199 29.00571 0.0662875000 29.130744
## [77,] 28.6243 28.86515 28.87837 28.87308 0.0052875000 29.071994
## [78,] 28.7148 28.78992 28.67308 28.71982 -0.0467375000 28.878369
## [79,] 28.6156 28.68020 28.46322 28.55001 -0.0867916667 28.673081
## [80,] 28.5756 28.63257 28.45026 28.52319 -0.0729250000 28.463221
## [81,] 28.5083 28.60357 28.48192 28.53058 -0.0486625000 28.450263
## [82,] 28.6951 28.59865 28.54848 28.56855 -0.0200666667 28.481919
## [83,] 28.8885 28.66687 28.73597 28.70833 0.0276375000 28.548483
## [84,] 29.0858 28.79442 29.00866 28.92297 0.0856958333 28.735969
## [85,] 29.3367 29.00152 29.39512 29.23768 0.1574375000 29.008665
## [86,] 29.3574 29.16710 29.59980 29.42672 0.1730791667 29.395119
## [87,] 29.3659 29.28645 29.65991 29.51052 0.1493833333 29.599798
## [88,] 29.5487 29.40217 29.71528 29.59004 0.1252416667 29.659908
## [89,] 29.3826 29.41365 29.57416 29.50996 0.0642041667 29.715279
## [90,] 29.2164 29.37840 29.39212 29.38663 0.0054875000 29.574160
## [91,] 29.1717 29.32985 29.24457 29.27868 -0.0341125000 29.392119
## [92,] 29.1913 29.24050 29.07367 29.14040 -0.0667333333 29.244569
## [93,] 29.0917 29.16777 28.98218 29.05642 -0.0742375000 29.073667
## [94,] 29.0579 29.12815 28.98079 29.03973 -0.0589458333 28.982181
## [95,] 29.0865 29.10685 29.01690 29.05288 -0.0359791667 28.980785
## [96,] 29.0657 29.07545 29.00194 29.03134 -0.0294041667 29.016902
## [97,] 28.6958 28.97647 28.81771 28.88122 -0.0635041667 29.001940
## [98,] 29.1813 29.00732 28.95032 28.97312 -0.0228000000 28.817715
## [99,] 29.0379 28.99517 28.96446 28.97674 -0.0122875000 28.950325
## [100,] 29.0966 29.00290 29.01529 29.01033 0.0049541667 28.964456
## [101,] 29.0987 29.10362 29.23091 29.17999 0.0509125000 29.015285
## [102,] 29.1217 29.08872 29.15726 29.12984 0.0274125000 29.230906
## [103,] 29.1019 29.10472 29.15428 29.13446 0.0198208333 29.157256
## [104,] 29.1644 29.12167 29.14999 29.13866 0.0113250000 29.154277
## [105,] 29.0476 29.10890 29.11372 29.11179 0.0019291667 29.149987
## [106,] 28.8890 29.05072 28.97442 29.00494 -0.0305208333 29.113723
## [107,] 28.9053 29.00157 28.88634 28.93243 -0.0460958333 28.974423
## [108,] 28.7631 28.90125 28.71065 28.78689 -0.0762416667 28.886335
## [109,] 28.8742 28.85790 28.69963 28.76294 -0.0633083333 28.710646
## [110,] 28.4464 28.74725 28.53101 28.61751 -0.0864958333 28.699629
## [111,] 28.5246 28.65207 28.42284 28.51453 -0.0916958333 28.531010
## [112,] 28.3630 28.55205 28.30160 28.40178 -0.1001791667 28.422835
## [113,] 28.6354 28.49235 28.29471 28.37377 -0.0790541667 28.301602
## [114,] 28.6541 28.54427 28.51775 28.52836 -0.0106083333 28.294715
## [115,] 28.8423 28.62370 28.74138 28.69431 0.0470708333 28.517754
## [116,] 28.9608 28.77315 29.04779 28.93793 0.1098541667 28.741377
## [117,] 28.9027 28.83998 29.08114 28.98468 0.0964666667 29.047785
## [118,] 29.1552 28.96525 29.23980 29.12998 0.1098208333 29.081142
## [119,] 29.0877 29.02660 29.23553 29.15196 0.0835708333 29.239802
## [120,] 29.6389 29.19613 29.51135 29.38526 0.1260916667 29.235527
## [121,] 29.6982 29.39500 29.81043 29.64426 0.1661708333 29.511354
## [122,] 29.7808 29.55140 29.98326 29.81052 0.1727458333 29.810427
## [123,] 29.4966 29.65363 29.99460 29.85821 0.1363916667 29.983265
## [124,] 29.5754 29.63775 29.76826 29.71606 0.0522041667 29.994604
## [125,] 29.0989 29.48793 29.33001 29.39318 -0.0631666667 29.768260
## [126,] 28.9608 29.28292 28.89521 29.05029 -0.1550875000 29.330008
## [127,] 29.1609 29.19900 28.86083 28.99610 -0.1352666667 28.895206
## [128,] 29.0164 29.05925 28.72921 28.86123 -0.1320166667 28.860833
## [129,] 28.9473 29.02135 28.82255 28.90207 -0.0795208333 28.729208
## [130,] 28.9675 29.02303 28.93531 28.97039 -0.0350875000 28.822548
## [131,] 28.8302 28.94035 28.82261 28.86971 -0.0470958333 28.935306
## [132,] 28.6650 28.85250 28.67449 28.74569 -0.0712041667 28.822610
## [133,] 28.4619 28.73115 28.47181 28.57554 -0.1037375000 28.674490
## [134,] 28.4709 28.60700 28.31408 28.43125 -0.1171666667 28.471806
## [135,] 28.4638 28.51540 28.24688 28.35429 -0.1074083333 28.314083
## [136,] 28.4209 28.45437 28.25003 28.33177 -0.0817375000 28.246879
## [137,] 28.2085 28.39102 28.22282 28.29010 -0.0672833333 28.250031
## [138,] 28.2293 28.33062 28.17691 28.23839 -0.0614875000 28.222817
## [139,] 28.2231 28.27045 28.11850 28.17928 -0.0607791667 28.176906
## [140,] 28.2874 28.23707 28.12004 28.16686 -0.0468125000 28.118502
## [141,] 28.3002 28.26000 28.23577 28.24546 -0.0096916667 28.120044
## [142,] 28.3738 28.29612 28.34648 28.32634 0.0201416667 28.235771
## [143,] 28.5223 28.37092 28.50408 28.45082 0.0532625000 28.346479
## [144,] 28.5414 28.43442 28.59119 28.52848 0.0627041667 28.504081
## [145,] 28.7043 28.53545 28.74581 28.66167 0.0841458333 28.591185
## [146,] 28.8556 28.65590 28.91711 28.81263 0.1044833333 28.745815
## [147,] 28.9272 28.75712 29.02613 28.91852 0.1076000000 28.917108
## [148,] 28.8710 28.83952 29.07707 28.98205 0.0950166667 29.026125
## [149,] 28.7337 28.84687 28.96691 28.91889 0.0480125000 29.077067
## [150,] 28.6112 28.78577 28.74986 28.76423 -0.0143666667 28.966906
## [151,] 28.6687 28.72115 28.59251 28.64397 -0.0514541667 28.749858
## [152,] 28.5697 28.64582 28.47236 28.54174 -0.0693875000 28.592515
## [153,] 28.5356 28.59630 28.44470 28.50534 -0.0606416667 28.472356
## [154,] 28.3534 28.53185 28.37863 28.43992 -0.0612875000 28.444696
## [155,] 28.3467 28.45135 28.27638 28.34637 -0.0699875000 28.378631
## [156,] 28.3951 28.40770 28.25920 28.31860 -0.0594000000 28.276381
## [157,] 28.4195 28.37867 28.27248 28.31496 -0.0424791667 28.259200
## [158,] 28.4098 28.39278 28.36803 28.37793 -0.0099000000 28.272477
## [159,] 28.3591 28.39588 28.39941 28.39799 0.0014125000 28.368025
## [160,] 28.2628 28.36280 28.32991 28.34307 -0.0131541667 28.399406
## [161,] 28.1886 28.30508 28.20665 28.24602 -0.0393708333 28.329915
## [162,] 28.0115 28.20550 28.01915 28.09369 -0.0745416667 28.206648
## [163,] 27.8257 28.07215 27.79843 27.90792 -0.1094875000 28.019146
## [164,] 28.1628 28.04715 27.86329 27.93683 -0.0735458333 27.798431
## [165,] 27.9451 27.98627 27.83379 27.89478 -0.0609958333 27.863285
## [166,] 27.7951 27.93217 27.80340 27.85491 -0.0515083333 27.833785
## [167,] 27.8084 27.92785 27.85200 27.88234 -0.0303416667 27.803404
## [168,] 28.0367 27.89632 27.83077 27.85699 -0.0262208333 27.851996
## [169,] 28.2775 27.97942 28.05523 28.02491 0.0303208333 27.830773
## [170,] 28.4582 28.14520 28.40853 28.30320 0.1053333333 28.055227
## [171,] 28.2903 28.26567 28.58904 28.45969 0.1293458333 28.408533
## [172,] 28.5323 28.38957 28.71392 28.58418 0.1297375000 28.589040
## [173,] 28.1721 28.36322 28.48374 28.43553 0.0482041667 28.713919
## [174,] 28.3573 28.33800 28.33614 28.33688 -0.0007458333 28.483735
## [175,] 28.0333 28.27375 28.16144 28.20636 -0.0449250000 28.336135
## [176,] 27.4726 28.00882 27.61362 27.77170 -0.1580833333 28.161438
## [177,] 27.8366 27.92495 27.57256 27.71352 -0.1409541667 27.613617
## [178,] 28.3183 27.91520 27.72273 27.79972 -0.0769875000 27.572565
## [179,] 28.1946 27.95552 27.96286 27.95993 0.0029333333 27.722731
## [180,] 28.2515 28.15025 28.42320 28.31402 0.1091791667 27.962858
## [181,] 28.3145 28.26972 28.59814 28.46678 0.1313666667 28.423198
## [182,] 28.3974 28.28950 28.49492 28.41275 0.0821666667 28.598142
## [183,] 28.6212 28.39615 28.59572 28.51589 0.0798291667 28.494917
## [184,] 28.9689 28.57550 28.89680 28.76828 0.1285208333 28.595723
## [185,] 28.8841 28.71790 29.08980 28.94104 0.1487583333 28.896802
## [186,] 28.8430 28.82930 29.16195 29.02889 0.1330583333 29.089796
## [187,] 28.7138 28.85245 29.03355 28.96111 0.0724416667 29.161946
## [188,] 28.3242 28.69127 28.55551 28.60982 -0.0543041667 29.033554
## [189,] 28.1319 28.50322 28.14350 28.28739 -0.1438916667 28.555515
## [190,] 28.1411 28.32775 27.88454 28.06183 -0.1772833333 28.143496
## [191,] 28.1120 28.17730 27.76465 27.92971 -0.1650583333 27.884542
## [192,] 28.2209 28.15148 27.92070 28.01301 -0.0923083333 27.764654
## [193,] 28.1866 28.16515 28.09804 28.12488 -0.0268458333 27.920704
## [194,] 28.2380 28.18938 28.22029 28.20793 0.0123666667 28.098035
## [195,] 27.9726 28.15453 28.13685 28.14392 -0.0070708333 28.220292
## [196,] 28.1896 28.14670 28.11797 28.12946 -0.0114916667 28.136848
## [197,] 28.1340 28.13355 28.09607 28.11106 -0.0149916667 28.117971
## [198,] 28.2772 28.14335 28.14138 28.14217 -0.0007875000 28.096071
## [199,] 28.6098 28.30265 28.50446 28.42374 0.0807250000 28.141381
## [200,] 28.7790 28.45000 28.77102 28.64261 0.1284083333 28.504463
## [201,] 28.4777 28.53592 28.83250 28.71387 0.1186291667 28.771021
## [202,] 28.4286 28.57377 28.75409 28.68196 0.0721250000 28.832498
## [203,] 28.9549 28.66005 28.83524 28.76516 0.0700750000 28.754088
## [204,] 28.6774 28.63465 28.69057 28.66820 0.0223666667 28.835238
## [205,] 28.8718 28.73318 28.87111 28.81594 0.0551750000 28.690567
## [206,] 29.1314 28.90887 29.20002 29.08356 0.1164583333 28.871113
## [207,] 28.7958 28.86910 29.00685 28.95175 0.0551000000 29.200021
## [208,] 28.5954 28.84860 28.86304 28.85726 0.0057750000 29.006850
## [209,] 28.6361 28.78967 28.68236 28.72529 -0.0429250000 28.863038
## [210,] 28.6365 28.66595 28.45365 28.53857 -0.0849208333 28.682363
## [211,] 28.9991 28.71677 28.65265 28.67830 -0.0256500000 28.453648
## [212,] 29.2690 28.88517 29.08648 29.00596 0.0805208333 28.652650
## [213,] 29.4928 29.09935 29.52858 29.35689 0.1716916667 29.086477
## [214,] 29.4490 29.30247 29.80503 29.60401 0.2010208333 29.528579
## [215,] 29.7932 29.50100 30.00767 29.80500 0.2026666667 29.805027
## [216,] 29.9821 29.67927 30.15219 29.96303 0.1891666667 30.007667
## [217,] 29.9750 29.79982 30.18179 30.02901 0.1527875000 30.152192
## [218,] 29.5781 29.83210 30.04718 29.96115 0.0860333333 30.181794
## [219,] 29.6100 29.78630 29.80618 29.79823 0.0079500000 30.047183
## [220,] 29.7066 29.71742 29.60661 29.65094 -0.0443250000 29.806175
## [221,] 29.6374 29.63302 29.45105 29.52384 -0.0727916667 29.606613
## [222,] 29.1732 29.53180 29.30624 29.39646 -0.0902250000 29.451046
## [223,] 29.1742 29.42285 29.16714 29.26943 -0.1022833333 29.306238
## [224,] 29.0042 29.24725 28.89478 29.03577 -0.1409875000 29.167142
## [225,] 29.1637 29.12883 28.78906 28.92497 -0.1359041667 28.894781
## [226,] 29.1321 29.11855 28.93385 29.00773 -0.0738791667 28.789065
## [227,] 29.1635 29.11587 29.05463 29.07913 -0.0245000000 28.933852
## [228,] 29.1499 29.15230 29.19132 29.17571 0.0156083333 29.054625
## [229,] 29.4553 29.22520 29.34556 29.29742 0.0481458333 29.191321
## [230,] 29.4804 29.31227 29.49705 29.42314 0.0739083333 29.345565
## [231,] 29.5822 29.41695 29.65073 29.55722 0.0935125000 29.497046
## [232,] 29.7202 29.55952 29.86125 29.74056 0.1206916667 29.650731
## [233,] 29.5103 29.57327 29.75289 29.68104 0.0718458333 29.861254
## [234,] 29.3410 29.53842 29.56573 29.55481 0.0109208333 29.752890
## [235,] 29.3616 29.48327 29.39103 29.42793 -0.0369000000 29.565727
## [236,] 29.3414 29.38857 29.20972 29.28126 -0.0715416667 29.391025
## [237,] 29.3577 29.35042 29.20084 29.26068 -0.0598333333 29.209721
## [238,] 29.2527 29.32835 29.22951 29.26904 -0.0395375000 29.200842
## [239,] 29.2538 29.30140 29.23342 29.26061 -0.0271916667 29.229506
## [240,] 29.2685 29.28317 29.22874 29.25051 -0.0217750000 29.233421
## [241,] 29.3493 29.28107 29.25203 29.26365 -0.0116166667 29.228738
## [242,] 29.6227 29.37357 29.47986 29.43734 0.0425125000 29.252033
## [243,] 29.6110 29.46287 29.65071 29.57558 0.0751333333 29.479856
## [244,] 29.4200 29.50075 29.66105 29.59693 0.0641208333 29.650708
## [245,] 29.3647 29.50460 29.57818 29.54875 0.0294333333 29.661052
## [246,] 29.2238 29.40487 29.29921 29.34148 -0.0422666667 29.578183
## [247,] 29.3553 29.34095 29.17954 29.24411 -0.0645625000 29.299208
## [248,] 29.6318 29.39390 29.36526 29.37672 -0.0114541667 29.179544
## [249,] 29.5630 29.44347 29.52293 29.49115 0.0317833333 29.365265
## [250,] 29.7900 29.58502 29.82534 29.72921 0.0961250000 29.522933
## [251,] 29.6213 29.65152 29.87326 29.78457 0.0886958333 29.825338
## [252,] 29.8209 29.69880 29.87229 29.80289 0.0693958333 29.873265
## [253,] 29.9359 29.79202 29.97566 29.90221 0.0734541667 29.872290
## [254,] 29.9424 29.83012 29.97514 29.91713 0.0580041667 29.975660
## [255,] 30.0357 29.93372 30.13382 30.05378 0.0800375000 29.975135
## [256,] 29.9694 29.97085 30.11946 30.06002 0.0594458333 30.133819
## [257,] 29.8404 29.94697 29.99124 29.97353 0.0177041667 30.119465
## [258,] 29.8999 29.93635 29.91864 29.92573 -0.0070833333 29.991235
## [259,] 30.3835 30.02330 30.11319 30.07723 0.0359541667 29.918642
## [260,] 30.5951 30.17972 30.44329 30.33786 0.1054250000 30.113185
## [261,] 30.4646 30.33577 30.69742 30.55276 0.1446583333 30.443288
## [262,] 30.5482 30.49785 30.89566 30.73654 0.1591250000 30.697421
## [263,] 30.5621 30.54250 30.79840 30.69604 0.1023583333 30.895663
## [264,] 30.4991 30.51850 30.59324 30.56334 0.0298958333 30.798396
## [265,] 30.7277 30.58427 30.66510 30.63277 0.0323291667 30.593240
## [266,] 30.2531 30.51050 30.46309 30.48206 -0.0189625000 30.665098
## [267,] 29.8751 30.33875 30.08999 30.18949 -0.0995041667 30.463094
## [268,] 29.7836 30.15987 29.76242 29.92140 -0.1589833333 30.089990
## [269,] 29.6953 29.90177 29.35853 29.57583 -0.2173000000 29.762417
## [270,] 29.5641 29.72952 29.22460 29.42657 -0.2019708333 29.358525
## [271,] 29.2289 29.56797 29.11495 29.29616 -0.1812083333 29.224598
## [272,] 28.9160 29.35107 28.87355 29.06456 -0.1910083333 29.114954
## [273,] 29.1891 29.22452 28.81828 28.98078 -0.1625000000 28.873554
## [274,] 29.2317 29.14142 28.84172 28.96160 -0.1198833333 28.818275
## [275,] 29.3304 29.16680 29.07654 29.11264 -0.0361041667 28.841717
## [276,] 29.3497 29.27522 29.39728 29.34846 0.0488208333 29.076540
## [277,] 29.3051 29.30422 29.44140 29.38653 0.0548708333 29.397277
## [278,] 29.2987 29.32097 29.41126 29.37514 0.0361125000 29.441402
## [279,] 29.1891 29.28565 29.26754 29.27478 -0.0072458333 29.411256
## [280,] 29.2876 29.27012 29.22826 29.24501 -0.0167458333 29.267535
## [281,] 29.3521 29.28187 29.26891 29.27409 -0.0051875000 29.228260
## [282,] 29.3497 29.29462 29.31389 29.30618 0.0077041667 29.268906
## [283,] 29.3897 29.34477 29.42298 29.39170 0.0312833333 29.313885
## [284,] 29.3810 29.36812 29.44442 29.41390 0.0305166667 29.422983
## [285,] 29.3717 29.37302 29.41950 29.40091 0.0185916667 29.444417
## [286,] 29.4535 29.39897 29.44523 29.42673 0.0185000000 29.419504
## [287,] 29.4503 29.41412 29.45673 29.43969 0.0170416667 29.445225
## [288,] 29.5522 29.45692 29.53386 29.50309 0.0307750000 29.456729
## [289,] 29.6012 29.51430 29.62800 29.58252 0.0454791667 29.533863
## [290,] 29.5907 29.54860 29.65712 29.61371 0.0434083333 29.627998
## [291,] 29.5852 29.58232 29.67697 29.63911 0.0378583333 29.657121
## [292,] 29.3691 29.53655 29.52173 29.52766 -0.0059291667 29.676971
## [293,] 29.4654 29.50260 29.43607 29.46268 -0.0266125000 29.521727
## [294,] 29.7915 29.55280 29.56819 29.56203 0.0061541667 29.436069
## [295,] 29.7173 29.58582 29.65479 29.62721 0.0275875000 29.568185
## [296,] 29.6484 29.65565 29.79137 29.73708 0.0542875000 29.654794
## [297,] 29.4692 29.65660 29.72974 29.70048 0.0292541667 29.791369
## [298,] 29.2980 29.53322 29.40889 29.45863 -0.0497333333 29.729735
## [299,] 29.0454 29.36525 29.05286 29.17782 -0.1249541667 29.408892
## [300,] 28.7391 29.13792 28.66238 28.85260 -0.1902166667 29.052865
## [301,] 28.3387 28.85530 28.24259 28.48768 -0.2450833333 28.662383
## [302,] 28.4903 28.65337 28.07073 28.30379 -0.2330583333 28.242592
## [303,] 28.3424 28.47762 27.97191 28.17419 -0.2022875000 28.070729
## [304,] 27.8457 28.25427 27.74449 27.94841 -0.2039125000 27.971906
## [305,] 28.3378 28.25405 27.99441 28.09827 -0.1038541667 27.744494
## [306,] 28.8275 28.33835 28.35048 28.34563 0.0048500000 27.994415
## [307,] 28.5514 28.39060 28.52607 28.47188 0.0541875000 28.350475
## [308,] 28.1074 28.45602 28.61647 28.55229 0.0641791667 28.526069
## [309,] 28.3067 28.44825 28.51482 28.48819 0.0266291667 28.616473
## [310,] 28.3499 28.32885 28.20038 28.25177 -0.0513875000 28.514823
## [311,] 28.4541 28.30452 28.17138 28.22464 -0.0532583333 28.200381
## [312,] 28.4575 28.39205 28.43144 28.41568 0.0157541667 28.171379
## [313,] 28.2260 28.37187 28.40946 28.39443 0.0150333333 28.431435
## [314,] 27.8899 28.25687 28.13278 28.18242 -0.0496375000 28.409458
## [315,] 27.8931 28.11662 27.83707 27.94889 -0.1118208333 28.132781
## [316,] NA NA NA NA NA 27.837073
## [317,] NA NA NA NA NA 27.725252
## [318,] NA NA NA NA NA 27.613431
## [319,] NA NA NA NA NA 27.501610
## [320,] NA NA NA NA NA 27.389790
## [321,] NA NA NA NA NA 27.277969
## [322,] NA NA NA NA NA 27.166148
## [323,] NA NA NA NA NA 27.054327
## [324,] NA NA NA NA NA 26.942506
## [325,] NA NA NA NA NA 26.830685
## [326,] NA NA NA NA NA 26.718865
## [327,] NA NA NA NA NA 26.607044
## [328,] NA NA NA NA NA 26.495223
## [329,] NA NA NA NA NA 26.383402
## [330,] NA NA NA NA NA 26.271581
## [331,] NA NA NA NA NA 26.159760
## [332,] NA NA NA NA NA 26.047940
## [333,] NA NA NA NA NA 25.936119
## [334,] NA NA NA NA NA 25.824298
## [335,] NA NA NA NA NA 25.712477
## [336,] NA NA NA NA NA 25.600656
## [337,] NA NA NA NA NA 25.488835
## [338,] NA NA NA NA NA 25.377015
## [339,] NA NA NA NA NA 25.265194
## [340,] NA NA NA NA NA 25.153373
## [341,] NA NA NA NA NA 25.041552
## [342,] NA NA NA NA NA 24.929731
## [343,] NA NA NA NA NA 24.817910
## [344,] NA NA NA NA NA 24.706090
## [345,] NA NA NA NA NA 24.594269
## [346,] NA NA NA NA NA 24.482448
## [347,] NA NA NA NA NA 24.370627
## [348,] NA NA NA NA NA 24.258806
## [349,] NA NA NA NA NA 24.146985
## [350,] NA NA NA NA NA 24.035165
## [351,] NA NA NA NA NA 23.923344
## [352,] NA NA NA NA NA 23.811523
## [353,] NA NA NA NA NA 23.699702
## [354,] NA NA NA NA NA 23.587881
## [355,] NA NA NA NA NA 23.476060
## [356,] NA NA NA NA NA 23.364240
## [357,] NA NA NA NA NA 23.252419
## [358,] NA NA NA NA NA 23.140598
## [359,] NA NA NA NA NA 23.028777
## [360,] NA NA NA NA NA 22.916956
## [361,] NA NA NA NA NA 22.805135
## [362,] NA NA NA NA NA 22.693315
## [363,] NA NA NA NA NA 22.581494
## [364,] NA NA NA NA NA 22.469673
## [365,] NA NA NA NA NA 22.357852
## [366,] NA NA NA NA NA 22.246031
## [367,] NA NA NA NA NA 22.134210
## [368,] NA NA NA NA NA 22.022390
## [369,] NA NA NA NA NA 21.910569
## [370,] NA NA NA NA NA 21.798748
## [371,] NA NA NA NA NA 21.686927
## [372,] NA NA NA NA NA 21.575106
## [373,] NA NA NA NA NA 21.463285
## [374,] NA NA NA NA NA 21.351465
## [375,] NA NA NA NA NA 21.239644
## [376,] NA NA NA NA NA 21.127823
## [377,] NA NA NA NA NA 21.016002
## [378,] NA NA NA NA NA 20.904181
## [379,] NA NA NA NA NA 20.792360
## [380,] NA NA NA NA NA 20.680540
## [381,] NA NA NA NA NA 20.568719
## [382,] NA NA NA NA NA 20.456898
## [383,] NA NA NA NA NA 20.345077
## [384,] NA NA NA NA NA 20.233256
## [385,] NA NA NA NA NA 20.121435
## [386,] NA NA NA NA NA 20.009615
## [387,] NA NA NA NA NA 19.897794
## [388,] NA NA NA NA NA 19.785973
## [389,] NA NA NA NA NA 19.674152
## [390,] NA NA NA NA NA 19.562331
## [391,] NA NA NA NA NA 19.450510
## [392,] NA NA NA NA NA 19.338690
## [393,] NA NA NA NA NA 19.226869
## [394,] NA NA NA NA NA 19.115048
## [395,] NA NA NA NA NA 19.003227
## [396,] NA NA NA NA NA 18.891406
## [397,] NA NA NA NA NA 18.779585
## [398,] NA NA NA NA NA 18.667765
## [399,] NA NA NA NA NA 18.555944
## [400,] NA NA NA NA NA 18.444123
## [401,] NA NA NA NA NA 18.332302
## [402,] NA NA NA NA NA 18.220481
## [403,] NA NA NA NA NA 18.108660
## [404,] NA NA NA NA NA 17.996840
## [405,] NA NA NA NA NA 17.885019
## [406,] NA NA NA NA NA 17.773198
## [407,] NA NA NA NA NA 17.661377
## [408,] NA NA NA NA NA 17.549556
## [409,] NA NA NA NA NA 17.437735
## [410,] NA NA NA NA NA 17.325915
## [411,] NA NA NA NA NA 17.214094
## [412,] NA NA NA NA NA 17.102273
## [413,] NA NA NA NA NA 16.990452
## [414,] NA NA NA NA NA 16.878631
## [415,] NA NA NA NA NA 16.766810
## [416,] NA NA NA NA NA 16.654990
## [417,] NA NA NA NA NA 16.543169
## [418,] NA NA NA NA NA 16.431348
## [419,] NA NA NA NA NA 16.319527
## [420,] NA NA NA NA NA 16.207706
## [421,] NA NA NA NA NA 16.095885
## [422,] NA NA NA NA NA 15.984065
## [423,] NA NA NA NA NA 15.872244
## [424,] NA NA NA NA NA 15.760423
## [425,] NA NA NA NA NA 15.648602
## [426,] NA NA NA NA NA 15.536781
## [427,] NA NA NA NA NA 15.424960
## [428,] NA NA NA NA NA 15.313140
## [429,] NA NA NA NA NA 15.201319
## [430,] NA NA NA NA NA 15.089498
## [431,] NA NA NA NA NA 14.977677
## [432,] NA NA NA NA NA 14.865856
## [433,] NA NA NA NA NA 14.754035
## [434,] NA NA NA NA NA 14.642215
## [435,] NA NA NA NA NA 14.530394
## [436,] NA NA NA NA NA 14.418573
## [437,] NA NA NA NA NA 14.306752
## [438,] NA NA NA NA NA 14.194931
## [439,] NA NA NA NA NA 14.083110
## [440,] NA NA NA NA NA 13.971290
## [441,] NA NA NA NA NA 13.859469
## [442,] NA NA NA NA NA 13.747648
## [443,] NA NA NA NA NA 13.635827
## [444,] NA NA NA NA NA 13.524006
## [445,] NA NA NA NA NA 13.412185
## [446,] NA NA NA NA NA 13.300365
## [447,] NA NA NA NA NA 13.188544
## [448,] NA NA NA NA NA 13.076723
## [449,] NA NA NA NA NA 12.964902
## [450,] NA NA NA NA NA 12.853081
## [451,] NA NA NA NA NA 12.741260
## [452,] NA NA NA NA NA 12.629440
## [453,] NA NA NA NA NA 12.517619
## [454,] NA NA NA NA NA 12.405798
## [455,] NA NA NA NA NA 12.293977
## [456,] NA NA NA NA NA 12.182156
## [457,] NA NA NA NA NA 12.070335
## [458,] NA NA NA NA NA 11.958515
## [459,] NA NA NA NA NA 11.846694
## [460,] NA NA NA NA NA 11.734873
## [461,] NA NA NA NA NA 11.623052
## [462,] NA NA NA NA NA 11.511231
## [463,] NA NA NA NA NA 11.399410
## [464,] NA NA NA NA NA 11.287590
## [465,] NA NA NA NA NA 11.175769
## [466,] NA NA NA NA NA 11.063948
## [467,] NA NA NA NA NA 10.952127
## [468,] NA NA NA NA NA 10.840306
## [469,] NA NA NA NA NA 10.728485
## [470,] NA NA NA NA NA 10.616665
## [471,] NA NA NA NA NA 10.504844
## [472,] NA NA NA NA NA 10.393023
## [473,] NA NA NA NA NA 10.281202
## [474,] NA NA NA NA NA 10.169381
## [475,] NA NA NA NA NA 10.057560
## [476,] NA NA NA NA NA 9.945740
## [477,] NA NA NA NA NA 9.833919
## [478,] NA NA NA NA NA 9.722098
## [479,] NA NA NA NA NA 9.610277
## [480,] NA NA NA NA NA 9.498456
## [481,] NA NA NA NA NA 9.386635
## [482,] NA NA NA NA NA 9.274815
## [483,] NA NA NA NA NA 9.162994
## [484,] NA NA NA NA NA 9.051173
## [485,] NA NA NA NA NA 8.939352
## [486,] NA NA NA NA NA 8.827531
## [487,] NA NA NA NA NA 8.715710
## [488,] NA NA NA NA NA 8.603890
## [489,] NA NA NA NA NA 8.492069
## [490,] NA NA NA NA NA 8.380248
## [491,] NA NA NA NA NA 8.268427
## [492,] NA NA NA NA NA 8.156606
## [493,] NA NA NA NA NA 8.044785
## [494,] NA NA NA NA NA 7.932965
## [495,] NA NA NA NA NA 7.821144
## [496,] NA NA NA NA NA 7.709323
## [497,] NA NA NA NA NA 7.597502
## [498,] NA NA NA NA NA 7.485681
## [499,] NA NA NA NA NA 7.373860
## [500,] NA NA NA NA NA 7.262040Hasil pemulusan menggunakan metode DMA divisualisasikan sebagai berikut
ts.plot(data.ts, xlab="Time Period ", ylab="Temperature", main= "DMA N=4 Data Temperature")
points(data.ts)
lines(data.gab2[,3],col="green",lwd=2)
lines(data.gab2[,6],col="red",lwd=2)
legend("topleft",c("data aktual","data pemulusan","data peramalan"), lty=8, col=c("black","green","red"), cex=0.8)
Selanjutnya perhitungan akurasi dilakukan baik pada data latih maupun data uji. Perhitungan akurasi dilakukan dengan ukuran akurasi SSE, MSE dan MAPE.
#Menghitung nilai keakuratan data latih
error_train.dma = train_ma.ts-data.ramal2[1:length(train_ma.ts)]
SSE_train.dma = sum(error_train.dma[8:length(train_ma.ts)]^2)
MSE_train.dma = mean(error_train.dma[8:length(train_ma.ts)]^2)
MAPE_train.dma = mean(abs((error_train.dma[8:length(train_ma.ts)]/train_ma.ts[8:length(train_ma.ts)])*100))
akurasi_train.dma <- matrix(c(SSE_train.dma, MSE_train.dma, MAPE_train.dma))
row.names(akurasi_train.dma)<- c("SSE", "MSE", "MAPE")
colnames(akurasi_train.dma) <- c("Akurasi m = 4")
akurasi_train.dma## Akurasi m = 4
## SSE 29.41270968
## MSE 0.09549581
## MAPE 0.83015255Perhitungan akurasi pada data latih menggunakan nilai MAPE menghasilkan nilai MAPE yang kurang dari 2% sehingga dikategorikan sangat baik. Selanjutnya, perhitungan nilai akurasi dilakukan pada data uji.
#Menghitung nilai keakuratan data uji
error_test.dma = test_ma.ts-data.gab2[316:500,6]
SSE_test.dma = sum(error_test.dma^2)
MSE_test.dma = mean(error_test.dma^2)
MAPE_test.dma = mean(abs((error_test.dma/test_ma.ts*100)))
akurasi_test.dma <- matrix(c(SSE_test.dma, MSE_test.dma, MAPE_test.dma))
row.names(akurasi_test.dma)<- c("SSE", "MSE", "MAPE")
colnames(akurasi_test.dma) <- c("Akurasi m = 4")
akurasi_test.dma## Akurasi m = 4
## SSE 28030.63888
## MSE 151.51697
## MAPE 37.34898Perhitungan akurasi menggunakan data latih menghasilkan nilai MAPE yang kurang dari 50% sehingga nilai akurasi ini dapat dikategorikan sebagai reasonable forecasting.
Pada data latih dan uji, metode SMA lebih baik dibandingkan dengan metode DMA.
Single Exponential Smoothing & Double Exponential Smoothing
Metode Exponential Smoothing adalah metode pemulusan dengan melakukan pembobotan menurun secara eksponensial. Nilai yang lebih baru diberi bobot yang lebih besar dari nilai terdahulu. Terdapat satu atau lebih parameter pemulusan yang ditentukan secara eksplisit, dan hasil pemilihan parameter tersebut akan menentukan bobot yang akan diberikan pada nilai pengamatan. Ada dua macam model, yaitu model tunggal dan ganda.
Pembagian Data
Pembagian data latih dan data uji dilakukan dengan perbandingan 63% data latih dan 37% data uji.
#membagi training dan testing
training<-data[1:315,]
testing<-data[316:500,]
train.ts <- ts(training$temperature)
test.ts <- ts(testing$temperature)Eksplorasi
Eksplorasi dilakukan dengan membuat plot data deret waktu untuk keseluruhan data, data latih, dan data uji.
#eksplorasi data
plot(data.ts, col="black",main="Plot semua data")
points(data.ts)
plot(train.ts, col="red",main="Plot data latih")
points(train.ts)
plot(test.ts, col="blue",main="Plot data uji")
points(test.ts)
Eksplorasi data juga dapat dilakukan menggunakan package
ggplot2 .
#Eksplorasi dengan GGPLOT
library(ggplot2)
ggplot() +
geom_line(data = training, aes(x = date, y = temperature, col = "Data Latih")) +
geom_line(data = testing, aes(x = date, y = temperature, col = "Data Uji")) +
labs(x = "Periode Waktu", y = "Temperature", color = "Legend") +
scale_colour_manual(name="Keterangan:", breaks = c("Data Latih", "Data Uji"),
values = c("blue", "red")) +
theme_bw() + theme(legend.position = "bottom",
plot.caption = element_text(hjust=0.5, size=12))
SES
Single Exponential Smoothing merupakan metode pemulusan yang tepat digunakan untuk data dengan pola stasioner atau konstan.
Nilai pemulusan pada periode ke-t didapat dari persamaan:
\[ \tilde{y}_T=\lambda y_t+(1-\lambda)\tilde{y}_{T-1} \]
Nilai parameter \(\lambda\) adalah nilai antara 0 dan 1.
Nilai pemulusan periode ke-t bertindak sebagai nilai ramalan pada periode ke-\((T+\tau)\).
\[ \tilde{y}_{T+\tau}(T)=\tilde{y}_T \]
Pemulusan dengan metode SES dapat dilakukan dengan dua fungsi dari
packages berbeda, yaitu (1) fungsi ses() dari
packages forecast dan (2) fungsi
HoltWinters dari packages stats .
#Cara 1 (fungsi ses)
ses.1 <- ses(train.ts, h = 185, alpha = 0.2)
plot(ses.1)
ses.1## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 316 28.22102 27.77763 28.66441 27.54292 28.89913
## 317 28.22102 27.76885 28.67319 27.52949 28.91255
## 318 28.22102 27.76024 28.68180 27.51632 28.92573
## 319 28.22102 27.75178 28.69026 27.50338 28.93866
## 320 28.22102 27.74348 28.69857 27.49068 28.95136
## 321 28.22102 27.73531 28.70673 27.47820 28.96385
## 322 28.22102 27.72729 28.71476 27.46592 28.97613
## 323 28.22102 27.71939 28.72266 27.45383 28.98821
## 324 28.22102 27.71161 28.73044 27.44194 29.00010
## 325 28.22102 27.70395 28.73810 27.43022 29.01182
## 326 28.22102 27.69640 28.74565 27.41868 29.02336
## 327 28.22102 27.68896 28.75309 27.40730 29.03475
## 328 28.22102 27.68162 28.76043 27.39607 29.04597
## 329 28.22102 27.67438 28.76767 27.38500 29.05704
## 330 28.22102 27.66723 28.77481 27.37407 29.06797
## 331 28.22102 27.66017 28.78187 27.36328 29.07876
## 332 28.22102 27.65321 28.78884 27.35262 29.08942
## 333 28.22102 27.64632 28.79572 27.34210 29.09994
## 334 28.22102 27.63952 28.80252 27.33170 29.11035
## 335 28.22102 27.63280 28.80924 27.32142 29.12063
## 336 28.22102 27.62615 28.81589 27.31125 29.13079
## 337 28.22102 27.61958 28.82246 27.30120 29.14085
## 338 28.22102 27.61308 28.82897 27.29125 29.15079
## 339 28.22102 27.60664 28.83540 27.28141 29.16063
## 340 28.22102 27.60028 28.84177 27.27168 29.17037
## 341 28.22102 27.59398 28.84807 27.26204 29.18001
## 342 28.22102 27.58774 28.85431 27.25250 29.18955
## 343 28.22102 27.58156 28.86049 27.24305 29.19900
## 344 28.22102 27.57544 28.86660 27.23369 29.20836
## 345 28.22102 27.56938 28.87267 27.22442 29.21763
## 346 28.22102 27.56337 28.87867 27.21523 29.22681
## 347 28.22102 27.55742 28.88462 27.20613 29.23591
## 348 28.22102 27.55152 28.89052 27.19711 29.24494
## 349 28.22102 27.54567 28.89637 27.18816 29.25388
## 350 28.22102 27.53988 28.90217 27.17930 29.26274
## 351 28.22102 27.53413 28.90792 27.17051 29.27154
## 352 28.22102 27.52843 28.91362 27.16179 29.28025
## 353 28.22102 27.52277 28.91927 27.15314 29.28890
## 354 28.22102 27.51716 28.92488 27.14457 29.29748
## 355 28.22102 27.51160 28.93044 27.13606 29.30599
## 356 28.22102 27.50608 28.93596 27.12761 29.31443
## 357 28.22102 27.50060 28.94144 27.11923 29.32281
## 358 28.22102 27.49516 28.94688 27.11092 29.33113
## 359 28.22102 27.48977 28.95228 27.10266 29.33938
## 360 28.22102 27.48441 28.95763 27.09447 29.34757
## 361 28.22102 27.47909 28.96295 27.08634 29.35571
## 362 28.22102 27.47381 28.96823 27.07826 29.36378
## 363 28.22102 27.46857 28.97348 27.07024 29.37180
## 364 28.22102 27.46336 28.97868 27.06228 29.37977
## 365 28.22102 27.45819 28.98386 27.05437 29.38768
## 366 28.22102 27.45305 28.98899 27.04651 29.39553
## 367 28.22102 27.44795 28.99410 27.03871 29.40334
## 368 28.22102 27.44288 28.99916 27.03095 29.41109
## 369 28.22102 27.43784 29.00420 27.02325 29.41879
## 370 28.22102 27.43284 29.00921 27.01560 29.42645
## 371 28.22102 27.42786 29.01418 27.00799 29.43405
## 372 28.22102 27.42292 29.01912 27.00043 29.44161
## 373 28.22102 27.41801 29.02403 26.99292 29.44912
## 374 28.22102 27.41313 29.02891 26.98546 29.45659
## 375 28.22102 27.40828 29.03377 26.97804 29.46401
## 376 28.22102 27.40345 29.03859 26.97066 29.47138
## 377 28.22102 27.39866 29.04338 26.96333 29.47872
## 378 28.22102 27.39389 29.04815 26.95604 29.48601
## 379 28.22102 27.38915 29.05289 26.94879 29.49326
## 380 28.22102 27.38444 29.05761 26.94158 29.50047
## 381 28.22102 27.37975 29.06229 26.93441 29.50763
## 382 28.22102 27.37509 29.06695 26.92728 29.51476
## 383 28.22102 27.37046 29.07159 26.92019 29.52185
## 384 28.22102 27.36585 29.07620 26.91314 29.52890
## 385 28.22102 27.36126 29.08078 26.90613 29.53591
## 386 28.22102 27.35670 29.08534 26.89915 29.54289
## 387 28.22102 27.35216 29.08988 26.89221 29.54983
## 388 28.22102 27.34765 29.09440 26.88531 29.55673
## 389 28.22102 27.34316 29.09889 26.87844 29.56360
## 390 28.22102 27.33869 29.10335 26.87161 29.57043
## 391 28.22102 27.33425 29.10780 26.86481 29.57723
## 392 28.22102 27.32982 29.11222 26.85805 29.58399
## 393 28.22102 27.32542 29.11662 26.85132 29.59072
## 394 28.22102 27.32104 29.12100 26.84462 29.59742
## 395 28.22102 27.31668 29.12536 26.83796 29.60409
## 396 28.22102 27.31235 29.12970 26.83132 29.61072
## 397 28.22102 27.30803 29.13401 26.82472 29.61732
## 398 28.22102 27.30373 29.13831 26.81815 29.62389
## 399 28.22102 27.29946 29.14259 26.81161 29.63043
## 400 28.22102 27.29520 29.14684 26.80510 29.63694
## 401 28.22102 27.29096 29.15108 26.79862 29.64342
## 402 28.22102 27.28674 29.15530 26.79217 29.64988
## 403 28.22102 27.28255 29.15950 26.78575 29.65630
## 404 28.22102 27.27837 29.16368 26.77935 29.66269
## 405 28.22102 27.27420 29.16784 26.77299 29.66906
## 406 28.22102 27.27006 29.17198 26.76665 29.67539
## 407 28.22102 27.26593 29.17611 26.76034 29.68170
## 408 28.22102 27.26183 29.18022 26.75406 29.68798
## 409 28.22102 27.25774 29.18431 26.74780 29.69424
## 410 28.22102 27.25366 29.18838 26.74157 29.70047
## 411 28.22102 27.24961 29.19244 26.73537 29.70667
## 412 28.22102 27.24557 29.19648 26.72919 29.71285
## 413 28.22102 27.24154 29.20050 26.72304 29.71900
## 414 28.22102 27.23754 29.20450 26.71691 29.72513
## 415 28.22102 27.23355 29.20849 26.71081 29.73123
## 416 28.22102 27.22958 29.21247 26.70474 29.73731
## 417 28.22102 27.22562 29.21643 26.69868 29.74336
## 418 28.22102 27.22168 29.22037 26.69265 29.74939
## 419 28.22102 27.21775 29.22429 26.68665 29.75540
## 420 28.22102 27.21384 29.22821 26.68067 29.76138
## 421 28.22102 27.20994 29.23210 26.67471 29.76734
## 422 28.22102 27.20606 29.23598 26.66877 29.77327
## 423 28.22102 27.20219 29.23985 26.66286 29.77919
## 424 28.22102 27.19834 29.24370 26.65697 29.78508
## 425 28.22102 27.19450 29.24754 26.65110 29.79095
## 426 28.22102 27.19068 29.25136 26.64525 29.79679
## 427 28.22102 27.18687 29.25517 26.63943 29.80262
## 428 28.22102 27.18308 29.25897 26.63362 29.80842
## 429 28.22102 27.17929 29.26275 26.62784 29.81421
## 430 28.22102 27.17553 29.26652 26.62208 29.81997
## 431 28.22102 27.17177 29.27027 26.61633 29.82571
## 432 28.22102 27.16803 29.27401 26.61061 29.83143
## 433 28.22102 27.16431 29.27774 26.60491 29.83713
## 434 28.22102 27.16059 29.28145 26.59923 29.84281
## 435 28.22102 27.15689 29.28515 26.59357 29.84847
## 436 28.22102 27.15320 29.28884 26.58793 29.85411
## 437 28.22102 27.14953 29.29252 26.58231 29.85973
## 438 28.22102 27.14586 29.29618 26.57671 29.86534
## 439 28.22102 27.14221 29.29983 26.57112 29.87092
## 440 28.22102 27.13857 29.30347 26.56556 29.87648
## 441 28.22102 27.13495 29.30710 26.56001 29.88203
## 442 28.22102 27.13133 29.31071 26.55449 29.88756
## 443 28.22102 27.12773 29.31431 26.54898 29.89307
## 444 28.22102 27.12414 29.31790 26.54349 29.89856
## 445 28.22102 27.12056 29.32148 26.53801 29.90403
## 446 28.22102 27.11699 29.32505 26.53256 29.90949
## 447 28.22102 27.11344 29.32861 26.52712 29.91492
## 448 28.22102 27.10989 29.33215 26.52170 29.92035
## 449 28.22102 27.10636 29.33568 26.51629 29.92575
## 450 28.22102 27.10284 29.33920 26.51091 29.93113
## 451 28.22102 27.09933 29.34272 26.50554 29.93650
## 452 28.22102 27.09583 29.34622 26.50019 29.94186
## 453 28.22102 27.09234 29.34970 26.49485 29.94719
## 454 28.22102 27.08886 29.35318 26.48953 29.95251
## 455 28.22102 27.08539 29.35665 26.48423 29.95782
## 456 28.22102 27.08194 29.36011 26.47894 29.96310
## 457 28.22102 27.07849 29.36355 26.47367 29.96837
## 458 28.22102 27.07505 29.36699 26.46841 29.97363
## 459 28.22102 27.07163 29.37042 26.46318 29.97887
## 460 28.22102 27.06821 29.37383 26.45795 29.98409
## 461 28.22102 27.06481 29.37724 26.45274 29.98930
## 462 28.22102 27.06141 29.38063 26.44755 29.99449
## 463 28.22102 27.05803 29.38402 26.44237 29.99967
## 464 28.22102 27.05465 29.38739 26.43721 30.00483
## 465 28.22102 27.05128 29.39076 26.43206 30.00998
## 466 28.22102 27.04793 29.39412 26.42693 30.01512
## 467 28.22102 27.04458 29.39746 26.42181 30.02023
## 468 28.22102 27.04124 29.40080 26.41670 30.02534
## 469 28.22102 27.03791 29.40413 26.41161 30.03043
## 470 28.22102 27.03460 29.40745 26.40654 30.03550
## 471 28.22102 27.03129 29.41076 26.40148 30.04057
## 472 28.22102 27.02799 29.41406 26.39643 30.04561
## 473 28.22102 27.02469 29.41735 26.39140 30.05065
## 474 28.22102 27.02141 29.42063 26.38638 30.05567
## 475 28.22102 27.01814 29.42390 26.38137 30.06067
## 476 28.22102 27.01488 29.42717 26.37638 30.06566
## 477 28.22102 27.01162 29.43042 26.37140 30.07064
## 478 28.22102 27.00837 29.43367 26.36644 30.07561
## 479 28.22102 27.00513 29.43691 26.36148 30.08056
## 480 28.22102 27.00191 29.44014 26.35654 30.08550
## 481 28.22102 26.99868 29.44336 26.35162 30.09043
## 482 28.22102 26.99547 29.44657 26.34671 30.09534
## 483 28.22102 26.99227 29.44978 26.34180 30.10024
## 484 28.22102 26.98907 29.45297 26.33692 30.10513
## 485 28.22102 26.98588 29.45616 26.33204 30.11000
## 486 28.22102 26.98271 29.45934 26.32718 30.11486
## 487 28.22102 26.97953 29.46251 26.32233 30.11971
## 488 28.22102 26.97637 29.46567 26.31749 30.12455
## 489 28.22102 26.97322 29.46883 26.31267 30.12938
## 490 28.22102 26.97007 29.47197 26.30786 30.13419
## 491 28.22102 26.96693 29.47511 26.30305 30.13899
## 492 28.22102 26.96380 29.47824 26.29827 30.14378
## 493 28.22102 26.96068 29.48137 26.29349 30.14856
## 494 28.22102 26.95756 29.48448 26.28872 30.15332
## 495 28.22102 26.95445 29.48759 26.28397 30.15807
## 496 28.22102 26.95135 29.49069 26.27923 30.16282
## 497 28.22102 26.94826 29.49379 26.27450 30.16755
## 498 28.22102 26.94517 29.49687 26.26978 30.17226
## 499 28.22102 26.94209 29.49995 26.26507 30.17697
## 500 28.22102 26.93902 29.50302 26.26037 30.18167ses.2<- ses(train.ts, h = 185, alpha = 0.7)
plot(ses.2)
ses.2## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 316 27.92831 27.62029 28.23634 27.45723 28.39940
## 317 27.92831 27.55232 28.30431 27.35328 28.50335
## 318 27.92831 27.49488 28.36175 27.26544 28.59119
## 319 27.92831 27.44421 28.41242 27.18794 28.66869
## 320 27.92831 27.39836 28.45826 27.11783 28.73880
## 321 27.92831 27.35618 28.50045 27.05331 28.80332
## 322 27.92831 27.31690 28.53973 26.99323 28.86340
## 323 27.92831 27.27999 28.57664 26.93679 28.91984
## 324 27.92831 27.24508 28.61155 26.88339 28.97324
## 325 27.92831 27.21186 28.64477 26.83259 29.02404
## 326 27.92831 27.18012 28.67651 26.78405 29.07258
## 327 27.92831 27.14967 28.70696 26.73748 29.11915
## 328 27.92831 27.12037 28.73626 26.69267 29.16396
## 329 27.92831 27.09209 28.76454 26.64942 29.20721
## 330 27.92831 27.06474 28.79189 26.60759 29.24904
## 331 27.92831 27.03823 28.81840 26.56704 29.28959
## 332 27.92831 27.01248 28.84415 26.52767 29.32896
## 333 27.92831 26.98744 28.86919 26.48938 29.36725
## 334 27.92831 26.96305 28.89358 26.45208 29.40455
## 335 27.92831 26.93926 28.91737 26.41569 29.44094
## 336 27.92831 26.91603 28.94060 26.38016 29.47646
## 337 27.92831 26.89332 28.96330 26.34543 29.51120
## 338 27.92831 26.87110 28.98553 26.31145 29.54518
## 339 27.92831 26.84934 29.00729 26.27816 29.57846
## 340 27.92831 26.82801 29.02862 26.24554 29.61109
## 341 27.92831 26.80708 29.04955 26.21353 29.64310
## 342 27.92831 26.78653 29.07009 26.18211 29.67452
## 343 27.92831 26.76635 29.09028 26.15125 29.70538
## 344 27.92831 26.74652 29.11011 26.12091 29.73572
## 345 27.92831 26.72701 29.12962 26.09108 29.76555
## 346 27.92831 26.70781 29.14882 26.06172 29.79491
## 347 27.92831 26.68891 29.16772 26.03281 29.82382
## 348 27.92831 26.67030 29.18633 26.00434 29.85229
## 349 27.92831 26.65195 29.20468 25.97629 29.88034
## 350 27.92831 26.63387 29.22276 25.94863 29.90800
## 351 27.92831 26.61603 29.24060 25.92135 29.93528
## 352 27.92831 26.59844 29.25819 25.89444 29.96219
## 353 27.92831 26.58107 29.27556 25.86788 29.98875
## 354 27.92831 26.56392 29.29271 25.84166 30.01497
## 355 27.92831 26.54699 29.30964 25.81576 30.04087
## 356 27.92831 26.53026 29.32636 25.79018 30.06645
## 357 27.92831 26.51374 29.34289 25.76490 30.09173
## 358 27.92831 26.49740 29.35923 25.73991 30.11672
## 359 27.92831 26.48124 29.37539 25.71521 30.14142
## 360 27.92831 26.46527 29.39136 25.69078 30.16585
## 361 27.92831 26.44946 29.40717 25.66661 30.19002
## 362 27.92831 26.43383 29.42280 25.64269 30.21394
## 363 27.92831 26.41835 29.43828 25.61903 30.23760
## 364 27.92831 26.40304 29.45359 25.59560 30.26103
## 365 27.92831 26.38787 29.46876 25.57241 30.28422
## 366 27.92831 26.37285 29.48378 25.54944 30.30719
## 367 27.92831 26.35798 29.49865 25.52669 30.32993
## 368 27.92831 26.34325 29.51338 25.50416 30.35247
## 369 27.92831 26.32865 29.52798 25.48184 30.37479
## 370 27.92831 26.31418 29.54245 25.45971 30.39692
## 371 27.92831 26.29984 29.55679 25.43778 30.41885
## 372 27.92831 26.28563 29.57100 25.41605 30.44058
## 373 27.92831 26.27154 29.58509 25.39450 30.46213
## 374 27.92831 26.25757 29.59906 25.37313 30.48350
## 375 27.92831 26.24371 29.61292 25.35194 30.50469
## 376 27.92831 26.22997 29.62666 25.33092 30.52571
## 377 27.92831 26.21634 29.64029 25.31007 30.54656
## 378 27.92831 26.20281 29.65382 25.28939 30.56724
## 379 27.92831 26.18939 29.66724 25.26886 30.58777
## 380 27.92831 26.17608 29.68055 25.24850 30.60813
## 381 27.92831 26.16286 29.69377 25.22828 30.62835
## 382 27.92831 26.14974 29.70689 25.20822 30.64841
## 383 27.92831 26.13672 29.71991 25.18830 30.66832
## 384 27.92831 26.12379 29.73284 25.16853 30.68810
## 385 27.92831 26.11095 29.74568 25.14890 30.70773
## 386 27.92831 26.09821 29.75842 25.12941 30.72722
## 387 27.92831 26.08555 29.77108 25.11005 30.74658
## 388 27.92831 26.07298 29.78365 25.09082 30.76581
## 389 27.92831 26.06049 29.79614 25.07172 30.78490
## 390 27.92831 26.04809 29.80854 25.05275 30.80388
## 391 27.92831 26.03576 29.82087 25.03391 30.82272
## 392 27.92831 26.02352 29.83311 25.01518 30.84145
## 393 27.92831 26.01136 29.84527 24.99658 30.86005
## 394 27.92831 25.99927 29.85736 24.97809 30.87854
## 395 27.92831 25.98725 29.86938 24.95972 30.89691
## 396 27.92831 25.97532 29.88131 24.94146 30.91517
## 397 27.92831 25.96345 29.89318 24.92331 30.93332
## 398 27.92831 25.95165 29.90498 24.90527 30.95136
## 399 27.92831 25.93993 29.91670 24.88734 30.96929
## 400 27.92831 25.92827 29.92836 24.86951 30.98712
## 401 27.92831 25.91668 29.93995 24.85179 31.00484
## 402 27.92831 25.90516 29.95147 24.83417 31.02246
## 403 27.92831 25.89370 29.96293 24.81664 31.03999
## 404 27.92831 25.88231 29.97432 24.79922 31.05741
## 405 27.92831 25.87098 29.98565 24.78189 31.07474
## 406 27.92831 25.85971 29.99692 24.76466 31.09197
## 407 27.92831 25.84850 30.00813 24.74752 31.10911
## 408 27.92831 25.83736 30.01927 24.73047 31.12616
## 409 27.92831 25.82627 30.03036 24.71351 31.14312
## 410 27.92831 25.81524 30.04139 24.69664 31.15999
## 411 27.92831 25.80427 30.05236 24.67986 31.17677
## 412 27.92831 25.79335 30.06328 24.66317 31.19346
## 413 27.92831 25.78249 30.07414 24.64656 31.21007
## 414 27.92831 25.77168 30.08495 24.63003 31.22660
## 415 27.92831 25.76093 30.09570 24.61359 31.24304
## 416 27.92831 25.75023 30.10640 24.59723 31.25940
## 417 27.92831 25.73959 30.11704 24.58094 31.27569
## 418 27.92831 25.72899 30.12764 24.56474 31.29189
## 419 27.92831 25.71845 30.13818 24.54861 31.30802
## 420 27.92831 25.70795 30.14868 24.53256 31.32406
## 421 27.92831 25.69751 30.15912 24.51659 31.34004
## 422 27.92831 25.68711 30.16952 24.50069 31.35594
## 423 27.92831 25.67676 30.17987 24.48487 31.37176
## 424 27.92831 25.66646 30.19017 24.46911 31.38752
## 425 27.92831 25.65621 30.20042 24.45343 31.40320
## 426 27.92831 25.64600 30.21063 24.43782 31.41881
## 427 27.92831 25.63584 30.22079 24.42228 31.43435
## 428 27.92831 25.62572 30.23091 24.40680 31.44983
## 429 27.92831 25.61565 30.24098 24.39140 31.46523
## 430 27.92831 25.60562 30.25101 24.37606 31.48057
## 431 27.92831 25.59563 30.26100 24.36078 31.49585
## 432 27.92831 25.58569 30.27094 24.34558 31.51105
## 433 27.92831 25.57579 30.28084 24.33043 31.52620
## 434 27.92831 25.56592 30.29070 24.31535 31.54128
## 435 27.92831 25.55611 30.30052 24.30033 31.55630
## 436 27.92831 25.54633 30.31030 24.28538 31.57125
## 437 27.92831 25.53659 30.32004 24.27048 31.58615
## 438 27.92831 25.52689 30.32974 24.25565 31.60098
## 439 27.92831 25.51723 30.33940 24.24087 31.61576
## 440 27.92831 25.50760 30.34902 24.22616 31.63047
## 441 27.92831 25.49802 30.35861 24.21150 31.64513
## 442 27.92831 25.48847 30.36815 24.19690 31.65973
## 443 27.92831 25.47897 30.37766 24.18236 31.67427
## 444 27.92831 25.46949 30.38714 24.16787 31.68876
## 445 27.92831 25.46006 30.39657 24.15344 31.70319
## 446 27.92831 25.45066 30.40597 24.13906 31.71756
## 447 27.92831 25.44129 30.41534 24.12474 31.73189
## 448 27.92831 25.43196 30.42467 24.11048 31.74615
## 449 27.92831 25.42267 30.43396 24.09626 31.76037
## 450 27.92831 25.41341 30.44322 24.08210 31.77453
## 451 27.92831 25.40418 30.45245 24.06799 31.78864
## 452 27.92831 25.39499 30.46164 24.05393 31.80270
## 453 27.92831 25.38583 30.47080 24.03992 31.81671
## 454 27.92831 25.37670 30.47993 24.02596 31.83067
## 455 27.92831 25.36761 30.48902 24.01205 31.84458
## 456 27.92831 25.35855 30.49808 23.99820 31.85843
## 457 27.92831 25.34952 30.50711 23.98439 31.87224
## 458 27.92831 25.34052 30.51611 23.97062 31.88601
## 459 27.92831 25.33155 30.52508 23.95691 31.89972
## 460 27.92831 25.32262 30.53401 23.94324 31.91339
## 461 27.92831 25.31371 30.54292 23.92962 31.92701
## 462 27.92831 25.30483 30.55180 23.91605 31.94058
## 463 27.92831 25.29599 30.56064 23.90252 31.95411
## 464 27.92831 25.28717 30.56946 23.88904 31.96759
## 465 27.92831 25.27839 30.57824 23.87560 31.98103
## 466 27.92831 25.26963 30.58700 23.86220 31.99443
## 467 27.92831 25.26090 30.59573 23.84885 32.00778
## 468 27.92831 25.25220 30.60443 23.83555 32.02108
## 469 27.92831 25.24353 30.61310 23.82228 32.03435
## 470 27.92831 25.23488 30.62175 23.80906 32.04757
## 471 27.92831 25.22626 30.63037 23.79589 32.06074
## 472 27.92831 25.21768 30.63895 23.78275 32.07388
## 473 27.92831 25.20911 30.64752 23.76965 32.08698
## 474 27.92831 25.20058 30.65605 23.75660 32.10003
## 475 27.92831 25.19207 30.66456 23.74359 32.11304
## 476 27.92831 25.18359 30.67304 23.73062 32.12601
## 477 27.92831 25.17513 30.68150 23.71768 32.13895
## 478 27.92831 25.16670 30.68993 23.70479 32.15184
## 479 27.92831 25.15830 30.69833 23.69194 32.16469
## 480 27.92831 25.14992 30.70671 23.67912 32.17751
## 481 27.92831 25.14156 30.71507 23.66634 32.19029
## 482 27.92831 25.13323 30.72340 23.65361 32.20302
## 483 27.92831 25.12493 30.73170 23.64091 32.21572
## 484 27.92831 25.11665 30.73998 23.62824 32.22839
## 485 27.92831 25.10839 30.74824 23.61562 32.24101
## 486 27.92831 25.10016 30.75647 23.60303 32.25360
## 487 27.92831 25.09195 30.76468 23.59048 32.26615
## 488 27.92831 25.08377 30.77286 23.57796 32.27867
## 489 27.92831 25.07561 30.78102 23.56548 32.29115
## 490 27.92831 25.06747 30.78916 23.55303 32.30359
## 491 27.92831 25.05936 30.79727 23.54063 32.31600
## 492 27.92831 25.05127 30.80536 23.52825 32.32838
## 493 27.92831 25.04320 30.81343 23.51591 32.34072
## 494 27.92831 25.03515 30.82148 23.50361 32.35302
## 495 27.92831 25.02713 30.82950 23.49134 32.36529
## 496 27.92831 25.01913 30.83750 23.47910 32.37753
## 497 27.92831 25.01115 30.84548 23.46689 32.38974
## 498 27.92831 25.00319 30.85344 23.45472 32.40191
## 499 27.92831 24.99525 30.86137 23.44259 32.41404
## 500 27.92831 24.98734 30.86929 23.43048 32.42615Untuk mendapatkan gambar hasil pemulusan pada data latih dengan
fungsi ses() , perlu digunakan fungsi
autoplot() dan autolayer() dari library
packages ggplot2 .
autoplot(ses.1) +
autolayer(fitted(ses.1), series="Fitted") +
ylab("Temperature") + xlab("Periode")
Pada fungsi ses() , terdapat beberapa argumen yang umum
digunakan, yaitu nilia y , gamma ,
beta , alpha , dan h .
Nilai y adalah nilai data deret waktu,
gamma adalah parameter pemulusan untuk komponen musiman,
beta adalah parameter pemulusan untuk tren, dan
alpha adalah parameter pemulusan untuk stasioner, serta
h adalah banyaknya periode yang akan diramalkan.
Kasus di atas merupakan contoh inisialisasi nilai parameter \(\lambda\) dengan nilai alpha
0,2 dan 0,7 dan banyak periode data yang akan diramalkan adalah sebanyak
185 periode. Selanjutnya akan digunakan fungsi
HoltWinters() dengan nilai inisialisasi parameter dan
panjang periode peramalan yang sama dengan fungsi ses()
.
#Cara 2 (fungsi Holtwinter)
ses1<- HoltWinters(train.ts, gamma = FALSE, beta = FALSE, alpha = 0.2)
plot(ses1)
#ramalan
ramalan1<- forecast(ses1, h=185)
ramalan1## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 316 28.22102 27.77843 28.66361 27.54413 28.89791
## 317 28.22102 27.76966 28.67238 27.53073 28.91131
## 318 28.22102 27.76107 28.68098 27.51758 28.92446
## 319 28.22102 27.75263 28.68942 27.50467 28.93737
## 320 28.22102 27.74433 28.69771 27.49199 28.95005
## 321 28.22102 27.73619 28.70586 27.47953 28.96251
## 322 28.22102 27.72817 28.71387 27.46727 28.97477
## 323 28.22102 27.72029 28.72176 27.45521 28.98683
## 324 28.22102 27.71252 28.72952 27.44334 28.99871
## 325 28.22102 27.70487 28.73717 27.43164 29.01040
## 326 28.22102 27.69734 28.74470 27.42012 29.02193
## 327 28.22102 27.68991 28.75213 27.40876 29.03329
## 328 28.22102 27.68258 28.75946 27.39755 29.04449
## 329 28.22102 27.67536 28.76669 27.38650 29.05554
## 330 28.22102 27.66822 28.77382 27.37559 29.06645
## 331 28.22102 27.66118 28.78086 27.36482 29.07722
## 332 28.22102 27.65423 28.78782 27.35418 29.08786
## 333 28.22102 27.64736 28.79469 27.34368 29.09837
## 334 28.22102 27.64057 28.80148 27.33329 29.10875
## 335 28.22102 27.63386 28.80819 27.32303 29.11901
## 336 28.22102 27.62722 28.81482 27.31288 29.12916
## 337 28.22102 27.62066 28.82138 27.30285 29.13920
## 338 28.22102 27.61417 28.82787 27.29292 29.14912
## 339 28.22102 27.60775 28.83430 27.28310 29.15894
## 340 28.22102 27.60139 28.84065 27.27338 29.16866
## 341 28.22102 27.59510 28.84694 27.26376 29.17828
## 342 28.22102 27.58887 28.85317 27.25423 29.18781
## 343 28.22102 27.58271 28.85934 27.24480 29.19724
## 344 28.22102 27.57660 28.86545 27.23546 29.20658
## 345 28.22102 27.57055 28.87150 27.22620 29.21584
## 346 28.22102 27.56455 28.87749 27.21704 29.22501
## 347 28.22102 27.55861 28.88343 27.20795 29.23409
## 348 28.22102 27.55272 28.88932 27.19894 29.24310
## 349 28.22102 27.54688 28.89516 27.19002 29.25203
## 350 28.22102 27.54110 28.90095 27.18117 29.26088
## 351 28.22102 27.53536 28.90668 27.17239 29.26965
## 352 28.22102 27.52967 28.91237 27.16369 29.27835
## 353 28.22102 27.52403 28.91802 27.15506 29.28698
## 354 28.22102 27.51843 28.92362 27.14650 29.29555
## 355 28.22102 27.51287 28.92917 27.13800 29.30404
## 356 28.22102 27.50736 28.93468 27.12957 29.31247
## 357 28.22102 27.50189 28.94015 27.12121 29.32083
## 358 28.22102 27.49647 28.94558 27.11291 29.32913
## 359 28.22102 27.49108 28.95096 27.10467 29.33737
## 360 28.22102 27.48573 28.95631 27.09649 29.34555
## 361 28.22102 27.48042 28.96162 27.08837 29.35367
## 362 28.22102 27.47515 28.96689 27.08031 29.36173
## 363 28.22102 27.46992 28.97213 27.07231 29.36974
## 364 28.22102 27.46472 28.97732 27.06436 29.37769
## 365 28.22102 27.45956 28.98249 27.05646 29.38558
## 366 28.22102 27.45443 28.98761 27.04862 29.39342
## 367 28.22102 27.44933 28.99271 27.04083 29.40121
## 368 28.22102 27.44427 28.99777 27.03309 29.40895
## 369 28.22102 27.43925 29.00280 27.02540 29.41664
## 370 28.22102 27.43425 29.00779 27.01776 29.42428
## 371 28.22102 27.42929 29.01276 27.01017 29.43187
## 372 28.22102 27.42435 29.01769 27.00262 29.43942
## 373 28.22102 27.41945 29.02259 26.99513 29.44692
## 374 28.22102 27.41458 29.02746 26.98767 29.45437
## 375 28.22102 27.40974 29.03231 26.98027 29.46178
## 376 28.22102 27.40492 29.03712 26.97290 29.46914
## 377 28.22102 27.40013 29.04191 26.96558 29.47646
## 378 28.22102 27.39538 29.04667 26.95830 29.48374
## 379 28.22102 27.39064 29.05140 26.95107 29.49097
## 380 28.22102 27.38594 29.05610 26.94387 29.49817
## 381 28.22102 27.38126 29.06078 26.93672 29.50532
## 382 28.22102 27.37661 29.06543 26.92960 29.51244
## 383 28.22102 27.37198 29.07006 26.92253 29.51952
## 384 28.22102 27.36738 29.07466 26.91549 29.52655
## 385 28.22102 27.36280 29.07924 26.90849 29.53355
## 386 28.22102 27.35825 29.08379 26.90153 29.54052
## 387 28.22102 27.35372 29.08832 26.89460 29.54744
## 388 28.22102 27.34921 29.09283 26.88771 29.55433
## 389 28.22102 27.34473 29.09731 26.88085 29.56119
## 390 28.22102 27.34027 29.10177 26.87403 29.56801
## 391 28.22102 27.33584 29.10621 26.86725 29.57480
## 392 28.22102 27.33142 29.11062 26.86050 29.58155
## 393 28.22102 27.32703 29.11502 26.85378 29.58827
## 394 28.22102 27.32266 29.11939 26.84709 29.59495
## 395 28.22102 27.31831 29.12374 26.84044 29.60161
## 396 28.22102 27.31398 29.12807 26.83382 29.60823
## 397 28.22102 27.30967 29.13238 26.82723 29.61482
## 398 28.22102 27.30538 29.13666 26.82067 29.62138
## 399 28.22102 27.30111 29.14093 26.81414 29.62791
## 400 28.22102 27.29686 29.14518 26.80764 29.63440
## 401 28.22102 27.29263 29.14941 26.80117 29.64087
## 402 28.22102 27.28842 29.15362 26.79473 29.64731
## 403 28.22102 27.28423 29.15781 26.78832 29.65372
## 404 28.22102 27.28006 29.16199 26.78194 29.66010
## 405 28.22102 27.27590 29.16614 26.77559 29.66646
## 406 28.22102 27.27177 29.17028 26.76926 29.67278
## 407 28.22102 27.26765 29.17440 26.76296 29.67908
## 408 28.22102 27.26355 29.17850 26.75669 29.68535
## 409 28.22102 27.25946 29.18258 26.75045 29.69160
## 410 28.22102 27.25540 29.18665 26.74423 29.69782
## 411 28.22102 27.25135 29.19069 26.73804 29.70401
## 412 28.22102 27.24732 29.19473 26.73187 29.71017
## 413 28.22102 27.24330 29.19874 26.72573 29.71631
## 414 28.22102 27.23930 29.20274 26.71961 29.72243
## 415 28.22102 27.23532 29.20672 26.71352 29.72852
## 416 28.22102 27.23135 29.21069 26.70746 29.73459
## 417 28.22102 27.22740 29.21464 26.70141 29.74063
## 418 28.22102 27.22347 29.21858 26.69540 29.74665
## 419 28.22102 27.21955 29.22249 26.68940 29.75264
## 420 28.22102 27.21564 29.22640 26.68343 29.75861
## 421 28.22102 27.21175 29.23029 26.67748 29.76456
## 422 28.22102 27.20788 29.23416 26.67156 29.77049
## 423 28.22102 27.20402 29.23802 26.66565 29.77639
## 424 28.22102 27.20018 29.24187 26.65977 29.78227
## 425 28.22102 27.19635 29.24570 26.65391 29.78813
## 426 28.22102 27.19253 29.24951 26.64808 29.79397
## 427 28.22102 27.18873 29.25332 26.64226 29.79978
## 428 28.22102 27.18494 29.25710 26.63647 29.80557
## 429 28.22102 27.18116 29.26088 26.63070 29.81135
## 430 28.22102 27.17740 29.26464 26.62494 29.81710
## 431 28.22102 27.17366 29.26839 26.61921 29.82283
## 432 28.22102 27.16992 29.27212 26.61350 29.82854
## 433 28.22102 27.16620 29.27584 26.60781 29.83423
## 434 28.22102 27.16249 29.27955 26.60214 29.83990
## 435 28.22102 27.15880 29.28324 26.59649 29.84555
## 436 28.22102 27.15512 29.28693 26.59086 29.85118
## 437 28.22102 27.15145 29.29060 26.58525 29.85679
## 438 28.22102 27.14779 29.29425 26.57966 29.86239
## 439 28.22102 27.14415 29.29790 26.57408 29.86796
## 440 28.22102 27.14051 29.30153 26.56853 29.87351
## 441 28.22102 27.13690 29.30515 26.56299 29.87905
## 442 28.22102 27.13329 29.30876 26.55748 29.88457
## 443 28.22102 27.12969 29.31235 26.55198 29.89007
## 444 28.22102 27.12611 29.31594 26.54649 29.89555
## 445 28.22102 27.12254 29.31951 26.54103 29.90101
## 446 28.22102 27.11897 29.32307 26.53559 29.90646
## 447 28.22102 27.11543 29.32662 26.53016 29.91189
## 448 28.22102 27.11189 29.33016 26.52475 29.91730
## 449 28.22102 27.10836 29.33368 26.51935 29.92269
## 450 28.22102 27.10485 29.33720 26.51398 29.92807
## 451 28.22102 27.10134 29.34070 26.50862 29.93343
## 452 28.22102 27.09785 29.34420 26.50327 29.93877
## 453 28.22102 27.09436 29.34768 26.49795 29.94410
## 454 28.22102 27.09089 29.35115 26.49264 29.94941
## 455 28.22102 27.08743 29.35461 26.48734 29.95470
## 456 28.22102 27.08398 29.35806 26.48207 29.95998
## 457 28.22102 27.08054 29.36150 26.47681 29.96524
## 458 28.22102 27.07711 29.36493 26.47156 29.97048
## 459 28.22102 27.07369 29.36835 26.46633 29.97571
## 460 28.22102 27.07028 29.37176 26.46111 29.98093
## 461 28.22102 27.06688 29.37516 26.45592 29.98613
## 462 28.22102 27.06349 29.37855 26.45073 29.99131
## 463 28.22102 27.06011 29.38193 26.44556 29.99648
## 464 28.22102 27.05674 29.38530 26.44041 30.00163
## 465 28.22102 27.05338 29.38866 26.43527 30.00677
## 466 28.22102 27.05003 29.39201 26.43015 30.01190
## 467 28.22102 27.04669 29.39535 26.42504 30.01701
## 468 28.22102 27.04336 29.39868 26.41994 30.02210
## 469 28.22102 27.04004 29.40201 26.41486 30.02718
## 470 28.22102 27.03672 29.40532 26.40979 30.03225
## 471 28.22102 27.03342 29.40862 26.40474 30.03730
## 472 28.22102 27.03013 29.41192 26.39970 30.04234
## 473 28.22102 27.02684 29.41520 26.39468 30.04736
## 474 28.22102 27.02356 29.41848 26.38967 30.05237
## 475 28.22102 27.02030 29.42175 26.38467 30.05737
## 476 28.22102 27.01704 29.42500 26.37969 30.06235
## 477 28.22102 27.01379 29.42825 26.37472 30.06732
## 478 28.22102 27.01055 29.43149 26.36976 30.07228
## 479 28.22102 27.00732 29.43473 26.36482 30.07722
## 480 28.22102 27.00409 29.43795 26.35989 30.08215
## 481 28.22102 27.00088 29.44117 26.35497 30.08707
## 482 28.22102 26.99767 29.44437 26.35007 30.09198
## 483 28.22102 26.99447 29.44757 26.34518 30.09687
## 484 28.22102 26.99128 29.45076 26.34030 30.10175
## 485 28.22102 26.98810 29.45394 26.33543 30.10661
## 486 28.22102 26.98493 29.45712 26.33058 30.11146
## 487 28.22102 26.98176 29.46028 26.32574 30.11631
## 488 28.22102 26.97860 29.46344 26.32091 30.12113
## 489 28.22102 26.97546 29.46659 26.31609 30.12595
## 490 28.22102 26.97231 29.46973 26.31129 30.13076
## 491 28.22102 26.96918 29.47286 26.30650 30.13555
## 492 28.22102 26.96605 29.47599 26.30171 30.14033
## 493 28.22102 26.96294 29.47911 26.29695 30.14510
## 494 28.22102 26.95983 29.48222 26.29219 30.14985
## 495 28.22102 26.95672 29.48532 26.28744 30.15460
## 496 28.22102 26.95363 29.48841 26.28271 30.15933
## 497 28.22102 26.95054 29.49150 26.27799 30.16405
## 498 28.22102 26.94746 29.49458 26.27328 30.16876
## 499 28.22102 26.94439 29.49765 26.26858 30.17346
## 500 28.22102 26.94132 29.50072 26.26389 30.17815ses2<- HoltWinters(train.ts, gamma = FALSE, beta = FALSE, alpha = 0.7)
plot(ses2)
#ramalan
ramalan2<- forecast(ses2, h=185)
ramalan2## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 316 27.92831 27.62036 28.23627 27.45733 28.39930
## 317 27.92831 27.55240 28.30423 27.35341 28.50322
## 318 27.92831 27.49498 28.36165 27.26558 28.59105
## 319 27.92831 27.44432 28.41231 27.18811 28.66852
## 320 27.92831 27.39848 28.45815 27.11801 28.73862
## 321 27.92831 27.35631 28.50032 27.05350 28.80313
## 322 27.92831 27.31703 28.53960 26.99344 28.86319
## 323 27.92831 27.28014 28.57649 26.93701 28.91962
## 324 27.92831 27.24523 28.61140 26.88363 28.97300
## 325 27.92831 27.21202 28.64461 26.83284 29.02379
## 326 27.92831 27.18029 28.67634 26.78430 29.07233
## 327 27.92831 27.14984 28.70679 26.73774 29.11888
## 328 27.92831 27.12055 28.73608 26.69294 29.16369
## 329 27.92831 27.09228 28.76435 26.64970 29.20693
## 330 27.92831 27.06493 28.79170 26.60788 29.24875
## 331 27.92831 27.03843 28.81820 26.56735 29.28928
## 332 27.92831 27.01269 28.84394 26.52798 29.32865
## 333 27.92831 26.98765 28.86898 26.48970 29.36693
## 334 27.92831 26.96327 28.89336 26.45240 29.40423
## 335 27.92831 26.93948 28.91715 26.41603 29.44060
## 336 27.92831 26.91626 28.94037 26.38051 29.47612
## 337 27.92831 26.89356 28.96307 26.34579 29.51084
## 338 27.92831 26.87134 28.98529 26.31181 29.54482
## 339 27.92831 26.84958 29.00705 26.27853 29.57810
## 340 27.92831 26.82825 29.02838 26.24591 29.61072
## 341 27.92831 26.80733 29.04930 26.21391 29.64272
## 342 27.92831 26.78679 29.06984 26.18250 29.67413
## 343 27.92831 26.76661 29.09002 26.15164 29.70499
## 344 27.92831 26.74678 29.10985 26.12131 29.73532
## 345 27.92831 26.72728 29.12935 26.09148 29.76515
## 346 27.92831 26.70808 29.14855 26.06213 29.79450
## 347 27.92831 26.68919 29.16744 26.03323 29.82340
## 348 27.92831 26.67058 29.18605 26.00477 29.85186
## 349 27.92831 26.65224 29.20439 25.97672 29.87991
## 350 27.92831 26.63416 29.22247 25.94907 29.90756
## 351 27.92831 26.61632 29.24031 25.92180 29.93483
## 352 27.92831 26.59873 29.25790 25.89489 29.96174
## 353 27.92831 26.58137 29.27526 25.86834 29.98829
## 354 27.92831 26.56423 29.29240 25.84212 30.01451
## 355 27.92831 26.54730 29.30933 25.81623 30.04040
## 356 27.92831 26.53058 29.32605 25.79066 30.06597
## 357 27.92831 26.51405 29.34258 25.76538 30.09125
## 358 27.92831 26.49771 29.35891 25.74040 30.11623
## 359 27.92831 26.48156 29.37507 25.71570 30.14093
## 360 27.92831 26.46559 29.39104 25.69127 30.16536
## 361 27.92831 26.44979 29.40684 25.66711 30.18952
## 362 27.92831 26.43416 29.42247 25.64320 30.21343
## 363 27.92831 26.41869 29.43794 25.61954 30.23709
## 364 27.92831 26.40337 29.45325 25.59612 30.26051
## 365 27.92831 26.38821 29.46842 25.57293 30.28370
## 366 27.92831 26.37320 29.48343 25.54997 30.30666
## 367 27.92831 26.35833 29.49830 25.52723 30.32940
## 368 27.92831 26.34360 29.51303 25.50470 30.35193
## 369 27.92831 26.32900 29.52763 25.48238 30.37425
## 370 27.92831 26.31454 29.54209 25.46026 30.39637
## 371 27.92831 26.30021 29.55642 25.43834 30.41829
## 372 27.92831 26.28600 29.57063 25.41661 30.44002
## 373 27.92831 26.27191 29.58472 25.39506 30.46157
## 374 27.92831 26.25794 29.59869 25.37370 30.48293
## 375 27.92831 26.24409 29.61254 25.35251 30.50412
## 376 27.92831 26.23035 29.62628 25.33150 30.52513
## 377 27.92831 26.21672 29.63991 25.31065 30.54598
## 378 27.92831 26.20320 29.65343 25.28997 30.56666
## 379 27.92831 26.18978 29.66685 25.26945 30.58718
## 380 27.92831 26.17647 29.68016 25.24909 30.60754
## 381 27.92831 26.16325 29.69338 25.22888 30.62775
## 382 27.92831 26.15014 29.70649 25.20883 30.64780
## 383 27.92831 26.13712 29.71951 25.18891 30.66772
## 384 27.92831 26.12419 29.73244 25.16915 30.68748
## 385 27.92831 26.11136 29.74527 25.14952 30.70711
## 386 27.92831 26.09861 29.75801 25.13003 30.72660
## 387 27.92831 26.08596 29.77067 25.11068 30.74595
## 388 27.92831 26.07339 29.78324 25.09145 30.76518
## 389 27.92831 26.06091 29.79572 25.07236 30.78427
## 390 27.92831 26.04850 29.80812 25.05339 30.80324
## 391 27.92831 26.03618 29.82044 25.03455 30.82208
## 392 27.92831 26.02394 29.83269 25.01583 30.84080
## 393 27.92831 26.01178 29.84485 24.99723 30.85940
## 394 27.92831 25.99970 29.85693 24.97875 30.87788
## 395 27.92831 25.98769 29.86894 24.96038 30.89625
## 396 27.92831 25.97575 29.88088 24.94212 30.91451
## 397 27.92831 25.96389 29.89274 24.92398 30.93265
## 398 27.92831 25.95209 29.90454 24.90594 30.95069
## 399 27.92831 25.94037 29.91626 24.88802 30.96861
## 400 27.92831 25.92872 29.92791 24.87019 30.98644
## 401 27.92831 25.91713 29.93950 24.85247 31.00416
## 402 27.92831 25.90561 29.95102 24.83485 31.02178
## 403 27.92831 25.89415 29.96247 24.81734 31.03929
## 404 27.92831 25.88276 29.97387 24.79991 31.05671
## 405 27.92831 25.87144 29.98519 24.78259 31.07404
## 406 27.92831 25.86017 29.99646 24.76536 31.09127
## 407 27.92831 25.84897 30.00766 24.74823 31.10840
## 408 27.92831 25.83782 30.01881 24.73118 31.12545
## 409 27.92831 25.82674 30.02989 24.71423 31.14240
## 410 27.92831 25.81571 30.04092 24.69736 31.15927
## 411 27.92831 25.80474 30.05189 24.68059 31.17604
## 412 27.92831 25.79383 30.06280 24.66390 31.19273
## 413 27.92831 25.78297 30.07366 24.64729 31.20934
## 414 27.92831 25.77216 30.08447 24.63077 31.22586
## 415 27.92831 25.76141 30.09522 24.61433 31.24230
## 416 27.92831 25.75072 30.10591 24.59797 31.25866
## 417 27.92831 25.74007 30.11656 24.58169 31.27494
## 418 27.92831 25.72948 30.12715 24.56549 31.29114
## 419 27.92831 25.71894 30.13769 24.54937 31.30726
## 420 27.92831 25.70845 30.14818 24.53332 31.32331
## 421 27.92831 25.69800 30.15862 24.51735 31.33928
## 422 27.92831 25.68761 30.16902 24.50145 31.35518
## 423 27.92831 25.67727 30.17936 24.48563 31.37100
## 424 27.92831 25.66697 30.18966 24.46988 31.38675
## 425 27.92831 25.65671 30.19991 24.45420 31.40243
## 426 27.92831 25.64651 30.21012 24.43859 31.41804
## 427 27.92831 25.63635 30.22028 24.42306 31.43357
## 428 27.92831 25.62623 30.23040 24.40758 31.44904
## 429 27.92831 25.61616 30.24047 24.39218 31.46445
## 430 27.92831 25.60613 30.25049 24.37685 31.47978
## 431 27.92831 25.59615 30.26048 24.36158 31.49505
## 432 27.92831 25.58621 30.27042 24.34637 31.51026
## 433 27.92831 25.57631 30.28032 24.33123 31.52540
## 434 27.92831 25.56645 30.29018 24.31615 31.54047
## 435 27.92831 25.55663 30.30000 24.30114 31.55549
## 436 27.92831 25.54686 30.30977 24.28619 31.57044
## 437 27.92831 25.53712 30.31951 24.27130 31.58533
## 438 27.92831 25.52742 30.32921 24.25647 31.60016
## 439 27.92831 25.51776 30.33887 24.24169 31.61494
## 440 27.92831 25.50814 30.34849 24.22698 31.62965
## 441 27.92831 25.49856 30.35807 24.21233 31.64430
## 442 27.92831 25.48902 30.36761 24.19773 31.65890
## 443 27.92831 25.47951 30.37712 24.18319 31.67344
## 444 27.92831 25.47004 30.38659 24.16871 31.68792
## 445 27.92831 25.46061 30.39602 24.15428 31.70235
## 446 27.92831 25.45121 30.40542 24.13991 31.71672
## 447 27.92831 25.44185 30.41478 24.12559 31.73104
## 448 27.92831 25.43252 30.42411 24.11132 31.74531
## 449 27.92831 25.42323 30.43340 24.09711 31.75952
## 450 27.92831 25.41397 30.44266 24.08295 31.77368
## 451 27.92831 25.40474 30.45189 24.06885 31.78778
## 452 27.92831 25.39555 30.46108 24.05479 31.80184
## 453 27.92831 25.38640 30.47023 24.04079 31.81584
## 454 27.92831 25.37727 30.47936 24.02683 31.82980
## 455 27.92831 25.36818 30.48845 24.01293 31.84370
## 456 27.92831 25.35912 30.49751 23.99907 31.85756
## 457 27.92831 25.35009 30.50654 23.98526 31.87137
## 458 27.92831 25.34110 30.51553 23.97150 31.88513
## 459 27.92831 25.33213 30.52450 23.95779 31.89884
## 460 27.92831 25.32320 30.53343 23.94413 31.91250
## 461 27.92831 25.31429 30.54234 23.93051 31.92612
## 462 27.92831 25.30542 30.55121 23.91694 31.93969
## 463 27.92831 25.29657 30.56006 23.90341 31.95322
## 464 27.92831 25.28776 30.56887 23.88993 31.96670
## 465 27.92831 25.27897 30.57765 23.87650 31.98013
## 466 27.92831 25.27022 30.58641 23.86311 31.99352
## 467 27.92831 25.26149 30.59514 23.84976 32.00687
## 468 27.92831 25.25279 30.60384 23.83646 32.02017
## 469 27.92831 25.24412 30.61251 23.82320 32.03343
## 470 27.92831 25.23548 30.62115 23.80998 32.04665
## 471 27.92831 25.22687 30.62976 23.79680 32.05982
## 472 27.92831 25.21828 30.63835 23.78367 32.07296
## 473 27.92831 25.20972 30.64691 23.77058 32.08605
## 474 27.92831 25.20118 30.65545 23.75753 32.09910
## 475 27.92831 25.19268 30.66395 23.74452 32.11211
## 476 27.92831 25.18420 30.67243 23.73155 32.12508
## 477 27.92831 25.17574 30.68089 23.71862 32.13801
## 478 27.92831 25.16731 30.68932 23.70573 32.15090
## 479 27.92831 25.15891 30.69772 23.69288 32.16375
## 480 27.92831 25.15053 30.70610 23.68007 32.17656
## 481 27.92831 25.14218 30.71445 23.66729 32.18934
## 482 27.92831 25.13385 30.72277 23.65456 32.20207
## 483 27.92831 25.12555 30.73108 23.64186 32.21477
## 484 27.92831 25.11727 30.73936 23.62920 32.22743
## 485 27.92831 25.10902 30.74761 23.61658 32.24005
## 486 27.92831 25.10079 30.75584 23.60399 32.25264
## 487 27.92831 25.09259 30.76404 23.59144 32.26519
## 488 27.92831 25.08440 30.77223 23.57893 32.27770
## 489 27.92831 25.07624 30.78038 23.56645 32.29018
## 490 27.92831 25.06811 30.78852 23.55401 32.30262
## 491 27.92831 25.06000 30.79663 23.54160 32.31503
## 492 27.92831 25.05191 30.80472 23.52923 32.32740
## 493 27.92831 25.04384 30.81279 23.51689 32.33974
## 494 27.92831 25.03580 30.82083 23.50459 32.35204
## 495 27.92831 25.02778 30.82885 23.49232 32.36431
## 496 27.92831 25.01978 30.83685 23.48009 32.37654
## 497 27.92831 25.01180 30.84483 23.46789 32.38874
## 498 27.92831 25.00384 30.85279 23.45572 32.40091
## 499 27.92831 24.99591 30.86072 23.44358 32.41304
## 500 27.92831 24.98799 30.86864 23.43148 32.42515Nilai parameter \(\alpha\) dari
kedua fungsi dapat dioptimalkan menyesuaikan dari error-nya
paling minimumnya. Caranya adalah dengan membuat parameter \(\alpha =\) NULL .
#SES
ses.opt <- ses(train.ts, h = 185, alpha = NULL)
plot(ses.opt)
ses.opt## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 316 27.8931 27.59752 28.18868 27.44105 28.34515
## 317 27.8931 27.47511 28.31109 27.25383 28.53237
## 318 27.8931 27.38117 28.40503 27.11017 28.67602
## 319 27.8931 27.30198 28.48422 26.98906 28.79714
## 320 27.8931 27.23221 28.55399 26.88236 28.90384
## 321 27.8931 27.16914 28.61706 26.78590 29.00030
## 322 27.8931 27.11113 28.67507 26.69719 29.08901
## 323 27.8931 27.05714 28.72906 26.61462 29.17158
## 324 27.8931 27.00644 28.77976 26.53707 29.24913
## 325 27.8931 26.95848 28.82772 26.46372 29.32248
## 326 27.8931 26.91286 28.87334 26.39395 29.39225
## 327 27.8931 26.86927 28.91693 26.32729 29.45891
## 328 27.8931 26.82747 28.95873 26.26335 29.52284
## 329 27.8931 26.78724 28.99896 26.20183 29.58437
## 330 27.8931 26.74843 29.03777 26.14247 29.64372
## 331 27.8931 26.71089 29.07531 26.08506 29.70114
## 332 27.8931 26.67450 29.11170 26.02942 29.75678
## 333 27.8931 26.63918 29.14702 25.97539 29.81081
## 334 27.8931 26.60482 29.18138 25.92284 29.86336
## 335 27.8931 26.57135 29.21485 25.87166 29.91454
## 336 27.8931 26.53871 29.24749 25.82174 29.96446
## 337 27.8931 26.50684 29.27936 25.77299 30.01321
## 338 27.8931 26.47568 29.31052 25.72534 30.06086
## 339 27.8931 26.44519 29.34100 25.67872 30.10748
## 340 27.8931 26.41534 29.37086 25.63306 30.15314
## 341 27.8931 26.38607 29.40013 25.58830 30.19790
## 342 27.8931 26.35737 29.42883 25.54440 30.24180
## 343 27.8931 26.32918 29.45701 25.50130 30.28490
## 344 27.8931 26.30150 29.48470 25.45896 30.32724
## 345 27.8931 26.27429 29.51191 25.41735 30.36885
## 346 27.8931 26.24754 29.53866 25.37643 30.40977
## 347 27.8931 26.22120 29.56499 25.33616 30.45004
## 348 27.8931 26.19528 29.59092 25.29651 30.48969
## 349 27.8931 26.16975 29.61645 25.25746 30.52874
## 350 27.8931 26.14459 29.64161 25.21899 30.56721
## 351 27.8931 26.11979 29.66641 25.18105 30.60515
## 352 27.8931 26.09533 29.69087 25.14364 30.64255
## 353 27.8931 26.07120 29.71500 25.10674 30.67946
## 354 27.8931 26.04738 29.73882 25.07031 30.71589
## 355 27.8931 26.02387 29.76233 25.03435 30.75185
## 356 27.8931 26.00064 29.78555 24.99884 30.78736
## 357 27.8931 25.97770 29.80849 24.96376 30.82244
## 358 27.8931 25.95504 29.83116 24.92909 30.85711
## 359 27.8931 25.93263 29.85357 24.89482 30.89138
## 360 27.8931 25.91048 29.87572 24.86094 30.92526
## 361 27.8931 25.88857 29.89763 24.82744 30.95876
## 362 27.8931 25.86690 29.91930 24.79429 30.99191
## 363 27.8931 25.84546 29.94074 24.76150 31.02470
## 364 27.8931 25.82424 29.96196 24.72905 31.05715
## 365 27.8931 25.80323 29.98297 24.69693 31.08927
## 366 27.8931 25.78244 30.00376 24.66512 31.12108
## 367 27.8931 25.76185 30.02435 24.63363 31.15257
## 368 27.8931 25.74145 30.04475 24.60244 31.18376
## 369 27.8931 25.72125 30.06495 24.57154 31.21466
## 370 27.8931 25.70123 30.08497 24.54092 31.24528
## 371 27.8931 25.68139 30.10481 24.51059 31.27561
## 372 27.8931 25.66173 30.12447 24.48052 31.30568
## 373 27.8931 25.64225 30.14395 24.45072 31.33548
## 374 27.8931 25.62292 30.16327 24.42117 31.36503
## 375 27.8931 25.60377 30.18243 24.39187 31.39433
## 376 27.8931 25.58477 30.20143 24.36281 31.42339
## 377 27.8931 25.56592 30.22028 24.33399 31.45221
## 378 27.8931 25.54723 30.23897 24.30540 31.48080
## 379 27.8931 25.52869 30.25751 24.27704 31.50916
## 380 27.8931 25.51029 30.27591 24.24890 31.53730
## 381 27.8931 25.49203 30.29417 24.22098 31.56522
## 382 27.8931 25.47391 30.31229 24.19326 31.59294
## 383 27.8931 25.45592 30.33028 24.16575 31.62045
## 384 27.8931 25.43806 30.34814 24.13845 31.64775
## 385 27.8931 25.42034 30.36586 24.11134 31.67486
## 386 27.8931 25.40274 30.38346 24.08442 31.70178
## 387 27.8931 25.38526 30.40094 24.05769 31.72851
## 388 27.8931 25.36791 30.41829 24.03115 31.75505
## 389 27.8931 25.35067 30.43553 24.00479 31.78141
## 390 27.8931 25.33355 30.45265 23.97860 31.80760
## 391 27.8931 25.31654 30.46966 23.95259 31.83361
## 392 27.8931 25.29965 30.48655 23.92675 31.85945
## 393 27.8931 25.28286 30.50334 23.90108 31.88512
## 394 27.8931 25.26618 30.52002 23.87557 31.91063
## 395 27.8931 25.24961 30.53659 23.85023 31.93597
## 396 27.8931 25.23314 30.55306 23.82504 31.96116
## 397 27.8931 25.21677 30.56943 23.80000 31.98620
## 398 27.8931 25.20050 30.58570 23.77512 32.01108
## 399 27.8931 25.18433 30.60187 23.75039 32.03581
## 400 27.8931 25.16825 30.61795 23.72580 32.06040
## 401 27.8931 25.15227 30.63393 23.70136 32.08484
## 402 27.8931 25.13638 30.64982 23.67706 32.10914
## 403 27.8931 25.12058 30.66562 23.65290 32.13330
## 404 27.8931 25.10487 30.68133 23.62887 32.15732
## 405 27.8931 25.08925 30.69695 23.60499 32.18121
## 406 27.8931 25.07372 30.71248 23.58123 32.20497
## 407 27.8931 25.05827 30.72793 23.55760 32.22860
## 408 27.8931 25.04290 30.74329 23.53410 32.25210
## 409 27.8931 25.02762 30.75858 23.51073 32.27547
## 410 27.8931 25.01242 30.77378 23.48748 32.29872
## 411 27.8931 24.99730 30.78890 23.46435 32.32184
## 412 27.8931 24.98226 30.80394 23.44135 32.34485
## 413 27.8931 24.96729 30.81891 23.41846 32.36774
## 414 27.8931 24.95240 30.83380 23.39569 32.39051
## 415 27.8931 24.93759 30.84861 23.37303 32.41317
## 416 27.8931 24.92284 30.86335 23.35049 32.43571
## 417 27.8931 24.90818 30.87802 23.32805 32.45815
## 418 27.8931 24.89358 30.89262 23.30573 32.48047
## 419 27.8931 24.87906 30.90714 23.28352 32.50268
## 420 27.8931 24.86460 30.92160 23.26141 32.52479
## 421 27.8931 24.85021 30.93599 23.23940 32.54679
## 422 27.8931 24.83589 30.95031 23.21750 32.56869
## 423 27.8931 24.82164 30.96456 23.19571 32.59049
## 424 27.8931 24.80745 30.97875 23.17401 32.61219
## 425 27.8931 24.79333 30.99287 23.15241 32.63379
## 426 27.8931 24.77927 31.00693 23.13091 32.65529
## 427 27.8931 24.76528 31.02092 23.10951 32.67669
## 428 27.8931 24.75135 31.03485 23.08820 32.69800
## 429 27.8931 24.73747 31.04872 23.06699 32.71921
## 430 27.8931 24.72366 31.06253 23.04587 32.74033
## 431 27.8931 24.70991 31.07629 23.02484 32.76136
## 432 27.8931 24.69622 31.08998 23.00390 32.78230
## 433 27.8931 24.68259 31.10361 22.98305 32.80315
## 434 27.8931 24.66901 31.11718 22.96229 32.82391
## 435 27.8931 24.65550 31.13070 22.94161 32.84459
## 436 27.8931 24.64203 31.14416 22.92102 32.86517
## 437 27.8931 24.62863 31.15757 22.90052 32.88568
## 438 27.8931 24.61528 31.17092 22.88010 32.90610
## 439 27.8931 24.60198 31.18422 22.85977 32.92643
## 440 27.8931 24.58874 31.19746 22.83951 32.94669
## 441 27.8931 24.57554 31.21066 22.81934 32.96686
## 442 27.8931 24.56241 31.22379 22.79924 32.98696
## 443 27.8931 24.54932 31.23688 22.77923 33.00697
## 444 27.8931 24.53628 31.24992 22.75929 33.02691
## 445 27.8931 24.52330 31.26290 22.73943 33.04677
## 446 27.8931 24.51036 31.27584 22.71965 33.06655
## 447 27.8931 24.49747 31.28873 22.69994 33.08626
## 448 27.8931 24.48464 31.30156 22.68030 33.10590
## 449 27.8931 24.47185 31.31435 22.66074 33.12546
## 450 27.8931 24.45910 31.32710 22.64126 33.14494
## 451 27.8931 24.44641 31.33979 22.62184 33.16436
## 452 27.8931 24.43376 31.35244 22.60250 33.18370
## 453 27.8931 24.42116 31.36504 22.58322 33.20298
## 454 27.8931 24.40860 31.37760 22.56402 33.22218
## 455 27.8931 24.39609 31.39011 22.54488 33.24132
## 456 27.8931 24.38362 31.40258 22.52582 33.26038
## 457 27.8931 24.37120 31.41500 22.50682 33.27938
## 458 27.8931 24.35882 31.42738 22.48789 33.29831
## 459 27.8931 24.34648 31.43972 22.46902 33.31718
## 460 27.8931 24.33419 31.45201 22.45022 33.33598
## 461 27.8931 24.32194 31.46426 22.43148 33.35472
## 462 27.8931 24.30973 31.47647 22.41281 33.37339
## 463 27.8931 24.29756 31.48864 22.39420 33.39200
## 464 27.8931 24.28544 31.50076 22.37565 33.41054
## 465 27.8931 24.27335 31.51285 22.35717 33.42903
## 466 27.8931 24.26130 31.52489 22.33875 33.44745
## 467 27.8931 24.24930 31.53690 22.32039 33.46581
## 468 27.8931 24.23733 31.54887 22.30209 33.48411
## 469 27.8931 24.22540 31.56079 22.28384 33.50236
## 470 27.8931 24.21352 31.57268 22.26566 33.52054
## 471 27.8931 24.20167 31.58453 22.24754 33.53866
## 472 27.8931 24.18985 31.59635 22.22947 33.55673
## 473 27.8931 24.17808 31.60812 22.21146 33.57474
## 474 27.8931 24.16634 31.61986 22.19351 33.59269
## 475 27.8931 24.15464 31.63156 22.17562 33.61058
## 476 27.8931 24.14297 31.64323 22.15778 33.62842
## 477 27.8931 24.13135 31.65485 22.13999 33.64621
## 478 27.8931 24.11975 31.66645 22.12226 33.66393
## 479 27.8931 24.10820 31.67800 22.10459 33.68161
## 480 27.8931 24.09667 31.68952 22.08697 33.69923
## 481 27.8931 24.08519 31.70101 22.06940 33.71680
## 482 27.8931 24.07374 31.71246 22.05189 33.73431
## 483 27.8931 24.06232 31.72388 22.03442 33.75178
## 484 27.8931 24.05093 31.73527 22.01701 33.76919
## 485 27.8931 24.03958 31.74662 21.99965 33.78655
## 486 27.8931 24.02827 31.75793 21.98235 33.80385
## 487 27.8931 24.01698 31.76922 21.96509 33.82111
## 488 27.8931 24.00573 31.78047 21.94788 33.83832
## 489 27.8931 23.99451 31.79169 21.93072 33.85548
## 490 27.8931 23.98332 31.80288 21.91361 33.87259
## 491 27.8931 23.97217 31.81403 21.89655 33.88965
## 492 27.8931 23.96105 31.82515 21.87954 33.90666
## 493 27.8931 23.94995 31.83625 21.86258 33.92362
## 494 27.8931 23.93889 31.84731 21.84566 33.94054
## 495 27.8931 23.92786 31.85834 21.82879 33.95741
## 496 27.8931 23.91686 31.86934 21.81197 33.97423
## 497 27.8931 23.90590 31.88030 21.79520 33.99100
## 498 27.8931 23.89496 31.89124 21.77847 34.00773
## 499 27.8931 23.88405 31.90215 21.76178 34.02442
## 500 27.8931 23.87317 31.91303 21.74514 34.04105#Lamda Optimum Holt Winter
sesopt<- HoltWinters(train.ts, gamma = FALSE, beta = FALSE,alpha = NULL)
sesopt## Holt-Winters exponential smoothing without trend and without seasonal component.
##
## Call:
## HoltWinters(x = train.ts, alpha = NULL, beta = FALSE, gamma = FALSE)
##
## Smoothing parameters:
## alpha: 0.9999261
## beta : FALSE
## gamma: FALSE
##
## Coefficients:
## [,1]
## a 27.8931plot(sesopt)
#ramalan
ramalanopt<- forecast(sesopt, h=185)
ramalanopt## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 316 27.8931 27.59759 28.18861 27.44116 28.34504
## 317 27.8931 27.47521 28.31099 27.25399 28.53221
## 318 27.8931 27.38129 28.40491 27.11036 28.67584
## 319 27.8931 27.30212 28.48408 26.98927 28.79693
## 320 27.8931 27.23237 28.55383 26.88260 28.90360
## 321 27.8931 27.16930 28.61690 26.78615 29.00005
## 322 27.8931 27.11131 28.67489 26.69746 29.08874
## 323 27.8931 27.05734 28.72886 26.61491 29.17129
## 324 27.8931 27.00664 28.77956 26.53737 29.24882
## 325 27.8931 26.95869 28.82751 26.46404 29.32216
## 326 27.8931 26.91308 28.87312 26.39429 29.39191
## 327 27.8931 26.86950 28.91669 26.32765 29.45855
## 328 27.8931 26.82771 28.95849 26.26372 29.52247
## 329 27.8931 26.78749 28.99871 26.20222 29.58398
## 330 27.8931 26.74869 29.03751 26.14287 29.64333
## 331 27.8931 26.71116 29.07504 26.08547 29.70073
## 332 27.8931 26.67478 29.11142 26.02984 29.75636
## 333 27.8931 26.63946 29.14674 25.97582 29.81038
## 334 27.8931 26.60511 29.18109 25.92329 29.86291
## 335 27.8931 26.57165 29.21455 25.87211 29.91409
## 336 27.8931 26.53901 29.24719 25.82220 29.96399
## 337 27.8931 26.50715 29.27905 25.77347 30.01273
## 338 27.8931 26.47600 29.31020 25.72583 30.06037
## 339 27.8931 26.44552 29.34068 25.67922 30.10698
## 340 27.8931 26.41567 29.37053 25.63357 30.15263
## 341 27.8931 26.38641 29.39979 25.58882 30.19738
## 342 27.8931 26.35771 29.42849 25.54493 30.24127
## 343 27.8931 26.32954 29.45666 25.50184 30.28436
## 344 27.8931 26.30186 29.48434 25.45951 30.32669
## 345 27.8931 26.27466 29.51154 25.41791 30.36829
## 346 27.8931 26.24791 29.53829 25.37699 30.40920
## 347 27.8931 26.22158 29.56462 25.33673 30.44946
## 348 27.8931 26.19567 29.59053 25.29710 30.48910
## 349 27.8931 26.17014 29.61606 25.25806 30.52814
## 350 27.8931 26.14499 29.64121 25.21959 30.56661
## 351 27.8931 26.12019 29.66601 25.18167 30.60453
## 352 27.8931 26.09573 29.69047 25.14427 30.64193
## 353 27.8931 26.07161 29.71459 25.10737 30.67883
## 354 27.8931 26.04780 29.73840 25.07095 30.71525
## 355 27.8931 26.02429 29.76191 25.03500 30.75120
## 356 27.8931 26.00107 29.78513 24.99949 30.78671
## 357 27.8931 25.97814 29.80806 24.96442 30.82178
## 358 27.8931 25.95547 29.83073 24.92976 30.85644
## 359 27.8931 25.93307 29.85313 24.89550 30.89070
## 360 27.8931 25.91093 29.87527 24.86163 30.92457
## 361 27.8931 25.88902 29.89718 24.82813 30.95807
## 362 27.8931 25.86736 29.91884 24.79499 30.99121
## 363 27.8931 25.84592 29.94028 24.76221 31.02399
## 364 27.8931 25.82470 29.96150 24.72976 31.05644
## 365 27.8931 25.80371 29.98249 24.69765 31.08855
## 366 27.8931 25.78291 30.00328 24.66585 31.12035
## 367 27.8931 25.76233 30.02387 24.63436 31.15184
## 368 27.8931 25.74194 30.04426 24.60318 31.18302
## 369 27.8931 25.72174 30.06446 24.57229 31.21391
## 370 27.8931 25.70172 30.08448 24.54168 31.24452
## 371 27.8931 25.68189 30.10431 24.51135 31.27485
## 372 27.8931 25.66224 30.12396 24.48129 31.30491
## 373 27.8931 25.64275 30.14345 24.45149 31.33471
## 374 27.8931 25.62344 30.16276 24.42195 31.36425
## 375 27.8931 25.60428 30.18192 24.39266 31.39354
## 376 27.8931 25.58529 30.20091 24.36361 31.42259
## 377 27.8931 25.56645 30.21975 24.33479 31.45141
## 378 27.8931 25.54776 30.23844 24.30621 31.47999
## 379 27.8931 25.52922 30.25698 24.27786 31.50834
## 380 27.8931 25.51082 30.27538 24.24972 31.53648
## 381 27.8931 25.49257 30.29363 24.22180 31.56440
## 382 27.8931 25.47445 30.31175 24.19410 31.59210
## 383 27.8931 25.45647 30.32973 24.16659 31.61961
## 384 27.8931 25.43862 30.34758 24.13929 31.64691
## 385 27.8931 25.42090 30.36530 24.11219 31.67401
## 386 27.8931 25.40330 30.38290 24.08528 31.70092
## 387 27.8931 25.38583 30.40037 24.05856 31.72764
## 388 27.8931 25.36848 30.41772 24.03202 31.75418
## 389 27.8931 25.35124 30.43496 24.00566 31.78053
## 390 27.8931 25.33413 30.45207 23.97949 31.80671
## 391 27.8931 25.31712 30.46908 23.95348 31.83272
## 392 27.8931 25.30023 30.48597 23.92765 31.85855
## 393 27.8931 25.28345 30.50275 23.90198 31.88422
## 394 27.8931 25.26677 30.51943 23.87648 31.90972
## 395 27.8931 25.25020 30.53600 23.85114 31.93506
## 396 27.8931 25.23374 30.55246 23.82595 31.96025
## 397 27.8931 25.21737 30.56883 23.80092 31.98527
## 398 27.8931 25.20110 30.58509 23.77605 32.01015
## 399 27.8931 25.18494 30.60126 23.75132 32.03488
## 400 27.8931 25.16886 30.61734 23.72674 32.05946
## 401 27.8931 25.15289 30.63331 23.70230 32.08390
## 402 27.8931 25.13700 30.64920 23.67801 32.10819
## 403 27.8931 25.12121 30.66499 23.65385 32.13235
## 404 27.8931 25.10550 30.68070 23.62984 32.15636
## 405 27.8931 25.08988 30.69632 23.60595 32.18025
## 406 27.8931 25.07435 30.71185 23.58220 32.20400
## 407 27.8931 25.05891 30.72729 23.55858 32.22762
## 408 27.8931 25.04355 30.74265 23.53509 32.25111
## 409 27.8931 25.02827 30.75793 23.51172 32.27448
## 410 27.8931 25.01307 30.77313 23.48847 32.29773
## 411 27.8931 24.99795 30.78825 23.46535 32.32085
## 412 27.8931 24.98291 30.80329 23.44235 32.34385
## 413 27.8931 24.96795 30.81825 23.41947 32.36673
## 414 27.8931 24.95306 30.83314 23.39670 32.38950
## 415 27.8931 24.93825 30.84795 23.37405 32.41215
## 416 27.8931 24.92351 30.86269 23.35151 32.43469
## 417 27.8931 24.90885 30.87735 23.32908 32.45712
## 418 27.8931 24.89426 30.89194 23.30676 32.47943
## 419 27.8931 24.87973 30.90647 23.28455 32.50164
## 420 27.8931 24.86528 30.92092 23.26245 32.52375
## 421 27.8931 24.85090 30.93530 23.24045 32.54575
## 422 27.8931 24.83658 30.94962 23.21856 32.56764
## 423 27.8931 24.82233 30.96387 23.19677 32.58943
## 424 27.8931 24.80815 30.97805 23.17507 32.61113
## 425 27.8931 24.79403 30.99217 23.15348 32.63272
## 426 27.8931 24.77997 31.00623 23.13199 32.65421
## 427 27.8931 24.76598 31.02022 23.11059 32.67561
## 428 27.8931 24.75205 31.03415 23.08928 32.69692
## 429 27.8931 24.73819 31.04801 23.06807 32.71812
## 430 27.8931 24.72438 31.06182 23.04696 32.73924
## 431 27.8931 24.71063 31.07557 23.02593 32.76027
## 432 27.8931 24.69694 31.08926 23.00500 32.78120
## 433 27.8931 24.68331 31.10289 22.98416 32.80204
## 434 27.8931 24.66974 31.11646 22.96340 32.82280
## 435 27.8931 24.65623 31.12997 22.94273 32.84347
## 436 27.8931 24.64277 31.14343 22.92215 32.86405
## 437 27.8931 24.62936 31.15684 22.90165 32.88455
## 438 27.8931 24.61602 31.17018 22.88123 32.90497
## 439 27.8931 24.60272 31.18348 22.86090 32.92530
## 440 27.8931 24.58948 31.19672 22.84065 32.94555
## 441 27.8931 24.57629 31.20991 22.82048 32.96572
## 442 27.8931 24.56316 31.22304 22.80039 32.98581
## 443 27.8931 24.55007 31.23613 22.78038 33.00582
## 444 27.8931 24.53704 31.24916 22.76045 33.02575
## 445 27.8931 24.52406 31.26214 22.74059 33.04561
## 446 27.8931 24.51112 31.27508 22.72081 33.06539
## 447 27.8931 24.49824 31.28796 22.70111 33.08509
## 448 27.8931 24.48540 31.30080 22.68148 33.10472
## 449 27.8931 24.47262 31.31358 22.66192 33.12428
## 450 27.8931 24.45988 31.32632 22.64244 33.14376
## 451 27.8931 24.44718 31.33901 22.62303 33.16317
## 452 27.8931 24.43454 31.35166 22.60369 33.18251
## 453 27.8931 24.42194 31.36426 22.58442 33.20178
## 454 27.8931 24.40939 31.37681 22.56522 33.22098
## 455 27.8931 24.39688 31.38932 22.54609 33.24011
## 456 27.8931 24.38441 31.40179 22.52703 33.25917
## 457 27.8931 24.37199 31.41421 22.50803 33.27817
## 458 27.8931 24.35962 31.42658 22.48910 33.29710
## 459 27.8931 24.34728 31.43892 22.47024 33.31596
## 460 27.8931 24.33499 31.45121 22.45144 33.33476
## 461 27.8931 24.32274 31.46346 22.43271 33.35349
## 462 27.8931 24.31054 31.47566 22.41404 33.37216
## 463 27.8931 24.29837 31.48783 22.39544 33.39076
## 464 27.8931 24.28625 31.49995 22.37690 33.40930
## 465 27.8931 24.27417 31.51203 22.35842 33.42778
## 466 27.8931 24.26212 31.52408 22.34000 33.44620
## 467 27.8931 24.25012 31.53608 22.32164 33.46456
## 468 27.8931 24.23816 31.54804 22.30334 33.48285
## 469 27.8931 24.22623 31.55997 22.28511 33.50109
## 470 27.8931 24.21434 31.57186 22.26693 33.51927
## 471 27.8931 24.20250 31.58370 22.24881 33.53739
## 472 27.8931 24.19069 31.59551 22.23075 33.55545
## 473 27.8931 24.17891 31.60729 22.21274 33.57346
## 474 27.8931 24.16718 31.61902 22.19480 33.59140
## 475 27.8931 24.15548 31.63072 22.17690 33.60929
## 476 27.8931 24.14382 31.64238 22.15907 33.62713
## 477 27.8931 24.13219 31.65401 22.14129 33.64491
## 478 27.8931 24.12060 31.66560 22.12356 33.66264
## 479 27.8931 24.10905 31.67715 22.10589 33.68031
## 480 27.8931 24.09753 31.68867 22.08828 33.69792
## 481 27.8931 24.08605 31.70015 22.07071 33.71549
## 482 27.8931 24.07460 31.71160 22.05320 33.73300
## 483 27.8931 24.06318 31.72302 22.03574 33.75046
## 484 27.8931 24.05180 31.73440 22.01834 33.76786
## 485 27.8931 24.04045 31.74575 22.00098 33.78522
## 486 27.8931 24.02914 31.75706 21.98368 33.80252
## 487 27.8931 24.01785 31.76835 21.96642 33.81978
## 488 27.8931 24.00660 31.77959 21.94922 33.83698
## 489 27.8931 23.99539 31.79081 21.93206 33.85413
## 490 27.8931 23.98420 31.80200 21.91496 33.87124
## 491 27.8931 23.97305 31.81315 21.89790 33.88830
## 492 27.8931 23.96193 31.82427 21.88090 33.90530
## 493 27.8931 23.95084 31.83536 21.86394 33.92226
## 494 27.8931 23.93978 31.84642 21.84702 33.93918
## 495 27.8931 23.92876 31.85744 21.83016 33.95604
## 496 27.8931 23.91776 31.86844 21.81334 33.97286
## 497 27.8931 23.90679 31.87941 21.79657 33.98963
## 498 27.8931 23.89586 31.89034 21.77984 34.00636
## 499 27.8931 23.88495 31.90125 21.76316 34.02304
## 500 27.8931 23.87407 31.91213 21.74653 34.03967Setelah dilakukan peramalan, akan dilakukan perhitungan keakuratan hasil peramalan. Perhitungan akurasi ini dilakukan baik pada data latih dan data uji.
Akurasi Data Latih
Perhitungan akurasi data dapat dilakukan dengan cara langsung maupun manual. Secara langsung, nilai akurasi dapat diambil dari objek yang tersimpan pada hasil SES, yaitu sum of squared errors (SSE). Nilai akurasi lain dapat dihitung pula dari nilai SSE tersebut.
#Keakuratan Metode
#Pada data training
SSE1<-ses1$SSE
MSE1<-ses1$SSE/length(train.ts)
RMSE1<-sqrt(MSE1)
akurasi1 <- matrix(c(SSE1,MSE1,RMSE1))
row.names(akurasi1)<- c("SSE", "MSE", "RMSE")
colnames(akurasi1) <- c("Akurasi lamda=0.2")
akurasi1## Akurasi lamda=0.2
## SSE 37.4662879
## MSE 0.1189406
## RMSE 0.3448777SSE2<-ses2$SSE
MSE2<-ses2$SSE/length(train.ts)
RMSE2<-sqrt(MSE2)
akurasi2 <- matrix(c(SSE2,MSE2,RMSE2))
row.names(akurasi2)<- c("SSE", "MSE", "RMSE")
colnames(akurasi2) <- c("Akurasi lamda=0.7")
akurasi2## Akurasi lamda=0.7
## SSE 18.09058324
## MSE 0.05743042
## RMSE 0.23964645#Cara Manual
fitted1<-ramalan1$fitted
sisaan1<-ramalan1$residuals
head(sisaan1)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA 0.2024000 0.4355200 0.5323160 0.2358528 -0.2518178resid1<-training$temperature-ramalan1$fitted
head(resid1)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA 0.2024000 0.4355200 0.5323160 0.2358528 -0.2518178#Cara Manual
SSE.1=sum(sisaan1[2:length(train.ts)]^2)
SSE.1## [1] 37.46629MSE.1 = SSE.1/length(train.ts)
MSE.1## [1] 0.1189406MAPE.1 = sum(abs(sisaan1[2:length(train.ts)]/train.ts[2:length(train.ts)])*
100)/length(train.ts)
MAPE.1## [1] 0.9248797akurasi.1 <- matrix(c(SSE.1,MSE.1,MAPE.1))
row.names(akurasi.1)<- c("SSE", "MSE", "MAPE")
colnames(akurasi.1) <- c("Akurasi lamda=0.2")
akurasi.1## Akurasi lamda=0.2
## SSE 37.4662879
## MSE 0.1189406
## MAPE 0.9248797fitted2<-ramalan2$fitted
sisaan2<-ramalan2$residuals
head(sisaan2)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA 0.2024000 0.3343200 0.2841960 -0.1047412 -0.4719224resid2<-training$temperature-ramalan2$fitted
head(resid2)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA 0.2024000 0.3343200 0.2841960 -0.1047412 -0.4719224SSE.2=sum(sisaan2[2:length(train.ts)]^2)
SSE.2## [1] 18.09058MSE.2 = SSE.2/length(train.ts)
MSE.2## [1] 0.05743042MAPE.2 = sum(abs(sisaan2[2:length(train.ts)]/train.ts[2:length(train.ts)])*
100)/length(train.ts)
MAPE.2## [1] 0.6111395akurasi.2 <- matrix(c(SSE.2,MSE.2,MAPE.2))
row.names(akurasi.2)<- c("SSE", "MSE", "MAPE")
colnames(akurasi.2) <- c("Akurasi lamda=0.7")
akurasi.2## Akurasi lamda=0.7
## SSE 18.09058324
## MSE 0.05743042
## MAPE 0.61113949Berdasarkan nilai SSE, MSE, RMSE, dan MAPE di antara kedua parameter, nilai parameter \(\lambda=0,7\) menghasilkan akurasi yang lebih baik dibanding \(\lambda=0,2\) . Hal ini dilihat dari nilai masing-masing ukuran akurasi yang lebih kecil. Berdasarkan nilai MAPE-nya, hasil ini dapat dikategorikan sebagai peramalan sangat baik.
Akurasi Data Uji
Akurasi data uji dapat dihitung dengan cara yang hampir sama dengan perhitungan akurasi data latih.
selisih1<-ramalan1$mean-testing$temperature
SSEtesting1<-sum(selisih1^2)
MSEtesting1<-SSEtesting1/length(testing)
selisih2<-ramalan2$mean-testing$temperature
SSEtesting2<-sum(selisih2^2)
MSEtesting2<-SSEtesting2/length(testing)
selisihopt<-ramalanopt$mean-testing$temperature
SSEtestingopt<-sum(selisihopt^2)
MSEtestingopt<-SSEtestingopt/length(testing)
akurasitesting1 <- matrix(c(SSEtesting1,SSEtesting2,SSEtestingopt))
row.names(akurasitesting1)<- c("SSE1", "SSE2", "SSEopt")
akurasitesting1## [,1]
## SSE1 73.50322
## SSE2 79.05504
## SSEopt 81.85931akurasitesting2 <- matrix(c(MSEtesting1,MSEtesting2,MSEtestingopt))
row.names(akurasitesting2)<- c("MSE1", "MSE2", "MSEopt")
akurasitesting2## [,1]
## MSE1 36.75161
## MSE2 39.52752
## MSEopt 40.92966Berdasarkan nilai SSE, MSE, di antara ketiga parameter, pada data uji nilai parameter \(\lambda=0,2\) menghasilkan akurasi yang lebih baik dibanding \(\lambda=0,7\) dan \(\lambda\) fungsi optimum. Hal ini dilihat dari nilai masing-masing ukuran akurasi yang lebih kecil.
DES
Metode pemulusan Double Exponential Smoothing (DES) digunakan untuk data yang memiliki pola tren. Metode DES adalah metode semacam SES, hanya saja dilakukan dua kali, yaitu pertama untuk tahapan ‘level’ dan kedua untuk tahapan ‘tren’. Pemulusan menggunakan metode ini akan menghasilkan peramalan tidak konstan untuk periode berikutnya.
Pemulusan dengan metode DES kali ini akan menggunakan fungsi
HoltWinters() . Jika sebelumnya nilai argumen
beta dibuat FALSE , kali ini argumen tersebut
akan diinisialisasi bersamaan dengan nilai alpha .
#Lamda=0.2 dan gamma=0.2
des.1<- HoltWinters(train.ts, gamma = FALSE, beta = 0.2, alpha = 0.2)
plot(des.1)
#ramalan
ramalandes1<- forecast(des.1, h=185)
ramalandes1## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 316 27.90237 27.3692869 28.43546 27.08708882 28.71765
## 317 27.85449 27.3062678 28.40271 27.01605623 28.69292
## 318 27.80661 27.2384300 28.37479 26.93765400 28.67556
## 319 27.75873 27.1654932 28.35196 26.85145356 28.66600
## 320 27.71085 27.0873429 28.33435 26.75727975 28.66441
## 321 27.66297 27.0040076 28.32192 26.65517606 28.67076
## 322 27.61508 26.9156255 28.31454 26.54535413 28.68482
## 323 27.56720 26.8224096 28.31200 26.42813938 28.70627
## 324 27.51932 26.7246148 28.31403 26.30392193 28.73472
## 325 27.47144 26.6225132 28.32037 26.17311776 28.76977
## 326 27.42356 26.5163758 28.33074 26.03614131 28.81098
## 327 27.37568 26.4064611 28.34490 25.89338804 28.85797
## 328 27.32780 26.2930090 28.36259 25.74522483 28.91037
## 329 27.27992 26.1762381 28.38360 25.59198581 28.96785
## 330 27.23204 26.0563449 28.40773 25.43397175 29.03010
## 331 27.18415 25.9335052 28.43480 25.27145145 29.09686
## 332 27.13627 25.8078756 28.46467 25.10466425 29.16788
## 333 27.08839 25.6795951 28.49719 24.93382297 29.24296
## 334 27.04051 25.5487877 28.53223 24.75911696 29.32191
## 335 26.99263 25.4155635 28.56970 24.58071494 29.40454
## 336 26.94475 25.2800212 28.60948 24.39876760 29.49073
## 337 26.89687 25.1422490 28.65149 24.21341001 29.58033
## 338 26.84899 25.0023264 28.69565 24.02476361 29.67321
## 339 26.80111 24.8603251 28.74189 23.83293802 29.76927
## 340 26.75322 24.7163099 28.79014 23.63803254 29.86842
## 341 26.70534 24.5703399 28.84035 23.44013750 29.97055
## 342 26.65746 24.4224691 28.89245 23.23933539 30.07559
## 343 26.60958 24.2727469 28.94641 23.03570180 30.18346
## 344 26.56170 24.1212188 29.00218 22.82930626 30.29409
## 345 26.51382 23.9679267 29.05971 22.62021296 30.40742
## 346 26.46594 23.8129095 29.11897 22.40848136 30.52339
## 347 26.41806 23.6562033 29.17991 22.19416670 30.64195
## 348 26.37018 23.4978418 29.24251 21.97732049 30.76303
## 349 26.32229 23.3378566 29.30673 21.75799085 30.88660
## 350 26.27441 23.1762770 29.37255 21.53622294 31.01260
## 351 26.22653 23.0131308 29.43993 21.31205915 31.14100
## 352 26.17865 22.8484442 29.50886 21.08553946 31.27176
## 353 26.13077 22.6822418 29.57930 20.85670161 31.40484
## 354 26.08289 22.5145470 29.65123 20.62558133 31.54020
## 355 26.03501 22.3453820 29.72463 20.39221249 31.67780
## 356 25.98713 22.1747678 29.79948 20.15662731 31.81762
## 357 25.93924 22.0027244 29.87577 19.91885643 31.95963
## 358 25.89136 21.8292710 29.95346 19.67892908 32.10380
## 359 25.84348 21.6544258 30.03254 19.43687321 32.25009
## 360 25.79560 21.4782063 30.11300 19.19271552 32.39849
## 361 25.74772 21.3006293 30.19481 18.94648162 32.54896
## 362 25.69984 21.1217108 30.27797 18.69819606 32.70148
## 363 25.65196 20.9414661 30.36245 18.44788245 32.85603
## 364 25.60408 20.7599103 30.44824 18.19556347 33.01259
## 365 25.55620 20.5770575 30.53533 17.94126099 33.17113
## 366 25.50831 20.3929215 30.62371 17.68499607 33.33163
## 367 25.46043 20.2075156 30.71335 17.42678903 33.49408
## 368 25.41255 20.0208528 30.80425 17.16665953 33.65844
## 369 25.36467 19.8329452 30.89640 16.90462653 33.82472
## 370 25.31679 19.6438051 30.98977 16.64070843 33.99287
## 371 25.26891 19.4534440 31.08437 16.37492300 34.16289
## 372 25.22103 19.2618732 31.18018 16.10728750 34.33477
## 373 25.17315 19.0691037 31.27719 15.83781867 34.50847
## 374 25.12527 18.8751460 31.37538 15.56653273 34.68400
## 375 25.07738 18.6800105 31.47476 15.29344547 34.86132
## 376 25.02950 18.4837072 31.57530 15.01857222 35.04043
## 377 24.98162 18.2862458 31.67700 14.74192789 35.22132
## 378 24.93374 18.0876359 31.77985 14.46352700 35.40395
## 379 24.88586 17.8878867 31.88383 14.18338369 35.58834
## 380 24.83798 17.6870072 31.98895 13.90151172 35.77444
## 381 24.79010 17.4850061 32.09519 13.61792451 35.96227
## 382 24.74222 17.2818921 32.20254 13.33263517 36.15180
## 383 24.69433 17.0776735 32.31100 13.04565646 36.34301
## 384 24.64645 16.8723584 32.42055 12.75700086 36.53591
## 385 24.59857 16.6659548 32.53119 12.46668053 36.73046
## 386 24.55069 16.4584704 32.64291 12.17470740 36.92668
## 387 24.50281 16.2499130 32.75571 11.88109308 37.12453
## 388 24.45493 16.0402899 32.86957 11.58584895 37.32401
## 389 24.40705 15.8296084 32.98449 11.28898614 37.52511
## 390 24.35917 15.6178756 33.10046 10.99051554 37.72782
## 391 24.31129 15.4050985 33.21747 10.69044781 37.93212
## 392 24.26340 15.1912840 33.33553 10.38879338 38.13802
## 393 24.21552 14.9764386 33.45461 10.08556248 38.34548
## 394 24.16764 14.7605690 33.57472 9.78076513 38.55452
## 395 24.11976 14.5436815 33.69584 9.47441116 38.76511
## 396 24.07188 14.3257825 33.81798 9.16651019 38.97725
## 397 24.02400 14.1068782 33.94112 8.85707166 39.19093
## 398 23.97612 13.8869746 34.06526 8.54610485 39.40613
## 399 23.92824 13.6660776 34.19040 8.23361884 39.62285
## 400 23.88036 13.4441932 34.31652 7.91962257 39.84109
## 401 23.83247 13.2213269 34.44362 7.60412479 40.06082
## 402 23.78459 12.9974845 34.57170 7.28713411 40.28205
## 403 23.73671 12.7726715 34.70075 6.96865899 40.50476
## 404 23.68883 12.5468932 34.83077 6.64870773 40.72895
## 405 23.64095 12.3201551 34.96174 6.32728850 40.95461
## 406 23.59307 12.0924624 35.09367 6.00440932 41.18173
## 407 23.54519 11.8638203 35.22655 5.68007809 41.41030
## 408 23.49731 11.6342338 35.36038 5.35430255 41.64031
## 409 23.44943 11.4037079 35.49514 5.02709034 41.87176
## 410 23.40154 11.1722475 35.63084 4.69844897 42.10464
## 411 23.35366 10.9398574 35.76747 4.36838583 42.33894
## 412 23.30578 10.7065425 35.90502 4.03690819 42.57466
## 413 23.25790 10.4723074 36.04349 3.70402320 42.81178
## 414 23.21002 10.2371566 36.18288 3.36973791 43.05030
## 415 23.16214 10.0010948 36.32318 3.03405926 43.29022
## 416 23.11426 9.7641264 36.46439 2.69699408 43.53152
## 417 23.06638 9.5262558 36.60650 2.35854910 43.77420
## 418 23.01849 9.2874873 36.74950 2.01873096 44.01826
## 419 22.97061 9.0478252 36.89340 1.67754619 44.26368
## 420 22.92273 8.8072737 37.03819 1.33500123 44.51046
## 421 22.87485 8.5658370 37.18387 0.99110243 44.75860
## 422 22.82697 8.3235192 37.33042 0.64585603 45.00808
## 423 22.77909 8.0803243 37.47785 0.29926822 45.25891
## 424 22.73121 7.8362562 37.62616 -0.04865492 45.51107
## 425 22.68333 7.5913189 37.77533 -0.39790740 45.76456
## 426 22.63545 7.3455163 37.92537 -0.74848330 46.01937
## 427 22.58756 7.0988522 38.07628 -1.10037678 46.27551
## 428 22.53968 6.8513303 38.22804 -1.45358209 46.53295
## 429 22.49180 6.6029544 38.38065 -1.80809353 46.79170
## 430 22.44392 6.3537281 38.53411 -2.16390550 47.05175
## 431 22.39604 6.1036551 38.68842 -2.52101246 47.31309
## 432 22.34816 5.8527389 38.84358 -2.87940896 47.57573
## 433 22.30028 5.6009830 38.99957 -3.23908959 47.83964
## 434 22.25240 5.3483909 39.15640 -3.60004903 48.10484
## 435 22.20452 5.0949662 39.31406 -3.96228203 48.37131
## 436 22.15663 4.8407121 39.47256 -4.32578339 48.63905
## 437 22.10875 4.5856320 39.63187 -4.69054797 48.90805
## 438 22.06087 4.3297292 39.79201 -5.05657072 49.17831
## 439 22.01299 4.0730071 39.95297 -5.42384663 49.44983
## 440 21.96511 3.8154687 40.11475 -5.79237075 49.72259
## 441 21.91723 3.5571174 40.27734 -6.16213820 49.99660
## 442 21.86935 3.2979563 40.44074 -6.53314415 50.27184
## 443 21.82147 3.0379886 40.60494 -6.90538383 50.54832
## 444 21.77358 2.7772172 40.76995 -7.27885252 50.82602
## 445 21.72570 2.5156452 40.93576 -7.65354555 51.10495
## 446 21.67782 2.2532757 41.10237 -8.02945833 51.38510
## 447 21.62994 1.9901116 41.26977 -8.40658630 51.66647
## 448 21.58206 1.7261559 41.43796 -8.78492494 51.94905
## 449 21.53418 1.4614115 41.60695 -9.16446982 52.23283
## 450 21.48630 1.1958813 41.77671 -9.54521651 52.51781
## 451 21.43842 0.9295681 41.94727 -9.92716068 52.80399
## 452 21.39054 0.6624747 42.11860 -10.31029800 53.09137
## 453 21.34265 0.3946040 42.29071 -10.69462421 53.37993
## 454 21.29477 0.1259586 42.46359 -11.08013511 53.66968
## 455 21.24689 -0.1434587 42.63724 -11.46682651 53.96061
## 456 21.19901 -0.4136451 42.81167 -11.85469429 54.25272
## 457 21.15113 -0.6845981 42.98686 -12.24373437 54.54599
## 458 21.10325 -0.9563150 43.16281 -12.63394271 54.84044
## 459 21.05537 -1.2287931 43.33953 -13.02531531 55.13605
## 460 21.00749 -1.5020299 43.51700 -13.41784821 55.43282
## 461 20.95961 -1.7760229 43.69523 -13.81153749 55.73075
## 462 20.91172 -2.0507694 43.87422 -14.20637928 56.02983
## 463 20.86384 -2.3262670 44.05395 -14.60236974 56.33006
## 464 20.81596 -2.6025131 44.23444 -14.99950506 56.63143
## 465 20.76808 -2.8795055 44.41567 -15.39778150 56.93394
## 466 20.72020 -3.1572415 44.59764 -15.79719531 57.23759
## 467 20.67232 -3.4357187 44.78036 -16.19774282 57.54238
## 468 20.62444 -3.7149349 44.96381 -16.59942037 57.84830
## 469 20.57656 -3.9948876 45.14800 -17.00222435 58.15534
## 470 20.52868 -4.2755745 45.33292 -17.40615117 58.46350
## 471 20.48079 -4.5569933 45.51858 -17.81119728 58.77279
## 472 20.43291 -4.8391416 45.70497 -18.21735917 59.08318
## 473 20.38503 -5.1220173 45.89208 -18.62463337 59.39470
## 474 20.33715 -5.4056179 46.07992 -19.03301641 59.70732
## 475 20.28927 -5.6899414 46.26848 -19.44250490 60.02104
## 476 20.24139 -5.9749855 46.45776 -19.85309543 60.33587
## 477 20.19351 -6.2607479 46.64776 -20.26478466 60.65180
## 478 20.14563 -6.5472266 46.83848 -20.67756926 60.96882
## 479 20.09774 -6.8344194 47.02991 -21.09144595 61.28694
## 480 20.04986 -7.1223241 47.22205 -21.50641146 61.60614
## 481 20.00198 -7.4109386 47.41490 -21.92246255 61.92643
## 482 19.95410 -7.7002609 47.60846 -22.33959602 62.24780
## 483 19.90622 -7.9902888 47.80273 -22.75780870 62.57025
## 484 19.85834 -8.2810203 47.99770 -23.17709743 62.89378
## 485 19.81046 -8.5724534 48.19337 -23.59745910 63.21838
## 486 19.76258 -8.8645860 48.38974 -24.01889061 63.54404
## 487 19.71470 -9.1574161 48.58681 -24.44138889 63.87078
## 488 19.66681 -9.4509418 48.78457 -24.86495091 64.19858
## 489 19.61893 -9.7451610 48.98303 -25.28957365 64.52744
## 490 19.57105 -10.0400719 49.18218 -25.71525412 64.85736
## 491 19.52317 -10.3356724 49.38201 -26.14198936 65.18833
## 492 19.47529 -10.6319607 49.58254 -26.56977642 65.52036
## 493 19.42741 -10.9289348 49.78375 -26.99861240 65.85343
## 494 19.37953 -11.2265929 49.98565 -27.42849441 66.18755
## 495 19.33165 -11.5249331 50.18823 -27.85941957 66.52271
## 496 19.28377 -11.8239534 50.39148 -28.29138505 66.85892
## 497 19.23588 -12.1236522 50.59542 -28.72438803 67.19616
## 498 19.18800 -12.4240276 50.80003 -29.15842571 67.53443
## 499 19.14012 -12.7250776 51.00532 -29.59349531 67.87374
## 500 19.09224 -13.0268006 51.21128 -30.02959409 68.21408#Lamda=0.6 dan gamma=0.3
des.2<- HoltWinters(train.ts, gamma = FALSE, beta = 0.3, alpha = 0.6)
plot(des.2)
#ramalan
ramalandes2<- forecast(des.2, h=185)
ramalandes2## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 316 27.814773 27.4732699 28.15628 27.2924890 28.33706
## 317 27.709460 27.2763558 28.14256 27.0470845 28.37183
## 318 27.604146 27.0609517 28.14734 26.7734020 28.43489
## 319 27.498832 26.8305320 28.16713 26.4767553 28.52091
## 320 27.393519 26.5873972 28.19964 26.1606623 28.62637
## 321 27.288205 26.3330941 28.24332 25.8274889 28.74892
## 322 27.182891 26.0687110 28.29707 25.4788995 28.88688
## 323 27.077578 25.7950521 28.36010 25.1161240 29.03903
## 324 26.972264 25.5127379 28.43179 24.7401115 29.20442
## 325 26.866950 25.2222654 28.51164 24.3516218 29.38228
## 326 26.761637 24.9240444 28.59923 23.9512817 29.57199
## 327 26.656323 24.6184210 28.69423 23.5396207 29.77303
## 328 26.551010 24.3056935 28.79633 23.1170949 29.98492
## 329 26.445696 23.9861228 28.90527 22.6841034 30.20729
## 330 26.340382 23.6599402 29.02082 22.2409999 30.43976
## 331 26.235069 23.3273530 29.14278 21.7881013 30.68204
## 332 26.129755 22.9885482 29.27096 21.3256938 30.93382
## 333 26.024441 22.6436966 29.40519 20.8540384 31.19484
## 334 25.919128 22.2929543 29.54530 20.3733741 31.46488
## 335 25.813814 21.9364655 29.69116 19.8839211 31.74371
## 336 25.708500 21.5743634 29.84264 19.3858835 32.03112
## 337 25.603187 21.2067724 29.99960 18.8794512 32.32692
## 338 25.497873 20.8338081 30.16194 18.3648012 32.63095
## 339 25.392559 20.4555791 30.32954 17.8420995 32.94302
## 340 25.287246 20.0721873 30.50230 17.3115021 33.26299
## 341 25.181932 19.6837290 30.68014 16.7731560 33.59071
## 342 25.076619 19.2902947 30.86294 16.2271999 33.92604
## 343 24.971305 18.8919705 31.05064 15.6737653 34.26884
## 344 24.865991 18.4888379 31.24314 15.1129768 34.61901
## 345 24.760678 18.0809742 31.44038 14.5449529 34.97640
## 346 24.655364 17.6684534 31.64227 13.9698063 35.34092
## 347 24.550050 17.2513457 31.84875 13.3876449 35.71246
## 348 24.444737 16.8297184 32.05976 12.7985712 36.09090
## 349 24.339423 16.4036357 32.27521 12.2026836 36.47616
## 350 24.234109 15.9731593 32.49506 11.6000764 36.86814
## 351 24.128796 15.5383482 32.71924 10.9908399 37.26675
## 352 24.023482 15.0992591 32.94771 10.3750608 37.67190
## 353 23.918169 14.6559466 33.18039 9.7528225 38.08351
## 354 23.812855 14.2084631 33.41725 9.1242052 38.50150
## 355 23.707541 13.7568592 33.65822 8.4892863 38.92580
## 356 23.602228 13.3011836 33.90327 7.8481402 39.35631
## 357 23.496914 12.8414832 34.15234 7.2008390 39.79299
## 358 23.391600 12.3778037 34.40540 6.5474519 40.23575
## 359 23.286287 11.9101887 34.66238 5.8880463 40.68453
## 360 23.180973 11.4386809 34.92327 5.2226870 41.13926
## 361 23.075659 10.9633214 35.18800 4.5514369 41.59988
## 362 22.970346 10.4841498 35.45654 3.8743570 42.06633
## 363 22.865032 10.0012050 35.72886 3.1915063 42.53856
## 364 22.759718 9.5145243 36.00491 2.5029421 43.01649
## 365 22.654405 9.0241441 36.28467 1.8087199 43.50009
## 366 22.549091 8.5300997 36.56808 1.1088939 43.98929
## 367 22.443778 8.0324254 36.85513 0.4035165 44.48404
## 368 22.338464 7.5311547 37.14577 -0.3073614 44.98429
## 369 22.233150 7.0263198 37.43998 -1.0236900 45.48999
## 370 22.127837 6.5179525 37.73772 -1.7454210 46.00109
## 371 22.022523 6.0060835 38.03896 -2.4725074 46.51755
## 372 21.917209 5.4907427 38.34368 -3.2049034 47.03932
## 373 21.811896 4.9719594 38.65183 -3.9425643 47.56636
## 374 21.706582 4.4497621 38.96340 -4.6854466 48.09861
## 375 21.601268 3.9241785 39.27836 -5.4335076 48.63604
## 376 21.495955 3.3952358 39.59667 -6.1867061 49.17862
## 377 21.390641 2.8629603 39.91832 -6.9450014 49.72628
## 378 21.285327 2.3273781 40.24328 -7.7083541 50.27901
## 379 21.180014 1.7885143 40.57151 -8.4767255 50.83675
## 380 21.074700 1.2463936 40.90301 -9.2500778 51.39948
## 381 20.969387 0.7010402 41.23773 -10.0283742 51.96715
## 382 20.864073 0.1524777 41.57567 -10.8115785 52.53972
## 383 20.758759 -0.3992709 41.91679 -11.5996555 53.11717
## 384 20.653446 -0.9541829 42.26107 -12.3925704 53.69946
## 385 20.548132 -1.5122361 42.60850 -13.1902896 54.28655
## 386 20.442818 -2.0734090 42.95905 -13.9927798 54.87842
## 387 20.337505 -2.6376804 43.31269 -14.8000087 55.47502
## 388 20.232191 -3.2050293 43.66941 -15.6119443 56.07633
## 389 20.126877 -3.7754354 44.02919 -16.4285555 56.68231
## 390 20.021564 -4.3488787 44.39201 -17.2498117 57.29294
## 391 19.916250 -4.9253397 44.75784 -18.0756830 57.90818
## 392 19.810937 -5.5047991 45.12667 -18.9061400 58.52801
## 393 19.705623 -6.0872381 45.49848 -19.7411539 59.15240
## 394 19.600309 -6.6726381 45.87326 -20.5806962 59.78131
## 395 19.494996 -7.2609809 46.25097 -21.4247393 60.41473
## 396 19.389682 -7.8522489 46.63161 -22.2732559 61.05262
## 397 19.284368 -8.4464243 47.01516 -23.1262192 61.69496
## 398 19.179055 -9.0434901 47.40160 -23.9836028 62.34171
## 399 19.073741 -9.6434293 47.79091 -24.8453810 62.99286
## 400 18.968427 -10.2462253 48.18308 -25.7115283 63.64838
## 401 18.863114 -10.8518619 48.57809 -26.5820198 64.30825
## 402 18.757800 -11.4603228 48.97592 -27.4568308 64.97243
## 403 18.652486 -12.0715925 49.37657 -28.3359374 65.64091
## 404 18.547173 -12.6856553 49.78000 -29.2193158 66.31366
## 405 18.441859 -13.3024960 50.18621 -30.1069426 66.99066
## 406 18.336546 -13.9220996 50.59519 -30.9987949 67.67189
## 407 18.231232 -14.5444514 51.00692 -31.8948500 68.35731
## 408 18.125918 -15.1695367 51.42137 -32.7950858 69.04692
## 409 18.020605 -15.7973413 51.83855 -33.6994804 69.74069
## 410 17.915291 -16.4278510 52.25843 -34.6080122 70.43859
## 411 17.809977 -17.0610521 52.68101 -35.5206600 71.14061
## 412 17.704664 -17.6969308 53.10626 -36.4374030 71.84673
## 413 17.599350 -18.3354738 53.53417 -37.3582205 72.55692
## 414 17.494036 -18.9766677 53.96474 -38.2830923 73.27117
## 415 17.388723 -19.6204995 54.39795 -39.2119984 73.98944
## 416 17.283409 -20.2669564 54.83377 -40.1449191 74.71174
## 417 17.178095 -20.9160256 55.27222 -41.0818352 75.43803
## 418 17.072782 -21.5676947 55.71326 -42.0227273 76.16829
## 419 16.967468 -22.2219513 56.15689 -42.9675768 76.90251
## 420 16.862155 -22.8787833 56.60309 -43.9163651 77.64067
## 421 16.756841 -23.5381788 57.05186 -44.8690737 78.38276
## 422 16.651527 -24.2001259 57.50318 -45.8256847 79.12874
## 423 16.546214 -24.8646129 57.95704 -46.7861803 79.87861
## 424 16.440900 -25.5316285 58.41343 -47.7505429 80.63234
## 425 16.335586 -26.2011611 58.87233 -48.7187551 81.38993
## 426 16.230273 -26.8731998 59.33375 -49.6907999 82.15135
## 427 16.124959 -27.5477334 59.79765 -50.6666603 82.91658
## 428 16.019645 -28.2247510 60.26404 -51.6463197 83.68561
## 429 15.914332 -28.9042419 60.73291 -52.6297617 84.45843
## 430 15.809018 -29.5861955 61.20423 -53.6169701 85.23501
## 431 15.703705 -30.2706013 61.67801 -54.6079288 86.01534
## 432 15.598391 -30.9574490 62.15423 -55.6026220 86.79940
## 433 15.493077 -31.6467283 62.63288 -56.6010340 87.58719
## 434 15.387764 -32.3384292 63.11396 -57.6031496 88.37868
## 435 15.282450 -33.0325417 63.59744 -58.6089533 89.17385
## 436 15.177136 -33.7290559 64.08333 -59.6184302 89.97270
## 437 15.071823 -34.4279622 64.57161 -60.6315655 90.77521
## 438 14.966509 -35.1292509 65.06227 -61.6483444 91.58136
## 439 14.861195 -35.8329126 65.55530 -62.6687524 92.39114
## 440 14.755882 -36.5389379 66.05070 -63.6927751 93.20454
## 441 14.650568 -37.2473174 66.54845 -64.7203985 94.02153
## 442 14.545254 -37.9580421 67.04855 -65.7516085 94.84212
## 443 14.439941 -38.6711029 67.55098 -66.7863912 95.66627
## 444 14.334627 -39.3864909 68.05575 -67.8247330 96.49399
## 445 14.229314 -40.1041972 68.56282 -68.8666204 97.32525
## 446 14.124000 -40.8242130 69.07221 -69.9120399 98.16004
## 447 14.018686 -41.5465298 69.58390 -70.9609784 98.99835
## 448 13.913373 -42.2711389 70.09788 -72.0134228 99.84017
## 449 13.808059 -42.9980320 70.61415 -73.0693601 100.68548
## 450 13.702745 -43.7272006 71.13269 -74.1287775 101.53427
## 451 13.597432 -44.4586364 71.65350 -75.1916625 102.38653
## 452 13.492118 -45.1923314 72.17657 -76.2580024 103.24224
## 453 13.386804 -45.9282774 72.70189 -77.3277850 104.10139
## 454 13.281491 -46.6664664 73.22945 -78.4009979 104.96398
## 455 13.176177 -47.4068904 73.75924 -79.4776291 105.82998
## 456 13.070863 -48.1495417 74.29127 -80.5576666 106.69939
## 457 12.965550 -48.8944124 74.82551 -81.6410984 107.57220
## 458 12.860236 -49.6414950 75.36197 -82.7279129 108.44839
## 459 12.754923 -50.3907817 75.90063 -83.8180984 109.32794
## 460 12.649609 -51.1422652 76.44148 -84.9116435 110.21086
## 461 12.544295 -51.8959379 76.98453 -86.0085367 111.09713
## 462 12.438982 -52.6517924 77.52976 -87.1087668 111.98673
## 463 12.333668 -53.4098215 78.07716 -88.2123226 112.87966
## 464 12.228354 -54.1700180 78.62673 -89.3191931 113.77590
## 465 12.123041 -54.9323747 79.17846 -90.4293674 114.67545
## 466 12.017727 -55.6968845 79.73234 -91.5428346 115.57829
## 467 11.912413 -56.4635404 80.28837 -92.6595839 116.48441
## 468 11.807100 -57.2323355 80.84654 -93.7796049 117.39380
## 469 11.701786 -58.0032629 81.40684 -94.9028869 118.30646
## 470 11.596473 -58.7763158 81.96926 -96.0294196 119.22236
## 471 11.491159 -59.5514874 82.53381 -97.1591926 120.14151
## 472 11.385845 -60.3287710 83.10046 -98.2921957 121.06389
## 473 11.280532 -61.1081602 83.66922 -99.4284188 121.98948
## 474 11.175218 -61.8896482 84.24008 -100.5678519 122.91829
## 475 11.069904 -62.6732285 84.81304 -101.7104850 123.85029
## 476 10.964591 -63.4588949 85.38808 -102.8563083 124.78549
## 477 10.859277 -64.2466408 85.96519 -104.0053121 125.72387
## 478 10.753963 -65.0364600 86.54439 -105.1574866 126.66541
## 479 10.648650 -65.8283462 87.12565 -106.3128223 127.61012
## 480 10.543336 -66.6222931 87.70897 -107.4713098 128.55798
## 481 10.438022 -67.4182948 88.29434 -108.6329395 129.50898
## 482 10.332709 -68.2163449 88.88176 -109.7977022 130.46312
## 483 10.227395 -69.0164376 89.47123 -110.9655887 131.42038
## 484 10.122082 -69.8185668 90.06273 -112.1365898 132.38075
## 485 10.016768 -70.6227266 90.65626 -113.3106964 133.34423
## 486 9.911454 -71.4289111 91.25182 -114.4878995 134.31081
## 487 9.806141 -72.2371144 91.84940 -115.6681901 135.28047
## 488 9.700827 -73.0473308 92.44898 -116.8515596 136.25321
## 489 9.595513 -73.8595546 93.05058 -118.0379990 137.22903
## 490 9.490200 -74.6737801 93.65418 -119.2274997 138.20790
## 491 9.384886 -75.4900016 94.25977 -120.4200531 139.18983
## 492 9.279572 -76.3082135 94.86736 -121.6156506 140.17480
## 493 9.174259 -77.1284104 95.47693 -122.8142838 141.16280
## 494 9.068945 -77.9505866 96.08848 -124.0159442 142.15383
## 495 8.963632 -78.7747368 96.70200 -125.2206235 143.14789
## 496 8.858318 -79.6008556 97.31749 -126.4283134 144.14495
## 497 8.753004 -80.4289375 97.93495 -127.6390057 145.14501
## 498 8.647691 -81.2589773 98.55436 -128.8526924 146.14807
## 499 8.542377 -82.0909697 99.17572 -130.0693653 147.15412
## 500 8.437063 -82.9249095 99.79904 -131.2890164 148.16314Selanjutnya jika ingin membandingkan plot data latih dan data uji adalah sebagai berikut.
#Visually evaluate the prediction
plot(data.ts)
lines(des.1$fitted[,1], lty=2, col="blue")
lines(ramalandes1$mean, col="red")
Untuk mendapatkan nilai parameter optimum dari DES, argumen
alpha dan beta dapat dibuat NULL
seperti berikut.
#Lamda dan gamma optimum
des.opt<- HoltWinters(train.ts, gamma = FALSE)
des.opt## Holt-Winters exponential smoothing with trend and without seasonal component.
##
## Call:
## HoltWinters(x = train.ts, gamma = FALSE)
##
## Smoothing parameters:
## alpha: 1
## beta : 0.04376793
## gamma: FALSE
##
## Coefficients:
## [,1]
## a 27.89310000
## b -0.04570657plot(des.opt)
#ramalan
ramalandesopt<- forecast(des.opt, h=185)
ramalandesopt## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 316 27.84739 27.5420464 28.15274 27.38040550 28.31438
## 317 27.80169 27.3603098 28.24306 27.12665884 28.47671
## 318 27.75598 27.2036325 28.30833 26.91123724 28.60072
## 319 27.71027 27.0588008 28.36175 26.71393180 28.70662
## 320 27.66457 26.9208214 28.40831 26.52710615 28.80203
## 321 27.61886 26.7871951 28.45053 26.34693791 28.89078
## 322 27.57315 26.6564733 28.48983 26.17121180 28.97510
## 323 27.52745 26.5277360 28.52716 25.99852066 29.05637
## 324 27.48174 26.4003606 28.56312 25.82791252 29.13557
## 325 27.43603 26.2739064 28.59816 25.65871305 29.21336
## 326 27.39033 26.1480498 28.63261 25.49042763 29.29023
## 327 27.34462 26.0225471 28.66670 25.32268335 29.36656
## 328 27.29891 25.8972103 28.70062 25.15519291 29.44264
## 329 27.25321 25.7718922 28.73452 24.98773097 29.51869
## 330 27.20750 25.6464754 28.76853 24.82011816 29.59488
## 331 27.16179 25.5208655 28.80272 24.65221000 29.67138
## 332 27.11609 25.3949857 28.83719 24.48388893 29.74829
## 333 27.07038 25.2687727 28.87199 24.31505843 29.82571
## 334 27.02468 25.1421745 28.90718 24.14563878 29.90371
## 335 26.97897 25.0151477 28.94279 23.97556366 29.98237
## 336 26.93326 24.8876561 28.97887 23.80477774 30.06175
## 337 26.88756 24.7596694 29.01544 23.63323458 30.14188
## 338 26.84185 24.6311621 29.05254 23.46089518 30.22280
## 339 26.79614 24.5021127 29.09017 23.28772669 30.30456
## 340 26.75044 24.3725030 29.12837 23.11370142 30.38717
## 341 26.70473 24.2423178 29.16714 22.93879600 30.47066
## 342 26.65902 24.1115443 29.20650 22.76299078 30.55505
## 343 26.61332 23.9801717 29.24646 22.58626922 30.64036
## 344 26.56761 23.8481908 29.28703 22.40861748 30.72660
## 345 26.52190 23.7155942 29.32821 22.23002401 30.81378
## 346 26.47620 23.5823755 29.37002 22.05047925 30.90191
## 347 26.43049 23.4485297 29.41245 21.86997535 30.99100
## 348 26.38478 23.3140526 29.45551 21.68850594 31.08106
## 349 26.33908 23.1789408 29.49921 21.50606595 31.17209
## 350 26.29337 23.0431919 29.54355 21.32265143 31.26409
## 351 26.24766 22.9068038 29.58852 21.13825942 31.35707
## 352 26.20196 22.7697751 29.63414 20.95288780 31.45103
## 353 26.15625 22.6321051 29.68040 20.76653523 31.54597
## 354 26.11054 22.4937932 29.72729 20.57920100 31.64189
## 355 26.06484 22.3548393 29.77484 20.39088500 31.73879
## 356 26.01913 22.2152437 29.82302 20.20158763 31.83667
## 357 25.97342 22.0750070 29.87184 20.01130970 31.93554
## 358 25.92772 21.9341300 29.92131 19.82005247 32.03538
## 359 25.88201 21.7926137 29.97141 19.62781750 32.13620
## 360 25.83630 21.6504593 30.02215 19.43460667 32.23800
## 361 25.79060 21.5076682 30.07353 19.24042214 32.34077
## 362 25.74489 21.3642420 30.12554 19.04526628 32.44452
## 363 25.69918 21.2201823 30.17819 18.84914169 32.54923
## 364 25.65348 21.0754911 30.23147 18.65205114 32.65491
## 365 25.60777 20.9301702 30.28537 18.45399755 32.76155
## 366 25.56207 20.7842215 30.33991 18.25498398 32.86915
## 367 25.51636 20.6376473 30.39507 18.05501362 32.97770
## 368 25.47065 20.4904496 30.45085 17.85408976 33.08721
## 369 25.42495 20.3426306 30.50726 17.65221577 33.19767
## 370 25.37924 20.1941927 30.56428 17.44939511 33.30908
## 371 25.33353 20.0451380 30.62193 17.24563130 33.42143
## 372 25.28783 19.8954690 30.68018 17.04092790 33.53472
## 373 25.24212 19.7451880 30.73905 16.83528853 33.64895
## 374 25.19641 19.5942974 30.79853 16.62871686 33.76411
## 375 25.15071 19.4427996 30.85861 16.42121656 33.88020
## 376 25.10500 19.2906970 30.91930 16.21279134 33.99721
## 377 25.05929 19.1379921 30.98059 16.00344494 34.11514
## 378 25.01359 18.9846873 31.04249 15.79318108 34.23399
## 379 24.96788 18.8307851 31.10497 15.58200352 34.35376
## 380 24.92217 18.6762879 31.16806 15.36991601 34.47443
## 381 24.87647 18.5211981 31.23173 15.15692229 34.59601
## 382 24.83076 18.3655183 31.29600 14.94302611 34.71849
## 383 24.78505 18.2092508 31.36086 14.72823120 34.84188
## 384 24.73935 18.0523981 31.42630 14.51254131 34.96615
## 385 24.69364 17.8949626 31.49232 14.29596014 35.09132
## 386 24.64793 17.7369468 31.55892 14.07849139 35.21738
## 387 24.60223 17.5783531 31.62610 13.86013876 35.34432
## 388 24.55652 17.4191838 31.69386 13.64090591 35.47214
## 389 24.51081 17.2594413 31.76219 13.42079649 35.60083
## 390 24.46511 17.0991280 31.83109 13.19981413 35.73040
## 391 24.41940 16.9382464 31.90056 12.97796243 35.86084
## 392 24.37369 16.7767986 31.97059 12.75524498 35.99214
## 393 24.32799 16.6147871 32.04119 12.53166534 36.12431
## 394 24.28228 16.4522141 32.11235 12.30722703 36.25734
## 395 24.23657 16.2890820 32.18407 12.08193358 36.39122
## 396 24.19087 16.1253930 32.25634 11.85578846 36.52595
## 397 24.14516 15.9611494 32.32917 11.62879513 36.66153
## 398 24.09945 15.7963534 32.40256 11.40095702 36.79795
## 399 24.05375 15.6310073 32.47649 11.17227754 36.93522
## 400 24.00804 15.4651132 32.55097 10.94276005 37.07332
## 401 23.96234 15.2986734 32.62600 10.71240790 37.21226
## 402 23.91663 15.1316900 32.70157 10.48122442 37.35203
## 403 23.87092 14.9641651 32.77768 10.24921288 37.49263
## 404 23.82522 14.7961010 32.85433 10.01637657 37.63405
## 405 23.77951 14.6274997 32.93152 9.78271870 37.77630
## 406 23.73380 14.4583633 33.00924 9.54824249 37.91936
## 407 23.68810 14.2886939 33.08750 9.31295112 38.06324
## 408 23.64239 14.1184935 33.16628 9.07684772 38.20793
## 409 23.59668 13.9477643 33.24560 8.83993543 38.35343
## 410 23.55098 13.7765081 33.32544 8.60221734 38.49973
## 411 23.50527 13.6047271 33.40581 8.36369651 38.64684
## 412 23.45956 13.4324231 33.48670 8.12437598 38.79475
## 413 23.41386 13.2595983 33.56811 7.88425876 38.94345
## 414 23.36815 13.0862544 33.65005 7.64334784 39.09295
## 415 23.32244 12.9123935 33.73249 7.40164616 39.24324
## 416 23.27674 12.7380175 33.81546 7.15915665 39.39432
## 417 23.23103 12.5631283 33.89893 6.91588223 39.54618
## 418 23.18532 12.3877277 33.98292 6.67182575 39.69882
## 419 23.13962 12.2118176 34.06742 6.42699008 39.85224
## 420 23.09391 12.0353999 34.15242 6.18137803 40.00644
## 421 23.04820 11.8584763 34.23793 5.93499239 40.16142
## 422 23.00250 11.6810487 34.32395 5.68783595 40.31716
## 423 22.95679 11.5031190 34.41046 5.43991143 40.47367
## 424 22.91108 11.3246888 34.49748 5.19122157 40.63095
## 425 22.86538 11.1457599 34.58500 4.94176906 40.78899
## 426 22.81967 10.9663341 34.67301 4.69155657 40.94779
## 427 22.77396 10.7864131 34.76152 4.44058674 41.10734
## 428 22.72826 10.6059986 34.85052 4.18886220 41.26765
## 429 22.68255 10.4250923 34.94001 3.93638553 41.42872
## 430 22.63684 10.2436960 35.02999 3.68315933 41.59053
## 431 22.59114 10.0618112 35.12046 3.42918614 41.75309
## 432 22.54543 9.8794396 35.21142 3.17446848 41.91639
## 433 22.49972 9.6965829 35.30287 2.91900886 42.08044
## 434 22.45402 9.5132426 35.39479 2.66280976 42.24523
## 435 22.40831 9.3294205 35.48720 2.40587365 42.41075
## 436 22.36261 9.1451180 35.58009 2.14820296 42.57701
## 437 22.31690 8.9603368 35.67346 1.88980011 42.74400
## 438 22.27119 8.7750785 35.76731 1.63066748 42.91172
## 439 22.22549 8.5893445 35.86163 1.37080747 43.08016
## 440 22.17978 8.4031364 35.95642 1.11022241 43.24934
## 441 22.13407 8.2164558 36.05169 0.84891464 43.41923
## 442 22.08837 8.0293042 36.14743 0.58688647 43.58985
## 443 22.04266 7.8416830 36.24364 0.32414020 43.76118
## 444 21.99695 7.6535937 36.34031 0.06067808 43.93323
## 445 21.95125 7.4650378 36.43745 -0.20349762 44.10599
## 446 21.90554 7.2760168 36.53506 -0.46838467 44.27946
## 447 21.85983 7.0865322 36.63313 -0.73398086 44.45365
## 448 21.81413 6.8965853 36.73167 -1.00028401 44.62854
## 449 21.76842 6.7061775 36.83066 -1.26729192 44.80413
## 450 21.72271 6.5153104 36.93012 -1.53500246 44.98043
## 451 21.67701 6.3239852 37.03003 -1.80341347 45.15743
## 452 21.63130 6.1322034 37.13040 -2.07252284 45.33512
## 453 21.58559 5.9399663 37.23122 -2.34232847 45.51352
## 454 21.53989 5.7472753 37.33250 -2.61282828 45.69260
## 455 21.49418 5.5541318 37.43423 -2.88402019 45.87238
## 456 21.44847 5.3605371 37.53641 -3.15590217 46.05285
## 457 21.40277 5.1664925 37.63904 -3.42847216 46.23401
## 458 21.35706 4.9719994 37.74212 -3.70172817 46.41585
## 459 21.31135 4.7770590 37.84565 -3.97566819 46.59838
## 460 21.26565 4.5816726 37.94962 -4.25029024 46.78159
## 461 21.21994 4.3858416 38.05404 -4.52559235 46.96547
## 462 21.17423 4.1895672 38.15890 -4.80157257 47.15004
## 463 21.12853 3.9928506 38.26421 -5.07822898 47.33528
## 464 21.08282 3.7956932 38.36995 -5.35555964 47.52120
## 465 21.03711 3.5980962 38.47613 -5.63356265 47.70779
## 466 20.99141 3.4000607 38.58276 -5.91223613 47.89505
## 467 20.94570 3.2015881 38.68982 -6.19157821 48.08298
## 468 20.90000 3.0026795 38.79731 -6.47158702 48.27158
## 469 20.85429 2.8033362 38.90524 -6.75226072 48.46084
## 470 20.80858 2.6035593 39.01360 -7.03359749 48.65076
## 471 20.76288 2.4033501 39.12240 -7.31559551 48.84135
## 472 20.71717 2.2027097 39.23163 -7.59825297 49.03259
## 473 20.67146 2.0016392 39.34129 -7.88156809 49.22449
## 474 20.62576 1.8001399 39.45137 -8.16553910 49.41705
## 475 20.58005 1.5982129 39.56189 -8.45016424 49.61026
## 476 20.53434 1.3958593 39.67283 -8.73544176 49.80413
## 477 20.48864 1.1930802 39.78419 -9.02136994 49.99864
## 478 20.44293 0.9898769 39.89598 -9.30794704 50.19381
## 479 20.39722 0.7862503 40.00820 -9.59517137 50.38962
## 480 20.35152 0.5822017 40.12083 -9.88304124 50.58607
## 481 20.30581 0.3777321 40.23389 -10.17155495 50.78317
## 482 20.26010 0.1728426 40.34736 -10.46071086 50.98092
## 483 20.21440 -0.0324658 40.46126 -10.75050728 51.17930
## 484 20.16869 -0.2381919 40.57557 -11.04094260 51.37832
## 485 20.12298 -0.4443347 40.69030 -11.33201517 51.57798
## 486 20.07728 -0.6508931 40.80545 -11.62372337 51.77828
## 487 20.03157 -0.8578660 40.92101 -11.91606561 51.97921
## 488 19.98586 -1.0652525 41.03698 -12.20904027 52.18077
## 489 19.94016 -1.2730515 41.15337 -12.50264579 52.38296
## 490 19.89445 -1.4812619 41.27016 -12.79688058 52.58578
## 491 19.84874 -1.6898828 41.38737 -13.09174309 52.78923
## 492 19.80304 -1.8989131 41.50499 -13.38723176 52.99331
## 493 19.75733 -2.1083518 41.62301 -13.68334506 53.19801
## 494 19.71162 -2.3181980 41.74145 -13.98008146 53.40333
## 495 19.66592 -2.5284506 41.86029 -14.27743944 53.60927
## 496 19.62021 -2.7391086 41.97953 -14.57541750 53.81584
## 497 19.57450 -2.9501711 42.09918 -14.87401414 54.02302
## 498 19.52880 -3.1616371 42.21923 -15.17322787 54.23082
## 499 19.48309 -3.3735056 42.33969 -15.47305722 54.43924
## 500 19.43738 -3.5857757 42.46055 -15.77350072 54.64827Selanjutnya akan dilakukan perhitungan akurasi pada data latih maupun data uji dengan ukuran akurasi SSE, MSE dan MAPE.
Akurasi Data Latih
#Akurasi Data Training
ssedes.train1<-des.1$SSE
msedes.train1<-ssedes.train1/length(train.ts)
sisaandes1<-ramalandes1$residuals
head(sisaandes1)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA NA 0.0712000 0.0356120 -0.3681829 -0.9269915mapedes.train1 <- sum(abs(sisaandes1[3:length(train.ts)]/train.ts[3:length(train.ts)])
*100)/length(train.ts)
akurasides.1 <- matrix(c(ssedes.train1,msedes.train1,mapedes.train1))
row.names(akurasides.1)<- c("SSE", "MSE", "MAPE")
colnames(akurasides.1) <- c("Akurasi lamda=0.2 dan gamma=0.2")
akurasides.1## Akurasi lamda=0.2 dan gamma=0.2
## SSE 54.1103299
## MSE 0.1717788
## MAPE 1.1003918ssedes.train2<-des.2$SSE
msedes.train2<-ssedes.train2/length(train.ts)
sisaandes2<-ramalandes2$residuals
head(sisaandes2)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] NA NA 0.0712000 -0.0028360 -0.4058399 -0.7444903mapedes.train2 <- sum(abs(sisaandes2[3:length(train.ts)]/train.ts[3:length(train.ts)])
*100)/length(train.ts)
akurasides.2 <- matrix(c(ssedes.train2,msedes.train2,mapedes.train2))
row.names(akurasides.2)<- c("SSE", "MSE", "MAPE")
colnames(akurasides.2) <- c("Akurasi lamda=0.6 dan gamma=0.3")
akurasides.2## Akurasi lamda=0.6 dan gamma=0.3
## SSE 22.16436202
## MSE 0.07036305
## MAPE 0.68015984Hasil akurasi dari data latih didapatkan skenario 2 dengan lamda=0.6 dan gamma=0.3 memiliki hasil yang lebih baik. Namun untuk kedua skenario dapat dikategorikan peramalan sangat baik berdasarkan nilai MAPE-nya.
Akurasi Data Uji
#Akurasi Data Testing
selisihdes1<-ramalandes1$mean-testing$temperature
selisihdes1## Time Series:
## Start = 316
## End = 500
## Frequency = 1
## [1] -0.1581283 -0.3951094 -0.5057906 -0.5996717 -0.7390528 -0.1806340
## [7] -0.9296151 -1.1184963 -1.0517774 -0.9406586 -0.9944397 -1.1767209
## [13] -1.1204020 -0.9952832 -0.7306643 -0.9497455 -0.9194266 -0.9572078
## [19] -0.9509889 -0.9470700 -0.9087512 -1.0473323 -1.3323135 -1.5344946
## [25] -1.5947758 -1.4707569 -1.5299381 -1.2745192 -1.2996004 -1.4180815
## [31] -1.5263627 -1.6030438 -1.7854250 -1.8196061 -1.9008872 -1.8454684
## [37] -1.9878495 -2.0808307 -2.1226118 -1.9102930 -1.9273741 -2.0572553
## [43] -2.0805364 -1.9826176 -1.9707987 -2.0495799 -2.0975610 -2.1887422
## [49] -2.0444233 -2.2536044 -2.3956856 -2.4592667 -2.4102479 -2.3496290
## [55] -2.3737102 -2.5779913 -2.5348725 -2.4824536 -2.4251348 -2.3317159
## [61] -2.3426971 -2.3854782 -2.5174593 -2.5636405 -2.4856216 -2.3678028
## [67] -2.2793839 -2.4969651 -2.7964462 -2.9220274 -2.7161085 -2.6850897
## [73] -2.9342708 -2.9833520 -3.0139331 -2.7921143 -2.8851954 -2.9257765
## [79] -2.9976577 -2.9757388 -2.7498200 -2.9702011 -3.1457823 -3.1311634
## [85] -3.2594446 -3.4803257 -3.5668069 -3.6707880 -3.4923692 -3.6903503
## [91] -3.7915315 -3.8565126 -3.7987937 -3.6349749 -3.8631560 -4.0086372
## [97] -3.9829183 -4.2145995 -4.4513806 -4.4323618 -4.2877429 -4.0228241
## [103] -4.5621052 -4.7995864 -5.1658675 -5.3794487 -5.3736298 -5.5082109
## [109] -5.5563921 -5.5585732 -5.1542544 -5.3783355 -5.2318167 -5.3876978
## [115] -5.5947790 -5.9283601 -6.0340413 -6.1681224 -6.3074036 -6.2438847
## [121] -6.2854659 -6.3791470 -6.3921281 -6.4968093 -6.7117904 -6.6707716
## [127] -6.5856527 -6.3034339 -6.6079150 -6.9483962 -7.2149773 -7.3978585
## [133] -7.4802396 -7.4713208 -7.3575019 -7.3153831 -7.0068642 -7.3554453
## [139] -7.6855265 -7.7526076 -8.0465888 -8.1174699 -8.1126511 -8.0742322
## [145] -7.9594134 -8.0857945 -8.1119757 -7.6562568 -8.0240380 -8.1902191
## [151] -7.9379003 -7.9816814 -8.2155625 -8.4178437 -8.3920248 -8.2095060
## [157] -7.7562871 -8.0669683 -7.8982494 -8.0517306 -8.2313117 -8.2022929
## [163] -8.1055740 -8.3883552 -8.2623363 -8.3876175 -8.5316986 -8.8343797
## [169] -9.0408609 -9.2348420 -9.3583232 -9.2960043 -9.3593855 -9.5755666
## [175] -9.5325478 -9.6701289 -9.8484101 -9.9355912 -9.9831724 -10.0014535
## [181] -9.4999347 -9.0761158 -8.5374969 -8.6891781 -9.7385592SSEtestingdes1<-sum(selisihdes1^2)
MSEtestingdes1<-SSEtestingdes1/length(testing$temperature)
MAPEtestingdes1<-sum(abs(selisihdes1/testing$temperature)*100)/length(testing$temperature)
selisihdes2<-ramalandes2$mean-testing$temperature
selisihdes2## Time Series:
## Start = 316
## End = 500
## Frequency = 1
## [1] -0.2457268 -0.5401404 -0.7082541 -0.8595677 -1.0563813 -0.5553950
## [7] -1.3618086 -1.6081223 -1.5988359 -1.5451496 -1.6563632 -1.8960768
## [13] -1.8971905 -1.8295041 -1.6223178 -1.8988314 -1.9259450 -2.0211587
## [19] -2.0723723 -2.1258860 -2.1449996 -2.3410132 -2.6834269 -2.9430405
## [25] -3.0607542 -2.9941678 -3.1107814 -2.9127951 -2.9953087 -3.1712224
## [31] -3.3369360 -3.4710497 -3.7108633 -3.8024769 -3.9411906 -3.9432042
## [37] -4.1430179 -4.2934315 -4.3926451 -4.2377588 -4.3122724 -4.4995861
## [43] -4.5802997 -4.5398133 -4.5854270 -4.7216406 -4.8270543 -4.9756679
## [49] -4.8887815 -5.1553952 -5.3549088 -5.4759225 -5.4843361 -5.4811498
## [55] -5.5626634 -5.8243770 -5.8386907 -5.8437043 -5.8438180 -5.8078316
## [61] -5.8762452 -5.9764589 -6.1658725 -6.2694862 -6.2488998 -6.1885134
## [67] -6.1575271 -6.4325407 -6.7894544 -6.9724680 -6.8239816 -6.8503953
## [73] -7.1570089 -7.2635226 -7.3515362 -7.1871498 -7.3376635 -7.4356771
## [79] -7.5649908 -7.6005044 -7.4320181 -7.7098317 -7.9428453 -7.9856590
## [85] -8.1713726 -8.4496863 -8.5935999 -8.7550135 -8.6340272 -8.8894408
## [91] -9.0480545 -9.1704681 -9.1701817 -9.0637954 -9.3494090 -9.5523227
## [97] -9.5840363 -9.8731499 -10.1673636 -10.2057772 -10.1185909 -9.9111045
## [103] -10.5078182 -10.8027318 -11.2264454 -11.4974591 -11.5490727 -11.7410864
## [109] -11.8467000 -11.9063136 -11.5594273 -11.8409409 -11.7518546 -11.9651682
## [115] -12.2296818 -12.6206955 -12.7838091 -12.9753228 -13.1720364 -13.1659500
## [121] -13.2649637 -13.4160773 -13.4864910 -13.6486046 -13.9210183 -13.9374319
## [127] -13.9097455 -13.6849592 -14.0468728 -14.4447865 -14.7688001 -15.0091137
## [133] -15.1489274 -15.1974410 -15.1410547 -15.1563683 -14.9052819 -15.3112956
## [139] -15.6988092 -15.8233229 -16.1747365 -16.3030501 -16.3556638 -16.3746774
## [145] -16.3172911 -16.5011047 -16.5847183 -16.1864320 -16.6116456 -16.8352593
## [151] -16.6403729 -16.7415866 -17.0329002 -17.2926138 -17.3242275 -17.1991411
## [157] -16.8033548 -17.1714684 -17.0601820 -17.2710957 -17.5081093 -17.5365230
## [163] -17.4972366 -17.8374502 -17.7688639 -17.9515775 -18.1530912 -18.5132048
## [169] -18.7771184 -19.0285321 -19.2094457 -19.2045594 -19.3253730 -19.5989867
## [175] -19.6134003 -19.8084139 -20.0441276 -20.1887412 -20.2937549 -20.3694685
## [181] -19.9253821 -19.5589958 -19.0778094 -19.2869231 -20.3937367SSEtestingdes2<-sum(selisihdes2^2)
MSEtestingdes2<-SSEtestingdes2/length(testing$temperature)
MAPEtestingdes2<-sum(abs(selisihdes2/testing$temperature)*100)/length(testing$temperature)
selisihdesopt<-ramalandesopt$mean-testing$temperature
selisihdesopt## Time Series:
## Start = 316
## End = 500
## Frequency = 1
## [1] -0.2131066 -0.4479131 -0.5564197 -0.6481263 -0.7853328 -0.2247394
## [7] -0.9715460 -1.1582525 -1.0893591 -0.9760657 -1.0276723 -1.2077788
## [13] -1.1492854 -1.0219920 -0.7551985 -0.9721051 -0.9396117 -0.9752182
## [19] -0.9668248 -0.9607314 -0.9202379 -1.0566445 -1.3394511 -1.5394576
## [25] -1.5975642 -1.4713708 -1.5283773 -1.2707839 -1.2936905 -1.4099970
## [31] -1.5161036 -1.5906102 -1.7708168 -1.8028233 -1.8819299 -1.8243365
## [37] -1.9645430 -2.0553496 -2.0949562 -1.8804627 -1.8953693 -2.0230759
## [43] -2.0441824 -1.9440890 -1.9300956 -2.0067021 -2.0525087 -2.1415153
## [49] -1.9950218 -2.2020284 -2.3419350 -2.4033416 -2.3521481 -2.2893547
## [55] -2.3112613 -2.5133678 -2.4680744 -2.4134810 -2.3539875 -2.2583941
## [61] -2.2672007 -2.3078072 -2.4376138 -2.4816204 -2.4014269 -2.2814335
## [67] -2.1908401 -2.4062466 -2.7035532 -2.8269598 -2.6188663 -2.5856729
## [73] -2.8326795 -2.8795861 -2.9079926 -2.6839992 -2.7749058 -2.8133123
## [79] -2.8830189 -2.8589255 -2.6308320 -2.8490386 -3.0224452 -3.0056517
## [85] -3.1317583 -3.3504649 -3.4347714 -3.5365780 -3.3559846 -3.5517911
## [91] -3.6507977 -3.7136043 -3.6537109 -3.4877174 -3.7137240 -3.8570306
## [97] -3.8291371 -4.0586437 -4.2932503 -4.2720568 -4.1252634 -3.8581700
## [103] -4.3952765 -4.6305831 -4.9946897 -5.2060962 -5.1981028 -5.3305094
## [109] -5.3765159 -5.3765225 -4.9700291 -5.1919356 -5.0432422 -5.1969488
## [115] -5.4018554 -5.7332619 -5.8367685 -5.9686751 -6.1057816 -6.0400882
## [121] -6.0794948 -6.1710013 -6.1818079 -6.2843145 -6.4971210 -6.4539276
## [127] -6.3666342 -6.0822407 -6.3845473 -6.7228539 -6.9872604 -7.1679670
## [133] -7.2481736 -7.2370802 -7.1210867 -7.0767933 -6.7660999 -7.1125064
## [139] -7.4404130 -7.5053196 -7.7971261 -7.8658327 -7.8588393 -7.8182458
## [145] -7.7012524 -7.8254590 -7.8494655 -7.3915721 -7.7571787 -7.9211852
## [151] -7.6666918 -7.7082984 -7.9400049 -8.1401115 -8.1121181 -7.9274247
## [157] -7.4720312 -7.7805378 -7.6096444 -7.7609509 -7.9383575 -7.9071641
## [163] -7.8082706 -8.0888772 -7.9606838 -8.0837903 -8.2256969 -8.5262035
## [169] -8.7305100 -8.9223166 -9.0436232 -8.9791297 -9.0403363 -9.2543429
## [175] -9.2091495 -9.3445560 -9.5206626 -9.6056692 -9.6510757 -9.6671823
## [181] -9.1634889 -8.7374954 -8.1967020 -8.3462086 -9.3934151SSEtestingdesopt<-sum(selisihdesopt^2)
MSEtestingdesopt<-SSEtestingdesopt/length(testing$temperature)
MAPEtestingdesopt<-sum(abs(selisihdesopt/testing$temperature)*100)/length(testing$temperature)
akurasitestingdes <-
matrix(c(SSEtestingdes1,MSEtestingdes1,MAPEtestingdes1,SSEtestingdes2,MSEtestingdes2,
MAPEtestingdes2,SSEtestingdesopt,MSEtestingdesopt,MAPEtestingdesopt),
nrow=3,ncol=3)
row.names(akurasitestingdes)<- c("SSE", "MSE", "MAPE")
colnames(akurasitestingdes) <- c("des ske1","des ske2","des opt")
akurasitestingdes## des ske1 des ske2 des opt
## SSE 5530.72677 25052.30650 5165.79518
## MSE 29.89582 135.41787 27.92322
## MAPE 16.31984 35.31179 15.80811Diperoleh yang paling bagus (dari nilai SSE, MSE, dan MAPE yang paling kecil) menggunakan fungsi optimum yaitu DES dengan nilai alpha = 1 dan beta = 0.04376
Perbandingan SES dan DES
MSEfull <-
matrix(c(MSEtesting1,MSEtesting2,MSEtestingopt,MSEtestingdes1,MSEtestingdes2,
MSEtestingdesopt),nrow=3,ncol=2)
row.names(MSEfull)<- c("ske 1", "ske 2", "ske opt")
colnames(MSEfull) <- c("ses","des")
MSEfull## ses des
## ske 1 36.75161 29.89582
## ske 2 39.52752 135.41787
## ske opt 40.92966 27.92322Kedua metode dapat dibandingkan dengan menggunakan ukuran akurasi yang sama. Contoh di atas adalah perbandingan kedua metode dengan ukuran akurasi MSE. Hasilnya didapatkan metode DES cenderung lebih baik dibandingkan metode SES dilihat dari MSE yang lebih kecil nilainya.