Prak01

Setting

Abaikan bagian ini. Lansung saja loncat ke 1. Tentang Data .

R Path Function

path <- function(){
  gsub  ( "\\\\",  "/",  readClipboard ()  )
}
#Copy path
#Panggil function di console
#Copy r path, paste ke var yang diinginkan

#Export chart
export.chart <- "C:/Users/Fathan/Documents/Obsidian Vault/2. Kuliah/Smt 5/6. Metode Peramalan Deret Waktu/@Proj/STA1341-MPDW/Pertemuan 1/Chart"

Install Load funcion

#                      -=( Install & Load Package Function )=-
install_load <- function (package1, ...)  {   

   # convert arguments to vector
   packages <- c(package1, ...)

   # start loop to determine if each package is installed
   for(package in packages){

       # if package is installed locally, load
       if(package %in% rownames(installed.packages()))
          do.call('library', list(package))

       # if package is not installed locally, download, then load
       else {
          install.packages(package)
          do.call("library", list(package))
       }
   } 
}

Theme 1

install_load('ggplot2','extrafont')

## Warning: package 'ggplot2' was built under R version 4.2.3

## Registering fonts with R

# font_import(); loadfonts() #Run ini sekali aja
theme1 <- list(
  guides(fill="none"), #No Legends
  theme(
  text = element_text(size = 66),
  axis.title = element_text(size=33),
  axis.text.y = element_text(vjust = .5, face = "bold"),
  plot.title = element_text(hjust = 0.5),
  panel.background = element_rect(fill = 'transparent'),
  plot.background = element_rect(fill='transparent', color=NA),
  panel.grid.major = element_line(colour = "grey90"),
  axis.line = element_line(linewidth = 2, colour = "grey90"))
)

Theme 2 - line plot

# This theme extends the 'theme_minimal' that comes with ggplot2.
# The "Lato" font is used as the base font. This is similar
# to the original font in Cedric's work, Avenir Next Condensed.
install_load('ggtext')

## Warning: package 'ggtext' was built under R version 4.2.3

## theme_set(theme_minimal(base_family = "Lato"))


theme_update(
  # Remove title for both x and y axes
  axis.title = element_blank(),
  # Axes labels are grey
  axis.text = element_text(color = "grey40"),
  # The size of the axes labels are different for x and y.
  axis.text.x = element_text(size = 20, margin = margin(t = 5)),
  axis.text.y = element_text(size = 17, margin = margin(r = 5)),
  # Also, the ticks have a very light grey color
  axis.ticks = element_line(color = "grey91", linewidth = .5),
  # The length of the axis ticks is increased.
  axis.ticks.length.x = unit(1.3, "lines"),
  axis.ticks.length.y = unit(.7, "lines"),
  # Remove the grid lines that come with ggplot2 plots by default
  panel.grid = element_blank(),
  # Customize margin values (top, right, bottom, left)
  plot.margin = margin(20, 40, 20, 40),
  # Use a light grey color for the background of both the plot and the panel
  plot.background = element_rect(fill = "grey98", color = "grey98"),
  panel.background = element_rect(fill = "grey98", color = "grey98"),
  # Customize title appearence
  plot.title = element_text(
    color = "grey10", 
    size = 28, 
    face = "bold",
    margin = margin(t = 15)
  ),
  # Customize subtitle appearence
  plot.subtitle = element_markdown(
    color = "grey30", 
    size = 16,
    lineheight = 1.35,
    margin = margin(t = 15, b = 40)
  ),
  # Title and caption are going to be aligned
  plot.title.position = "plot",
  plot.caption.position = "plot",
  plot.caption = element_text(
    color = "grey30", 
    size = 13,
    lineheight = 1.2, 
    hjust = 0,
    margin = margin(t = 40) # Large margin on the top of the caption.
  ),
  # Remove legend
  legend.position = "none"
)

A. Tentang Data

Dataset yang saya gunakan merupakan koleksi data harga saham historis periode Juli 2018 hingga Juli 2023 dari beberapa raksasa teknologi paling berpengaruh di dunia: Microsoft, Apple, Amazon, Nvidia, Google, Netflix, dan Meta (sebelumnya dikenal sebagai Facebook). Dataset ini menjadi sumber daya berharga bagi analis keuangan, ilmuwan data, dan penggemar pasar saham yang ingin menganalisis dan memahami tren harga perusahaan-perusahaan terkemuka di industri ini.

Dataset ini memilki data :

1. Open: yakni Harga saham pada awal periode perdagangan tertentu. Ini adalah harga saham pertama pada hari perdagangan tersebut.
2. High: Harga tertinggi yang saham capai selama periode perdagangan tersebut. Ini mencerminkan harga tertinggi yang pembeli bersedia bayar selama hari tersebut.
3. Low: Harga terendah yang saham capai selama periode perdagangan tersebut. Ini mencerminkan harga terendah yang penjual bersedia terima selama hari tersebut.
4. Close: Harga saham pada akhir periode perdagangan tertentu. Ini adalah harga saham terakhir pada hari perdagangan tersebut.
5. Adj Close (Adjusted Close): Harga penutup yang telah disesuaikan untuk memperhitungkan perubahan seperti pembagian saham atau dividen. Ini adalah harga penutup yang paling relevan untuk analisis jangka panjang, karena mencerminkan harga saham yang sebenarnya setelah penyesuaian.
6. Volume: Volume perdagangan saham selama periode tertentu. Ini mencerminkan jumlah saham yang diperdagangkan selama hari perdagangan tersebut.

Karena tugas kali ini hanya menggunakan satu peubah dan satu kategori saja. Maka kali ini saya akan menggunakan peubah Adj Close (Adjusted Close) .Karena Adj Close Adalah peubah yang paling sesuai untuk dianalisis dibandingkan peubah lainnya. Untuk pemilihan data sahamnya, saya ingin mengeksplorasi terlebih dahulu.

Import Data

install_load('rio')
raw.data <- import("https://raw.githubusercontent.com/Zen-Rofiqy/STA1341-MPDW/main/Data/MAANG%20Stock%20Prices.csv")

## Warning in (function (input = "", file = NULL, text = NULL, cmd = NULL, :
## Stopped early on line 8815. Expected 8 fields but found 1. Consider fill=TRUE
## and comment.char=. First discarded non-empty line: <<=======>>

Cleaning Data

Melihat tipe data.

str(raw.data)

## 'data.frame':    8812 obs. of  8 variables:
##  $ Name     : chr  "AMZN" "AMZN" "AMZN" "AMZN" ...
##  $ Date     : chr  "7/30/18" "7/31/18" "8/1/18" "8/2/18" ...
##  $ Open     : chr  "91.366501" "89.324501" "89.199997" "89.438499" ...
##  $ High     : chr  "91.474998" "90.091499" "89.921997" "91.828003" ...
##  $ Low      : chr  "88.301003" "86.966003" "88.801003" "89.300003" ...
##  $ Close    : chr  "88.960999" "88.872002" "89.858498" "91.716499" ...
##  $ Adj Close: chr  "88.960999" "88.872002" "89.858498" "91.716499" ...
##  $ Volume   : chr  "131246000" "114774000" "83062000" "87094000" ...

Cek Data kosong.

sum(is.na(raw.data))

## [1] 0

Tidak ada data kosong.

Semua tipe data masih berupa character. Harus diubah menjadi tipe data yang sesuai.

install_load('dplyr')

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

data <- raw.data %>%  
  mutate(
    Date = as.Date(raw.data[, 2], format = "%m/%d/%y"), #Mengubah menjadi Date 
    across(3:ncol(raw.data), as.numeric)                #Mengubah menjadi Numerik
  )

## Warning in mask$eval_all_mutate(quo): NAs introduced by coercion

## Warning in mask$eval_all_mutate(quo): NAs introduced by coercion

## Warning in mask$eval_all_mutate(quo): NAs introduced by coercion

## Warning in mask$eval_all_mutate(quo): NAs introduced by coercion

## Warning in mask$eval_all_mutate(quo): NAs introduced by coercion

## Warning in mask$eval_all_mutate(quo): NAs introduced by coercion

str(data)

## 'data.frame':    8812 obs. of  8 variables:
##  $ Name     : chr  "AMZN" "AMZN" "AMZN" "AMZN" ...
##  $ Date     : Date, format: "2018-07-30" "2018-07-31" ...
##  $ Open     : num  91.4 89.3 89.2 89.4 91.9 ...
##  $ High     : num  91.5 90.1 89.9 91.8 92.1 ...
##  $ Low      : num  88.3 87 88.8 89.3 91.1 ...
##  $ Close    : num  89 88.9 89.9 91.7 91.2 ...
##  $ Adj Close: num  89 88.9 89.9 91.7 91.2 ...
##  $ Volume   : num  1.31e+08 1.15e+08 8.31e+07 8.71e+07 6.92e+07 ...

Ternyata ada data kosong. Harus cek ulang.

# Mencari indeks baris dan kolom yang mengandung NA
na.idx <- which(is.na(data), arr.ind = TRUE)

# Menampilkan data raw dengan baris dan kolom yang mengandung NA
install_load('kableExtra','dplyr')

## Warning in !is.null(rmarkdown::metadata$output) && rmarkdown::metadata$output
## %in% : 'length(x) = 2 > 1' in coercion to 'logical(1)'

## 
## Attaching package: 'kableExtra'

## The following object is masked from 'package:dplyr':
## 
##     group_rows

kable(raw.data[                        # Subsetting
                unique(na.idx[, 1]),   # Vektor indeks baris yang mengandung NA
                unique(na.idx[, 2])  ] # Vektor indeks kolom yang mengandung NA
      ) %>% kable_styling()            # Style Tabel

	Date	Open	High	Low	Close	Adj Close	Volume
1259	Date	Open	High	Low	Close	Adj Close	Volume
2518	Date	Open	High	Low	Close	Adj Close	Volume
3777	Date	Open	High	Low	Close	Adj Close	Volume
5036	Date	Open	High	Low	Close	Adj Close	Volume
6295	Date	Open	High	Low	Close	Adj Close	Volume
7554	Date	Open	High	Low	Close	Adj Close	Volume

Ternyata pada baris tersebut ada data karakter text. Sehingga ketika diubah ke numerik akan menjadi NA. Maka saya akan menghapus baris tersebut.

data <- data %>%
  filter(!row_number() %in% unique(na.idx[, 1]))

Time Series MAANG

install_load('viridis','ggrepel')

## Loading required package: viridisLite

#Plot
cts.maang <-
ggplot(data, aes(x=Date, y=`Adj Close`)) + #Data
  geom_line(aes(color=Name), linewidth=1) + #Timeseries
  #Color
    scale_color_viridis(alpha = 0.75, #Opacity
                     begin = 0, #Color pallte scale begins
                     end = 0.9, #Color pallte scale ends
                     direction = -1, #Flip color scale
                     discrete = T, #Discrete Value
                     option = "D") + #Color Palette
  theme1 + #THeme
  labs(x = "Tahun", y = "Harga Saham (USD)") + #Label X & Y
  # Label / legend
  geom_text_repel(
    data=data[data$Date == max(data$Date),], #Posisi di ujung data
    aes(color = Name, label = Name), #Warna garis & label saham
    size = 8, #Ukuran text
    nudge_x = 80, #Posisi Text (kanan 50)
    hjust = 0, #Ujung
    segment.size = 1,               #Ukuran garis
    segment.alpha = .75,             #transparasi garis
    segment.linetype = "dotted",    #Time garis
    box.padding = .4, #Biar label saham nggak dempetan
    segment.curvature = -0.1, #biar garis mulus
    segment.ncp = 8, 
    segment.angle = 60 
  ) +
  #Axis
    coord_cartesian(clip = "off"
  ) +
    scale_x_date( #Sumbu x
    date_breaks = "1 year",  # Menampilkan label setiap tahun
    date_labels = "%Y",  # Format label tahun
    limits = c(as.Date("2018-07-30"), as.Date("2023-12-28"))
    #Tampilin lebih dari 20023-07-28 agar label saham bisa masuk
  ) +
    scale_y_continuous( #Sumbu y
    labels = scales::dollar_format(prefix = "$") #tambahin dolar
  ) +
    annotate( #Buat nandain batas data
    "text", x = as.Date("2023-7-28"), y = 50, 
    label = "28 Juli", size=6
  ) +
  geom_vline( #Buat garis batas data
    xintercept = as.numeric(as.Date("2023-07-28")), 
             linetype = "dotted", color = "red")
cts.maang

#Export Chart
ggsave("01_Time Series MAANG.png", cts.maang, path = export.chart,
        dpi = 300, height = 9, width = 16)

Jika dilihat dari tahun 2019-2022, semua saham cenderung memiliki pola trend naik. Lalu dari 2021-2023 polanya cenderung trend turun. Untuk tugas praktikum kali ini, saya hanya akan menggunakan rentang tahun 2022-2023 dengan tren cenderung turun. Agar pengerjaannya tidak terlalu sulit, karena masih tahap awal pembelajaran.

Ada yang menarik perhatian saya. Kenapa dulu Pendiri Amazon, Jeff Bezos yang pernah menjadi orang terkaya di dunia pada tahun 2017 lalu, harga saham sekarang tidak setinggi yang saya kira?. Oleh karena itu saya memutuskan untuk menggunakan data saham Amazon untuk praktikum kali ini.

amzn <- data %>%
  select(1, 2, 7) %>%  # Memilih kolom 1, 2, dan 7
  filter(Name == "AMZN", Date >= as.Date("2022-01-01"))  # Filter data saham Amazon tahun 2022 ke atas

rownames(amzn) <- NULL
str(amzn)

## 'data.frame':    394 obs. of  3 variables:
##  $ Name     : chr  "AMZN" "AMZN" "AMZN" "AMZN" ...
##  $ Date     : Date, format: "2022-01-03" "2022-01-04" ...
##  $ Adj Close: num  170 168 164 163 163 ...

kable(amzn) %>% kable_styling()

Name	Date	Adj Close
AMZN	2022-01-03	170.4045
AMZN	2022-01-04	167.5220
AMZN	2022-01-05	164.3570
AMZN	2022-01-06	163.2540
AMZN	2022-01-07	162.5540
AMZN	2022-01-10	161.4860
AMZN	2022-01-11	165.3620
AMZN	2022-01-12	165.2070
AMZN	2022-01-13	161.2140
AMZN	2022-01-14	162.1380
AMZN	2022-01-18	158.9175
AMZN	2022-01-19	156.2990
AMZN	2022-01-20	151.6675
AMZN	2022-01-21	142.6430
AMZN	2022-01-24	144.5440
AMZN	2022-01-25	139.9860
AMZN	2022-01-26	138.8725
AMZN	2022-01-27	139.6375
AMZN	2022-01-28	143.9780
AMZN	2022-01-31	149.5735
AMZN	2022-02-01	151.1935
AMZN	2022-02-02	150.6125
AMZN	2022-02-03	138.8455
AMZN	2022-02-04	157.6395
AMZN	2022-02-07	157.9355
AMZN	2022-02-08	161.4135
AMZN	2022-02-09	161.1895
AMZN	2022-02-10	159.0035
AMZN	2022-02-11	153.2935
AMZN	2022-02-14	155.1670
AMZN	2022-02-15	156.5105
AMZN	2022-02-16	158.1005
AMZN	2022-02-17	154.6525
AMZN	2022-02-18	152.6015
AMZN	2022-02-22	150.1975
AMZN	2022-02-23	144.8270
AMZN	2022-02-24	151.3580
AMZN	2022-02-25	153.7885
AMZN	2022-02-28	153.5630
AMZN	2022-03-01	151.1420
AMZN	2022-03-02	152.0525
AMZN	2022-03-03	147.8985
AMZN	2022-03-04	145.6410
AMZN	2022-03-07	137.4530
AMZN	2022-03-08	136.0145
AMZN	2022-03-09	139.2790
AMZN	2022-03-10	146.8175
AMZN	2022-03-11	145.5245
AMZN	2022-03-14	141.8530
AMZN	2022-03-15	147.3665
AMZN	2022-03-16	153.1040
AMZN	2022-03-17	157.2390
AMZN	2022-03-18	161.2505
AMZN	2022-03-21	161.4915
AMZN	2022-03-22	164.8890
AMZN	2022-03-23	163.4080
AMZN	2022-03-24	163.6495
AMZN	2022-03-25	164.7735
AMZN	2022-03-28	168.9905
AMZN	2022-03-29	169.3150
AMZN	2022-03-30	166.3010
AMZN	2022-03-31	162.9975
AMZN	2022-04-01	163.5600
AMZN	2022-04-04	168.3465
AMZN	2022-04-05	164.0550
AMZN	2022-04-06	158.7560
AMZN	2022-04-07	157.7845
AMZN	2022-04-08	154.4605
AMZN	2022-04-11	151.1220
AMZN	2022-04-12	150.7875
AMZN	2022-04-13	155.5410
AMZN	2022-04-14	151.7065
AMZN	2022-04-18	152.7850
AMZN	2022-04-19	158.1155
AMZN	2022-04-20	153.9980
AMZN	2022-04-21	148.2960
AMZN	2022-04-22	144.3500
AMZN	2022-04-25	146.0740
AMZN	2022-04-26	139.3910
AMZN	2022-04-27	138.1670
AMZN	2022-04-28	144.5965
AMZN	2022-04-29	124.2815
AMZN	2022-05-02	124.5000
AMZN	2022-05-03	124.2535
AMZN	2022-05-04	125.9285
AMZN	2022-05-05	116.4070
AMZN	2022-05-06	114.7725
AMZN	2022-05-09	108.7890
AMZN	2022-05-10	108.8590
AMZN	2022-05-11	105.3720
AMZN	2022-05-12	106.9305
AMZN	2022-05-13	113.0550
AMZN	2022-05-16	110.8105
AMZN	2022-05-17	115.3685
AMZN	2022-05-18	107.1125
AMZN	2022-05-19	107.3190
AMZN	2022-05-20	107.5910
AMZN	2022-05-23	107.5570
AMZN	2022-05-24	104.1000
AMZN	2022-05-25	106.7750
AMZN	2022-05-26	111.0775
AMZN	2022-05-27	115.1465
AMZN	2022-05-31	120.2095
AMZN	2022-06-01	121.6840
AMZN	2022-06-02	125.5110
AMZN	2022-06-03	122.3500
AMZN	2022-06-06	124.7900
AMZN	2022-06-07	123.0000
AMZN	2022-06-08	121.1800
AMZN	2022-06-09	116.1500
AMZN	2022-06-10	109.6500
AMZN	2022-06-13	103.6700
AMZN	2022-06-14	102.3100
AMZN	2022-06-15	107.6700
AMZN	2022-06-16	103.6600
AMZN	2022-06-17	106.2200
AMZN	2022-06-21	108.6800
AMZN	2022-06-22	108.9500
AMZN	2022-06-23	112.4400
AMZN	2022-06-24	116.4600
AMZN	2022-06-27	113.2200
AMZN	2022-06-28	107.4000
AMZN	2022-06-29	108.9200
AMZN	2022-06-30	106.2100
AMZN	2022-07-01	109.5600
AMZN	2022-07-05	113.5000
AMZN	2022-07-06	114.3300
AMZN	2022-07-07	116.3300
AMZN	2022-07-08	115.5400
AMZN	2022-07-11	111.7500
AMZN	2022-07-12	109.2200
AMZN	2022-07-13	110.4000
AMZN	2022-07-14	110.6300
AMZN	2022-07-15	113.5500
AMZN	2022-07-18	113.7600
AMZN	2022-07-19	118.2100
AMZN	2022-07-20	122.7700
AMZN	2022-07-21	124.6300
AMZN	2022-07-22	122.4200
AMZN	2022-07-25	121.1400
AMZN	2022-07-26	114.8100
AMZN	2022-07-27	120.9700
AMZN	2022-07-28	122.2800
AMZN	2022-07-29	134.9500
AMZN	2022-08-01	135.3900
AMZN	2022-08-02	134.1600
AMZN	2022-08-03	139.5200
AMZN	2022-08-04	142.5700
AMZN	2022-08-05	140.8000
AMZN	2022-08-08	139.4100
AMZN	2022-08-09	137.8300
AMZN	2022-08-10	142.6900
AMZN	2022-08-11	140.6400
AMZN	2022-08-12	143.5500
AMZN	2022-08-15	143.1800
AMZN	2022-08-16	144.7800
AMZN	2022-08-17	142.1000
AMZN	2022-08-18	142.3000
AMZN	2022-08-19	138.2300
AMZN	2022-08-22	133.2200
AMZN	2022-08-23	133.6200
AMZN	2022-08-24	133.8000
AMZN	2022-08-25	137.2800
AMZN	2022-08-26	130.7500
AMZN	2022-08-29	129.7900
AMZN	2022-08-30	128.7300
AMZN	2022-08-31	126.7700
AMZN	2022-09-01	127.8200
AMZN	2022-09-02	127.5100
AMZN	2022-09-06	126.1100
AMZN	2022-09-07	129.4800
AMZN	2022-09-08	129.8200
AMZN	2022-09-09	133.2700
AMZN	2022-09-12	136.4500
AMZN	2022-09-13	126.8200
AMZN	2022-09-14	128.5500
AMZN	2022-09-15	126.2800
AMZN	2022-09-16	123.5300
AMZN	2022-09-19	124.6600
AMZN	2022-09-20	122.1900
AMZN	2022-09-21	118.5400
AMZN	2022-09-22	117.3100
AMZN	2022-09-23	113.7800
AMZN	2022-09-26	115.1500
AMZN	2022-09-27	114.4100
AMZN	2022-09-28	118.0100
AMZN	2022-09-29	114.8000
AMZN	2022-09-30	113.0000
AMZN	2022-10-03	115.8800
AMZN	2022-10-04	121.0900
AMZN	2022-10-05	120.9500
AMZN	2022-10-06	120.3000
AMZN	2022-10-07	114.5600
AMZN	2022-10-10	113.6700
AMZN	2022-10-11	112.2100
AMZN	2022-10-12	112.9000
AMZN	2022-10-13	112.5300
AMZN	2022-10-14	106.9000
AMZN	2022-10-17	113.7900
AMZN	2022-10-18	116.3600
AMZN	2022-10-19	115.0700
AMZN	2022-10-20	115.2500
AMZN	2022-10-21	119.3200
AMZN	2022-10-24	119.8200
AMZN	2022-10-25	120.6000
AMZN	2022-10-26	115.6600
AMZN	2022-10-27	110.9600
AMZN	2022-10-28	103.4100
AMZN	2022-10-31	102.4400
AMZN	2022-11-01	96.7900
AMZN	2022-11-02	92.1200
AMZN	2022-11-03	89.3000
AMZN	2022-11-04	90.9800
AMZN	2022-11-07	90.5300
AMZN	2022-11-08	89.9800
AMZN	2022-11-09	86.1400
AMZN	2022-11-10	96.6300
AMZN	2022-11-11	100.7900
AMZN	2022-11-14	98.4900
AMZN	2022-11-15	98.9400
AMZN	2022-11-16	97.1200
AMZN	2022-11-17	94.8500
AMZN	2022-11-18	94.1400
AMZN	2022-11-21	92.4600
AMZN	2022-11-22	93.2000
AMZN	2022-11-23	94.1300
AMZN	2022-11-25	93.4100
AMZN	2022-11-28	93.9500
AMZN	2022-11-29	92.4200
AMZN	2022-11-30	96.5400
AMZN	2022-12-01	95.5000
AMZN	2022-12-02	94.1300
AMZN	2022-12-05	91.0100
AMZN	2022-12-06	88.2500
AMZN	2022-12-07	88.4600
AMZN	2022-12-08	90.3500
AMZN	2022-12-09	89.0900
AMZN	2022-12-12	90.5500
AMZN	2022-12-13	92.4900
AMZN	2022-12-14	91.5800
AMZN	2022-12-15	88.4500
AMZN	2022-12-16	87.8600
AMZN	2022-12-19	84.9200
AMZN	2022-12-20	85.1900
AMZN	2022-12-21	86.7700
AMZN	2022-12-22	83.7900
AMZN	2022-12-23	85.2500
AMZN	2022-12-27	83.0400
AMZN	2022-12-28	81.8200
AMZN	2022-12-29	84.1800
AMZN	2022-12-30	84.0000
AMZN	2023-01-03	85.8200
AMZN	2023-01-04	85.1400
AMZN	2023-01-05	83.1200
AMZN	2023-01-06	86.0800
AMZN	2023-01-09	87.3600
AMZN	2023-01-10	89.8700
AMZN	2023-01-11	95.0900
AMZN	2023-01-12	95.2700
AMZN	2023-01-13	98.1200
AMZN	2023-01-17	96.0500
AMZN	2023-01-18	95.4600
AMZN	2023-01-19	93.6800
AMZN	2023-01-20	97.2500
AMZN	2023-01-23	97.5200
AMZN	2023-01-24	96.3200
AMZN	2023-01-25	97.1800
AMZN	2023-01-26	99.2200
AMZN	2023-01-27	102.2400
AMZN	2023-01-30	100.5500
AMZN	2023-01-31	103.1300
AMZN	2023-02-01	105.1500
AMZN	2023-02-02	112.9100
AMZN	2023-02-03	103.3900
AMZN	2023-02-06	102.1800
AMZN	2023-02-07	102.1100
AMZN	2023-02-08	100.0500
AMZN	2023-02-09	98.2400
AMZN	2023-02-10	97.6100
AMZN	2023-02-13	99.5400
AMZN	2023-02-14	99.7000
AMZN	2023-02-15	101.1600
AMZN	2023-02-16	98.1500
AMZN	2023-02-17	97.2000
AMZN	2023-02-21	94.5800
AMZN	2023-02-22	95.7900
AMZN	2023-02-23	95.8200
AMZN	2023-02-24	93.5000
AMZN	2023-02-27	93.7600
AMZN	2023-02-28	94.2300
AMZN	2023-03-01	92.1700
AMZN	2023-03-02	92.1300
AMZN	2023-03-03	94.9000
AMZN	2023-03-06	93.7500
AMZN	2023-03-07	93.5500
AMZN	2023-03-08	93.9200
AMZN	2023-03-09	92.2500
AMZN	2023-03-10	90.7300
AMZN	2023-03-13	92.4300
AMZN	2023-03-14	94.8800
AMZN	2023-03-15	96.2000
AMZN	2023-03-16	100.0400
AMZN	2023-03-17	98.9500
AMZN	2023-03-20	97.7100
AMZN	2023-03-21	100.6100
AMZN	2023-03-22	98.7000
AMZN	2023-03-23	98.7100
AMZN	2023-03-24	98.1300
AMZN	2023-03-27	98.0400
AMZN	2023-03-28	97.2400
AMZN	2023-03-29	100.2500
AMZN	2023-03-30	102.0000
AMZN	2023-03-31	103.2900
AMZN	2023-04-03	102.4100
AMZN	2023-04-04	103.9500
AMZN	2023-04-05	101.1000
AMZN	2023-04-06	102.0600
AMZN	2023-04-10	102.1700
AMZN	2023-04-11	99.9200
AMZN	2023-04-12	97.8300
AMZN	2023-04-13	102.4000
AMZN	2023-04-14	102.5100
AMZN	2023-04-17	102.7400
AMZN	2023-04-18	102.3000
AMZN	2023-04-19	104.3000
AMZN	2023-04-20	103.8100
AMZN	2023-04-21	106.9600
AMZN	2023-04-24	106.2100
AMZN	2023-04-25	102.5700
AMZN	2023-04-26	104.9800
AMZN	2023-04-27	109.8200
AMZN	2023-04-28	105.4500
AMZN	2023-05-01	102.0500
AMZN	2023-05-02	103.6300
AMZN	2023-05-03	103.6500
AMZN	2023-05-04	104.0000
AMZN	2023-05-05	105.6600
AMZN	2023-05-08	105.8300
AMZN	2023-05-09	106.6200
AMZN	2023-05-10	110.1900
AMZN	2023-05-11	112.1800
AMZN	2023-05-12	110.2600
AMZN	2023-05-15	111.2000
AMZN	2023-05-16	113.4000
AMZN	2023-05-17	115.5000
AMZN	2023-05-18	118.1500
AMZN	2023-05-19	116.2500
AMZN	2023-05-22	115.0100
AMZN	2023-05-23	114.9900
AMZN	2023-05-24	116.7500
AMZN	2023-05-25	115.0000
AMZN	2023-05-26	120.1100
AMZN	2023-05-30	121.6600
AMZN	2023-05-31	120.5800
AMZN	2023-06-01	122.7700
AMZN	2023-06-02	124.2500
AMZN	2023-06-05	125.3000
AMZN	2023-06-06	126.6100
AMZN	2023-06-07	121.2300
AMZN	2023-06-08	124.2500
AMZN	2023-06-09	123.4300
AMZN	2023-06-12	126.5700
AMZN	2023-06-13	126.6600
AMZN	2023-06-14	126.4200
AMZN	2023-06-15	127.1100
AMZN	2023-06-16	125.4900
AMZN	2023-06-20	125.7800
AMZN	2023-06-21	124.8300
AMZN	2023-06-22	130.1500
AMZN	2023-06-23	129.3300
AMZN	2023-06-26	127.3300
AMZN	2023-06-27	129.1800
AMZN	2023-06-28	129.0400
AMZN	2023-06-29	127.9000
AMZN	2023-06-30	130.3600
AMZN	2023-07-03	130.2200
AMZN	2023-07-05	130.3800
AMZN	2023-07-06	128.3600
AMZN	2023-07-07	129.7800
AMZN	2023-07-10	127.1300
AMZN	2023-07-11	128.7800
AMZN	2023-07-12	130.8000
AMZN	2023-07-13	134.3000
AMZN	2023-07-14	134.6800
AMZN	2023-07-17	133.5600
AMZN	2023-07-18	132.8300
AMZN	2023-07-19	135.3600
AMZN	2023-07-20	129.9600
AMZN	2023-07-21	130.0000
AMZN	2023-07-24	128.8000
AMZN	2023-07-25	129.1300
AMZN	2023-07-26	128.1500
AMZN	2023-07-27	128.2500
AMZN	2023-07-28	132.2100

Mengubah Ajd Close Menjadi Time series

amzn.ts <- ts(amzn[,3])

Ringkasan Data Ajd CLose

summary(amzn.ts)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   81.82  102.01  115.77  119.81  134.88  170.40

Time Series Amazon

Cara manual

ts.plot(amzn.ts, xlab="Time Period", ylab="Harga Saham", 
        main = "Time Series Amazon", col='orange', lwd=2)
points(amzn.ts, col='orange', lwd=1.5)

# Membuka file PNG untuk menyimpan plot
png("C:/Users/Fathan/Documents/Obsidian Vault/2. Kuliah/Smt 5/6. Metode Peramalan Deret Waktu/@Proj/STA1341-MPDW/Pertemuan 1/Chart/02_Time Series Amazon.png",
    height = 9*300, width = 16*300, res=300)

# Plot time series dengan warna dan pengaturan lainnya
ts.plot(amzn.ts, xlab = "Time Period", ylab = "Harga Saham",
        main = "Time Series Amazon", col = 'orange', lwd = 2)
points(amzn.ts, col = 'orange', lwd = 1.5)

# Menyimpan plot sebagai file PNG
dev.off() # Menutup file PNG

## png 
##   2

Agar lebih menarik, saya coba menggunakan ggplot2. Dengan ggplot2, tipe data tidak perlu dibuah ke Time Series dulu.

cts.amzn <-
ggplot(amzn, aes(x=Date, y=`Adj Close`)) + 
  geom_line(aes(color=Name), linewidth=0.5) +
  scale_color_manual(values = c("cyan4")) +
  theme_minimal()
cts.amzn

#Export Chart
ggsave("03_Time Series Amazon_ggplot.png", cts.amzn, path = export.chart,
        dpi = 300, height = 5, width = 10)

Terlihat bahwa data berpola trend turun karena terjadi penurunan sekuler jangka panjang (perubahan sistematis selama periode waktu yang panjang) dalam data dan cendrung membentuk pola musiman. Oleh karena itu, metode pemulusan yang cocok adalah Double Moving Average (DMA), Double Exponential Smoothing (DES), dan Holt-Winter atau Holt-Winter Multiplikatif.

B. Pemulusan (Smoothing)

Pembagian data

#membagi 80% data latih (training) dan 20% data uji (testing)
training <- amzn[1: round(nrow(amzn) *80/100),]
testing <- amzn[round(nrow(amzn) *80/100): nrow(amzn),]
train.ts <- ts(training[,3])
test.ts <- ts(testing[,3])

Eksplorasi Data

Eksplorasi data dilakukan pada keseluruhan data, data latih serta data uji menggunakan plot data deret waktu.

Menggunakan ggplot2 .

ctsa.train_test <-
ggplot() + 
  geom_line(data = training, 
            aes(x = Date, y = `Adj Close`, col = "Data Latih")) +
  geom_line(data = testing, 
            aes(x = Date, y = `Adj Close`, col = "Data Uji")) +
  labs(x = "Periode Waktu", y = "Harga Saham", color = "Legend") +
  scale_colour_manual(name="Keterangan:", 
                      breaks = c("Data Latih", "Data Uji"),
                      values = c("orange", "cyan4")) + 
  theme_bw() + theme(legend.position = "bottom",
                     plot.caption = element_text(hjust=0.5, size=12))
ctsa.train_test

#Export Chart
ggsave("04_TSA_train-test.png", ctsa.train_test, path = export.chart,
        dpi = 300, height = 5, width = 10)

1. Double Moving Average (DMA)

Metode pemulusan Double Moving Average (DMA) pada dasarnya mirip dengan Single Moving Average (SMA). Namun demikian, metode ini lebih cocok digunakan untuk pola data trend. Proses pemulusan dengan rata rata dalam metode ini dilakukan sebanyak 2 kali.

install_load('TTR')
data.sma <- SMA(train.ts, n=4)

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:nrow(testing)
f = c()

for (i in t) {
  f[i] = At[length(At)] + Bt[length(Bt)]*(i)
}

data.gab2 <- cbind(aktual = c(train.ts,rep(NA, nrow(testing))), 
                   pemulusan1 = c(data.sma,rep(NA, nrow(testing))),
                   pemulusan2 = c(data.dma, rep(NA, nrow(testing))),
                   At = c(At, rep(NA, nrow(testing))), 
                   Bt = c(Bt,rep(NA, nrow(testing))),
                   ramalan = c(data.ramal2, f[-1]))
kable(data.gab2) %>% kable_styling() 

aktual	pemulusan1	pemulusan2	At	Bt	ramalan
170.4045	NA	NA	NA	NA	NA
167.5220	NA	NA	NA	NA	NA
164.3570	NA	NA	NA	NA	NA
163.2540	166.3844	NA	NA	NA	NA
162.5540	164.4217	NA	NA	NA	NA
161.4860	162.9127	NA	NA	NA	NA
165.3620	163.1640	161.40280	162.10728	-0.7044792	NA
165.2070	163.6522	163.84319	163.76681	0.0763753	161.40280
161.2140	163.3172	163.41006	163.37294	0.0371260	163.84319
162.1380	163.4803	163.60828	163.55707	0.0512098	163.41006
158.9175	161.8691	159.85147	160.65853	-0.8070622	163.60828
156.2990	159.6421	155.58369	157.20706	-1.6233756	159.85147
151.6675	157.2555	151.74508	153.94924	-2.2041684	155.58369
142.6430	152.3817	143.37279	146.97637	-3.6035837	151.74508
144.5440	148.7884	139.24077	143.05982	-3.8190404	143.37279
139.9860	144.7101	134.58711	138.63631	-4.0492078	139.24077
138.8725	141.5114	132.61716	136.17484	-3.5576872	134.58711
139.6375	140.7600	135.45588	137.57753	-2.1216468	132.61716
143.9780	140.6185	138.48266	139.33699	-0.8543350	135.45588
149.5735	143.0154	145.58048	144.55444	1.0260418	138.48266
151.1935	146.0956	151.88437	149.56887	2.3155003	145.58048
150.6125	148.8394	155.83464	153.03653	2.7981052	151.88437
138.8455	147.5563	149.52224	148.73585	0.7863973	155.83464
157.6395	149.5728	152.16733	151.12950	1.0378335	149.52224
157.9355	151.2583	154.51091	153.20985	1.3010628	152.16733
161.4135	153.9585	159.57860	157.33056	2.2480411	154.51091
161.1895	159.5445	169.47950	165.50550	3.9739990	159.57860
159.0035	159.8855	166.09185	163.60931	2.4825407	169.47950
153.2935	158.7250	159.88604	159.42162	0.4644165	166.09185
155.1670	157.1634	154.38635	155.49716	-1.1108113	159.88604
156.5105	155.9936	152.74654	154.04538	-1.2988326	154.38635
158.1005	155.7679	153.86022	154.62328	-0.7630622	152.74654
154.6525	156.1076	155.85679	155.95712	-0.1003343	153.86022
152.6015	155.4662	154.85359	155.09865	-0.2450638	155.85679
150.1975	153.8880	151.52226	152.46856	-0.9462928	154.85359
144.8270	150.5696	144.83920	147.13137	-2.2921669	151.52226
151.3580	149.7460	145.29355	147.07453	-1.7809784	144.83920
153.7885	150.0427	148.34468	149.02390	-0.6792290	145.29355
153.5630	150.8841	151.83996	151.45763	0.3823345	148.34468
151.1420	152.4629	155.26111	154.14181	1.1192925	151.83996
152.0525	152.6365	154.51973	153.76644	0.7532926	155.26111
147.8985	151.1640	150.12588	150.54113	-0.4152495	154.51973
145.6410	149.1835	145.55314	147.00528	-1.4521454	150.12588
137.4530	145.7613	139.21948	141.83619	-2.6167075	145.55314
136.0145	141.7518	133.06279	136.53838	-3.4755840	139.21948
139.2790	139.5969	132.13610	135.12041	-2.9843120	133.06279
146.8175	139.8910	136.79231	138.03178	-1.2394790	132.13610
145.5245	141.9089	143.77846	143.03063	0.7478340	136.79231
141.8530	143.3685	146.99715	145.54569	1.4514587	143.77846
147.3665	145.3904	149.97486	148.14106	1.8337911	146.99715
153.1040	146.9620	151.21960	149.51656	1.7030411	149.97486
157.2390	149.8906	155.70354	153.37837	2.3251653	151.21960
161.2505	154.7400	163.89709	160.23425	3.6628335	155.70354
161.4915	158.2713	167.94672	164.07653	3.8701877	163.89709
164.8890	161.2175	169.86360	166.40516	3.4584383	167.94672
163.4080	162.7598	168.61413	166.27238	2.3417512	169.86360
163.6495	163.3595	166.62201	165.31701	1.3050010	168.61413
164.7735	164.1800	166.34803	165.48082	0.8672085	166.62201
168.9905	165.2054	167.42074	166.53459	0.8861440	166.34803
169.3150	166.6821	169.72441	168.50750	1.2169150	167.42074
166.3010	167.3450	169.83145	168.83687	0.9945811	169.72441
162.9975	166.9010	167.51370	167.26862	0.2450822	169.83145
163.5600	165.5434	163.75254	164.46887	-0.7163334	167.51370
168.3465	165.3012	163.68224	164.32984	-0.6476045	163.75254
164.0550	164.7397	163.27042	163.85815	-0.5877297	163.68224
158.7560	163.6794	161.78510	162.54281	-0.7577088	163.27042
157.7845	162.2355	159.31305	160.48203	-1.1689791	161.78510
154.4605	158.7640	152.77957	155.17334	-2.3937710	159.31305
151.1220	155.5307	147.99465	151.00909	-3.0144375	152.77957
150.7875	153.5386	146.90764	149.56003	-2.6523947	147.99465
155.5410	152.9777	149.26937	150.75272	-1.4833534	146.90764
151.7065	152.2892	150.13118	150.99441	-0.8632285	149.26937
152.7850	152.7050	152.41724	152.53235	-0.1151028	150.13118
158.1155	154.5370	156.88658	155.94675	0.9398327	152.41724
153.9980	154.1512	155.36896	154.88187	0.4870829	156.88658
148.2960	153.2986	152.67472	152.92428	-0.2495619	155.36896
144.3500	151.1899	147.68269	149.08557	-1.4028740	152.67472
146.0740	148.1795	142.30399	144.65419	-2.3502065	147.68269
139.3910	144.5278	136.57578	139.75657	-3.1807900	142.30399
138.1670	141.9955	134.53275	137.51785	-2.9851030	136.57578
144.5965	142.0571	138.50239	139.92428	-1.4218966	134.53275
124.2815	136.6090	128.79509	131.92066	-3.1255635	138.50239
124.5000	132.8863	123.71838	127.38553	-3.6671472	128.79509
124.2535	129.4079	119.68756	123.57569	-3.8881263	123.71838
125.9285	124.7409	114.45733	118.57075	-4.1134173	119.68756
116.4070	122.7722	114.97298	118.09269	-3.1197090	114.45733
114.7725	120.3404	113.71542	116.36540	-2.6499796	114.97298
108.7890	116.4742	108.79477	111.86656	-3.0717920	113.71542
108.8590	112.2069	102.63760	106.46531	-3.8277080	108.79477
105.3720	109.4481	100.83266	104.27885	-3.4461867	102.63760
106.9305	107.4876	100.95997	103.57103	-2.6110624	100.83266
113.0550	108.5541	107.10402	107.68406	-0.5800419	100.95997
110.8105	109.0420	109.72372	109.45103	0.2726873	107.10402
115.3685	111.5411	115.51597	113.92603	1.5899372	109.72372
107.1125	111.5866	113.92939	112.99228	0.9371049	115.51597
107.3190	110.1526	109.43935	109.72466	-0.2853120	113.92939
107.5910	109.3478	107.16562	108.03847	-0.8728536	109.43935
107.5570	107.3949	103.68555	105.16928	-1.4837291	107.16562
104.1000	106.6418	103.73758	104.89925	-1.1616673	103.68555
106.7750	106.5058	104.89445	105.53897	-0.6445210	103.73758
111.0775	107.3774	108.03977	107.77481	0.2649578	104.89445
115.1465	109.2747	112.31616	111.09959	1.2165624	108.03977
120.2095	113.3021	120.28067	117.48925	2.7914172	112.31616
121.6840	117.0294	125.83516	122.31284	3.5223125	120.28067
125.5110	120.6378	129.93233	126.21450	3.7178336	125.83516
122.3500	122.4386	129.24972	126.52528	2.7244373	129.93233
124.7900	123.5837	128.01937	126.24512	1.7742497	129.24972
123.0000	123.9128	126.02864	125.18228	0.8463542	128.01937
121.1800	122.8300	122.22786	122.46872	-0.2408543	126.02864
116.1500	121.2800	118.57729	119.65838	-1.0810829	122.22786
109.6500	117.4950	111.02094	113.61056	-2.5896246	118.57729
103.6700	112.6625	102.82188	106.75813	-3.9362500	111.02094
102.3100	107.9450	96.44396	101.04437	-4.6004170	102.82188
107.6700	105.8250	97.23021	100.66812	-3.4379174	96.44396
103.6600	104.3275	98.72333	100.96500	-2.2416668	97.23021
106.2200	104.9650	103.63063	104.16438	-0.5337496	98.72333
108.6800	106.5575	108.45542	107.69625	0.7591672	103.63063
108.9500	106.8775	108.87021	108.07313	0.7970835	108.45542
112.4400	109.0725	112.74646	111.27687	1.4695831	108.87021
116.4600	111.6325	116.79500	114.73000	2.0649995	112.74646
113.2200	112.7675	117.23417	115.44750	1.7866665	116.79500
107.4000	112.3800	113.90813	113.29688	0.6112506	117.23417
108.9200	111.5000	110.55000	110.93000	-0.3800000	113.90813
106.2100	108.9375	104.83958	106.47875	-1.6391668	110.55000
109.5600	108.0225	104.37666	105.83500	-1.4583339	104.83958
113.5000	109.5475	109.62354	109.59312	0.0304162	104.37666
114.3300	110.9000	113.48021	112.44813	1.0320835	109.62354
116.3300	113.4300	118.35500	116.38500	1.9700006	113.48021
115.5400	114.9250	119.46563	117.64938	1.8162508	118.35500
111.7500	114.4875	116.24063	115.53938	0.7012504	119.46563
109.2200	113.2100	111.87146	112.40688	-0.5354167	116.24063
110.4000	111.7275	108.62750	109.86750	-1.2400001	111.87146
110.6300	110.5000	107.19792	108.51875	-1.3208339	108.62750
113.5500	110.9500	109.87188	110.30313	-0.4312500	107.19792
113.7600	112.0850	113.36729	112.85438	0.5129169	109.87188
118.2100	114.0375	117.61146	116.18188	1.4295832	113.36729
122.7700	117.0725	122.96625	120.60875	2.3574998	117.61146
124.6300	119.8425	126.64770	123.92562	2.7220825	122.96625
122.4200	122.0075	128.28666	125.77500	2.5116657	126.64770
121.1400	122.7400	126.61395	125.06437	1.5495827	128.28666
114.8100	120.7500	119.77500	120.16500	-0.3900000	126.61395
120.9700	119.8350	117.33813	118.33687	-0.9987494	119.77500
122.2800	119.8000	118.16458	118.81875	-0.6541662	117.33813
134.9500	123.2525	127.15771	125.59562	1.5620833	118.16458
135.3900	128.3975	137.69125	133.97375	3.7175000	127.15771
134.1600	131.6950	141.54292	137.60375	3.9391670	137.69125
139.5200	136.0050	146.28417	142.17250	4.1116676	141.54292
142.5700	137.9100	145.25688	142.31813	2.9387518	146.28417
140.8000	139.2625	144.33647	142.30688	2.0295849	145.25688
139.4100	140.5750	144.13646	142.71188	1.4245841	144.33647
137.8300	140.1525	141.28167	140.83000	0.4516666	144.13646
142.6900	140.1825	140.41479	140.32188	0.0929159	141.28167
140.6400	140.1425	139.94146	140.02188	-0.0804177	140.41479
143.5500	141.1775	142.45042	141.94125	0.5091660	139.94146
143.1800	142.5150	145.03270	144.02562	1.0070820	142.45042
144.7800	143.0375	145.23645	144.35687	0.8795822	145.03270
142.1000	143.4025	144.85146	144.27188	0.5795836	145.23645
142.3000	143.0900	143.22125	143.16875	0.0525005	144.85146
138.2300	141.8525	140.19729	140.85938	-0.6620827	143.22125
133.2200	138.9625	134.18854	136.09813	-1.9095828	140.19729
133.6200	136.8425	131.26854	133.49812	-2.2295844	134.18854
133.8000	134.7175	129.09041	131.34125	-2.2508342	131.26854
137.2800	134.4800	131.52896	132.70937	-1.1804168	129.09041
130.7500	133.8625	132.00729	132.74937	-0.7420832	131.52896
129.7900	132.9050	131.09458	131.81875	-0.7241669	132.00729
128.7300	131.6375	128.99791	130.05375	-1.0558344	131.09458
126.7700	129.0100	124.27041	126.16625	-1.8958343	128.99791
127.8200	128.2775	124.64416	126.09750	-1.4533338	124.27041
127.5100	127.7075	125.28979	126.25688	-0.9670823	124.64416
126.1100	127.0525	125.45355	126.09313	-0.6395820	125.28979
129.4800	127.7300	127.79354	127.76813	0.0254173	125.45355
129.8200	128.2300	129.14667	128.78000	0.3666677	127.79354
133.2700	129.6700	132.16896	131.16938	0.9995841	129.14667
136.4500	132.2550	136.89458	135.03875	1.8558333	132.16896
126.8200	131.5900	133.51292	132.74375	0.7691669	136.89458
128.5500	131.2725	131.39854	131.34813	0.0504163	133.51292
126.2800	129.5250	126.79896	127.88937	-1.0904175	131.39854
123.5300	126.2950	120.66896	122.91937	-2.2504170	126.79896
124.6600	125.7550	121.66021	123.29813	-1.6379162	120.66896
122.1900	124.1650	120.38167	121.89500	-1.5133330	121.66021
118.5400	122.2300	118.26125	119.84875	-1.5874997	120.38167
117.3100	120.6750	116.45625	118.14375	-1.6875000	118.26125
113.7800	117.9550	112.45292	114.65375	-2.2008340	116.45625
115.1500	116.1950	111.08042	113.12625	-2.0458338	112.45292
114.4100	115.1625	111.27188	112.82813	-1.5562498	111.08042
118.0100	115.3375	113.96250	114.51250	-0.5499993	111.27188
114.8000	115.5925	115.62688	115.61313	0.0137510	113.96250
113.0000	115.0550	114.66854	114.82313	-0.1545831	115.62688
115.8800	115.4225	115.54021	115.49312	0.0470825	114.66854
121.0900	116.1925	117.23729	116.81937	0.4179152	115.54021
120.9500	117.7300	120.44666	119.36000	1.0866651	117.23729
120.3000	119.5550	123.43833	121.88500	1.5533330	120.44666
114.5600	119.2250	120.97396	120.27437	0.6995835	123.43833
113.6700	117.3700	115.53667	116.27000	-0.7333329	120.97396
112.2100	115.1850	110.77042	112.53625	-1.7658329	115.53667
112.9000	113.3350	108.42875	110.39125	-1.9624999	110.77042
112.5300	112.8275	109.74104	110.97562	-1.2345832	108.42875
106.9000	111.1350	107.82563	109.14938	-1.3237495	109.74104
113.7900	111.5300	110.40188	110.85313	-0.4512494	107.82563
116.3600	112.3950	113.10021	112.81813	0.2820835	110.40188
115.0700	113.0300	114.70917	114.03750	0.6716668	113.10021
115.2500	115.1175	118.61646	117.21688	1.3995831	114.70917
119.3200	116.5000	120.23229	118.73937	1.4929164	118.61646
119.8200	117.3650	120.46812	119.22687	1.2412497	120.23229
120.6000	118.7475	121.77250	120.56250	1.2099996	120.46812
115.6600	118.8500	120.49063	119.83438	0.6562503	121.77250
110.9600	116.7600	114.80896	115.58938	-0.7804165	120.49063
103.4100	112.6575	105.83042	108.56125	-2.7308328	114.80896
102.4400	108.1175	98.15292	102.13875	-3.9858325	105.83042
96.7900	103.4000	92.01042	96.56625	-4.5558332	98.15292
92.1200	98.6900	86.97959	91.66375	-4.6841663	92.01042
89.3000	95.1625	84.86250	88.98250	-4.1199999	86.97959
90.9800	92.2975	83.81417	87.20750	-3.3933331	84.86250
90.5300	90.7325	84.91896	87.24438	-2.3254169	83.81417
89.9800	90.1975	87.03083	88.29750	-1.2666668	84.91896
86.1400	89.4075	87.32208	88.15625	-0.8341673	87.03083
96.6300	90.8200	91.70437	91.35062	0.3537489	87.32208
100.7900	93.3850	97.43917	95.81750	1.6216662	91.70437
98.4900	95.5125	100.89791	98.74375	2.1541660	97.43917
98.9400	98.7125	105.55417	102.81750	2.7366667	100.89791
97.1200	98.8350	102.54125	101.05875	1.4825008	105.55417
94.8500	97.3500	96.92917	97.09750	-0.1683331	102.54125
94.1400	96.2625	93.71667	94.73500	-1.0183332	96.92917
92.4600	94.6425	91.09250	92.51250	-1.4200004	93.71667
93.2000	93.6625	90.63437	91.84562	-1.2112510	91.09250
94.1300	93.4825	91.76583	92.45250	-0.6866674	90.63437
93.4100	93.3000	92.51354	92.82812	-0.3145830	91.76583
93.9500	93.6725	93.91104	93.81562	0.0954168	92.51354
92.4200	93.4775	93.46812	93.47187	-0.0037498	93.91104
96.5400	94.0800	94.82583	94.52750	0.2983338	93.46812
95.5000	94.6025	95.67646	95.24687	0.4295832	94.82583
94.1300	94.6475	95.39021	95.09312	0.2970832	95.67646
91.0100	94.2950	94.10958	94.18375	-0.0741663	95.39021
88.2500	92.2225	89.35688	90.50313	-1.1462498	94.10958
88.4600	90.4625	86.38854	88.01812	-1.6295834	89.35688
90.3500	89.5175	86.00604	87.41062	-1.4045833	86.38854
89.0900	89.0375	86.91666	87.76500	-0.8483340	86.00604
90.5500	89.6125	89.53750	89.56750	-0.0300001	86.91666
92.4900	90.6200	92.15854	91.54312	0.6154165	89.53750
91.5800	90.9275	92.39104	91.80563	0.5854172	92.15854
88.4500	90.7675	91.24354	91.05313	0.1904171	92.39104
87.8600	90.0950	89.24917	89.58750	-0.3383333	91.24354
84.9200	88.2025	85.20979	86.40687	-1.1970835	89.24917
85.1900	86.6050	82.75083	84.29250	-1.5416668	85.20979
86.7700	86.1850	83.54021	84.59812	-1.0579167	82.75083
83.7900	85.1675	82.88000	83.79500	-0.9150000	83.54021
85.2500	85.2500	84.33021	84.69813	-0.3679164	82.88000
83.0400	84.7125	83.68542	84.09625	-0.4108333	84.33021
81.8200	83.4750	81.51458	82.29875	-0.7841663	83.68542
84.1800	83.5725	82.43917	82.89250	-0.4533333	81.51458
84.0000	83.2600	82.43500	82.76500	-0.3300000	82.43917
85.8200	83.9550	84.60396	84.34437	0.2595832	82.43500
85.1400	84.7850	86.27146	85.67687	0.5945831	84.60396
83.1200	84.5200	85.17000	84.91000	0.2600002	86.27146
86.0800	85.0400	85.81500	85.50500	0.3100005	85.17000
87.3600	85.4250	86.22917	85.90750	0.3216671	85.81500
89.8700	86.6075	88.62313	87.81688	0.8062507	86.22917
95.0900	89.6000	94.48646	92.53187	1.9545828	88.62313
95.2700	91.8975	97.75583	95.41250	2.3433323	94.48646
98.1200	94.5875	101.11146	98.50187	2.6095829	97.75583
96.0500	96.1325	101.26271	99.21062	2.0520833	101.11146
95.4600	96.2250	98.74896	97.73938	1.0095838	101.26271
93.6800	95.8275	96.05146	95.96188	0.0895840	98.74896
97.2500	95.6100	95.04542	95.27125	-0.2258333	96.05146
97.5200	95.9775	96.09000	96.04500	0.0449991	95.04542
96.3200	96.1925	96.67687	96.48312	0.1937495	96.09000
97.1800	97.0675	98.49354	97.92312	0.5704165	96.67687
99.2200	97.5600	98.99437	98.42062	0.5737502	98.49354
102.2400	98.7400	100.99000	100.09000	0.9000002	98.99437
100.5500	99.7975	102.30792	101.30375	1.0041672	100.99000
103.1300	101.2850	104.51729	103.22437	1.2929166	102.30792
105.1500	102.7675	106.30083	104.88750	1.4133333	104.51729
112.9100	105.4350	110.62459	108.54875	2.0758340	106.30083
103.3900	106.1450	109.87313	108.38188	1.4912500	110.62459
102.1800	105.9075	107.31375	106.75125	0.5625003	109.87313
102.1100	105.1475	104.29542	104.63625	-0.3408334	107.31375
100.0500	101.9325	97.18146	99.08188	-1.9004168	104.29542
98.2400	100.6450	96.03979	97.88188	-1.8420836	97.18146
97.6100	99.5025	95.66188	97.19813	-1.5362500	96.03979
99.5400	98.8600	96.56833	97.48500	-0.9166666	95.66188
99.7000	98.7725	97.65166	98.10000	-0.4483340	96.56833
101.1600	99.5025	100.07438	99.84563	0.2287502	97.65166
98.1500	99.6375	100.37813	100.08188	0.2962504	100.07438
97.2000	99.0525	98.73792	98.86375	-0.1258335	100.37813
94.5800	97.7725	95.74125	96.55375	-0.8124997	98.73792
95.7900	96.4300	93.44146	94.63688	-1.1954168	95.74125
95.8200	95.8475	93.46729	94.41937	-0.9520836	93.44146
93.5000	94.9225	92.72146	93.60188	-0.8804166	93.46729
93.7600	94.7175	93.44771	93.95563	-0.5079165	92.72146
94.2300	94.3275	93.28375	93.70125	-0.4174996	93.44771
92.1700	93.4150	91.86396	92.48438	-0.6204168	93.28375
92.1300	93.0725	91.72146	92.26187	-0.5404171	91.86396
94.9000	93.3575	93.04812	93.17187	-0.1237503	91.72146
93.7500	93.2375	93.18229	93.20437	-0.0220838	93.04812
93.5500	93.5825	94.03250	93.85250	0.1800004	93.18229
93.9200	94.0300	94.82688	94.50813	0.3187504	94.03250
92.2500	93.3675	93.05604	93.18063	-0.1245833	94.82688
90.7300	92.6125	91.30313	91.82688	-0.5237498	93.05604
92.4300	92.3325	91.07729	91.57937	-0.5020835	91.30313
94.8800	92.5725	92.32458	92.42375	-0.0991669	91.07729
96.2000	93.5600	94.87771	94.35062	0.5270827	92.32458
100.0400	95.8875	99.71979	98.18687	1.5329161	94.87771
98.9500	97.5175	101.90604	100.15062	1.7554160	99.71979
97.7100	98.2250	101.43750	100.15250	1.2849999	101.90604
100.6100	99.3275	101.97438	100.91563	1.0587505	101.43750
98.7000	98.9925	99.78729	99.46937	0.3179166	101.97438
98.7100	98.9325	99.03771	98.99562	0.0420834	99.78729
98.1300	99.0375	98.97916	99.00250	-0.0233336	99.03771
98.0400	98.3950	97.65437	97.95062	-0.2962501	98.97916
97.2400	98.0300	97.08208	97.46125	-0.3791666	97.65437
100.2500	98.4150	98.32437	98.36062	-0.0362498	97.08208
102.0000	99.3825	100.76063	100.20938	0.5512505	98.32437
103.2900	100.6950	103.30229	102.25938	1.0429170	100.76063
102.4100	101.9875	105.10000	103.85500	1.2450009	103.30229
103.9500	102.9125	105.69271	104.58063	1.1120835	105.10000
NA	NA	NA	NA	NA	105.69271
NA	NA	NA	NA	NA	106.80479
NA	NA	NA	NA	NA	107.91688
NA	NA	NA	NA	NA	109.02896
NA	NA	NA	NA	NA	110.14104
NA	NA	NA	NA	NA	111.25313
NA	NA	NA	NA	NA	112.36521
NA	NA	NA	NA	NA	113.47729
NA	NA	NA	NA	NA	114.58938
NA	NA	NA	NA	NA	115.70146
NA	NA	NA	NA	NA	116.81354
NA	NA	NA	NA	NA	117.92563
NA	NA	NA	NA	NA	119.03771
NA	NA	NA	NA	NA	120.14979
NA	NA	NA	NA	NA	121.26188
NA	NA	NA	NA	NA	122.37396
NA	NA	NA	NA	NA	123.48604
NA	NA	NA	NA	NA	124.59813
NA	NA	NA	NA	NA	125.71021
NA	NA	NA	NA	NA	126.82229
NA	NA	NA	NA	NA	127.93438
NA	NA	NA	NA	NA	129.04646
NA	NA	NA	NA	NA	130.15855
NA	NA	NA	NA	NA	131.27063
NA	NA	NA	NA	NA	132.38271
NA	NA	NA	NA	NA	133.49480
NA	NA	NA	NA	NA	134.60688
NA	NA	NA	NA	NA	135.71896
NA	NA	NA	NA	NA	136.83105
NA	NA	NA	NA	NA	137.94313
NA	NA	NA	NA	NA	139.05521
NA	NA	NA	NA	NA	140.16730
NA	NA	NA	NA	NA	141.27938
NA	NA	NA	NA	NA	142.39146
NA	NA	NA	NA	NA	143.50355
NA	NA	NA	NA	NA	144.61563
NA	NA	NA	NA	NA	145.72771
NA	NA	NA	NA	NA	146.83980
NA	NA	NA	NA	NA	147.95188
NA	NA	NA	NA	NA	149.06396
NA	NA	NA	NA	NA	150.17605
NA	NA	NA	NA	NA	151.28813
NA	NA	NA	NA	NA	152.40021
NA	NA	NA	NA	NA	153.51230
NA	NA	NA	NA	NA	154.62438
NA	NA	NA	NA	NA	155.73646
NA	NA	NA	NA	NA	156.84855
NA	NA	NA	NA	NA	157.96063
NA	NA	NA	NA	NA	159.07272
NA	NA	NA	NA	NA	160.18480
NA	NA	NA	NA	NA	161.29688
NA	NA	NA	NA	NA	162.40897
NA	NA	NA	NA	NA	163.52105
NA	NA	NA	NA	NA	164.63313
NA	NA	NA	NA	NA	165.74522
NA	NA	NA	NA	NA	166.85730
NA	NA	NA	NA	NA	167.96938
NA	NA	NA	NA	NA	169.08147
NA	NA	NA	NA	NA	170.19355
NA	NA	NA	NA	NA	171.30563
NA	NA	NA	NA	NA	172.41772
NA	NA	NA	NA	NA	173.52980
NA	NA	NA	NA	NA	174.64188
NA	NA	NA	NA	NA	175.75397
NA	NA	NA	NA	NA	176.86605
NA	NA	NA	NA	NA	177.97813
NA	NA	NA	NA	NA	179.09022
NA	NA	NA	NA	NA	180.20230
NA	NA	NA	NA	NA	181.31438
NA	NA	NA	NA	NA	182.42647
NA	NA	NA	NA	NA	183.53855
NA	NA	NA	NA	NA	184.65063
NA	NA	NA	NA	NA	185.76272
NA	NA	NA	NA	NA	186.87480
NA	NA	NA	NA	NA	187.98689
NA	NA	NA	NA	NA	189.09897
NA	NA	NA	NA	NA	190.21105
NA	NA	NA	NA	NA	191.32314
NA	NA	NA	NA	NA	192.43522
NA	NA	NA	NA	NA	193.54730

Visualisasi hasil pemulusan menggunakan metode DMA

ts.plot(amzn.ts, xlab="Time Period ", ylab="Average Price", 
        main= "DMA N=4 Data Saham Amazon Periode 2022-2023")
points(amzn.ts)
lines(data.gab2[,3],col="cyan4",lwd=2)
lines(data.gab2[,6],col="orange",lwd=2)
legend("topleft",c("data aktual","data pemulusan","data peramalan"), 
       lty=8, col=c("black","cyan4","orange"), cex=0.8)

# Membuka file PNG untuk menyimpan plot
png("C:/Users/Fathan/Documents/Obsidian Vault/2. Kuliah/Smt 5/6. Metode Peramalan Deret Waktu/@Proj/STA1341-MPDW/Pertemuan 1/Chart/05_TSA_DMA-n4.png",
    height = 9*300, width = 16*300, res=300)

# Plot time series dengan warna dan pengaturan lainnya
ts.plot(amzn.ts, xlab="Time Period ", ylab="Average Price", 
        main= "DMA N=4 Data Saham Amazon Periode 2022-2023")
points(amzn.ts)
lines(data.gab2[,3],col="cyan4",lwd=2)
lines(data.gab2[,6],col="orange",lwd=2)
legend("topleft",c("data aktual","data pemulusan","data peramalan"), 
       lty=8, col=c("black","cyan4","orange"), cex=0.8)

# Menyimpan plot sebagai file PNG
dev.off() # Menutup file PNG

## png 
##   2

Akurasi Data Latih

Selanjutnya perhitungan akurasi dilakukan baik pada data latih maupun data uji. Perhitungan akurasi dilakukan dengan ukuran Sum Squares Error (SSE), Mean Square Error (MSE) dan Mean Absolute Percentage Error (MAPE).

#Menghitung nilai keakuratan data latih

error_train.dma = train.ts - data.ramal2[1:length(train.ts)]
SSE_train.dma = sum(error_train.dma[8:length(train.ts)]^2)
MSE_train.dma = mean(error_train.dma[8:length(train.ts)]^2)
MAPE_train.dma = mean(abs((error_train.dma[8:length(train.ts)]/
                             train.ts[8:length(train.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")
kable(akurasi_train.dma) %>% kable_styling()

	Akurasi m = 4
SSE	7582.684345
MSE	24.619105
MAPE	3.284713

Semakin kecil SSE, MSE, dan MAPE maka semakin akurat sebuah model dalam melakukan peramalan. Perhitungan akurasi pada data latih menggunakan nilai MAPE menghasilkan nilai MAPE diantara 10-20 sehingga nilai akurasi ini dapat dikategorikan baik. Selanjutnya, perhitungan nilai akurasi dilakukan pada data uji.

Akurasi Data Uji

#Menghitung nilai keakuratan data uji

error_test.dma = test.ts - 
  data.gab2[nrow(training) : nrow(amzn),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.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")
kable(akurasi_test.dma) %>% kable_styling()

	Akurasi m = 4
SSE	91763.86806
MSE	1147.04835
MAPE	24.73109

Perhitungan akurasi pada data uji menghasilkan nilai MAPE di antara 20-50 sehingga nilai akurasi ini dapat dikategorikan sebagai layak (cukup baik).

2. Double Exponential Smoothing (DES)

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. Model tunggal atau Single Exponential Smoothing (SES) merupakan metode pemulusan yang tepat untuk data dengan pola stasioner atau konstan. Sedangkan model ganda atau Double Exponential Smoothing (DES) untuk data berpola tren. Data harga saham amazon periode 2022-2023 cenderung berpola tren sehingga menggunakan metode pemulusan DES.

Metode pemulusan 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 ini akan menggunakan fungsi HoltWinters() . Nilai argumen beta diinisialisasi bersamaan dengan nilai alpha dan nilai argumen gamma dibuat FALSE.

install_load('forecast')

## Warning: package 'forecast' was built under R version 4.2.3

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

#beta=0.2 dan alpha=0.2
des.1<- HoltWinters(train.ts, gamma = FALSE, beta = 0.2, alpha = 0.2)
plot(des.1, lwd=2)

#ramalan
ramalandes1<- forecast(des.1, h= nrow(testing))     #h = panjang periode
kable(ramalandes1) %>% kable_styling()

	Point Forecast	Lo 80	Hi 80	Lo 95	Hi 95
316	103.8783	95.547935	112.2087	91.1380900	116.6186
317	104.5073	95.940312	113.0742	91.4052420	117.6093
318	105.1362	96.257388	114.0150	91.5572300	118.7152
319	105.7651	96.494784	115.0355	91.5873575	119.9429
320	106.3941	96.650709	116.1374	91.4928868	121.2952
321	107.0230	96.725608	117.3204	91.2744975	122.7715
322	107.6519	96.721644	118.5822	90.9354973	124.3684
323	108.2809	96.642141	119.9196	90.4809711	126.0808
324	108.9098	96.491087	121.3285	89.9170153	127.9026
325	109.5387	96.272730	122.8047	89.2501304	129.8273
326	110.1677	95.991307	124.3440	88.4867927	131.8486
327	110.7966	95.650857	125.9424	87.6331818	133.9600
328	111.4255	95.255129	127.5960	86.6950311	136.1560
329	112.0545	94.807538	129.3014	85.6775619	138.4314
330	112.6834	94.311157	131.0557	84.5854743	140.7813
331	113.3123	93.768731	132.8560	83.4229686	143.2017
332	113.9413	93.182708	134.6998	82.1937850	145.6888
333	114.5702	92.555260	136.5852	80.9012493	148.2392
334	115.1991	91.888324	138.5100	79.5483204	150.8500
335	115.8281	91.183622	140.4725	78.1376346	153.5185
336	116.4570	90.442695	142.4713	76.6715471	156.2425
337	117.0859	89.666923	144.5050	75.1521684	159.0197
338	117.7149	88.857546	146.5722	73.5813962	161.8484
339	118.3438	88.015686	148.6719	71.9609433	164.7267
340	118.9727	87.142355	150.8031	70.2923619	167.6531
341	119.6017	86.238478	152.9649	68.5770633	170.6263
342	120.2306	85.304897	155.1563	66.8163366	173.6449
343	120.8596	84.342384	157.3767	65.0113629	176.7077
344	121.4885	83.351650	159.6253	63.1632289	179.8137
345	122.1174	82.333352	161.9015	61.2729377	182.9619
346	122.7464	81.288095	164.2046	59.3414183	186.1513
347	123.3753	80.216446	166.5341	57.3695340	189.3810
348	124.0042	79.118929	168.8895	55.3580897	192.6504
349	124.6332	77.996037	171.2703	53.3078376	195.9585
350	125.2621	76.848232	173.6760	51.2194830	199.3047
351	125.8910	75.675946	176.1061	49.0936886	202.6884
352	126.5200	74.479588	178.5603	46.9310791	206.1088
353	127.1489	73.259543	181.0382	44.7322443	209.5655
354	127.7778	72.016177	183.5395	42.4977424	213.0579
355	128.4068	70.749836	186.0637	40.2281029	216.5854
356	129.0357	69.460848	188.6105	37.9238290	220.1476
357	129.6646	68.149528	191.1797	35.5853997	223.7439
358	130.2936	66.816173	193.7710	33.2132719	227.3739
359	130.9225	65.461069	196.3839	30.8078821	231.0371
360	131.5514	64.084490	199.0184	28.3696476	234.7332
361	132.1804	62.686696	201.6740	25.8989686	238.4618
362	132.8093	61.267939	204.3507	23.3962289	242.2224
363	133.4382	59.828459	207.0480	20.8617973	246.0147
364	134.0672	58.368489	209.7658	18.2960283	249.8383
365	134.6961	56.888252	212.5040	15.6992634	253.6929
366	135.3250	55.387963	215.2621	13.0718320	257.5782
367	135.9540	53.867830	218.0401	10.4140516	261.4939
368	136.5829	52.328054	220.8378	7.7262292	265.4396
369	137.2118	50.768828	223.6549	5.0086615	269.4150
370	137.8408	49.190340	226.4912	2.2616355	273.4199
371	138.4697	47.592773	229.3466	-0.5145707	277.4540
372	139.0986	45.976302	232.2210	-3.3196875	281.5170
373	139.7276	44.341098	235.1141	-6.1534535	285.6086
374	140.3565	42.687328	238.0257	-9.0156148	289.7286
375	140.9854	41.015152	240.9557	-11.9059251	293.8768
376	141.6144	39.324727	243.9040	-14.8241446	298.0529
377	142.2433	37.616205	246.8704	-17.7700403	302.2567
378	142.8722	35.889736	249.8548	-20.7433854	306.4879
379	143.5012	34.145462	252.8569	-23.7439590	310.7463
380	144.1301	32.383526	255.8767	-26.7715459	315.0318
381	144.7591	30.604063	258.9140	-29.8259364	319.3440
382	145.3880	28.807209	261.9688	-32.9069258	323.6829
383	146.0169	26.993093	265.0407	-36.0143146	328.0482
384	146.6459	25.161842	268.1299	-39.1479078	332.4396
385	147.2748	23.313582	271.2360	-42.3075151	336.8571
386	147.9037	21.448434	274.3590	-45.4929506	341.3004
387	148.5327	19.566517	277.4988	-48.7040325	345.7693
388	149.1616	17.667947	280.6552	-51.9405831	350.2638
389	149.7905	15.752837	283.8282	-55.2024284	354.7835
390	150.4195	13.821299	287.0176	-58.4893983	359.3283
391	151.0484	11.873442	290.2233	-61.8013262	363.8981
392	151.6773	9.909372	293.4453	-65.1380491	368.4927
393	152.3063	7.929195	296.6833	-68.4994071	373.1119
394	152.9352	5.933011	299.9374	-71.8852436	377.7556
395	153.5641	3.920923	303.2073	-75.2954052	382.4237

#beta=0.3 dan aplha=0.6
des.2<- HoltWinters(train.ts, gamma = FALSE, beta = 0.3, alpha = 0.6)
plot(des.2, lwd=2)

#ramalan
ramalandes2<- forecast(des.2, h=nrow(testing))
kable(ramalandes2) %>% kable_styling()

	Point Forecast	Lo 80	Hi 80	Lo 95	Hi 95
316	104.6853	99.3200698	110.0506	96.4798745	112.8908
317	105.5228	98.7184684	112.3272	95.1164557	115.9292
318	106.3603	97.8263750	114.8943	93.3087678	119.4119
319	107.1978	96.6983780	117.6973	91.1402965	123.2554
320	108.0353	95.3706163	120.7001	88.6663114	127.4044
321	108.8729	93.8673923	123.8783	85.9239800	131.8217
322	109.7104	92.2058056	127.2149	82.9394535	136.4813
323	110.5479	90.3984889	130.6972	79.7320524	141.3637
324	111.3854	88.4551926	134.3156	76.3166883	146.4541
325	112.2229	86.3837226	138.0620	72.7052996	151.7405
326	113.0604	84.1905175	141.9303	68.9077330	157.2130
327	113.8979	81.8810165	145.9148	64.9323072	162.8635
328	114.7354	79.4599049	150.0109	60.7861878	168.6846
329	115.5729	76.9312823	154.2145	56.4756445	174.6702
330	116.4104	74.2987823	158.5220	52.0062344	180.8146
331	117.2479	71.5656598	162.9302	47.3829355	187.1129
332	118.0854	68.7348569	167.4360	42.6102471	193.5606
333	118.9229	65.8090525	172.0368	37.6922666	200.1536
334	119.7604	62.7907022	176.7302	32.6327494	206.8881
335	120.5979	59.6820692	181.5138	27.4351567	213.7607
336	121.4354	56.4852494	186.3856	22.1026941	220.7682
337	122.2729	53.2021925	191.3437	16.6383430	227.9076
338	123.1105	49.8347185	196.3862	11.0448871	235.1760
339	123.9480	46.3845324	201.5114	5.3249341	242.5710
340	124.7855	42.8532365	206.7177	-0.5190659	250.0900
341	125.6230	39.2423400	212.0036	-6.4848042	257.7307
342	126.4605	35.5532690	217.3677	-12.5701002	265.4911
343	127.2980	31.7873733	222.8086	-18.7728896	273.3689
344	128.1355	27.9459333	228.3250	-25.0912138	281.3622
345	128.9730	24.0301663	233.9158	-31.5232114	289.4692
346	129.8105	20.0412313	239.5798	-38.0671098	297.6881
347	130.6480	15.9802337	245.3158	-44.7212185	306.0172
348	131.4855	11.8482295	251.1228	-51.4839224	314.4549
349	132.3230	7.6462288	256.9998	-58.3536767	322.9997
350	133.1605	3.3751991	262.9458	-65.3290017	331.6500
351	133.9980	-0.9639315	268.9600	-72.4084781	340.4045
352	134.8355	-5.3702719	275.0413	-79.5907431	349.2618
353	135.6730	-9.8429657	281.1890	-86.8744866	358.2206
354	136.5105	-14.3811883	287.4023	-94.2584481	367.2795
355	137.3481	-18.9841460	293.6803	-101.7414131	376.4375
356	138.1856	-23.6510729	300.0222	-109.3222107	385.6933
357	139.0231	-28.3812304	306.4274	-116.9997112	395.0458
358	139.8606	-33.1739049	312.8950	-124.7728231	404.4940
359	140.6981	-38.0284066	319.4246	-132.6404915	414.0366
360	141.5356	-42.9440683	326.0152	-140.6016961	423.6729
361	142.3731	-47.9202439	332.6664	-148.6554487	433.4016
362	143.2106	-52.9563077	339.3775	-156.8007924	443.2220
363	144.0481	-58.0516529	346.1479	-165.0367994	453.1330
364	144.8856	-63.2056913	352.9769	-173.3625695	463.1338
365	145.7231	-68.4178514	359.8641	-181.7772294	473.2235
366	146.5606	-73.6875786	366.8088	-190.2799304	483.4012
367	147.3981	-79.0143337	373.8106	-198.8698481	493.6661
368	148.2356	-84.3975925	380.8688	-207.5461809	504.0174
369	149.0731	-89.8368453	387.9831	-216.3081489	514.4544
370	149.9106	-95.3315955	395.1529	-225.1549930	524.9763
371	150.7481	-100.8813601	402.3777	-234.0859742	535.5823
372	151.5857	-106.4856680	409.6570	-243.1003724	546.2717
373	152.4232	-112.1440606	416.9904	-252.1974858	557.0438
374	153.2607	-117.8560902	424.3774	-261.3766300	567.8980
375	154.0982	-123.6213203	431.8177	-270.6371374	578.8335
376	154.9357	-129.4393250	439.3107	-279.9783566	589.8497
377	155.7732	-135.3096884	446.8560	-289.3996514	600.9460
378	156.6107	-141.2320042	454.4534	-298.9004007	612.1218
379	157.4482	-147.2058757	462.1023	-308.4799975	623.3764
380	158.2857	-153.2309149	469.8023	-318.1378486	634.7092
381	159.1232	-159.3067427	477.5532	-327.8733741	646.1198
382	159.9607	-165.4329881	485.3544	-337.6860067	657.6074
383	160.7982	-171.6092883	493.2057	-347.5751915	669.1716
384	161.6357	-177.8352880	501.1067	-357.5403853	680.8118
385	162.4732	-184.1106398	509.0571	-367.5810564	692.5275
386	163.3107	-190.4350030	517.0565	-377.6966841	704.3182
387	164.1482	-196.8080443	525.1045	-387.8867584	716.1832
388	164.9857	-203.2294368	533.2009	-398.1507795	728.1223
389	165.8233	-209.6988603	541.3454	-408.4882578	740.1348
390	166.6608	-216.2160008	549.5375	-418.8987129	752.2202
391	167.4983	-222.7805505	557.7771	-429.3816740	764.3782
392	168.3358	-229.3922073	566.0637	-439.9366793	776.6082
393	169.1733	-236.0506750	574.3972	-450.5632756	788.9098
394	170.0108	-242.7556627	582.7772	-461.2610183	801.2826
395	170.8483	-249.5068852	591.2035	-472.0294709	813.7260

# Membuka file PNG untuk menyimpan plot
png("C:/Users/Fathan/Documents/Obsidian Vault/2. Kuliah/Smt 5/6. Metode Peramalan Deret Waktu/@Proj/STA1341-MPDW/Pertemuan 1/Chart/06_TSA_DES-1.png",
    height = 9*300, width = 16*300, res=300)

# Plot time series dengan warna dan pengaturan lainnya
plot(des.1, lwd=2)

# Menyimpan plot sebagai file PNG
dev.off() # Menutup file PNG

## png 
##   2

# Membuka file PNG untuk menyimpan plot
png("C:/Users/Fathan/Documents/Obsidian Vault/2. Kuliah/Smt 5/6. Metode Peramalan Deret Waktu/@Proj/STA1341-MPDW/Pertemuan 1/Chart/07_TSA_DES-2.png",
    height = 9*300, width = 16*300, res=300)

# Plot time series dengan warna dan pengaturan lainnya
plot(des.2, lwd=2)

# Menyimpan plot sebagai file PNG
dev.off() # Menutup file PNG

## png 
##   2

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.

Plot Data Latih dan Data Uji

Selanjutnya jika ingin membandingkan plot data latih dan data uji adalah sebagai berikut.

#Visually evaluate the prediction
plot(amzn.ts)
lines(des.1$fitted[,1], lty=2, col="purple1", lwd=2)
lines(ramalandes1$mean, col="orange", lwd=2)

# Membuka file PNG untuk menyimpan plot
png("C:/Users/Fathan/Documents/Obsidian Vault/2. Kuliah/Smt 5/6. Metode Peramalan Deret Waktu/@Proj/STA1341-MPDW/Pertemuan 1/Chart/08_TSA_DES_Train-Test.png",
    height = 9*300, width = 16*300, res=300)

# Plot time series dengan warna dan pengaturan lainnya
plot(amzn.ts)
lines(des.1$fitted[,1], lty=2, col="purple1", lwd=2)
lines(ramalandes1$mean, col="orange", lwd=2)

# Menyimpan plot sebagai file PNG
dev.off() # Menutup file PNG

## png 
##   2

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: 0.9851685
##  beta : 0.0426844
##  gamma: FALSE
## 
## Coefficients:
##          [,1]
## a 103.9307404
## b   0.2793775

plot(des.opt, lwd=2)

#ramalan
ramalandesopt<- forecast(des.opt, h=nrow(testing))   #h = panjang periode
kable(ramalandesopt) %>% kable_styling()

	Point Forecast	Lo 80	Hi 80	Lo 95	Hi 95
316	104.2101	99.357915	109.0623	96.7893134	111.6309
317	104.4895	97.533425	111.4456	93.8511035	115.1279
318	104.7689	96.090993	113.4468	91.4972014	118.0405
319	105.0483	94.831442	115.2651	89.4229907	120.6735
320	105.3276	93.678469	116.9768	87.5117763	123.1435
321	105.6070	92.593625	118.6204	85.7047568	125.5093
322	105.8864	91.554532	120.2182	83.9677084	127.8051
323	106.1658	90.546932	121.7846	82.2788245	130.0527
324	106.4451	89.561156	123.3291	80.6233159	132.2670
325	106.7245	88.590338	124.8587	78.9906838	134.4583
326	107.0039	87.629432	126.3784	77.3732125	136.6346
327	107.2833	86.674630	127.8919	75.7650746	138.8015
328	107.5626	85.722989	129.4023	74.1617719	140.9635
329	107.8420	84.772199	130.9119	72.5597703	143.1243
330	108.1214	83.820417	132.4224	70.9562520	145.2866
331	108.4008	82.866156	133.9354	69.3489427	147.4526
332	108.6802	81.908204	135.4521	67.7359881	149.6243
333	108.9595	80.945564	136.9735	66.1158634	151.8032
334	109.2389	79.977410	138.5004	64.4873055	153.9905
335	109.5183	79.003053	140.0335	62.8492623	156.1873
336	109.7977	78.021918	141.5734	61.2008526	158.3945
337	110.0770	77.033521	143.1206	59.5413359	160.6128
338	110.3564	76.037453	144.6754	57.8700877	162.8428
339	110.6358	75.033369	146.2382	56.1865806	165.0850
340	110.9152	74.020978	147.8094	54.4903680	167.3400
341	111.1946	73.000032	149.3891	52.7810720	169.6080
342	111.4739	71.970321	150.9775	51.0583729	171.8895
343	111.7533	70.931671	152.5749	49.3220003	174.1846
344	112.0327	69.883931	154.1814	47.5717262	176.4936
345	112.3121	68.826975	155.7972	45.8073593	178.8168
346	112.5914	67.760701	157.4222	44.0287395	181.1541
347	112.8708	66.685020	159.0566	42.2357340	183.5059
348	113.1502	65.599861	160.7005	40.4282337	185.8722
349	113.4296	64.505167	162.3540	38.6061498	188.2530
350	113.7090	63.400891	164.0170	36.7694117	190.6485
351	113.9883	62.286997	165.6897	34.9179645	193.0587
352	114.2677	61.163458	167.3720	33.0517669	195.4836
353	114.5471	60.030256	169.0639	31.1707896	197.9234
354	114.8265	58.887377	170.7655	29.2750142	200.3779
355	115.1058	57.734817	172.4769	27.3644312	202.8472
356	115.3852	56.572573	174.1979	25.4390398	205.3314
357	115.6646	55.400651	175.9285	23.4988460	207.8303
358	115.9440	54.219058	177.6689	21.5438624	210.3441
359	116.2233	53.027807	179.4189	19.5741072	212.8726
360	116.5027	51.826912	181.1785	17.5896037	215.4159
361	116.7821	50.616392	182.9478	15.5903793	217.9738
362	117.0615	49.396267	184.7267	13.5764654	220.5465
363	117.3409	48.166560	186.5152	11.5478970	223.1338
364	117.6202	46.927295	188.3132	9.5047117	225.7358
365	117.8996	45.678499	190.1207	7.4469500	228.3523
366	118.1790	44.420200	191.9378	5.3746548	230.9833
367	118.4584	43.152428	193.7643	3.2878707	233.6289
368	118.7377	41.875212	195.6003	1.1866443	236.2889
369	119.0171	40.588585	197.4457	-0.9289764	238.9632
370	119.2965	39.292578	199.3004	-3.0589418	241.6519
371	119.5759	37.987224	201.1645	-5.2032016	244.3550
372	119.8553	36.672557	203.0380	-7.3617041	247.0722
373	120.1346	35.348612	204.9207	-9.5343970	249.8037
374	120.4140	34.015423	206.8126	-11.7212273	252.5493
375	120.6934	32.673025	208.7138	-13.9221413	255.3089
376	120.9728	31.321454	210.6241	-16.1370849	258.0826
377	121.2521	29.960744	212.5435	-18.3660038	260.8703
378	121.5315	28.590933	214.4721	-20.6088430	263.6719
379	121.8109	27.212055	216.4097	-22.8655477	266.4873
380	122.0903	25.824148	218.3564	-25.1360627	269.3166
381	122.3697	24.427246	220.3121	-27.4203329	272.1596
382	122.6490	23.021387	222.2767	-29.7183030	275.0164
383	122.9284	21.606605	224.2502	-32.0299178	277.8867
384	123.2078	20.182938	226.2326	-34.3551223	280.7707
385	123.4872	18.750421	228.2239	-36.6938615	283.6682
386	123.7665	17.309090	230.2240	-39.0460805	286.5792
387	124.0459	15.858981	232.2329	-41.4117247	289.5036
388	124.3253	14.400129	234.2505	-43.7907396	292.4413
389	124.6047	12.932570	236.2768	-46.1830711	295.3924
390	124.8841	11.456339	238.3118	-48.5886652	298.3568
391	125.1634	9.971471	240.3554	-51.0074683	301.3343
392	125.4428	8.478001	242.4076	-53.4394270	304.3250
393	125.7222	6.975964	244.4684	-55.8844882	307.3289
394	126.0016	5.465394	246.5377	-58.3425994	310.3457
395	126.2809	3.946325	248.6156	-60.8137082	313.3756

# Membuka file PNG untuk menyimpan plot
png("C:/Users/Fathan/Documents/Obsidian Vault/2. Kuliah/Smt 5/6. Metode Peramalan Deret Waktu/@Proj/STA1341-MPDW/Pertemuan 1/Chart/09_TSA_DES-Opt.png",
    height = 9*300, width = 16*300, res=300)

# Plot time series dengan warna dan pengaturan lainnya
plot(des.opt, lwd=2)

# Menyimpan plot sebagai file PNG
dev.off() # Menutup file PNG

## png 
##   2

Selanjutnya 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 -0.282516  1.564783  3.383031  4.334296

mapedes.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                     13207.601464
## MSE                        41.928894
## MAPE                        4.090672

ssedes.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 -0.282516  1.717341  2.611163  2.130670

mapedes.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                      5469.804193
## MSE                        17.364458
## MAPE                        2.666762

Hasil akurasi dari data latih skenario 2 dengan lamda=0.6 dan gamma=0.3 memiliki hasil yang lebih baik karena memiliki nilai SSE, MSE, dan MAPE yang lebih kecil. Berdasarkan nilai MAPE-nya, baik skenario 1 dan 2dapat dikategorikan peramalan sangat baik.

Akurasi Data Uji

#Akurasi Data Testing
selisihdes1 <- ramalandes1$mean - testing[,3]
selisihdes1

## Time Series:
## Start = 316 
## End = 395 
## Frequency = 1 
##  [1] -0.07166725  3.40726591  3.07620007  3.59513423  6.47406839  9.19299856
##  [7]  5.25193272  5.77086688  6.16980504  7.23873420  5.86766836  6.98660752
## [13]  4.46554068  5.84447484 10.11340800  8.33233916  4.12127632  9.12021348
## [19] 13.14914164 12.19808181 12.80701097 13.08594713 12.05487729 12.51381345
## [25] 12.35274661  9.41168177  8.05061793 10.59955009 10.28848925  8.71741841
## [31]  7.24635457  5.22528673  7.75422289  9.62315505 10.27209322  9.14102538
## [37] 11.51995954  7.03889270  6.11782386  7.82676002  6.26569918  5.41463034
## [43]  4.99356150  4.31249766 10.32142982  7.93036698  9.37930114  6.86823530
## [49]  7.40716546  8.27610563  8.21503679 10.46397395 10.80290711 12.38183827
## [55]  7.69078043  9.13970659 11.76864075 10.54758391 11.31651807 13.08544323
## [61] 11.25437839 12.02331255 12.49224271 15.14118088 14.35011704 17.62905320
## [67] 16.60798536 15.21691552 12.34584968 12.59479384 14.34372300 15.70265316
## [73] 13.80158832 19.83051648 20.41945764 22.24838880 22.54732096 24.15626612
## [79] 24.68519429 21.35412145

SSEtestingdes1<-sum(selisihdes1^2)
MSEtestingdes1<-SSEtestingdes1/
                length(testing[,3])
MAPEtestingdes1<-sum(abs(selisihdes1/
                         testing[,3])*100)/
                 length(testing[,3])

selisihdes2<-ramalandes2$mean - testing[,3]
selisihdes2

## Time Series:
## Start = 316 
## End = 395 
## Frequency = 1 
##  [1]  0.7353294  4.4228343  4.3003401  5.0278459  8.1153517 11.0428535
##  [7]  7.3103593  8.0378651  8.6453749  9.9228757  8.7603815 10.0878923
## [13]  7.7753971  9.3629030 13.8404078 12.2679106  8.2654194 13.4729282
## [19] 17.7104280 16.9679398 17.7854406 18.2729484 17.4504502 18.1179580
## [25] 18.1654628 15.4329696 14.2804775 17.0379813 16.9354921 15.5729929
## [31] 14.3105007 12.4980045 15.2355123 17.3130161 18.1705259 17.2480297
## [37] 19.8355355 15.5630403 14.8505431 16.7680510 15.4155618 14.7730646
## [43] 14.5605674 14.0880752 20.3055790 18.1230878 19.7805936 17.4780994
## [49] 18.2256012 19.3031130 19.4506158 21.9081246 22.4556295 24.2431323
## [55] 19.7606461 21.4181439 24.2556497 23.2431645 24.2206703 26.1981671
## [61] 24.5756739 25.5531797 26.2306815 29.0881913 28.5056992 31.9932070
## [67] 31.1807108 29.9982126 27.3357184 27.7932342 29.7507350 31.3182368
## [73] 29.6257436 35.8632434 36.6607562 38.6982590 39.2057628 41.0232797
## [79] 41.7607795 38.6382783

SSEtestingdes2<-sum(selisihdes2^2)
MSEtestingdes2<-SSEtestingdes2/
                length(testing[,3])
MAPEtestingdes2<-sum(abs(selisihdes2/
                         testing[,3])*100)/
                 length(testing[,3])

selisihdesopt<-ramalandesopt$mean - testing[,3]
selisihdesopt

## Time Series:
## Start = 316 
## End = 395 
## Frequency = 1 
##  [1]   0.2601209   3.3894974   2.7088749   2.8782524   5.4076299   7.7770034
##  [7]   3.4863808   3.6557583   3.7051398   4.4245123   2.7038898   3.4732723
## [13]   0.6026488   1.6320262   5.5514027   3.4207772  -1.1398423   3.5095382
## [19]   7.1889097   5.8882932   6.1476657   6.0770451   4.6964186   4.8057981
## [25]   4.2951746   1.0045531  -0.7060674   1.4933081   0.8326905  -1.0879370
## [31]  -2.9085575  -5.2791820  -3.0998025  -1.5804270  -1.2810455  -2.7616700
## [37]  -0.7322926  -5.5629161  -6.8335416  -5.4741621  -7.3847796  -8.5854051
## [43]  -9.3560306 -10.3866512  -4.7272757  -7.4678952  -6.3685177  -9.2291402
## [49]  -9.0397667  -8.5203832  -8.9310087  -7.0316283  -7.0422518  -5.8128773
## [55] -10.8534918  -9.7541223  -7.4747448  -9.0453583  -8.6259809  -7.2066124
## [61]  -9.3872339  -8.9678564  -8.8484829  -6.5491014  -7.6897219  -4.7603425
## [67]  -6.1309670  -7.8715935 -11.0922160 -11.1928285  -9.7934560  -8.7840825
## [73] -11.0347040  -5.3553326  -5.1159481  -3.6365736  -3.6871981  -2.4278096
## [79]  -2.2484381  -5.9290676

SSEtestingdesopt<-sum(selisihdesopt^2)
MSEtestingdesopt<-SSEtestingdesopt/
                  length(testing[,3])
MAPEtestingdesopt<-sum(abs(selisihdesopt/
                           testing[,3])*100)/
                  length(testing[,3])

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")
kable(akurasitestingdes) %>% kable_styling()

	des ske1	des ske2	des opt
SSE	10758.291043	37152.67055	3163.79939
MSE	134.478638	464.40838	39.54749
MAPE	8.728892	16.06336	4.57769

Hasil akurasi dari data latih DES Opt memiliki hasil yang lebih baik karena memiliki nilai SSE, MSE, dan MAPE yang lebih kecil dibandingkan hasil akurasi pada DES skenario 1 dan 2. Berdasarkan nilai MAPE-nya, DES Opt dan DES skenario 1 dapat dikategorikan peramalan sangat baik, sedangkan DES skenario 2 peramalan baik.

3. Winter Aditif

Metode Holt-Winter untuk peramalan data musiman menggunakan tiga persamaan pemulusan yang terdiri atas persamaan untuk level \((L_t)\), trend \((B_t)\), dan komponen seasonal / musiman \((S_t)\) dengan parameter pemulusan berupa \(\alpha\), \(\beta\), dan \(\gamma\). Metode Holt-Winter musiman terbagi menjadi dua, yaitu metode aditif dan metode multiplikatif. Perbedaan persamaan dan contoh datanya adalah sebagai berikut.

Pemulusan data musiman dengan metode Winter dilakukan menggunakan fungsi HoltWinters() dengan memasukkan argumen tambahan, yaitu gamma() dan seasonal() . Arguman seasonal() diinisialisasi menyesuaikan jenis musiman, aditif atau multiplikatif.

Penentuan Frekuensi

ts.plot(amzn.ts, xlab="Time Period", ylab="Harga Saham", 
        main = "Time Series Amazon", col='orange', lwd=2)
points(amzn.ts, col='orange', lwd=1.5)
# Tambahkan garis vertikal
abline(v = 100, col = "red", lty = 2)
abline(v = 200, col = "blue", lty = 2)
abline(v = 300, col = "purple", lty = 2)

Nampak bahwa pola frekuensi data nya cenderung diangka 100.

# Membuka file PNG untuk menyimpan plot
png("C:/Users/Fathan/Documents/Obsidian Vault/2. Kuliah/Smt 5/6. Metode Peramalan Deret Waktu/@Proj/STA1341-MPDW/Pertemuan 1/Chart/10_TSA_Frekuensi.png",
    height = 9*300, width = 16*300, res=300)

# Plot time series dengan warna dan pengaturan lainnya
ts.plot(amzn.ts, xlab="Time Period", ylab="Harga Saham", 
        main = "Time Series Amazon", col='orange', lwd=2)
points(amzn.ts, col='orange', lwd=1.5)
# Tambahkan garis vertikal
abline(v = 100, col = "red", lty = 2)
abline(v = 200, col = "blue", lty = 2)
abline(v = 300, col = "purple", lty = 2)

# Menyimpan plot sebagai file PNG
dev.off() # Menutup file PNG

## png 
##   2

Pembagian data Musiman

training.ts<-ts(training[,3], frequency = 100) #Kebentuk puncak berapakali
testing.ts<-ts(testing[,3], frequency = 100)

Pemulusan

Perhitungan dengan model aditif dilakukan jika plot data asli menunjukkan fluktuasi musiman yang relatif stabil (konstan).

#Pemulusan dengan winter aditif 
winter1 <- HoltWinters(training.ts,
                       alpha=0.2, beta=0.1, gamma=0.1, 
                       seasonal = "additive")
kable(winter1$fitted) %>% kable_styling()

xhat	level	trend	season
125.61952	142.61579	-0.2524484268	-16.7438230
126.38595	139.45494	-0.5432889035	-12.5257070
128.60878	136.66376	-0.7680778065	-7.2869065
127.66012	134.21583	-0.9360633229	-5.6196515
129.43456	132.08454	-1.0555856698	-1.5943949
124.55647	130.24425	-1.1340568853	-4.5537138
125.57788	128.66889	-1.1781864220	-1.9128233
122.65648	127.33313	-1.1939440736	-3.4827093
119.98428	126.20789	-1.1870736130	-5.0365393
114.36454	125.25996	-1.1631591716	-9.7322598
107.43806	124.45389	-1.1274499850	-15.8883798
101.12663	123.76883	-1.0832112361	-21.5589914
99.52035	123.19429	-1.0323438618	-22.6416039
104.78111	122.71988	-0.9765508345	-16.9622214
100.78943	122.32111	-0.9187730456	-20.6129079
103.38363	121.97645	-0.8613615032	-17.7314559
105.91147	121.68236	-0.8046341394	-14.9662544
106.27419	121.43143	-0.7492636159	-14.4079824
109.85487	121.21733	-0.6957474246	-10.6667150
113.98930	121.03861	-0.6440447718	-6.4052705
110.90250	120.88871	-0.5946307038	-9.3915760
105.23746	120.75758	-0.5482806862	-14.9718375
106.89194	120.64180	-0.5050298078	-13.2448340
104.32899	120.54239	-0.4644686580	-15.7489305
107.87256	120.45412	-0.4268484146	-12.1547141
111.99157	120.36476	-0.3930996014	-7.9800920
112.94941	120.27335	-0.3629309592	-6.9610100
115.09328	120.18653	-0.3353190271	-4.7579399
114.42641	120.09856	-0.3105845022	-5.3615659
110.72435	120.01069	-0.2883126930	-8.9980269
108.34185	119.92751	-0.2677997925	-11.3178584
109.61239	119.83534	-0.2502368263	-9.9727174
109.85388	119.74263	-0.2344845169	-9.6542648
112.80926	119.66337	-0.2189621295	-6.6351413
113.06637	119.59255	-0.2041473271	-6.3220324
117.51440	119.52713	-0.1902747379	-1.8224579
122.02900	119.47598	-0.1763627207	2.7293875
123.85446	119.44781	-0.1615428018	4.5681950
121.59738	119.44138	-0.1460321602	2.3020361
120.23863	119.45987	-0.1295798043	0.9083421
113.82866	119.51056	-0.1115524245	-5.5703464
119.98668	119.59528	-0.0919257227	0.4833341
121.36611	119.70001	-0.0722593963	1.7383596
134.15465	119.81053	-0.0539816974	14.3981026
134.69865	119.91562	-0.0380748047	14.8211097
133.52929	120.01581	-0.0242478951	13.5377222
138.95120	120.11771	-0.0116335597	18.8451222
142.09329	120.21984	-0.0002574204	21.8737152
140.38274	120.31492	0.0092768393	20.0585462
138.99744	120.40765	0.0176220109	18.5721722
128.70267	120.50778	0.0258732082	8.1690173
135.43007	122.35912	0.2084197594	12.8625238
141.72979	124.01953	0.3536184752	17.3566447
142.51324	124.15519	0.3318225989	18.0262292
146.86372	124.69436	0.3525578366	21.8168012
145.30575	124.31018	0.2788832302	20.7166932
146.10901	124.48391	0.2683681611	21.3567341
147.03329	123.95048	0.1881880634	22.8946221
150.80835	123.19201	0.0935224039	27.5228222
148.88925	120.76986	-0.1580447123	28.2774402
142.74624	117.47796	-0.4714297714	25.7397106
137.47302	115.18128	-0.6539547524	22.9456961
137.08344	113.79272	-0.7274151914	24.0181286
141.60742	113.10462	-0.7234839683	29.2262801
134.58308	110.20965	-0.9406323210	25.3140611
127.66222	108.31040	-1.0364941177	20.3883151
126.20894	107.48746	-1.0151386919	19.7366106
122.29763	106.58454	-1.0039174664	16.7170055
119.48126	106.68509	-0.8934699764	13.6896320
120.34288	107.39737	-0.7328950744	13.6784015
125.98768	107.81790	-0.6175526611	18.7873305
122.70986	107.89881	-0.5477063572	15.3587575
125.17059	108.77314	-0.4055035066	16.8029545
132.28422	109.98752	-0.2435151568	22.5402196
129.33871	110.57716	-0.1601996142	18.9217516
123.40384	109.91321	-0.2105737678	13.7012006
120.85329	110.73187	-0.1076505355	10.2290665
124.11118	111.70956	0.0008836616	12.4007305
117.70334	111.59421	-0.0107399329	6.1198664
118.40492	112.97481	0.1283933708	5.3017200
126.24906	113.86022	0.2040950354	12.1847475
104.91712	112.52250	0.0499138960	-7.6552925
108.37058	115.05099	0.2977714477	-6.9781796
110.02730	116.43064	0.4059598210	-6.8093076
113.61269	117.86114	0.5084139435	-4.7568676
105.09029	118.52902	0.5243602035	-13.9630942
107.09851	121.63732	0.7827544984	-15.3215682
103.88083	123.96038	0.9367843442	-21.0163337
107.19534	126.72100	1.1191677834	-20.6448261
107.04386	129.57710	1.2928609683	-23.8261001
113.32158	133.67918	1.5737837564	-21.9313836
123.01898	136.77865	1.7263520012	-15.4860245
122.15410	137.96121	1.6719724965	-17.4790760
126.84269	138.11436	1.5200903722	-12.7917570
117.22443	136.99991	1.2566364841	-21.0321164
117.61311	137.25366	1.1563478537	-20.7969019
118.06666	137.46739	1.0620857622	-20.4628164
117.92793	137.42214	0.9513526034	-20.4455604
113.01618	136.16791	0.7307939643	-23.8825240
116.63726	137.05347	0.7462704244	-21.1624725
120.57782	137.74428	0.7407251549	-17.9071849
124.58915	137.38344	0.6305686645	-13.4248626
128.63112	136.14618	0.4437856531	-7.9588486
128.88757	134.72774	0.2575632500	-6.0977409
131.33973	133.17179	0.0762119086	-1.9082798
126.23125	131.10006	-0.1385826645	-4.7302320
126.52137	128.84723	-0.3500075061	-1.9758539
121.26849	125.38495	-0.6612348907	-3.4552275
115.19273	121.15202	-1.0184045291	-4.9408816
106.72018	117.58307	-1.2734591071	-9.5894231
97.14008	114.32357	-1.4720627769	-15.7114248
88.91951	111.84749	-1.5724643823	-21.3555219
86.36784	110.35113	-1.5648544384	-22.4184318
91.50498	109.70871	-1.4726111963	-16.7311103
86.16572	108.04110	-1.4921108891	-20.3832618
88.39147	107.31184	-1.4158253156	-17.5045465
89.24010	105.44572	-1.4608547363	-14.7447723
89.95587	105.46285	-1.3130567013	-14.1939177
94.76034	106.31662	-1.0963741525	-10.4599044
98.73678	105.96617	-1.0217809560	-6.2076142
94.76115	104.98504	-1.0177165026	-9.2061759
88.66972	104.43909	-0.9705393567	-14.7988340
90.77509	104.70461	-0.8469337912	-13.0825894
88.15257	104.53066	-0.7796355336	-15.5984496
91.89930	104.61251	-0.6934870140	-12.0197188
95.65227	104.17916	-0.6674731135	-7.8594175
95.65875	103.20723	-0.6979185574	-6.8505623
96.65767	102.05956	-0.7428935055	-4.6590018
94.70561	100.77514	-0.7970469426	-5.2724787
89.76223	99.52097	-0.8427591969	-8.9159753
88.07895	100.03376	-0.7072038245	-11.2476065
90.34228	100.81077	-0.5587828454	-9.9097081
90.93432	101.00953	-0.4830284327	-9.5921753
93.48424	100.54164	-0.4815148906	-6.5758821
92.16053	99.01327	-0.5861996624	-6.2665420
95.25995	97.68697	-0.6602103088	-1.7668098
98.07502	96.04477	-0.7584092830	2.7886672
97.18148	93.48935	-0.9381098579	4.6302376
92.52205	91.22495	-1.0707393883	2.3678455
90.05687	90.14780	-1.0713804824	0.9804516
82.84829	89.38104	-1.0409177910	-5.4918396
89.09358	89.46047	-0.9288835583	0.5619994
89.14278	88.28487	-0.9535552005	1.8114704
99.91047	86.48676	-1.0380108901	14.4617302
96.04865	82.50465	-1.3324203400	14.8764173
91.38669	79.31650	-1.5179933350	13.5881795
93.49987	76.27917	-1.6699270287	18.8906267
93.03620	72.95927	-1.8349244075	21.9118522
87.18218	69.12510	-2.0348483121	20.0919268
82.48090	66.01782	-2.1420919819	18.6051769
71.00664	64.21555	-2.1081100800	8.8992035
76.30118	64.70611	-1.8482428877	13.4433186
80.37322	64.76163	-1.6578665791	17.2694612
80.60376	64.05712	-1.5625310728	18.1091702
83.00773	62.99784	-1.5122061447	21.5221028
81.32396	62.10008	-1.4507607516	20.6746329
81.56251	61.85653	-1.3300398444	21.0360137
83.54006	62.18799	-1.1638898988	22.5159595
88.91775	63.33409	-0.9328911994	26.5165537
89.88970	63.67165	-0.8058462799	27.0238999
88.88023	64.51186	-0.6412402236	25.0096107
87.45858	65.30457	-0.4978447895	22.6518543
90.10305	66.40701	-0.3378164991	24.0338535
94.87600	66.78459	-0.2662774993	28.3576867
91.70493	66.99311	-0.2187974139	24.9306140
88.30857	67.93733	-0.1024960027	20.4737368
89.27635	69.43712	0.0577326493	19.7814955
88.45018	71.07558	0.2158057449	17.1587955
88.20848	73.44535	0.4312021256	14.3319316
91.53446	76.68286	0.7118324052	14.1397712
99.15666	79.19780	0.8921432900	19.0667157
97.78379	80.88461	0.9716101210	15.9275689
101.89930	83.32946	1.1189344199	17.4509079
110.86317	86.65054	1.3391484298	22.8734817
106.40499	86.49505	1.1896850934	18.7202549
102.05782	86.83974	1.1051852781	14.1128935
99.72479	87.95536	1.1062289693	10.6632033
102.59360	89.12663	1.1127331862	12.3542361
97.07070	89.36864	1.0256611404	6.6763997
97.14314	90.50216	1.0364470697	5.6045266
104.67039	92.01798	1.0843843320	11.5680230
86.42940	92.10829	0.9849764491	-6.6638623
90.77355	96.03939	1.2795884596	-6.5454261
93.82189	98.79427	1.4271175340	-6.3994911
97.69860	100.89700	1.4946796432	-4.6930826
90.27075	101.76796	1.4323076676	-12.9295170
91.14136	104.30412	1.5426926020	-14.7054488
88.13201	106.78254	1.6362653132	-20.2867999
91.28598	109.49240	1.7436251978	-19.9500534
90.82153	111.73083	1.7931057112	-22.7024089
94.74580	114.20563	1.8612751389	-21.3211106
101.65797	115.55175	1.8097591111	-15.7035426
98.98851	115.45591	1.6191997262	-18.0866045
103.94927	116.25741	1.5374295628	-13.8455725
95.65516	115.75499	1.3334441606	-21.4332710
96.78479	116.66740	1.2913409847	-21.1739503
97.71408	117.38578	1.2340451112	-20.9057491
97.32398	117.52701	1.1247635252	-21.3277950
94.50525	117.33298	0.9928839643	-23.8206181
97.67754	117.91082	0.9513790390	-21.1846536
100.85030	118.30269	0.8954281673	-18.3478109
104.89848	118.26805	0.8024220525	-14.1719947
110.10029	118.09878	0.7052524756	-8.7037382
110.23307	116.57397	0.4822465548	-6.8231462
112.01593	114.55160	0.2317850883	-2.7674581
106.92994	112.50220	0.0036664901	-5.5759313
107.47819	110.85988	-0.1609323332	-3.2207634
103.72511	108.94531	-0.3362960631	-4.8839060
101.08069	107.48999	-0.4481983141	-5.9610999
95.54081	106.43366	-0.5090121913	-10.3838378
89.67642	106.26448	-0.4750283514	-16.1130313
86.31553	107.90417	-0.2635568027	-21.3250821
88.77818	110.77751	0.0501325889	-22.0494588
97.26126	113.73000	0.3403690048	-16.8091090
95.46534	115.10012	0.4433438218	-20.0781195

xhat1 <- winter1$fitted[,2]

winter1.opt<- HoltWinters(training.ts, 
                          #Supaya optimum
                          alpha= NULL,  beta = NULL, gamma = NULL, 
                          seasonal = "additive")
winter1.opt

## Holt-Winters exponential smoothing with trend and additive seasonal component.
## 
## Call:
## HoltWinters(x = training.ts, alpha = NULL, beta = NULL, gamma = NULL,     seasonal = "additive")
## 
## Smoothing parameters:
##  alpha: 0.7420479
##  beta : 0
##  gamma: 1
## 
## Coefficients:
##             [,1]
## a    123.2905107
## b     -0.2524484
## s1   -19.2876168
## s2   -13.3250480
## s3   -13.0011951
## s4   -11.7996186
## s5    -7.6141066
## s6    -9.3372915
## s7   -14.0363594
## s8   -13.5577012
## s9   -15.5406209
## s10  -12.7676174
## s11   -8.9054573
## s12   -7.5698796
## s13   -5.2659891
## s14   -5.6504876
## s15   -6.9835867
## s16  -10.3889352
## s17  -10.3480238
## s18  -10.5362762
## s19   -8.2494766
## s20   -6.6613377
## s21   -2.4692209
## s22    1.1909620
## s23    4.2072540
## s24    3.4357758
## s25    1.4805628
## s26   -4.3938540
## s27   -0.7673580
## s28    0.4819545
## s29   11.0149194
## s30   14.3820602
## s31   13.1285641
## s32   17.8904078
## s33   20.4138383
## s34   19.9763015
## s35   19.6945504
## s36   12.9201875
## s37   13.9460345
## s38   15.3000328
## s39   17.0691065
## s40   20.7248327
## s41   21.4997279
## s42   21.6185003
## s43   23.6435010
## s44   24.9310224
## s45   26.7202025
## s46   25.7489695
## s47   24.2574069
## s48   24.3692679
## s49   26.9371993
## s50   25.9592980
## s51   22.3928903
## s52   20.7161039
## s53   19.1691146
## s54   16.7295645
## s55   14.0789406
## s56   18.0148444
## s57   17.3253220
## s58   19.6161246
## s59   19.1119466
## s60   17.5483423
## s61   15.8161747
## s62   11.7598726
## s63   11.0832825
## s64    8.5761005
## s65    6.7699066
## s66    8.9421620
## s67    0.1747336
## s68   -5.7999172
## s69   -6.4391645
## s70   -6.2129900
## s71   -9.1932354
## s72  -13.3565791
## s73  -18.6996793
## s74  -19.2569201
## s75  -20.6121073
## s76  -21.9215303
## s77  -18.3660640
## s78  -17.9259556
## s79  -15.6242748
## s80  -18.6067578
## s81  -19.6737124
## s82  -20.6087935
## s83  -21.8431072
## s84  -21.0930765
## s85  -19.9739418
## s86  -20.1591745
## s87  -15.4525678
## s88  -10.4268448
## s89   -7.5235989
## s90   -2.9873597
## s91   -5.0749462
## s92   -4.1367066
## s93   -5.2059725
## s94   -5.2576193
## s95   -8.9218233
## s96  -12.9852472
## s97  -18.1808502
## s98  -20.3549702
## s99  -18.9450275
## s100 -19.3405137

kable(winter1.opt$fitted) %>% kable_styling()

xhat	level	trend	season
125.61952	142.61579	-0.2524484	-16.7438230
118.79431	131.57247	-0.2524484	-12.5257070
121.07381	128.61317	-0.2524484	-7.2869065
121.84726	127.71936	-0.2524484	-5.6196515
125.49892	127.34576	-0.2524484	-1.5943949
122.29612	127.10228	-0.2524484	-4.5537138
124.72454	126.88981	-0.2524484	-1.9128233
122.95078	126.68594	-0.2524484	-3.4827093
121.18103	126.47001	-0.2524484	-5.0365393
116.23210	126.21680	-0.2524484	-9.7322598
109.76261	125.90344	-0.2524484	-15.8883798
103.75599	125.56743	-0.2524484	-21.5589914
102.35712	125.25117	-0.2524484	-22.6416039
107.74909	124.96376	-0.2524484	-16.9622214
103.78726	124.65262	-0.2524484	-20.6129079
106.32183	124.30574	-0.2524484	-17.7314559
108.75902	123.97773	-0.2524484	-14.9662544
109.00621	123.66664	-0.2524484	-14.4079824
112.45332	123.37248	-0.2524484	-10.6667150
116.45243	123.11015	-0.2524484	-6.4052705
113.21929	122.86332	-0.2524484	-9.3915760
107.38711	122.61139	-0.2524484	-14.9718375
108.87123	122.36851	-0.2524484	-13.2448340
106.15087	122.15225	-0.2524484	-15.7489305
109.53652	121.94368	-0.2524484	-12.1547141
113.47611	121.70865	-0.2524484	-7.9800920
114.26047	121.47393	-0.2524484	-6.9610100
116.26269	121.27308	-0.2524484	-4.7579399
115.45656	121.07058	-0.2524484	-5.3615659
111.62957	120.88004	-0.2524484	-8.9980269
109.14665	120.71696	-0.2524484	-11.3178584
110.29377	120.51894	-0.2524484	-9.9727174
110.43860	120.34532	-0.2524484	-9.6542648
113.34730	120.23489	-0.2524484	-6.6351413
113.55838	120.13286	-0.2524484	-6.3220324
117.95512	120.03002	-0.2524484	-1.8224579
122.44365	119.96671	-0.2524484	2.7293875
124.27217	119.95643	-0.2524484	4.5681950
122.01909	119.96950	-0.2524484	2.3020361
120.67044	120.01455	-0.2524484	0.9083421
114.28774	120.11053	-0.2524484	-5.5703464
120.47651	120.24563	-0.2524484	0.4833341
121.84528	120.35937	-0.2524484	1.7383596
134.57516	120.42950	-0.2524484	14.3981026
135.02386	120.45520	-0.2524484	14.8211097
133.75972	120.47444	-0.2524484	13.5377222
139.11170	120.51903	-0.2524484	18.8451222
142.19083	120.56956	-0.2524484	21.8737152
140.40458	120.59848	-0.2524484	20.0585462
138.95918	120.63946	-0.2524484	18.5721722
128.63811	120.72154	-0.2524484	8.1690173
139.89999	127.28992	-0.2524484	12.8625238
146.21199	129.10779	-0.2524484	17.3566447
142.49444	124.72066	-0.2524484	18.0262292
146.81584	125.25149	-0.2524484	21.8168012
142.76531	122.30107	-0.2524484	20.7166932
144.64790	123.54361	-0.2524484	21.3567341
144.04268	121.40051	-0.2524484	22.8946221
147.12528	119.85491	-0.2524484	27.5228222
141.02672	113.00173	-0.2524484	28.2774402
132.44358	106.95632	-0.2524484	25.7397106
130.27007	107.57683	-0.2524484	22.9456961
133.70943	109.94375	-0.2524484	24.0181286
141.31467	112.34084	-0.2524484	29.2262801
129.31051	104.24890	-0.2524484	25.3140611
124.48812	104.35225	-0.2524484	20.3883151
126.73164	107.24748	-0.2524484	19.7366106
123.48805	107.02349	-0.2524484	16.7170055
123.42274	109.98556	-0.2524484	13.6896320
126.19201	112.76605	-0.2524484	13.6784015
130.98763	112.45275	-0.2524484	18.7873305
126.18787	111.08156	-0.2524484	15.3587575
130.07484	113.52433	-0.2524484	16.8029545
137.93062	115.64285	-0.2524484	22.5402196
132.96101	114.29171	-0.2524484	18.9217516
122.93109	109.48234	-0.2524484	13.7012006
123.37601	113.39939	-0.2524484	10.2290665
127.45012	115.30184	-0.2524484	12.4007305
118.00789	112.14047	-0.2524484	6.1198664
121.87348	116.82421	-0.2524484	5.3017200
128.73893	116.80664	-0.2524484	12.1847475
101.07835	108.98609	-0.2524484	-7.6552925
113.54767	120.77830	-0.2524484	-6.9781796
113.63649	120.69825	-0.2524484	-6.8093076
116.55958	121.56890	-0.2524484	-4.7568676
105.50582	119.72136	-0.2524484	-13.9630942
113.17360	128.74762	-0.2524484	-15.3215682
108.43325	129.70204	-0.2524484	-21.0163337
111.94106	132.83833	-0.2524484	-20.6448261
111.43022	135.50877	-0.2524484	-23.8261001
120.24050	142.42434	-0.2524484	-21.9313836
126.95989	142.69837	-0.2524484	-15.4860245
119.77244	137.50396	-0.2524484	-17.4790760
120.33943	133.38363	-0.2524484	-12.7917570
106.89758	128.18215	-0.2524484	-21.0321164
110.82242	131.87177	-0.2524484	-20.7969019
112.44572	133.16099	-0.2524484	-20.4628164
112.27307	132.97108	-0.2524484	-20.4455604
104.59658	128.73156	-0.2524484	-23.8825240
113.88614	135.30106	-0.2524484	-21.1624725
116.13692	136.88434	-0.2524484	-20.4949691
122.12107	135.84018	-0.2524484	-13.4666681
122.72677	130.48907	-0.2524484	-7.5098571
121.79443	127.70864	-0.2524484	-5.6617653
124.14735	125.99107	-0.2524484	-1.5912783
118.31406	123.10632	-0.2524484	-4.5398154
118.73605	120.88444	-0.2524484	-1.8959379
111.13932	114.86179	-0.2524484	-3.4700132
103.58456	108.87381	-0.2524484	-5.0368039
97.76616	107.77205	-0.2524484	-9.7534361
90.62536	106.79524	-0.2524484	-15.9174273
85.81826	107.65189	-0.2524484	-21.5811731
87.07685	109.98305	-0.2524484	-22.6537588
95.39186	112.62693	-0.2524484	-16.9826226
87.86857	108.76675	-0.2524484	-20.6457350
92.07092	110.08109	-0.2524484	-17.7577241
90.18853	105.42762	-0.2524484	-14.9866384
95.28011	109.95504	-0.2524484	-14.4224820
102.86860	113.79120	-0.2524484	-10.6701493
103.63385	110.28962	-0.2524484	-6.4033187
96.91027	106.55411	-0.2524484	-9.3913934
91.23633	106.45729	-0.2524484	-14.9685116
95.40165	108.88636	-0.2524484	-13.2322545
91.71157	107.69770	-0.2524484	-15.7336790
95.59951	108.00062	-0.2524484	-12.1486567
97.74124	105.96761	-0.2524484	-7.9739307
95.83993	103.03545	-0.2524484	-6.9430746
95.98686	100.97988	-0.2524484	-4.7405762
93.62349	99.21599	-0.2524484	-5.3400431
88.85108	98.07049	-0.2524484	-8.9669614
91.97220	103.52359	-0.2524484	-11.2989385
95.69117	105.88894	-0.2524484	-9.9453155
94.62068	104.47802	-0.2524484	-9.6048947
94.71098	101.54628	-0.2524484	-6.5828541
89.97701	96.49948	-0.2524484	-6.2700226
93.11218	95.12134	-0.2524484	-1.7567109
95.38034	92.81922	-0.2524484	2.8135697
92.30708	87.89903	-0.2524484	4.6604963
88.49575	86.34275	-0.2524484	2.4054516
89.83124	89.05422	-0.2524484	1.0294658
84.41136	90.09944	-0.2524484	-5.4356284
93.20203	92.84385	-0.2524484	0.6106306
90.22541	88.62736	-0.2524484	1.8504959
98.68039	84.43804	-0.2524484	14.4947933
88.83819	74.17508	-0.2524484	14.9155547
85.77647	72.38794	-0.2524484	13.6409768
89.35943	70.66144	-0.2524484	18.9504448
89.07867	67.35959	-0.2524484	21.9715258
82.53426	62.62616	-0.2524484	20.1605466
80.27971	61.84370	-0.2524484	18.6884631
74.77309	64.48545	-0.2524484	10.5400855
84.40958	71.07981	-0.2524484	13.5822128
87.54086	71.87397	-0.2524484	15.9193390
87.88603	69.83997	-0.2524484	18.2985137
86.67737	66.05090	-0.2524484	20.8789262
86.33911	65.35517	-0.2524484	21.2363861
86.30732	65.86027	-0.2524484	20.6994998
90.44415	68.25150	-0.2524484	22.4450949
96.42231	71.44649	-0.2524484	25.2282642
96.35021	70.33897	-0.2524484	26.2636794
97.19052	71.39980	-0.2524484	26.0431684
93.90483	70.30103	-0.2524484	23.8562487
95.88931	71.20259	-0.2524484	24.9391633
95.55939	69.31073	-0.2524484	26.5011016
95.49810	70.31280	-0.2524484	25.4377445
92.79077	71.56070	-0.2524484	21.4825173
93.42117	73.92711	-0.2524484	19.7465046
94.04589	76.46390	-0.2524484	17.8344414
94.54239	80.05089	-0.2524484	14.7439494
98.91523	85.51043	-0.2524484	13.6572482
104.61705	86.47106	-0.2524484	18.3984318
101.15838	85.11515	-0.2524484	16.2956741
105.19939	87.82468	-0.2524484	17.6271542
115.19972	93.29388	-0.2524484	22.1582894
101.36327	84.27805	-0.2524484	17.3376647
99.52982	84.63166	-0.2524484	15.1506118
97.01953	86.29383	-0.2524484	10.9781569
99.42721	88.29013	-0.2524484	11.3895258
94.74006	87.15672	-0.2524484	7.8357931
94.16482	89.03390	-0.2524484	5.3833669
102.07156	92.77009	-0.2524484	9.5539109
87.03708	90.75784	-0.2524484	-3.4683041
93.81457	100.98527	-0.2524484	-6.9182509
97.27858	103.94992	-0.2524484	-6.4188949
98.07536	103.63916	-0.2524484	-5.3113556
89.80293	100.79299	-0.2524484	-10.7376130
89.82875	104.98324	-0.2524484	-14.9020337
89.08580	109.17658	-0.2524484	-19.8383319
92.31846	112.19968	-0.2524484	-19.6287683
91.43013	113.01692	-0.2524484	-21.3343394
92.84129	114.84211	-0.2524484	-21.7483682
96.63512	114.09153	-0.2524484	-17.2039572
91.41998	110.49606	-0.2524484	-18.8236354
98.06136	112.82596	-0.2524484	-14.5121507
89.46006	109.37427	-0.2524484	-19.6617676
91.64333	112.15676	-0.2524484	-20.2609843
92.90019	113.59371	-0.2524484	-20.4410768
90.77479	112.85879	-0.2524484	-21.8315540
90.80960	112.57311	-0.2524484	-21.5110623
92.74629	113.52308	-0.2524484	-20.5243354
93.83131	114.85394	-0.2524484	-20.7701831
100.86765	116.35917	-0.2524484	-15.2390743
106.85148	115.49257	-0.2524484	-8.3886404
102.95332	109.37684	-0.2524484	-6.1710729
102.47483	105.23360	-0.2524484	-2.5063244
98.12048	103.59736	-0.2524484	-5.2244344
99.62071	103.77494	-0.2524484	-3.9017874
97.13045	102.84671	-0.2524484	-5.4638080
97.75148	103.33597	-0.2524484	-5.3320450
93.03993	103.29762	-0.2524484	-10.0052390
90.37749	106.16182	-0.2524484	-15.5318820
92.29975	113.23525	-0.2524484	-20.6830509
98.28147	120.18085	-0.2524484	-21.6469313
105.15577	123.64497	-0.2524484	-18.2367508
101.00150	121.35503	-0.2524484	-20.1010854

xhat1.opt <- winter1.opt$fitted[,2]

Peramalan

#Forecast
forecast1 <- predict(winter1, n.ahead = nrow(testing))
forecast1.opt <- predict(winter1.opt, nrow(testing))

Plot Deret Waktu

#Plot time series
plot(training.ts,main="Winter 0.2;0.1;0.1",type="l",col="black",
     xlim=c(1,4.8), ylim=c(60,180), pch=12)
lines(xhat1,type="l",col="orange", lwd=2)
lines(xhat1.opt,type="l",col="cyan4", lwd=2)
lines(forecast1,type="l",col="orange", lwd=2)
lines(forecast1.opt,type="l",col="cyan4", lwd=2)
legend("topleft",c("Actual Data",expression(paste(winter1)),
                   expression(paste(winter1.opt))),cex=0.5,
       col=c("black","orange","cyan4"),lty=1)

Hasil pemulusan pada forecasting model Winter1 opt terlihat lebih baik dibandingkan model Winter. Hal ini dapat dilihat dari pola pergerakan hasil pemulusan Winter1 opt yang lebih mirip dengan data aktual-nya. Ini dikarenakan Winter1 opt menggunakan parameter beta , alpha , dan gamma yang optimum (dengan pemberian value NULL ) Sehingga lebih mirip dengan data aslinya.

# Membuka file PNG untuk menyimpan plot
png("C:/Users/Fathan/Documents/Obsidian Vault/2. Kuliah/Smt 5/6. Metode Peramalan Deret Waktu/@Proj/STA1341-MPDW/Pertemuan 1/Chart/11_TSA_Winter 0.2;0.1;0.1.png",
    height = 9*300, width = 16*300, res=300)

# Plot time series dengan warna dan pengaturan lainnya
#Plot time series
plot(training.ts,main="Winter 0.2;0.1;0.1",type="l",col="black",
     xlim=c(1,4.8), ylim=c(60,180), pch=12)
lines(xhat1,type="l",col="orange", lwd=2)
lines(xhat1.opt,type="l",col="cyan4", lwd=2)
lines(forecast1,type="l",col="orange", lwd=2)
lines(forecast1.opt,type="l",col="cyan4", lwd=2)
legend("topleft",c("Actual Data",expression(paste(winter1)),
                   expression(paste(winter1.opt))),cex=0.5,
       col=c("black","orange","cyan4"),lty=1)

# Menyimpan plot sebagai file PNG
dev.off() # Menutup file PNG

## png 
##   2

Akurasi Data Latih

#Akurasi data training
SSE1<-winter1$SSE
MSE1<-winter1$SSE/length(training.ts)
RMSE1<-sqrt(MSE1)

SSE1.opt<-winter1.opt$SSE
MSE1.opt<-winter1.opt$SSE/length(training.ts)
RMSE1.opt<-sqrt(MSE1.opt)

akurasi1.train = data.frame(Model_Winter = c("Winter 1","Winter1 optimal"),
                            Nilai_SSE=c(SSE1,SSE1.opt),
                            Nilai_MSE=c(MSE1,MSE1.opt),
                            Nilai_RMSE=c(RMSE1,RMSE1.opt))
kable(akurasi1.train) %>% kable_styling()

Model_Winter	Nilai_SSE	Nilai_MSE	Nilai_RMSE
Winter 1	9431.981	29.94280	5.472001
Winter1 optimal	4127.961	13.10464	3.620033

Akurasi pada model Winter1 optimal dengan data training lebih baik dibandingkan model Winter1. Ditandai dengan ketiga nilai SSE, MSE, dan RMSE yang lebih kecil.

Akurasi Data Uji

#Akurasi Data Testing
forecast1<-data.frame(forecast1)
testing.ts<-data.frame(testing.ts)
selisih1<-forecast1 - testing.ts
SSEtesting1<-sum(selisih1^2)
MSEtesting1<-SSEtesting1/length(testing.ts)
RMSEtesting1<-sqrt(MSEtesting1)

forecast1.opt<-data.frame(forecast1.opt)
selisih1.opt<-forecast1.opt - testing.ts
SSEtesting1.opt<-sum(selisih1.opt^2)
MSEtesting1.opt<-SSEtesting1.opt/length(testing.ts)
RMSEtesting1.opt<-sqrt(MSEtesting1.opt)


akurasi1.test = data.frame(Model_Winter = c("Winter 1","winter1 optimal"),
                            Nilai_SSE=c(SSEtesting1, SSEtesting1.opt),
                            Nilai_MSE=c(MSEtesting1, MSEtesting1.opt),
                            Nilai_RMSE=c(RMSEtesting1,RMSEtesting1.opt))
kable(akurasi1.test) %>% kable_styling()

Model_Winter	Nilai_SSE	Nilai_MSE	Nilai_RMSE
Winter 1	76727.42	76727.42	276.9971
winter1 optimal	30622.33	30622.33	174.9924

Sama seperti sebelumnya, Akurasi pada model Winter1 dengan data testing lebih baik dibandingkan model Winter1 optimal. Ditandai dengan ketiga nilai SSE, MSE, dan RMSE yang lebih kecil.

4. Winter Multiplikatif

Model multiplikatif digunakan cocok digunakan jika plot data asli menunjukkan fluktuasi musiman yang bervariasi.

#Pemulusan dengan winter multiplikatif 
winter2 <- HoltWinters(training.ts,
                       alpha=0.2,beta=0.1,gamma=0.3,
                       seasonal = "multiplicative")
kable(winter2$fitted) %>% kable_styling()

xhat	level	trend	season
124.17101	142.61579	-0.2524484268	0.8722119
125.65077	139.36098	-0.5526852965	0.9052108
128.41627	136.48745	-0.7847697084	0.9463061
127.60349	133.96819	-0.9582180898	0.9593528
129.52540	131.77592	-1.0816240984	0.9910563
124.55353	129.88417	-1.1626366991	0.9676201
125.59289	128.26607	-1.2081821971	0.9884698
122.65158	126.89544	-1.2244273314	0.9759735
119.98548	125.74241	-1.2172874787	0.9635443
114.43345	124.77307	-1.1924931317	0.9259825
107.63534	123.95133	-1.1554178444	0.8765385
101.47487	123.25560	-1.1094491923	0.8307660
99.93028	122.67461	-1.0566032596	0.8216734
105.06937	122.19724	-0.9986795495	0.8669193
101.16289	121.79853	-0.9386825072	0.8370265
103.68514	121.45651	-0.8790162230	0.8599046
106.14293	121.16706	-0.8200593704	0.8819740
106.48741	120.92232	-0.7625278210	0.8862150
109.98249	120.71555	-0.7069524177	0.9164551
114.02541	120.54490	-0.6533215476	0.9510711
110.99715	120.40355	-0.6021248392	0.9265095
105.43061	120.28126	-0.5541415298	0.8805909
107.04689	120.17440	-0.5094126562	0.8945548
104.51572	120.08377	-0.4675347004	0.8737586
107.98989	120.00405	-0.4287531882	0.9031120
112.04438	119.92301	-0.3939821077	0.9373822
112.98875	119.83960	-0.3629250124	0.9456972
115.10747	119.76032	-0.3345597328	0.9638412
114.44736	119.67944	-0.3091918523	0.9587595
110.77853	119.59818	-0.2863991186	0.9284794
108.40667	119.52104	-0.2654730729	0.9090282
109.66385	119.43451	-0.2475786584	0.9200996
109.90644	119.34695	-0.2315770567	0.9226890
112.84365	119.27221	-0.2158934064	0.9478174
113.09926	119.20536	-0.2009885824	0.9503790
117.52410	119.14342	-0.1870838634	0.9879600
122.01418	119.09519	-0.1731987627	1.0260018
123.82945	119.06932	-0.1584654973	1.0413637
121.58814	119.06461	-0.1430905112	1.0224234
120.24028	119.08424	-0.1268181963	1.0107842
113.88371	119.13545	-0.1090157595	0.9567934
119.99370	119.22005	-0.0896533267	1.0072467
121.36404	119.32426	-0.0702678765	1.0176937
134.07128	119.43400	-0.0522671244	1.1230469
134.62465	119.53822	-0.0366183968	1.1265511
133.46895	119.63747	-0.0230309857	1.1158264
138.87266	119.73830	-0.0106446461	1.1599045
142.01643	119.83928	0.0005174386	1.1850523
140.32209	119.93322	0.0098601220	1.1699057
138.94233	120.02479	0.0180301663	1.1574398
127.50511	120.12363	0.0261113322	1.0612184
133.82223	122.09559	0.2206969255	1.0940671
139.94927	123.93736	0.3828035181	1.1257166
141.15978	124.44288	0.3950753682	1.1307441
145.51855	125.26073	0.4373524412	1.1576832
144.58573	125.29407	0.3969517890	1.1503266
145.70368	125.72480	0.4003294378	1.1552312
146.79587	125.50124	0.3379406676	1.1665355
150.37550	125.06838	0.2608600058	1.1998438
148.74984	123.30472	0.0584085784	1.2057884
143.29589	120.78725	-0.1991794849	1.1883090
138.62997	118.95955	-0.3620310125	1.1689112
138.11685	117.77112	-0.4446714752	1.1772014
141.85613	117.18427	-0.4588891620	1.2152981
135.68270	114.89766	-0.6416612892	1.1875324
129.65458	113.26357	-0.7409042000	1.1522530
128.10450	112.36218	-0.7569524441	1.1478360
124.54047	111.37271	-0.7802048986	1.1261203
121.96848	111.17495	-0.7219600659	1.1042570
122.40536	111.45665	-0.6215935959	1.1043920
126.72288	111.50595	-0.5545043102	1.1421471
123.93798	111.43424	-0.5062247501	1.1172829
125.88792	111.98094	-0.4009330776	1.1282301
131.88427	112.88862	-0.2700717218	1.1710707
129.59370	113.39830	-0.1920965403	1.1447580
124.43624	112.72161	-0.2405557461	1.1062862
122.17404	113.22476	-0.1661850693	1.0806260
124.77901	113.81850	-0.0901928277	1.0971676
119.06921	113.50063	-0.1129606632	1.0501073
119.48646	114.45247	-0.0064802558	1.0440423
126.08928	114.96389	0.0453096595	1.0963409
107.37193	113.63202	-0.0924081156	0.9456782
110.04306	115.64140	0.1177704239	0.9506207
111.10582	116.54538	0.1963914946	0.9517229
114.02064	117.59164	0.2813781279	0.9673176
105.98405	117.95352	0.2894286099	0.8963245
107.58632	120.92634	0.5577678567	0.8856000
104.17942	123.11321	0.7206784901	0.8412836
107.04168	125.93083	0.9303717519	0.8437701
106.50445	128.95616	1.1398676201	0.8186603
112.57368	133.65930	1.4961949415	0.8329198
122.59025	137.16681	1.6973263953	0.8828071
121.36687	138.34528	1.6454408787	0.8669637
126.41165	138.42044	1.4884131222	0.9035286
116.02545	137.08843	1.2063711638	0.8389719
116.44807	137.38525	1.1154157250	0.8407763
116.95710	137.65667	1.0310158241	0.8433128
116.86209	137.63775	0.9260228389	0.8433813
111.75805	136.20136	0.6897811053	0.8164009
115.70638	137.38892	0.7395593923	0.8376721
118.13689	138.28454	0.7551650761	0.8496630
123.25755	138.31780	0.6829743292	0.8867401
128.27913	137.19471	0.5023677749	0.9316039
129.08518	135.77370	0.3100300548	0.9485718
132.04846	134.13022	0.1146798972	0.9836385
126.98797	131.91713	-0.1180978902	0.9634970
127.40985	129.44760	-0.3532406181	0.9869513
122.15239	125.76089	-0.6865873230	0.9766386
116.06114	121.23616	-1.0704014941	0.9658420
107.79276	117.34519	-1.3524587524	0.9293062
98.64295	113.62478	-1.5892538928	0.8804614
90.86828	110.55382	-1.7374250525	0.8350606
88.14299	108.44078	-1.7749857324	0.8263473
92.12803	107.35244	-1.7063217968	0.8720437
87.17379	105.27961	-1.7429720959	0.8419608
88.67814	104.20323	-1.6763131362	0.8649255
88.88279	101.94001	-1.7350035258	0.8870095
89.45997	101.95182	-1.5603220691	0.8911110
93.63509	102.93440	-1.3060320258	0.9213479
97.00869	102.68224	-1.2006448716	0.9559239
93.76981	101.88567	-1.1602375397	0.9309448
88.76809	101.44517	-1.0882635696	0.8845240
90.53172	101.73209	-0.9507454180	0.8982984
88.34125	101.58470	-0.8704095586	0.8771471
91.42014	101.65342	-0.7764970787	0.9062543
94.53044	101.26972	-0.7372176482	0.9402973
94.55550	100.44732	-0.7457350124	0.9483851
95.36356	99.46002	-0.7698917347	0.9662928
93.78740	98.39756	-0.7991492284	0.9609521
89.77367	97.31381	-0.8276084440	0.9304301
88.56967	97.94066	-0.6821632625	0.9106626
90.54576	98.78054	-0.5299591154	0.9215800
91.09874	99.02842	-0.4521745417	0.9241449
93.12320	98.55704	-0.4540949357	0.9492395
91.85850	97.07619	-0.5567707852	0.9517100
94.16266	95.80523	-0.6281895945	0.9893422
96.28018	94.40629	-0.7052643688	1.0275253
95.38685	92.30152	-0.8452157731	1.0429774
91.74995	90.52879	-0.9379665381	1.0240999
89.93057	89.73535	-0.9235139668	1.0125967
84.59840	89.13762	-0.8909357052	0.9586581
89.05236	89.05022	-0.8105818019	1.0092104
88.87193	88.00335	-0.8342113464	1.0195343
96.15128	86.39389	-0.9117355272	1.1248111
92.98424	83.53316	-1.1066354740	1.1280864
89.49756	81.32479	-1.2168086407	1.1172115
90.30340	79.08623	-1.3189837699	1.1612010
89.54423	76.89687	-1.4060213023	1.1861601
85.33058	74.39416	-1.5156900113	1.1708613
81.90071	72.27882	-1.5756558329	1.1583742
75.23052	71.09669	-1.5363026385	1.0815137
77.57334	71.18209	-1.3741320964	1.1112392
78.96834	71.29219	-1.2257093836	1.1270487
79.52430	71.16167	-1.1161904002	1.1353237
80.29302	70.67890	-1.0528479882	1.1532037
80.17738	70.62969	-0.9524844882	1.1506975
80.49627	70.92560	-0.8276451251	1.1483397
82.28806	71.73053	-0.6643879292	1.1579081
85.66773	73.27736	-0.4432661244	1.1762038
87.16445	74.46685	-0.2799905902	1.1749312
88.77907	76.05174	-0.0935022038	1.1687880
89.51872	77.20242	0.0309160612	1.1590684
92.14875	78.25852	0.1334342244	1.1754874
93.95170	78.65248	0.1594871807	1.1920994
93.51034	79.36533	0.2148231491	1.1750461
92.64994	80.26262	0.2830699200	1.1502781
93.34939	81.18380	0.3468815420	1.1449602
93.61774	82.19981	0.4137940477	1.1332001
93.88831	83.60236	0.5126690356	1.1161895
95.96802	85.61149	0.6623154358	1.1123657
100.85048	87.09763	0.7446980620	1.1480852
100.58709	88.23943	0.7844079647	1.1298894
103.75015	89.83151	0.8651754499	1.1439243
110.19019	92.29817	1.0253234287	1.1807337
106.00639	92.17163	0.9101375844	1.1388524
103.97737	92.40979	0.8429402140	1.1150061
102.09556	92.91778	0.8094450543	1.0892840
103.02070	93.35165	0.7718871379	1.0945265
99.74255	93.24997	0.6845305258	1.0618308
98.85651	93.53283	0.6443631604	1.0496863
102.59961	94.30742	0.6573860124	1.0803962
91.82950	94.42804	0.6037091585	0.9663035
93.68474	96.96292	0.7968265384	0.9583161
95.59610	98.69164	0.8900163402	0.9599769
97.62346	99.91581	0.9234317521	0.9681098
93.00480	100.21050	0.8605574864	0.9201922
92.30313	101.67641	0.9210927719	0.8996625
89.56664	103.37933	0.9992748122	0.8580939
91.51554	105.29537	1.0909513748	0.8602190
91.28716	106.90815	1.1431349793	0.8448502
93.20006	108.74794	1.2128005004	0.8475758
97.46813	109.71768	1.1884944011	0.8788341
94.71630	109.69136	1.0670123364	0.8551616
98.58461	110.80133	1.0713085610	0.8812218
92.99942	110.77539	0.9615833316	0.8323066
94.17858	111.86927	0.9748136188	0.8345903
95.04934	112.78212	0.9686169117	0.8355932
94.12969	113.08071	0.9016143372	0.8258271
93.45653	113.15898	0.8192801123	0.8199504
96.06190	113.72788	0.7942413271	0.8388065
97.10466	114.24031	0.7660607713	0.8443415
100.83261	114.79209	0.7446320326	0.8727321
106.30369	115.35508	0.7264682303	0.9157673
107.21784	114.47553	0.5658665284	0.9319935
109.14695	113.00107	0.3618342200	0.9628101
105.34646	111.58957	0.1845002414	0.9424946
105.50049	110.36367	0.0434605146	0.9555587
102.30345	108.98587	-0.0986656570	0.9395360
101.12520	107.99880	-0.1875063382	0.9379834
96.85860	107.15346	-0.2532899987	0.9060660
92.46849	106.98435	-0.2448712522	0.8663008
90.20316	108.53597	-0.0652221966	0.8315897
92.86691	111.30793	0.2184957266	0.8326898
99.43080	114.02990	0.4688431796	0.8684008
98.18161	115.18488	0.5374568066	0.8484240

xhat2 <- winter2$fitted[,2]

winter2.opt<- HoltWinters(training.ts, alpha= NULL,  beta = NULL, gamma = NULL, seasonal = "multiplicative")
kable(winter2.opt$fitted) %>% kable_styling()

xhat	level	trend	season
124.17101	142.61579	-0.2524484	0.8722119
118.11312	130.73379	-0.2524484	0.9052108
120.83384	127.94247	-0.2524484	0.9463061
121.76725	127.17891	-0.2524484	0.9593528
125.47445	126.85923	-0.2524484	0.9910563
122.29063	126.63535	-0.2524484	0.9676201
124.72313	126.43043	-0.2524484	0.9884698
122.95114	126.23039	-0.2524484	0.9759735
121.17946	126.01673	-0.2524484	0.9635443
116.22216	125.76471	-0.2524484	0.9259825
109.74213	125.45190	-0.2524484	0.8765385
103.73408	125.11802	-0.2524484	0.8307660
102.34220	124.80582	-0.2524484	0.8216734
107.73255	124.52302	-0.2524484	0.8669193
103.75966	124.21467	-0.2524484	0.8370265
106.29929	123.86999	-0.2524484	0.8599046
108.74181	123.54611	-0.2524484	0.8819740
108.99286	123.23937	-0.2524484	0.8862150
112.44630	122.94946	-0.2524484	0.9164551
116.44842	122.69169	-0.2524484	0.9510711
113.21596	122.44867	-0.2524484	0.9265095
107.38556	122.19961	-0.2524484	0.8805909
108.87395	121.95986	-0.2524484	0.8945548
106.15716	121.74729	-0.2524484	0.8737586
109.53777	121.54169	-0.2524484	0.9031120
113.47561	121.30831	-0.2524484	0.9373822
114.26251	121.07602	-0.2524484	0.9456972
116.26470	120.87886	-0.2524484	0.9638412
115.46000	120.67889	-0.2524484	0.9587595
111.63910	120.49109	-0.2524484	0.9284794
109.15495	120.33117	-0.2524484	0.9090282
110.30312	120.13416	-0.2524484	0.9200996
110.45587	119.96329	-0.2524484	0.9226890
113.36331	119.85704	-0.2524484	0.9478174
113.57479	119.75718	-0.2524484	0.9503790
117.96564	119.65570	-0.2524484	0.9879600
122.44554	119.59487	-0.2524484	1.0260018
124.27109	119.58740	-0.2524484	1.0413637
122.02572	119.60195	-0.2524484	1.0224234
120.68338	119.64825	-0.2524484	1.0107842
114.33042	119.74576	-0.2524484	0.9567934
120.49609	119.88162	-0.2524484	1.0072467
121.85989	119.99367	-0.2524484	1.0176937
134.55065	120.06102	-0.2524484	1.1230469
134.99642	120.08405	-0.2524484	1.1265511
133.73158	120.10225	-0.2524484	1.1158264
139.06653	120.14725	-0.2524484	1.1599045
142.14137	120.19768	-0.2524484	1.1850523
140.35708	120.22544	-0.2524484	1.1699057
138.90879	120.26629	-0.2524484	1.1574398
127.44899	120.34931	-0.2524484	1.0612184
139.40884	127.67502	-0.2524484	1.0940671
145.77294	129.74591	-0.2524484	1.1257166
142.14430	125.96109	-0.2524484	1.1307441
146.35346	126.67171	-0.2524484	1.1576832
142.69021	124.29566	-0.2524484	1.1503266
144.63279	125.45059	-0.2524484	1.1552312
143.77225	123.49967	-0.2524484	1.1665355
146.40140	122.26950	-0.2524484	1.1998438
140.46067	116.74110	-0.2524484	1.2057884
132.59655	111.83668	-0.2524484	1.1883090
130.91688	112.25144	-0.2524484	1.1689112
133.79756	113.90978	-0.2524484	1.1772014
140.60586	115.94905	-0.2524484	1.2152981
129.63286	109.41398	-0.2524484	1.1875324
125.60893	109.26404	-0.2524484	1.1522530
127.24625	111.10997	-0.2524484	1.1478360
124.19265	110.53609	-0.2524484	1.1261203
124.25823	112.77900	-0.2524484	1.1042570
126.51406	114.80784	-0.2524484	1.1043920
130.22705	114.27196	-0.2524484	1.1421471
126.54385	113.51280	-0.2524484	1.1172829
130.06180	115.53194	-0.2524484	1.1282301
137.28455	117.48239	-0.2524484	1.1710707
133.27893	116.67787	-0.2524484	1.1447580
123.68504	112.05447	-0.2524484	1.1062862
124.22480	115.20878	-0.2524484	1.0806260
127.46589	116.42968	-0.2524484	1.0971676
118.81514	113.39816	-0.2524484	1.0501073
122.36717	117.45763	-0.2524484	1.0440423
128.07593	117.07372	-0.2524484	1.0963409
103.86438	110.08303	-0.2524484	0.9456782
114.63789	120.84512	-0.2524484	0.9506207
113.86518	119.89355	-0.2524484	0.9517229
116.49839	120.68694	-0.2524484	0.9673176
106.22298	118.76197	-0.2524484	0.8963245
113.75051	128.69702	-0.2524484	0.8856000
108.61828	129.36263	-0.2524484	0.8412836
112.13081	133.14507	-0.2524484	0.8437701
111.40527	136.33486	-0.2524484	0.8186603
120.76883	145.24700	-0.2524484	0.8329198
127.92812	145.16306	-0.2524484	0.8828071
119.60998	138.21669	-0.2524484	0.8669637
120.34935	133.45173	-0.2524484	0.9035286
106.73392	127.47235	-0.2524484	0.8389719
111.00262	132.27642	-0.2524484	0.8407763
112.59893	133.77222	-0.2524484	0.8433128
112.34176	133.45645	-0.2524484	0.8433813
104.46094	128.20545	-0.2524484	0.8164009
114.38664	136.80545	-0.2524484	0.8376721
117.35788	138.37799	-0.2524484	0.8496464
122.20652	136.03950	-0.2524484	0.8999866
122.44740	129.79900	-0.2524484	0.9452000
121.56087	126.98332	-0.2524484	0.9592049
123.96195	125.32487	-0.2524484	0.9911214
118.24852	122.44461	-0.2524484	0.9677259
118.49975	120.11999	-0.2524484	0.9885892
110.98465	113.95913	-0.2524484	0.9760609
103.52552	107.69475	-0.2524484	0.9635453
98.43399	106.56954	-0.2524484	0.9258529
91.74662	104.94151	-0.2524484	0.8763726
87.02447	105.01912	-0.2524484	0.8306503
87.61413	106.88891	-0.2524484	0.8216152
94.96521	109.81010	-0.2524484	0.8668058
88.15437	105.59376	-0.2524484	0.8368452
91.80423	107.03135	-0.2524484	0.8597600
89.44070	101.67512	-0.2524484	0.8818610
95.24711	107.73828	-0.2524484	0.8861365
102.71423	112.33162	-0.2524484	0.9164435
102.96134	108.50832	-0.2524484	0.9510924
97.03220	104.98038	-0.2524484	0.9265169
92.06760	104.80135	-0.2524484	0.8806176
95.49760	106.99661	-0.2524484	0.8946400
92.03119	105.56858	-0.2524484	0.8738565
95.23194	105.69628	-0.2524484	0.9031533
96.97543	103.70090	-0.2524484	0.9374276
95.38107	101.09698	-0.2524484	0.9458230
95.41080	99.23009	-0.2524484	0.9639631
93.54275	97.80367	-0.2524484	0.9589091
89.51773	96.64416	-0.2524484	0.9286870
92.73068	102.24955	-0.2524484	0.9091502
95.80536	104.35685	-0.2524484	0.9202816
94.55530	102.69408	-0.2524484	0.9230163
94.07123	99.46605	-0.2524484	0.9481687
89.56329	94.45742	-0.2524484	0.9507278
91.97599	93.30597	-0.2524484	0.9884203
93.96248	91.77912	-0.2524484	1.0266131
91.27998	87.84985	-0.2524484	1.0420398
88.81311	87.05471	-0.2524484	1.0231658
90.37392	89.58623	-0.2524484	1.0116433
86.19724	90.25737	-0.2524484	0.9576948
92.31986	91.82721	-0.2524484	1.0081366
89.51967	88.14762	-0.2524484	1.0184821
94.56078	84.39651	-0.2524484	1.1237962
87.28810	77.68429	-0.2524484	1.1272894
85.78324	77.07580	-0.2524484	1.1166298
87.27486	75.44048	-0.2524484	1.1607546
87.26022	73.83664	-0.2524484	1.1858556
82.62438	70.82722	-0.2524484	1.1707354
80.84327	70.04250	-0.2524484	1.1583781
77.47747	72.02157	-0.2524484	1.0795377
83.79915	76.44978	-0.2524484	1.0997649
86.38455	77.62085	-0.2524484	1.1165352
86.41265	76.50489	-0.2524484	1.1332443
84.95388	74.00157	-0.2524484	1.1519307
85.69506	74.50646	-0.2524484	1.1540799
86.43291	75.37163	-0.2524484	1.1506104
89.82485	77.43333	-0.2524484	1.1638225
95.23873	80.68560	-0.2524484	1.1840731
95.53572	80.45361	-0.2524484	1.1912013
97.16862	81.88183	-0.2524484	1.1903633
94.73136	80.90139	-0.2524484	1.1746139
95.75586	81.12950	-0.2524484	1.1839683
94.72347	79.51877	-0.2524484	1.1950027
95.80272	80.90422	-0.2524484	1.1878564
94.44677	81.77173	-0.2524484	1.1585819
94.63861	82.77183	-0.2524484	1.1468652
95.18425	84.23606	-0.2524484	1.1333670
96.05882	86.74217	-0.2524484	1.1106385
99.92920	90.80122	-0.2524484	1.1035954
103.49487	90.98455	-0.2524484	1.1406643
101.39100	90.48430	-0.2524484	1.1236720
105.01091	92.82341	-0.2524484	1.1343828
114.27131	97.96541	-0.2524484	1.1694591
102.14498	90.50478	-0.2524484	1.1317710
100.44866	90.27631	-0.2524484	1.1158004
98.61740	91.17732	-0.2524484	1.0846031
99.88845	91.94813	-0.2524484	1.0893474
95.80624	90.52338	-0.2524484	1.0613189
95.32657	91.58755	-0.2524484	1.0437014
101.44765	94.46254	-0.2524484	1.0768236
89.98855	92.95279	-0.2524484	0.9707467
96.19447	101.61558	-0.2524484	0.9490085
97.99497	102.95946	-0.2524484	0.9541215
98.07836	102.06154	-0.2524484	0.9633556
90.54374	98.99585	-0.2524484	0.9169599
91.33696	103.17570	-0.2524484	0.8874278
90.45795	106.83678	-0.2524484	0.8486984
92.73866	109.36112	-0.2524484	0.8499660
91.52768	110.03956	-0.2524484	0.8336833
93.35664	112.29822	-0.2524484	0.8332009
96.34154	110.94245	-0.2524484	0.8703725
91.58586	106.94144	-0.2524484	0.8584377
97.57888	109.67982	-0.2524484	0.8917228
89.79126	106.10100	-0.2524484	0.8482993
92.01717	109.28115	-0.2524484	0.8439720
93.19250	110.77533	-0.2524484	0.8431964
91.22344	109.65696	-0.2524484	0.8338179
90.40756	108.94606	-0.2524484	0.8317651
92.77051	110.57728	-0.2524484	0.8408852
94.74939	112.26826	-0.2524484	0.8458573
100.41560	113.34438	-0.2524484	0.8879113
105.72180	112.76422	-0.2524484	0.9396510
101.99060	106.92878	-0.2524484	0.9560752
101.40437	103.20784	-0.2524484	0.9849351
98.28803	102.33058	-0.2524484	0.9628706
99.46860	102.40958	-0.2524484	0.9736824
97.27075	101.55357	-0.2524484	0.9602140
97.79943	101.99435	-0.2524484	0.9612503
93.78490	101.93578	-0.2524484	0.9223233
91.51810	104.58539	-0.2524484	0.8771736
93.39647	112.04468	-0.2524484	0.8354469
99.02291	119.77010	-0.2524484	0.8285212
105.67177	123.50751	-0.2524484	0.8573423
100.92907	120.30773	-0.2524484	0.8406883

xhat2.opt <- winter2.opt$fitted[,2]

Peramalan

#Forecast
forecast2 <- predict(winter2, n.ahead = nrow(testing))
forecast2.opt <- predict(winter2.opt, n.ahead = nrow(testing))

Plot Deret Waktu

#Plot time series
plot(training.ts, main="Winter 0.2;0.1;0.1",
     type="l",col="black", xlim=c(1,4.8), ylim=c(60,180), pch=12)
lines(xhat2,type="l",col="orange", lwd=2)
lines(xhat2.opt,type="l",col="cyan4", lwd=2)
lines(forecast2,type="l",col="orange", lwd=2)
lines(forecast2.opt,type="l",col="cyan4", lwd=2)
legend("topleft",c("Actual Data", expression(paste(winter2)),
                   expression(paste(winter2.opt))), 
                   cex=0.5, col=c("black","orange","cyan4"),lty=1)

Hasil pemulusan pada forecasting model Winter2 opt terlihat lebih baik dibandingkan model Winter. Hal ini dapat dilihat dari pola pergerakan hasil pemulusan Winter2 opt yang lebih mirip dengan data aktual-nya. Ini dikarenakan Winter2 opt menggunakan parameter beta , alpha , dan gamma yang optimum (dengan pemberian value NULL ) Sehingga lebih mirip dengan data aslinya.

# Membuka file PNG untuk menyimpan plot
png("C:/Users/Fathan/Documents/Obsidian Vault/2. Kuliah/Smt 5/6. Metode Peramalan Deret Waktu/@Proj/STA1341-MPDW/Pertemuan 1/Chart/12_TSA_Winter 0.2;0.1;0.1.png",
    height = 9*300, width = 16*300, res=300)

# Plot time series dengan warna dan pengaturan lainnya
#Plot time series
plot(training.ts, main="Winter 0.2;0.1;0.1",
     type="l",col="black", xlim=c(1,4.8), ylim=c(60,180), pch=12)
lines(xhat2,type="l",col="orange", lwd=2)
lines(xhat2.opt,type="l",col="cyan4", lwd=2)
lines(forecast2,type="l",col="orange", lwd=2)
lines(forecast2.opt,type="l",col="cyan4", lwd=2)
legend("topleft",c("Actual Data", expression(paste(winter2)),
                   expression(paste(winter2.opt))), 
                   cex=0.5, col=c("black","orange","cyan4"),lty=1)

# Menyimpan plot sebagai file PNG
dev.off() # Menutup file PNG

## png 
##   2

Akurasi Data Latih

#Akurasi data training
SSE2<-winter2$SSE
MSE2<-winter2$SSE/length(training.ts)
RMSE2<-sqrt(MSE2)

SSE2.opt<-winter2.opt$SSE
MSE2.opt<-winter2.opt$SSE/length(training.ts)
RMSE2.opt<-sqrt(MSE2.opt)

akurasi2.train = data.frame(Model_Winter = c("Winter 2","winter2 optimal"),
                            Nilai_SSE=c(SSE2,SSE2.opt),
                            Nilai_MSE=c(MSE2,MSE2.opt),
                            Nilai_RMSE=c(RMSE2,RMSE2.opt))
kable(akurasi2.train) %>% kable_styling()

Model_Winter	Nilai_SSE	Nilai_MSE	Nilai_RMSE
Winter 2	7343.858	23.31384	4.828440
winter2 optimal	3299.752	10.47540	3.236573

Akurasi pada model Winter2 optimal dengan data training lebih baik dibandingkan model Winter2. Ditandai dengan ketiga nilai SSE, MSE, dan RMSE yang lebih kecil.

Akurasi Data Uji

#Akurasi Data Testing
forecast2<-data.frame(forecast2)
testing.ts<-data.frame(testing.ts)
selisih2<-forecast2-testing.ts
SSEtesting2<-sum(selisih2^2)
MSEtesting2<-SSEtesting2/length(testing.ts)
RMSEtesting2<-sqrt(MSEtesting2)

forecast2.opt<-data.frame(forecast2.opt)
selisih2.opt<-forecast2.opt-testing.ts
SSEtesting2.opt<-sum(selisih2.opt^2)
MSEtesting2.opt<-SSEtesting2.opt/length(testing.ts)
RMSEtesting2.opt<-sqrt(MSEtesting2.opt)


akurasi2.test = data.frame(Model_Winter = c("Winter 2","winter2 optimal"),
                            Nilai_SSE=c(SSEtesting2, SSEtesting2.opt),
                            Nilai_MSE=c(MSEtesting2, MSEtesting2.opt),
                            Nilai_RMSE=c(RMSEtesting1,RMSEtesting1.opt))
kable(akurasi2.test) %>% kable_styling()

Model_Winter	Nilai_SSE	Nilai_MSE	Nilai_RMSE
Winter 2	99159.71	99159.71	276.9971
winter2 optimal	26956.06	26956.06	174.9924

Sama seperti sebelumnya, Akurasi pada model Winter2 dengan data testing lebih baik dibandingkan model Winter2 optimal. Ditandai dengan ketiga nilai SSE, MSE, dan RMSE yang lebih kecil.

5. Perbandingan Metode

banding.dma_des <- data.frame(
  cbind(rbind(SSE_test.dma, MSE_test.dma, MAPE_test.dma),
        rbind(SSEtestingdesopt, MSEtestingdesopt, MAPEtestingdesopt)))
row.names(banding.dma_des) <- c("SSE", "MSE", "MAPE")
colnames(banding.dma_des) <- c("DMA","DES")
kable(banding.dma_des) %>% kable_styling()

	DMA	DES
SSE	91763.86806	3163.79939
MSE	1147.04835	39.54749
MAPE	24.73109	4.57769

banding.wa_wm <- 
  cbind.data.frame(  t( akurasi1.test[2,-1]), 
                     t( akurasi2.test[2,-1]) )
row.names(banding.wa_wm) <- c("SSE", "MSE", "RMSE")
colnames(banding.wa_wm) <- c("Winter Aditif","Winter Multiplikatif")
kable(banding.wa_wm) %>% kable_styling()

	Winter Aditif	Winter Multiplikatif
SSE	30622.3302	26956.0560
MSE	30622.3302	26956.0560
RMSE	174.9924	174.9924

Metode DMA dan DES dapat dibandingkan hasilnya dengan menggunakan ukuran akurasi yang sama, yaitu SSE, MSE, dan MAPE. Didapatkan hasil bahwa metode DES lebih baik dibandingkan metode DMA dilihat dari SSE, MSE, dan MAPE yang lebih kecil nilainya.

Lalu metode Winter Aditif dan Winter Multifplikatif dapat dibandingkan hasilnya dengan menggunakan ukuran akurasi yang sama, yaitu SSE, MSE, dan RMSE. Didapatkan hasil bahwa metode Winter Multifplikatif lebih baik dibandingkan metode Winter Aditif dilihat dari SSE, MSE, dan RMSE yang lebih kecil nilainya.

C. Kesimpulan

Jika kita bandingkan keempatnya serta melihat nilai SSE dan MSE nya. Maka kita akan melihat bahwa metode DES adalah metode pemulusan terbaik untuk data deret waktu saham amazon periode 2022-2023. Hal ini juga dapat ditinjau langsung dari plot pemulusan yang sudah dibuat.

Referensi

• Legend/Label Time Series : https://r-graph-gallery.com/web-line-chart-with-labels-at-end-of-line.html

• Color : https://bookdown.org/hneth/ds4psy/ds4psy_files/figure-html/apx-color-sample-1.png

• Asisten praktikum : https://github.com/rizkynurhambali/Praktikum-MPDW-2324