Time-Series Candy Dataset

library(readr)
library(dplyr)
library(lubridate)
library(purrr)
library(zoo)
library(recipes)
library(imputeTS)
library(tidyr)
# Data Set
library(fpp2)

# model and evaluation
library(forecast)
library(TTR)
library(tseries)

# visualization
library(ggplot2)
library(TSstudio)
library(plotly)

options(scipen = 999)

candy <- read.csv("candy_production.csv")
candy

Exploratory Data

candy_ts <- ts(data = candy$IPG3113N, 
               start = c(1972, 1),
               end = c(2017,8),# opsional
               frequency = 12 # sesuai pola musiman
               )

#Cross Validation.

# data test
candy_test <- tail(candy_ts, 12)

# data train
candy_train <- head(candy_ts, length(candy_ts) - 12)

candy_train %>% 
  autoplot() +
  autolayer(candy_test, series = "Data Test") +
  theme(legend.position = "top")

candy_single_decomp <- candy_ts %>%
   mstl()

candy_single_decomp %>%
   tail(4*12) %>%
   autoplot()

Terlihat pola multi seasonal ketika di lakukan decompose pola trend penjualan naik selalu terlihat ketika ingin tahun baru.

Time-series Model

candy_ses <- HoltWinters(candy_train,
                         beta = F,
                         gamma = F
                         )

candy_ses

## Holt-Winters exponential smoothing without trend and without seasonal component.
## 
## Call:
## HoltWinters(x = candy_train, beta = F, gamma = F)
## 
## Smoothing parameters:
##  alpha: 0.9999339
##  beta : FALSE
##  gamma: FALSE
## 
## Coefficients:
##       [,1]
## a 104.6976

Model SES

Membuat model SES menggunakan function HoltWinters() dari package stats.

• alpha : koefisien untuk komponen random/residual.
  • ~ 1 observasi yang paling baru diberikan bobot yang paling tinggi tinggi dibandingkan dengan data periode lama
  • ~ 0 observasi yang paling baru diberikan bobot yang paling tinggi tinggi namun perbedaannya sangat sedikit dengan data periode lama
• beta : koefisien untuk komponen trend.
• gamma : koefisien untuk komponen seasonality.
• seasonality : menentukan jenis model seasonality (additive/multiplicative).

forecast_ses1 <- forecast(candy_ses, # nama model
                         h = 12 # meramal data untuk 12 bulan ke depan (1 tahun)
                         )

forecast_ses1 %>% 
  autoplot()

plot_forecast(forecast_ses1)

## Warning: `arrange_()` is deprecated as of dplyr 0.7.0.
## Please use `arrange()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.

accuracy(forecast_ses1, # hasil forecast
         candy_test # data test
         )

##                      ME     RMSE      MAE        MPE     MAPE     MASE
## Training set 0.03552213 9.078150 6.387317 -0.3747221 6.419526 1.232895
## Test set     5.30428212 7.748825 6.201541  4.5710061 5.447342 1.197037
##                   ACF1 Theil's U
## Training set 0.2634750        NA
## Test set     0.4462207  1.268245

dengan menggunakan model ses MAE yang didapat cukup besar.

Boleh juga dicoba bandingkan seasonal additive dan multiplicative

Holt Linear Method (hanya menggunakan trend)

Model Additive

Jika seasonal tidak ditulis, by default seasonal = “additive”

# dengan seasonal = "additive"
candy_seasonal <- HoltWinters(candy_train)

forecast_candy_seasonal <- forecast(candy_seasonal, 12)

accuracy(forecast_candy_seasonal, candy_test)

##                      ME     RMSE      MAE        MPE     MAPE      MASE
## Training set -0.2265730 3.878871 2.972647 -0.2802264 3.029201 0.5737876
## Test set      0.2096428 6.018426 5.343807  0.3599105 4.800096 1.0314747
##                   ACF1 Theil's U
## Training set 0.1076271        NA
## Test set     0.6409968 0.9945754

Model Multiplicative

# dengan seasonal = "multiplicative"
candy_seasonal <- HoltWinters(candy_train, seasonal = "multiplicative")

forecast_candy_seasonal <- forecast(candy_seasonal, 12)

accuracy(forecast_candy_seasonal, candy_test)

##                      ME     RMSE      MAE        MPE     MAPE      MASE
## Training set -0.3078917 4.220722 3.189807 -0.3479162 3.223621 0.6157043
## Test set     -0.5221824 7.650147 6.746691 -0.2419717 6.049466 1.3022627
##                   ACF1 Theil's U
## Training set 0.1791895        NA
## Test set     0.7126994   1.25342

Kesimpulannya Model terbaik ada pada Model Additive dikarnakan memiliki nilai MAE yang kecil maka model dapat disimpulkan mengalami sedikit kehilangan informasi, maka hasil forecast nya akan cukup akurat.