PERAMALAN ANGKA KEMATIAN PENYAKIT TUBERKULOSIS DI INDONESIA MENGGUNAKAN BOX-JENKIN’S METHOD BERBASIS R

ANALISIS RUNTUN WAKTU

Email             : brigita.melantika@student.matanauniversity.ac.id
RPubs            : https://rpubs.com/brigitatiaraem/
Jurusan          : Statistika
Address         : ARA Center, Matana University Tower
                         Jl. CBD Barat Kav, RT.1, Curug Sangereng, Kelapa Dua, Tangerang, Banten 15810.

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1 Import Data

print(getwd())

## [1] "D:/KULIAH/kuliahsem5/Runtun Waktu"

library(readxl)
data<-read_excel("Data_ARIMA_Tuberkulosis.xlsx",sheet = "Sheet4") 
data

## # A tibble: 30 × 2
##    Tahun Jumlah_Kematian_Penderita_Tuberkulosis
##    <dbl>                                  <dbl>
##  1  1990                                 128009
##  2  1991                                 125100
##  3  1992                                 123350
##  4  1993                                 122167
##  5  1994                                 120251
##  6  1995                                 118083
##  7  1996                                 115789
##  8  1997                                 115176
##  9  1998                                 116838
## 10  1999                                 117608
## # … with 20 more rows

class(data)

## [1] "tbl_df"     "tbl"        "data.frame"

str(data)

## tibble [30 × 2] (S3: tbl_df/tbl/data.frame)
##  $ Tahun                                 : num [1:30] 1990 1991 1992 1993 1994 ...
##  $ Jumlah_Kematian_Penderita_Tuberkulosis: num [1:30] 128009 125100 123350 122167 120251 ...

Mengubah bentuk data dari data frame ke bentuk vektor atau matriks.

dat<-ts(data$Jumlah_Kematian_Penderita_Tuberkulosis,start=c(1990,1),frequency=1)
dat

## Time Series:
## Start = 1990 
## End = 2019 
## Frequency = 1 
##  [1] 128009 125100 123350 122167 120251 118083 115789 115176 116838 117608
## [11] 117563 117026 116569 115703 114201 112034 110253 109058 106904 104609
## [21] 101631  97484  92813  89584  86953  83909  82533  80770  78494  76549

summary(dat)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   76549   93981  113118  106567  117429  128009

DATA<-data[,2]

plot(DATA)

Actual<-ts.plot(DATA, main = "Grafik 01",
        xlab=" Penyakit Tuberkulosis tahun 2000-2022 di Indonesia",
        ylab=" Tahun")

Actual

## NULL

par(mfrow=c(2,1)) # mempartisi grafik
acf(DATA)
pacf(DATA)

2 Difference Method dan Dickey-Fuller Test

#install.packages("fUnitRoots") 
library(fUnitRoots) 

library(urca)
library(tseries)
DDIF2<-diff(log(dat),differences=3)
ts.plot(dat,main="TS: DATA DIFF ORDE 3")

adf.test(DDIF2)

## 
##  Augmented Dickey-Fuller Test
## 
## data:  DDIF2
## Dickey-Fuller = -3.8739, Lag order = 2, p-value = 0.03004
## alternative hypothesis: stationary

library(dplyr)
library(forecast)
library(ggplot2)
DDIF2 %>% diff() %>% ggtsdisplay(main="")

3 Fitted Models

library(forecast)
fitar <- Arima(dat, order=c(2,3,1))
fitar

## Series: dat 
## ARIMA(2,3,1) 
## 
## Coefficients:
##          ar1      ar2      ma1
##       0.2294  -0.2967  -0.9999
## s.e.  0.1875   0.1839   0.1772
## 
## sigma^2 = 815875:  log likelihood = -222.27
## AIC=452.54   AICc=454.36   BIC=457.72

library(lmtest)
coeftest(fitar) 

## 
## z test of coefficients:
## 
##     Estimate Std. Error z value  Pr(>|z|)    
## ar1  0.22943    0.18747  1.2238    0.2210    
## ar2 -0.29670    0.18393 -1.6131    0.1067    
## ma1 -0.99992    0.17721 -5.6425 1.676e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

confint(fitar)

##          2.5 %      97.5 %
## ar1 -0.1380130  0.59686750
## ar2 -0.6571936  0.06379284
## ma1 -1.3472537 -0.65258843

4 Ljung-Box test

checkresiduals(fitar)

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(2,3,1)
## Q* = 2.0643, df = 3, p-value = 0.5592
## 
## Model df: 3.   Total lags used: 6

qqnorm(fitar$residuals)

tsdiag(fitar)

5 Peramalan 6 Tahun ke Depan

autoplot(forecast(fitar))

6 Predict 5th

predict(fitar, n.ahead = 5, se.fit = TRUE)

## $pred
## Time Series:
## Start = 2020 
## End = 2024 
## Frequency = 1 
## [1] 74865.50 73177.14 71443.44 69734.12 68077.21
## 
## $se
## Time Series:
## Start = 2020 
## End = 2024 
## Frequency = 1 
## [1]  919.6057 2276.4286 3813.4179 5491.9469 7367.2122

7 Perbandingan Nilai Error

accuracy(fitar)

##                     ME     RMSE      MAE        MPE      MAPE      MASE
## Training set -149.4619 807.8987 638.5377 -0.1136616 0.6167537 0.3287691
##                     ACF1
## Training set -0.01783563

auto.arima(dat)

## Series: dat 
## ARIMA(0,2,0) 
## 
## sigma^2 = 803288:  log likelihood = -230.06
## AIC=462.12   AICc=462.27   BIC=463.45