Membangkitkan Data Time Series

library(tseries)

## Warning: package 'tseries' was built under R version 4.4.3

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

library(TSA)

## Warning: package 'TSA' was built under R version 4.4.3

## 
## Attaching package: 'TSA'

## The following objects are masked from 'package:stats':
## 
##     acf, arima

## The following object is masked from 'package:utils':
## 
##     tar

library(forecast)

## Warning: package 'forecast' was built under R version 4.4.3

## Registered S3 methods overwritten by 'forecast':
##   method       from
##   fitted.Arima TSA 
##   plot.Arima   TSA

Data Simulasi Time Series

coba simulasikan data time series dengan model ARIMA(1,1,1). Tentukan nilai AR dan MA

set.seed(123)

n = 200

ar = 0.7
ma = -0.5

ts_arima = arima.sim(model = list(order = c(1,1,1), ar = ar, ma = ma), n = n)

ts.plot(ts_arima, main="simulasi data ARIAMA(1,1,1)")

### Melakukan Pemodelan 1. Buat plot ACF dan PACF

2. Cek kestasioneritas dengan dengan ADF Test

3. Melakukan differencing

4. Buat Plot ACF daan PACF

5. Cek kestasioneritas dengan ADF Test

6. Ubah ke data ts

7. Buat Kandidat Model melalui ACF, PACF, dan EACF

8. Bandingkan dengan hasil auto.arima

9. Cek AIC Terkecil

acf(ts_arima)

pacf(ts_arima)

adf.test(ts_arima)

## 
##  Augmented Dickey-Fuller Test
## 
## data:  ts_arima
## Dickey-Fuller = -2.449, Lag order = 5, p-value = 0.388
## alternative hypothesis: stationary

diff1 = diff(ts_arima)

acf(diff1)

pacf(diff1)

adf.test(diff1)

## Warning in adf.test(diff1): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  diff1
## Dickey-Fuller = -5.4572, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary

data.ts = ts(diff1)
head(data.ts)

## Time Series:
## Start = 1 
## End = 6 
## Frequency = 1 
## [1] -0.4362295 -1.1367886 -0.4798151 -1.2528876 -1.0929103 -1.0256309

Kandidat Model

acf(data.ts)

pacf(data.ts)

eacf(data.ts)

## AR/MA
##   0 1 2 3 4 5 6 7 8 9 10 11 12 13
## 0 x o o o o o o o o o o  o  o  o 
## 1 x o o o o o o o o o o  o  o  o 
## 2 x x o o o o o o o o o  o  o  o 
## 3 x x o o o o o o o o o  o  o  o 
## 4 x x o o o o o o o o o  o  o  o 
## 5 x o o o o o o o o o o  o  o  o 
## 6 x o o x o o o o o o o  o  o  o 
## 7 o x x x x o o o o o o  o  o  o

auto.arima(data.ts)

## Series: data.ts 
## ARIMA(2,0,2) with zero mean 
## 
## Coefficients:
##           ar1     ar2     ma1      ma2
##       -0.1116  0.6336  0.3108  -0.6250
## s.e.   0.2175  0.1701  0.2294   0.2122
## 
## sigma^2 = 0.8631:  log likelihood = -267.28
## AIC=544.57   AICc=544.88   BIC=561.06

auto.arima(ts_arima)

## Series: ts_arima 
## ARIMA(2,1,2) 
## 
## Coefficients:
##           ar1     ar2     ma1      ma2
##       -0.1116  0.6336  0.3108  -0.6250
## s.e.   0.2175  0.1701  0.2294   0.2122
## 
## sigma^2 = 0.8631:  log likelihood = -267.28
## AIC=544.57   AICc=544.88   BIC=561.06

Penentuan Model Terbaik Berdasarkan AIC

arima(data.ts, order=c(1,1,1), method="ML")

## 
## Call:
## arima(x = data.ts, order = c(1, 1, 1), method = "ML")
## 
## Coefficients:
##          ar1      ma1
##       0.1488  -1.0000
## s.e.  0.0706   0.0164
## 
## sigma^2 estimated as 0.8926:  log likelihood = -273.56,  aic = 551.13

arima(data.ts, order=c(0,1,2), method="ML")

## 
## Call:
## arima(x = data.ts, order = c(0, 1, 2), method = "ML")
## 
## Coefficients:
##           ma1      ma2
##       -0.8590  -0.1410
## s.e.   0.0722   0.0703
## 
## sigma^2 estimated as 0.8938:  log likelihood = -273.72,  aic = 551.44

arima(data.ts, order=c(1,1,2), method="ML")

## 
## Call:
## arima(x = data.ts, order = c(1, 1, 2), method = "ML")
## 
## Coefficients:
##           ar1      ma1      ma2
##       -0.8162  -0.0500  -0.9500
## s.e.   0.0731   0.0457   0.0454
## 
## sigma^2 estimated as 0.8643:  log likelihood = -270.66,  aic = 547.31

arima(data.ts, order=c(2,0,2), method="ML")

## 
## Call:
## arima(x = data.ts, order = c(2, 0, 2), method = "ML")
## 
## Coefficients:
##           ar1     ar2     ma1      ma2  intercept
##       -0.1096  0.6350  0.3087  -0.6269    -0.0214
## s.e.   0.2164  0.1692  0.2283   0.2112     0.0931
## 
## sigma^2 estimated as 0.8456:  log likelihood = -267.26,  aic = 544.51

Berdasarkan hasil pemodelan, diperoleh model dengan nilai AIC terkecil adalah ARIMA(2,0,2)