0.1 Soal

Dari data yang kalian miliki dan sudah melakukan plot data serta uji stasioneritasnya, selanjutnya adalah a. Transformasi awal dan identifikasi model. (jika data kalian tidak stasioner) b. Estimasi parameter dari model yang memungkinkan.

library(readxl)
library(ggplot2)
library(tseries)

## Warning: package 'tseries' was built under R version 3.6.3

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

library(forecast)

## Warning: package 'forecast' was built under R version 3.6.3

0.2 Import Data

HB <- read_xlsx("Harga Beras.xlsx")

Data saya tidak bersifat stasioner maka saya melakukan proses differencing

0.3 Diff

HB_diff <- diff(HB$Harga.Beras,
                        differences = 1)

ts.plot(HB_diff,
        col = "Green",
        xlab = "Time",
        ylab = "Differencing",
        main = "Time Series Plot (Differencing)")

0.4 Estimasi Parameter

1 AR(1)

HB_log <- log(HB$Harga.Beras)
AR1 <- arima(HB_log,
             order = c(1,2,0),
             seasonal = list(order = c(0,0,0),
                             period = NA),
             include.mean = F)
summary(AR1)

## 
## Call:
## arima(x = HB_log, order = c(1, 2, 0), seasonal = list(order = c(0, 0, 0), period = NA), 
##     include.mean = F)
## 
## Coefficients:
##          ar1
##       0.1138
## s.e.  0.2043
## 
## sigma^2 estimated as 4.492e-05:  log likelihood = 114.76,  aic = -225.51
## 
## Training set error measures:
##                         ME        RMSE         MAE          MPE       MAPE
## Training set -0.0005328198 0.006890307 0.004987783 -0.005629061 0.05302794
##               MASE      ACF1
## Training set 1.098 0.1248957

Dari summary(arima) terdapat bahwa nilai koefisien AR1 = 0.1138 dan s.e. = 0.2043 dan sigma^2 = 4.492e-05

2 MA(1)

MA1 <- arima(HB_log,
             order = c(0,2,1),
             seasonal = list(order = c(0,0,0),
                             period = NA),
             include.mean = F)
summary(MA1)

## 
## Call:
## arima(x = HB_log, order = c(0, 2, 1), seasonal = list(order = c(0, 0, 0), period = NA), 
##     include.mean = F)
## 
## Coefficients:
##          ma1
##       0.2665
## s.e.  0.2227
## 
## sigma^2 estimated as 4.399e-05:  log likelihood = 115.06,  aic = -226.13
## 
## Training set error measures:
##                         ME        RMSE         MAE          MPE     MAPE
## Training set -0.0004844921 0.006826072 0.005032781 -0.005116356 0.053504
##                  MASE       ACF1
## Training set 1.107906 0.02282901

Dari summary(arima) terdapat bahwa nilai koefisien ma1 = 0.2665 dan s.e. = 0.2227 serta sigma^2 = 4.399e-05

3 ARMA(1,1)

ARMA1 <- arima(HB_log,
               order = c(1,2,1),
               seasonal = list(order = c(0,0,0),
                               period = NA),
               include.mean = F)
summary(ARMA1)

## 
## Call:
## arima(x = HB_log, order = c(1, 2, 1), seasonal = list(order = c(0, 0, 0), period = NA), 
##     include.mean = F)
## 
## Coefficients:
##          ar1      ma1
##       0.5226  -1.0000
## s.e.  0.1681   0.0821
## 
## sigma^2 estimated as 3.481e-05:  log likelihood = 117.64,  aic = -229.29
## 
## Training set error measures:
##                         ME        RMSE         MAE          MPE       MAPE
## Training set -0.0005328956 0.006161243 0.004549772 -0.005641721 0.04837094
##                  MASE      ACF1
## Training set 1.001577 0.3426282

Dari summary(arima) terdapat bahwa nilai koefisien AR1 = 0.5226, ma1 = -1 dan s.e.ar = 0.1681, s.e.ma = 0.0821 serta sigma^2 = 3.481e-05

4 AR(2)

AR2 <- arima(HB_log,
             order = c(2,2,0),
             seasonal = list(order = c(0,0,0),
                             period = NA),
             include.mean = F)
summary(AR2)

## 
## Call:
## arima(x = HB_log, order = c(2, 2, 0), seasonal = list(order = c(0, 0, 0), period = NA), 
##     include.mean = F)
## 
## Coefficients:
##          ar1      ar2
##       0.0585  -0.4731
## s.e.  0.1910   0.1933
## 
## sigma^2 estimated as 3.758e-05:  log likelihood = 117.36,  aic = -228.73
## 
## Training set error measures:
##                         ME        RMSE         MAE          MPE       MAPE
## Training set -0.0006140288 0.006369246 0.004948726 -0.006496628 0.05260887
##                  MASE      ACF1
## Training set 1.089402 0.1158287

Dari summary(arima) terdapat bahwa nilai koefisien AR1 = 0.0585, AR2 = -0.4731 dan s.e.1 = 0.1910, s.e.2 = 0.1933 serta sigma^2 = 3.758e-05

5 Model MA(2)

MA2 <- arima(HB_log,
             order = c(0,2,2),
             seasonal = list(order = c(0,0,0),
                             period = NA),
             include.mean = F)
summary(MA2)

## 
## Call:
## arima(x = HB_log, order = c(0, 2, 2), seasonal = list(order = c(0, 0, 0), period = NA), 
##     include.mean = F)
## 
## Coefficients:
##           ma1      ma2
##       -0.3519  -0.6480
## s.e.   0.1474   0.1268
## 
## sigma^2 estimated as 2.995e-05:  log likelihood = 119.72,  aic = -233.44
## 
## Training set error measures:
##                         ME        RMSE         MAE          MPE      MAPE
## Training set -0.0001839687 0.005777596 0.004429301 -0.001934603 0.0470879
##                   MASE      ACF1
## Training set 0.9750569 0.2695166

Dari summary(arima) terdapat bahwa nilai koefisien MA1 = -0.3519, MA2 = -0.6480 dan s.e.1 = 0.1474, s.e.2 = 0.1268 serta sigma^2 = 2.995e-05

6 ARMA(2,2)

ARMA2 <- arima(HB_log,
               order = c(2,2,2),
               seasonal = list(order = c(0,0,0),
                               period = NA),
               include.mean = F)
summary(ARMA2)

## 
## Call:
## arima(x = HB_log, order = c(2, 2, 2), seasonal = list(order = c(0, 0, 0), period = NA), 
##     include.mean = F)
## 
## Coefficients:
##          ar1      ar2      ma1      ma2
##       0.5842  -0.3511  -0.7970  -0.2029
## s.e.  0.5470   0.3635   0.5521   0.5440
## 
## sigma^2 estimated as 2.829e-05:  log likelihood = 120.48,  aic = -230.96
## 
## Training set error measures:
##                         ME        RMSE         MAE          MPE      MAPE
## Training set -0.0002308872 0.005641318 0.004467831 -0.002436394 0.0474975
##                   MASE      ACF1
## Training set 0.9835388 0.1267005

Dari summary(arima) didapatkan nilai koefisien AR1 = 0.5842, AR2 = -0.3511, MA1 = -0.7970, MA2 = -0.2029 dan s.e.AR1 = 0.5470, s.e.AR2 = 0.3635, s.e.MA1 = 0.5521, s.e.MA2 = 0.5440 serta sigma^2 = 2.829e-05

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Project UAS 4 Analisis Runtun Waktu

Abraham (20184920009)

Desember 13, 2020