RStudio for FEB Universitas Jambi
M. Ammar Alwandi (BPS Kota Sungai Penuh)
RStudio untuk Penelitian Ekonomi dan Bisnis
Data Input merupakan file excel berformat (.xlsx) yang berisi data IHK, Uang Beredar, BI Rate, dan IHSG.
Tahapan Analisis Data
1. Persiapan Data
- Install Packages ‘openxlsx’ agar dapat membuka data berformat .xlsx
install.packages('openxlsx')- Panggil Packages ‘openxlsx’
library(openxlsx)- Masukkan File Data Input ke dalam R
dt <- read.xlsx('dataset.xlsx')- Install Packages ‘DT’ untuk menampilkan data secara rapi
install.packages('DT')- Tampilan Data
library(DT)Registered S3 method overwritten by 'htmlwidgets':
method from
print.htmlwidget tools:rstudiodatatable(dt)2. Mengubah Format Data Menjadi Time-Series dan Plotting Data
- Ubah format data menjadi time series
ts_dt <- ts(dt, start=c(2018,1),frequency = 12)- Install Packages untuk plotting data
install.packages('ggplot2')
install.packages('forecast')- Plotting Data Laju IHK
library(ggplot2)
library(forecast)
autoplot(ts_dt[,'IHK']) +
ggtitle('IHK Indonesia Januari 2018 - Juli 2023') +
xlab('Tahun') +
ylab('IHK') +
theme_bw()
- Dekomposisi IHK
autoplot(decompose(ts_dt[,'IHK'])) +
theme_bw()
- Plotting Data M2
autoplot(ts_dt[,'M2']) +
ggtitle('Uang Beredar (M2) di Indonesia Januari 2018 - Juli 2023') +
xlab('Tahun') +
ylab('Jumlah Uang Beredar (Trilyun Rupiah)') +
theme_bw()
- Dekomposisi Data M2
autoplot(decompose(ts_dt[,'M2'])) +
theme_bw()
- Plotting Data IHSG
autoplot(ts_dt[,'IHSG']) +
ggtitle('IHSG di Indonesia Januari 2018 - Juli 2023') +
xlab('Tahun') +
ylab('IHSG (Rupiah)') +
theme_bw()
- Dekomposisi Data IHSG
autoplot(decompose(ts_dt[,'IHSG'])) +
theme_bw()
- Plotting Semua Grafik
autoplot(ts_dt[,c('M2','Suku.Bunga','IHSG','IHK')],facets=T) +
ggtitle('IHK, Uang Beredar M2, Suku Bunga, dan IHSG di Indonesia') +
xlab('Tahun') +
ylab(NULL) +
theme_bw()
3. Menampilkan Korelasi Antar Variabel
- Install packages menampilkan korelasi ‘GGally’
install.packages('GGally')- Menampilkan Analisis Korelasi antarvariabel
library(GGally)
ggpairs(as.data.frame(ts_dt[,c('M2','Suku.Bunga','IHSG','IHK')])) +
theme_bw()
4. Cek Autokrelasi
ggtsdisplay(ts_dt[,'IHK']) + ggtitle('Cek Autokorelasi IHK')
Data IHK tidak Stasioner
ggtsdisplay(ts_dt[,'M2']) + ggtitle('Cek Autokorelasi M2')
Data M2 tidak stasioner
ggtsdisplay(ts_dt[,'Suku.Bunga']) + ggtitle('Cek Suku Bunga IHK')
Data suku bunga tidak stasioner
ggtsdisplay(ts_dt[,'IHSG']) + ggtitle('Cek Autokorelasi IHSG')
Data IHSG tidak stasioner
5. Membuat Model Autoregressive Integrated Moving Average (ARIMA)
- Auto Arima untuk IHK
fit <- auto.arima(ts_dt[,"IHK"], seasonal=F,trace=T,stepwise = F)
ARIMA(0,1,0) : 63.96537
ARIMA(0,1,0) with drift : 30.1593
ARIMA(0,1,1) : 53.75137
ARIMA(0,1,1) with drift : 31.18333
ARIMA(0,1,2) : 52.96979
ARIMA(0,1,2) with drift : 33.39428
ARIMA(0,1,3) : 47.72036
ARIMA(0,1,3) with drift : 34.36805
ARIMA(0,1,4) : 50.0605
ARIMA(0,1,4) with drift : 35.69836
ARIMA(0,1,5) : 51.36456
ARIMA(0,1,5) with drift : 37.74061
ARIMA(1,1,0) : 47.53273
ARIMA(1,1,0) with drift : 31.09527
ARIMA(1,1,1) : Inf
ARIMA(1,1,1) with drift : 32.62519
ARIMA(1,1,2) : Inf
ARIMA(1,1,2) with drift : 34.9523
ARIMA(1,1,3) : Inf
ARIMA(1,1,3) with drift : 36.19476
ARIMA(1,1,4) : Inf
ARIMA(1,1,4) with drift : 38.13893
ARIMA(2,1,0) : 44.61598
ARIMA(2,1,0) with drift : 33.21201
ARIMA(2,1,1) : Inf
ARIMA(2,1,1) with drift : 34.95499
ARIMA(2,1,2) : 39.27146
ARIMA(2,1,2) with drift : 36.74261
ARIMA(2,1,3) : Inf
ARIMA(2,1,3) with drift : Inf
ARIMA(3,1,0) : 41.30163
ARIMA(3,1,0) with drift : 34.41963
ARIMA(3,1,1) : 43.61032
ARIMA(3,1,1) with drift : 35.85304
ARIMA(3,1,2) : Inf
ARIMA(3,1,2) with drift : 36.98618
ARIMA(4,1,0) : 43.63873
ARIMA(4,1,0) with drift : 35.90691
ARIMA(4,1,1) : 45.86665
ARIMA(4,1,1) with drift : 37.97268
ARIMA(5,1,0) : 41.33319
ARIMA(5,1,0) with drift : 36.67773
Best model: ARIMA(0,1,0) with drift summary(fit)Series: ts_dt[, "IHK"]
ARIMA(0,1,0) with drift
Coefficients:
drift
0.2506
s.e. 0.0363
sigma^2 = 0.08826: log likelihood = -12.98
AIC=29.97 AICc=30.16 BIC=34.35
Training set error measures:
ME RMSE MAE MPE
Training set 0.001469404 0.2926206 0.2256332 -0.0009377039
MAPE MASE ACF1
Training set 0.2114929 0.07371692 0.1368385checkresiduals(fit)
Ljung-Box test
data: Residuals from ARIMA(0,1,0) with drift
Q* = 11.129, df = 13, p-value = 0.6
Model df: 0. Total lags used: 13
forecast(fit,h=10) %>% autoplot() + theme_bw() + ylab('IHK')
forecast(fit,h=10) %>% as.data.frame() %>% datatable() %>%
formatRound(columns=colnames(forecast(fit,h=10) %>% as.data.frame()),digits = 3)- Arima Manual untuk IHK
fit_manual <- Arima(ts_dt[,'IHK'], order=c(1,1,0))
checkresiduals(fit_manual)
Ljung-Box test
data: Residuals from ARIMA(1,1,0)
Q* = 18.881, df = 12, p-value = 0.09144
Model df: 1. Total lags used: 13
forecast(fit_manual,h=10) %>% autoplot() + theme_bw() + ylab('IHK')
forecast(fit_manual,h=10) %>% as.data.frame() %>% datatable() %>%
formatRound(columns=colnames(forecast(fit,h=10) %>% as.data.frame()),digits = 3)- Auto Seasonal Arima untuk IHK
fit_S <- auto.arima(ts_dt[,"IHK"], seasonal=T,trace=T,stepwise = F)
ARIMA(0,1,0) : 63.96537
ARIMA(0,1,0) with drift : 30.1593
ARIMA(0,1,0)(0,0,1)[12] : 54.13993
ARIMA(0,1,0)(0,0,1)[12] with drift : 31.42573
ARIMA(0,1,0)(1,0,0)[12] : 50.56691
ARIMA(0,1,0)(1,0,0)[12] with drift : 31.39962
ARIMA(0,1,0)(1,0,1)[12] : Inf
ARIMA(0,1,0)(1,0,1)[12] with drift : 33.52479
ARIMA(0,1,1) : 53.75137
ARIMA(0,1,1) with drift : 31.18333
ARIMA(0,1,1)(0,0,1)[12] : 49.72827
ARIMA(0,1,1)(0,0,1)[12] with drift : 32.66809
ARIMA(0,1,1)(1,0,0)[12] : 47.40822
ARIMA(0,1,1)(1,0,0)[12] with drift : 32.62651
ARIMA(0,1,1)(1,0,1)[12] : Inf
ARIMA(0,1,1)(1,0,1)[12] with drift : 34.8635
ARIMA(0,1,2) : 52.96979
ARIMA(0,1,2) with drift : 33.39428
ARIMA(0,1,2)(0,0,1)[12] : 49.06578
ARIMA(0,1,2)(0,0,1)[12] with drift : 34.82526
ARIMA(0,1,2)(1,0,0)[12] : 46.44393
ARIMA(0,1,2)(1,0,0)[12] with drift : 34.73816
ARIMA(0,1,2)(1,0,1)[12] : Inf
ARIMA(0,1,2)(1,0,1)[12] with drift : 36.89772
ARIMA(0,1,3) : 47.72036
ARIMA(0,1,3) with drift : 34.36805
ARIMA(0,1,3)(0,0,1)[12] : 43.72743
ARIMA(0,1,3)(0,0,1)[12] with drift : 34.9602
ARIMA(0,1,3)(1,0,0)[12] : 41.53349
ARIMA(0,1,3)(1,0,0)[12] with drift : 34.7085
ARIMA(0,1,3)(1,0,1)[12] : 42.4861
ARIMA(0,1,3)(1,0,1)[12] with drift : 36.90096
ARIMA(0,1,4) : 50.0605
ARIMA(0,1,4) with drift : 35.69836
ARIMA(0,1,4)(0,0,1)[12] : 46.04979
ARIMA(0,1,4)(0,0,1)[12] with drift : 36.24567
ARIMA(0,1,4)(1,0,0)[12] : 43.84213
ARIMA(0,1,4)(1,0,0)[12] with drift : 36.05335
ARIMA(0,1,5) : 51.36456
ARIMA(0,1,5) with drift : 37.74061
ARIMA(1,1,0) : 47.53273
ARIMA(1,1,0) with drift : 31.09527
ARIMA(1,1,0)(0,0,1)[12] : 46.27816
ARIMA(1,1,0)(0,0,1)[12] with drift : 32.54956
ARIMA(1,1,0)(1,0,0)[12] : 44.74604
ARIMA(1,1,0)(1,0,0)[12] with drift : 32.49737
ARIMA(1,1,0)(1,0,1)[12] : 44.9799
ARIMA(1,1,0)(1,0,1)[12] with drift : 34.71532
ARIMA(1,1,1) : Inf
ARIMA(1,1,1) with drift : 32.62519
ARIMA(1,1,1)(0,0,1)[12] : 36.22448
ARIMA(1,1,1)(0,0,1)[12] with drift : 33.69162
ARIMA(1,1,1)(1,0,0)[12] : 35.85543
ARIMA(1,1,1)(1,0,0)[12] with drift : 33.50995
ARIMA(1,1,1)(1,0,1)[12] : 37.2407
ARIMA(1,1,1)(1,0,1)[12] with drift : 35.48998
ARIMA(1,1,2) : Inf
ARIMA(1,1,2) with drift : 34.9523
ARIMA(1,1,2)(0,0,1)[12] : 38.53287
ARIMA(1,1,2)(0,0,1)[12] with drift : 36.05997
ARIMA(1,1,2)(1,0,0)[12] : 38.05073
ARIMA(1,1,2)(1,0,0)[12] with drift : 35.83026
ARIMA(1,1,2)(1,0,1)[12] : 39.22798
ARIMA(1,1,2)(1,0,1)[12] with drift : 37.74478
ARIMA(1,1,3) : Inf
ARIMA(1,1,3) with drift : 36.19476
ARIMA(1,1,3)(0,0,1)[12] : 45.93221
ARIMA(1,1,3)(0,0,1)[12] with drift : 36.56609
ARIMA(1,1,3)(1,0,0)[12] : 40.0253
ARIMA(1,1,3)(1,0,0)[12] with drift : 36.2986
ARIMA(1,1,4) : Inf
ARIMA(1,1,4) with drift : 38.13893
ARIMA(2,1,0) : 44.61598
ARIMA(2,1,0) with drift : 33.21201
ARIMA(2,1,0)(0,0,1)[12] : 43.39623
ARIMA(2,1,0)(0,0,1)[12] with drift : 34.53657
ARIMA(2,1,0)(1,0,0)[12] : 41.99017
ARIMA(2,1,0)(1,0,0)[12] with drift : 34.41978
ARIMA(2,1,0)(1,0,1)[12] : 42.51044
ARIMA(2,1,0)(1,0,1)[12] with drift : 36.54602
ARIMA(2,1,1) : Inf
ARIMA(2,1,1) with drift : 34.95499
ARIMA(2,1,1)(0,0,1)[12] : 38.53893
ARIMA(2,1,1)(0,0,1)[12] with drift : 36.07173
ARIMA(2,1,1)(1,0,0)[12] : 38.0803
ARIMA(2,1,1)(1,0,0)[12] with drift : 35.85353
ARIMA(2,1,1)(1,0,1)[12] : 39.30966
ARIMA(2,1,1)(1,0,1)[12] with drift : 37.80028
ARIMA(2,1,2) : 39.27146
ARIMA(2,1,2) with drift : 36.74261
ARIMA(2,1,2)(0,0,1)[12] : Inf
ARIMA(2,1,2)(0,0,1)[12] with drift : 37.95994
ARIMA(2,1,2)(1,0,0)[12] : 40.28788
ARIMA(2,1,2)(1,0,0)[12] with drift : 37.8167
ARIMA(2,1,3) : Inf
ARIMA(2,1,3) with drift : Inf
ARIMA(3,1,0) : 41.30163
ARIMA(3,1,0) with drift : 34.41963
ARIMA(3,1,0)(0,0,1)[12] : 38.54012
ARIMA(3,1,0)(0,0,1)[12] with drift : 34.76954
ARIMA(3,1,0)(1,0,0)[12] : 37.05266
ARIMA(3,1,0)(1,0,0)[12] with drift : 34.38598
ARIMA(3,1,0)(1,0,1)[12] : 38.16694
ARIMA(3,1,0)(1,0,1)[12] with drift : 36.28734
ARIMA(3,1,1) : 43.61032
ARIMA(3,1,1) with drift : 35.85304
ARIMA(3,1,1)(0,0,1)[12] : 39.60608
ARIMA(3,1,1)(0,0,1)[12] with drift : 35.49473
ARIMA(3,1,1)(1,0,0)[12] : 37.91567
ARIMA(3,1,1)(1,0,0)[12] with drift : 35.10857
ARIMA(3,1,2) : Inf
ARIMA(3,1,2) with drift : 36.98618
ARIMA(4,1,0) : 43.63873
ARIMA(4,1,0) with drift : 35.90691
ARIMA(4,1,0)(0,0,1)[12] : 40.63615
ARIMA(4,1,0)(0,0,1)[12] with drift : 35.84255
ARIMA(4,1,0)(1,0,0)[12] : 38.9049
ARIMA(4,1,0)(1,0,0)[12] with drift : 35.46566
ARIMA(4,1,1) : 45.86665
ARIMA(4,1,1) with drift : 37.97268
ARIMA(5,1,0) : 41.33319
ARIMA(5,1,0) with drift : 36.67773
Best model: ARIMA(0,1,0) with drift summary(fit_S)Series: ts_dt[, "IHK"]
ARIMA(0,1,0) with drift
Coefficients:
drift
0.2506
s.e. 0.0363
sigma^2 = 0.08826: log likelihood = -12.98
AIC=29.97 AICc=30.16 BIC=34.35
Training set error measures:
ME RMSE MAE MPE
Training set 0.001469404 0.2926206 0.2256332 -0.0009377039
MAPE MASE ACF1
Training set 0.2114929 0.07371692 0.1368385checkresiduals(fit_S)
Ljung-Box test
data: Residuals from ARIMA(0,1,0) with drift
Q* = 11.129, df = 13, p-value = 0.6
Model df: 0. Total lags used: 13
forecast(fit_S,h=10) %>% autoplot() + theme_bw() + ylab('IHK')
forecast(fit_S,h=10) %>% as.data.frame() %>% datatable() %>%
formatRound(columns=colnames(forecast(fit_S,h=10) %>% as.data.frame()),digits = 3)- Auto Arima untuk M2
fit_M2 <- auto.arima(ts_dt[,"M2"], seasonal=F,trace=T,stepwise = F)
ARIMA(0,1,0) : 816.7799
ARIMA(0,1,0) with drift : 807.9048
ARIMA(0,1,1) : 817.9273
ARIMA(0,1,1) with drift : 801.2732
ARIMA(0,1,2) : 815.024
ARIMA(0,1,2) with drift : 803.4078
ARIMA(0,1,3) : 817.2804
ARIMA(0,1,3) with drift : 803.7743
ARIMA(0,1,4) : 819.5586
ARIMA(0,1,4) with drift : 805.3923
ARIMA(0,1,5) : 818.9004
ARIMA(0,1,5) with drift : 807.8882
ARIMA(1,1,0) : 817.3944
ARIMA(1,1,0) with drift : 800.7321
ARIMA(1,1,1) : 816.9464
ARIMA(1,1,1) with drift : 802.9981
ARIMA(1,1,2) : 817.2764
ARIMA(1,1,2) with drift : 804.0087
ARIMA(1,1,3) : Inf
ARIMA(1,1,3) with drift : Inf
ARIMA(1,1,4) : Inf
ARIMA(1,1,4) with drift : 807.8953
ARIMA(2,1,0) : 815.2402
ARIMA(2,1,0) with drift : 802.9992
ARIMA(2,1,1) : Inf
ARIMA(2,1,1) with drift : Inf
ARIMA(2,1,2) : Inf
ARIMA(2,1,2) with drift : 805.6541
ARIMA(2,1,3) : Inf
ARIMA(2,1,3) with drift : Inf
ARIMA(3,1,0) : 816.2715
ARIMA(3,1,0) with drift : 804.9364
ARIMA(3,1,1) : Inf
ARIMA(3,1,1) with drift : 805.9745
ARIMA(3,1,2) : Inf
ARIMA(3,1,2) with drift : Inf
ARIMA(4,1,0) : 817.6938
ARIMA(4,1,0) with drift : 806.8768
ARIMA(4,1,1) : Inf
ARIMA(4,1,1) with drift : Inf
ARIMA(5,1,0) : 819.9861
ARIMA(5,1,0) with drift : 807.5715
Best model: ARIMA(1,1,0) with drift summary(fit_M2)Series: ts_dt[, "M2"]
ARIMA(1,1,0) with drift
Coefficients:
ar1 drift
-0.3625 45.8975
s.e. 0.1140 9.0043
sigma^2 = 10161: log likelihood = -397.17
AIC=800.34 AICc=800.73 BIC=806.91
Training set error measures:
ME RMSE MAE MPE MAPE
Training set -0.1224509 98.5202 74.01026 -0.02690376 1.067594
MASE ACF1
Training set 0.1234757 -0.00296349checkresiduals(fit_M2)
Ljung-Box test
data: Residuals from ARIMA(1,1,0) with drift
Q* = 21.628, df = 12, p-value = 0.04191
Model df: 1. Total lags used: 13
forecast(fit_M2,h=10) %>% autoplot() + theme_bw() + ylab('M2')
forecast(fit_M2,h=10) %>% as.data.frame() %>% datatable() %>%
formatRound(columns=colnames(forecast(fit_M2,h=10) %>% as.data.frame()),digits = 3)- Auto Seasonal Arima untuk M2
fit_M2_S <- auto.arima(ts_dt[,"M2"], seasonal=T,trace=T,stepwise = F)
ARIMA(0,1,0) : 816.7799
ARIMA(0,1,0) with drift : 807.9048
ARIMA(0,1,0)(0,0,1)[12] : 803.8486
ARIMA(0,1,0)(0,0,1)[12] with drift : 798.8955
ARIMA(0,1,0)(1,0,0)[12] : 799.193
ARIMA(0,1,0)(1,0,0)[12] with drift : 796.9098
ARIMA(0,1,0)(1,0,1)[12] : Inf
ARIMA(0,1,0)(1,0,1)[12] with drift : 799.1764
ARIMA(0,1,1) : 817.9273
ARIMA(0,1,1) with drift : 801.2732
ARIMA(0,1,1)(0,0,1)[12] : 803.0051
ARIMA(0,1,1)(0,0,1)[12] with drift : 791.5686
ARIMA(0,1,1)(1,0,0)[12] : 795.9565
ARIMA(0,1,1)(1,0,0)[12] with drift : 789.7735
ARIMA(0,1,1)(1,0,1)[12] : Inf
ARIMA(0,1,1)(1,0,1)[12] with drift : 792.0481
ARIMA(0,1,2) : 815.024
ARIMA(0,1,2) with drift : 803.4078
ARIMA(0,1,2)(0,0,1)[12] : 800.6183
ARIMA(0,1,2)(0,0,1)[12] with drift : 793.4395
ARIMA(0,1,2)(1,0,0)[12] : 794.6645
ARIMA(0,1,2)(1,0,0)[12] with drift : 791.3371
ARIMA(0,1,2)(1,0,1)[12] : Inf
ARIMA(0,1,2)(1,0,1)[12] with drift : 793.7393
ARIMA(0,1,3) : 817.2804
ARIMA(0,1,3) with drift : 803.7743
ARIMA(0,1,3)(0,0,1)[12] : 802.451
ARIMA(0,1,3)(0,0,1)[12] with drift : 792.7162
ARIMA(0,1,3)(1,0,0)[12] : 794.3209
ARIMA(0,1,3)(1,0,0)[12] with drift : 789.2983
ARIMA(0,1,3)(1,0,1)[12] : Inf
ARIMA(0,1,3)(1,0,1)[12] with drift : 791.7786
ARIMA(0,1,4) : 819.5586
ARIMA(0,1,4) with drift : 805.3923
ARIMA(0,1,4)(0,0,1)[12] : 804.8714
ARIMA(0,1,4)(0,0,1)[12] with drift : 794.5953
ARIMA(0,1,4)(1,0,0)[12] : 796.7426
ARIMA(0,1,4)(1,0,0)[12] with drift : 791.3529
ARIMA(0,1,5) : 818.9004
ARIMA(0,1,5) with drift : 807.8882
ARIMA(1,1,0) : 817.3944
ARIMA(1,1,0) with drift : 800.7321
ARIMA(1,1,0)(0,0,1)[12] : 801.4298
ARIMA(1,1,0)(0,0,1)[12] with drift : 790.2275
ARIMA(1,1,0)(1,0,0)[12] : 793.2994
ARIMA(1,1,0)(1,0,0)[12] with drift : 787.8235
ARIMA(1,1,0)(1,0,1)[12] : Inf
ARIMA(1,1,0)(1,0,1)[12] with drift : 790.1607
ARIMA(1,1,1) : 816.9464
ARIMA(1,1,1) with drift : 802.9981
ARIMA(1,1,1)(0,0,1)[12] : 802.0482
ARIMA(1,1,1)(0,0,1)[12] with drift : 792.4549
ARIMA(1,1,1)(1,0,0)[12] : 793.8329
ARIMA(1,1,1)(1,0,0)[12] with drift : 789.6291
ARIMA(1,1,1)(1,0,1)[12] : Inf
ARIMA(1,1,1)(1,0,1)[12] with drift : 792.3657
ARIMA(1,1,2) : 817.2764
ARIMA(1,1,2) with drift : 804.0087
ARIMA(1,1,2)(0,0,1)[12] : 802.5546
ARIMA(1,1,2)(0,0,1)[12] with drift : 794.4904
ARIMA(1,1,2)(1,0,0)[12] : 795.459
ARIMA(1,1,2)(1,0,0)[12] with drift : 791.6121
ARIMA(1,1,2)(1,0,1)[12] : Inf
ARIMA(1,1,2)(1,0,1)[12] with drift : 794.375
ARIMA(1,1,3) : Inf
ARIMA(1,1,3) with drift : Inf
ARIMA(1,1,3)(0,0,1)[12] : 804.8742
ARIMA(1,1,3)(0,0,1)[12] with drift : 794.8219
ARIMA(1,1,3)(1,0,0)[12] : 796.744
ARIMA(1,1,3)(1,0,0)[12] with drift : 791.5384
ARIMA(1,1,4) : Inf
ARIMA(1,1,4) with drift : 807.8953
ARIMA(2,1,0) : 815.2402
ARIMA(2,1,0) with drift : 802.9992
ARIMA(2,1,0)(0,0,1)[12] : 800.7882
ARIMA(2,1,0)(0,0,1)[12] with drift : 792.4816
ARIMA(2,1,0)(1,0,0)[12] : 793.4842
ARIMA(2,1,0)(1,0,0)[12] with drift : 789.7552
ARIMA(2,1,0)(1,0,1)[12] : Inf
ARIMA(2,1,0)(1,0,1)[12] with drift : Inf
ARIMA(2,1,1) : Inf
ARIMA(2,1,1) with drift : Inf
ARIMA(2,1,1)(0,0,1)[12] : Inf
ARIMA(2,1,1)(0,0,1)[12] with drift : 794.5513
ARIMA(2,1,1)(1,0,0)[12] : 795.8261
ARIMA(2,1,1)(1,0,0)[12] with drift : 791.6086
ARIMA(2,1,1)(1,0,1)[12] : Inf
ARIMA(2,1,1)(1,0,1)[12] with drift : 793.9977
ARIMA(2,1,2) : Inf
ARIMA(2,1,2) with drift : 805.6541
ARIMA(2,1,2)(0,0,1)[12] : Inf
ARIMA(2,1,2)(0,0,1)[12] with drift : Inf
ARIMA(2,1,2)(1,0,0)[12] : Inf
ARIMA(2,1,2)(1,0,0)[12] with drift : Inf
ARIMA(2,1,3) : Inf
ARIMA(2,1,3) with drift : Inf
ARIMA(3,1,0) : 816.2715
ARIMA(3,1,0) with drift : 804.9364
ARIMA(3,1,0)(0,0,1)[12] : 802.5371
ARIMA(3,1,0)(0,0,1)[12] with drift : 794.6623
ARIMA(3,1,0)(1,0,0)[12] : 795.8251
ARIMA(3,1,0)(1,0,0)[12] with drift : 791.7634
ARIMA(3,1,0)(1,0,1)[12] : Inf
ARIMA(3,1,0)(1,0,1)[12] with drift : 794.3689
ARIMA(3,1,1) : Inf
ARIMA(3,1,1) with drift : 805.9745
ARIMA(3,1,1)(0,0,1)[12] : Inf
ARIMA(3,1,1)(0,0,1)[12] with drift : Inf
ARIMA(3,1,1)(1,0,0)[12] : Inf
ARIMA(3,1,1)(1,0,0)[12] with drift : 793.2387
ARIMA(3,1,2) : Inf
ARIMA(3,1,2) with drift : Inf
ARIMA(4,1,0) : 817.6938
ARIMA(4,1,0) with drift : 806.8768
ARIMA(4,1,0)(0,0,1)[12] : 804.9205
ARIMA(4,1,0)(0,0,1)[12] with drift : 796.1133
ARIMA(4,1,0)(1,0,0)[12] : 798.154
ARIMA(4,1,0)(1,0,0)[12] with drift : 793.2257
ARIMA(4,1,1) : Inf
ARIMA(4,1,1) with drift : Inf
ARIMA(5,1,0) : 819.9861
ARIMA(5,1,0) with drift : 807.5715
Best model: ARIMA(1,1,0)(1,0,0)[12] with drift summary(fit_M2_S)Series: ts_dt[, "M2"]
ARIMA(1,1,0)(1,0,0)[12] with drift
Coefficients:
ar1 sar1 drift
-0.3973 0.4935 42.6043
s.e. 0.1124 0.1117 12.9758
sigma^2 = 7793: log likelihood = -389.58
AIC=787.17 AICc=787.82 BIC=795.93
Training set error measures:
ME RMSE MAE MPE MAPE
Training set 2.704755 85.6001 65.44454 0.02983104 0.9494215
MASE ACF1
Training set 0.109185 0.01805996checkresiduals(fit_M2_S)
Ljung-Box test
data: Residuals from ARIMA(1,1,0)(1,0,0)[12] with drift
Q* = 11.727, df = 11, p-value = 0.3845
Model df: 2. Total lags used: 13
forecast(fit_M2_S,h=10) %>% autoplot() + theme_bw() + ylab('M2')
forecast(fit_M2_S,h=10) %>% as.data.frame() %>% datatable() %>%
formatRound(columns=colnames(forecast(fit_M2_S,h=10) %>% as.data.frame()),digits = 3)- Manual Sarima untuk M2
fit_M2_manual <- Arima(ts_dt[,'M2'], order=c(1,1,0),seasonal=c(1,0,0))
summary(fit_M2_manual)Series: ts_dt[, "M2"]
ARIMA(1,1,0)(1,0,0)[12]
Coefficients:
ar1 sar1
-0.3541 0.6249
s.e. 0.1190 0.0956
sigma^2 = 8298: log likelihood = -393.46
AIC=792.91 AICc=793.3 BIC=799.48
Training set error measures:
ME RMSE MAE MPE MAPE
Training set 27.91175 89.03268 65.95447 0.4248966 0.9617459
MASE ACF1
Training set 0.1100358 -0.04705863- Auto SArima untuk IHSG
fit_IHSG_S <- auto.arima(ts_dt[,"IHSG"], seasonal=T,trace=T,stepwise = F)
ARIMA(0,1,0) : 938.6773
ARIMA(0,1,0) with drift : 940.7864
ARIMA(0,1,0)(0,0,1)[12] : 940.7322
ARIMA(0,1,0)(0,0,1)[12] with drift : 942.9115
ARIMA(0,1,0)(1,0,0)[12] : 940.7177
ARIMA(0,1,0)(1,0,0)[12] with drift : 942.8974
ARIMA(0,1,0)(1,0,1)[12] : 942.962
ARIMA(0,1,0)(1,0,1)[12] with drift : 945.2075
ARIMA(0,1,1) : 939.9251
ARIMA(0,1,1) with drift : 942.1006
ARIMA(0,1,1)(0,0,1)[12] : 942.0862
ARIMA(0,1,1)(0,0,1)[12] with drift : 944.3352
ARIMA(0,1,1)(1,0,0)[12] : 942.0798
ARIMA(0,1,1)(1,0,0)[12] with drift : 944.329
ARIMA(0,1,1)(1,0,1)[12] : 944.3536
ARIMA(0,1,1)(1,0,1)[12] with drift : 946.6782
ARIMA(0,1,2) : 942.0624
ARIMA(0,1,2) with drift : 944.3071
ARIMA(0,1,2)(0,0,1)[12] : 944.2931
ARIMA(0,1,2)(0,0,1)[12] with drift : 946.615
ARIMA(0,1,2)(1,0,0)[12] : 944.2864
ARIMA(0,1,2)(1,0,0)[12] with drift : 946.6086
ARIMA(0,1,2)(1,0,1)[12] : 946.6545
ARIMA(0,1,2)(1,0,1)[12] with drift : 949.0539
ARIMA(0,1,3) : 944.1653
ARIMA(0,1,3) with drift : 946.4761
ARIMA(0,1,3)(0,0,1)[12] : 946.4993
ARIMA(0,1,3)(0,0,1)[12] with drift : 948.8914
ARIMA(0,1,3)(1,0,0)[12] : 946.4973
ARIMA(0,1,3)(1,0,0)[12] with drift : 948.8897
ARIMA(0,1,3)(1,0,1)[12] : 948.8648
ARIMA(0,1,3)(1,0,1)[12] with drift : 951.3424
ARIMA(0,1,4) : 945.5913
ARIMA(0,1,4) with drift : 947.9968
ARIMA(0,1,4)(0,0,1)[12] : 948.015
ARIMA(0,1,4)(0,0,1)[12] with drift : 950.5041
ARIMA(0,1,4)(1,0,0)[12] : 948.015
ARIMA(0,1,4)(1,0,0)[12] with drift : 950.5041
ARIMA(0,1,5) : 939.0305
ARIMA(0,1,5) with drift : 941.0672
ARIMA(1,1,0) : 939.9801
ARIMA(1,1,0) with drift : 942.1567
ARIMA(1,1,0)(0,0,1)[12] : 942.1415
ARIMA(1,1,0)(0,0,1)[12] with drift : 944.3914
ARIMA(1,1,0)(1,0,0)[12] : 942.1349
ARIMA(1,1,0)(1,0,0)[12] with drift : 944.385
ARIMA(1,1,0)(1,0,1)[12] : 944.398
ARIMA(1,1,0)(1,0,1)[12] with drift : 946.7278
ARIMA(1,1,1) : 941.9961
ARIMA(1,1,1) with drift : Inf
ARIMA(1,1,1)(0,0,1)[12] : 944.2371
ARIMA(1,1,1)(0,0,1)[12] with drift : Inf
ARIMA(1,1,1)(1,0,0)[12] : 944.2321
ARIMA(1,1,1)(1,0,0)[12] with drift : 946.5477
ARIMA(1,1,1)(1,0,1)[12] : 946.5864
ARIMA(1,1,1)(1,0,1)[12] with drift : 948.9791
ARIMA(1,1,2) : Inf
ARIMA(1,1,2) with drift : Inf
ARIMA(1,1,2)(0,0,1)[12] : Inf
ARIMA(1,1,2)(0,0,1)[12] with drift : Inf
ARIMA(1,1,2)(1,0,0)[12] : Inf
ARIMA(1,1,2)(1,0,0)[12] with drift : Inf
ARIMA(1,1,2)(1,0,1)[12] : Inf
ARIMA(1,1,2)(1,0,1)[12] with drift : Inf
ARIMA(1,1,3) : 938.1728
ARIMA(1,1,3) with drift : 940.529
ARIMA(1,1,3)(0,0,1)[12] : 940.2546
ARIMA(1,1,3)(0,0,1)[12] with drift : 942.6798
ARIMA(1,1,3)(1,0,0)[12] : 940.202
ARIMA(1,1,3)(1,0,0)[12] with drift : 942.626
ARIMA(1,1,4) : 939.1764
ARIMA(1,1,4) with drift : 941.6579
ARIMA(2,1,0) : 942.1143
ARIMA(2,1,0) with drift : 944.3611
ARIMA(2,1,0)(0,0,1)[12] : 944.3384
ARIMA(2,1,0)(0,0,1)[12] with drift : 946.6623
ARIMA(2,1,0)(1,0,0)[12] : 944.3304
ARIMA(2,1,0)(1,0,0)[12] with drift : 946.6546
ARIMA(2,1,0)(1,0,1)[12] : 946.7088
ARIMA(2,1,0)(1,0,1)[12] with drift : 949.1042
ARIMA(2,1,1) : Inf
ARIMA(2,1,1) with drift : Inf
ARIMA(2,1,1)(0,0,1)[12] : Inf
ARIMA(2,1,1)(0,0,1)[12] with drift : Inf
ARIMA(2,1,1)(1,0,0)[12] : Inf
ARIMA(2,1,1)(1,0,0)[12] with drift : Inf
ARIMA(2,1,1)(1,0,1)[12] : Inf
ARIMA(2,1,1)(1,0,1)[12] with drift : Inf
ARIMA(2,1,2) : Inf
ARIMA(2,1,2) with drift : Inf
ARIMA(2,1,2)(0,0,1)[12] : Inf
ARIMA(2,1,2)(0,0,1)[12] with drift : Inf
ARIMA(2,1,2)(1,0,0)[12] : Inf
ARIMA(2,1,2)(1,0,0)[12] with drift : Inf
ARIMA(2,1,3) : 943.5181
ARIMA(2,1,3) with drift : Inf
ARIMA(3,1,0) : 944.035
ARIMA(3,1,0) with drift : 946.347
ARIMA(3,1,0)(0,0,1)[12] : 946.3789
ARIMA(3,1,0)(0,0,1)[12] with drift : 948.7706
ARIMA(3,1,0)(1,0,0)[12] : 946.3788
ARIMA(3,1,0)(1,0,0)[12] with drift : 948.7706
ARIMA(3,1,0)(1,0,1)[12] : 948.6612
ARIMA(3,1,0)(1,0,1)[12] with drift : 951.1362
ARIMA(3,1,1) : 941.4681
ARIMA(3,1,1) with drift : 943.8501
ARIMA(3,1,1)(0,0,1)[12] : 943.6367
ARIMA(3,1,1)(0,0,1)[12] with drift : 946.0934
ARIMA(3,1,1)(1,0,0)[12] : 943.5912
ARIMA(3,1,1)(1,0,0)[12] with drift : 946.0466
ARIMA(3,1,2) : 937.5612
ARIMA(3,1,2) with drift : 940.0436
ARIMA(4,1,0) : 945.8152
ARIMA(4,1,0) with drift : 948.219
ARIMA(4,1,0)(0,0,1)[12] : 948.2389
ARIMA(4,1,0)(0,0,1)[12] with drift : 950.7263
ARIMA(4,1,0)(1,0,0)[12] : 948.2389
ARIMA(4,1,0)(1,0,0)[12] with drift : 950.7263
ARIMA(4,1,1) : 942.252
ARIMA(4,1,1) with drift : 944.7392
ARIMA(5,1,0) : 943.2228
ARIMA(5,1,0) with drift : 945.6396
Best model: ARIMA(3,1,2) summary(fit_IHSG_S)Series: ts_dt[, "IHSG"]
ARIMA(3,1,2)
Coefficients:
ar1 ar2 ar3 ma1 ma2
-1.5408 -0.9915 -0.2914 1.5673 0.8543
s.e. 0.1400 0.2194 0.1227 0.0907 0.1225
sigma^2 = 74739: log likelihood = -462.07
AIC=936.14 AICc=937.56 BIC=949.28
Training set error measures:
ME RMSE MAE MPE MAPE
Training set 4.391526 260.8553 177.1598 -0.06077829 3.017928
MASE ACF1
Training set 0.2513588 0.02987347checkresiduals(fit_IHSG_S)
Ljung-Box test
data: Residuals from ARIMA(3,1,2)
Q* = 8.2026, df = 8, p-value = 0.4139
Model df: 5. Total lags used: 13
forecast(fit_IHSG_S,h=10) %>% autoplot() + theme_bw() + ylab('IHSG')
forecast(fit_IHSG_S,h=10) %>% as.data.frame() %>% datatable() %>%
formatRound(columns=colnames(forecast(fit_IHSG_S,h=10) %>% as.data.frame()),digits = 3)6. Analisa Tematik Simulasi Forecasting IHK berdasarkan Kebijakan Moneter
Grafik Jumlah Uang Beredar dan Suku Bunga
Analisis Korelasi antara Jumlah Uang Beredar dan IHSG
ggpairs(dt[,c('IHK','M2','IHSG')]) + theme_bw()
Membuat Model ARIMA X Jumlah Uang Beredar berdasarkan Suku Bunga
fit_M2_arimax <- auto.arima(ts_dt[,'IHK'],
xreg = ts_dt[,c('IHSG','M2')],
seasonal=T,trace=T,stepwise=T)
Regression with ARIMA(2,0,2)(1,0,1)[12] errors : Inf
Regression with ARIMA(0,0,0) errors : 219.1605
Regression with ARIMA(1,0,0)(1,0,0)[12] errors : Inf
Regression with ARIMA(0,0,1)(0,0,1)[12] errors : 182.6329
Regression with ARIMA(0,0,0) errors : 466.0125
Regression with ARIMA(0,0,1) errors : 180.3338
Regression with ARIMA(0,0,1)(1,0,0)[12] errors : 182.7234
Regression with ARIMA(0,0,1)(1,0,1)[12] errors : 181.7997
Regression with ARIMA(1,0,1) errors : Inf
Regression with ARIMA(0,0,2) errors : 154.8949
Regression with ARIMA(0,0,2)(1,0,0)[12] errors : 155.4894
Regression with ARIMA(0,0,2)(0,0,1)[12] errors : 153.7999
Regression with ARIMA(0,0,2)(1,0,1)[12] errors : 154.9567
Regression with ARIMA(1,0,2)(0,0,1)[12] errors : Inf
Regression with ARIMA(0,0,3)(0,0,1)[12] errors : 138.0388
Regression with ARIMA(0,0,3) errors : 141.1436
Regression with ARIMA(0,0,3)(1,0,1)[12] errors : 140.6475
Regression with ARIMA(0,0,3)(1,0,0)[12] errors : 139.0141
Regression with ARIMA(1,0,3)(0,0,1)[12] errors : Inf
Regression with ARIMA(0,0,4)(0,0,1)[12] errors : 135.3759
Regression with ARIMA(0,0,4) errors : 136.2502
Regression with ARIMA(0,0,4)(1,0,1)[12] errors : 138.1449
Regression with ARIMA(0,0,4)(1,0,0)[12] errors : 135.3891
Regression with ARIMA(1,0,4)(0,0,1)[12] errors : Inf
Regression with ARIMA(0,0,5)(0,0,1)[12] errors : 131.1132
Regression with ARIMA(0,0,5) errors : 135.6046
Regression with ARIMA(0,0,5)(1,0,1)[12] errors : 133.6008
Regression with ARIMA(0,0,5)(1,0,0)[12] errors : 131.1261
Regression with ARIMA(1,0,5)(0,0,1)[12] errors : Inf
Regression with ARIMA(0,0,5)(0,0,1)[12] errors : 317.0066
Best model: Regression with ARIMA(0,0,5)(0,0,1)[12] errors summary(fit_M2_arimax)Series: ts_dt[, "IHK"]
Regression with ARIMA(0,0,5)(0,0,1)[12] errors
Coefficients:
ma1 ma2 ma3 ma4 ma5 sma1 intercept
0.8291 1.2565 0.9479 0.5875 0.4091 0.5339 81.5252
s.e. 0.1412 0.2280 0.2712 0.2225 0.1809 0.1779 5.1057
IHSG M2
-2e-04 0.0038
s.e. 2e-04 0.0008
sigma^2 = 0.2997: log likelihood = -53.59
AIC=127.18 AICc=131.11 BIC=149.23
Training set error measures:
ME RMSE MAE MPE MAPE
Training set 0.03836652 0.5093184 0.3984354 0.02762542 0.373614
MASE ACF1
Training set 0.1301734 0.094414checkresiduals(fit_M2_arimax)
Ljung-Box test
data: Residuals from Regression with ARIMA(0,0,5)(0,0,1)[12] errors
Q* = 19.471, df = 7, p-value = 0.006832
Model df: 6. Total lags used: 13
Forecasting Indeks Harga Konsumen 12 bulan ke depan berdasarkan simulasi kebijakan yang dibuat oleh peneliti
- Simulasi Menambah Uang Beredar (Menurunkan Suku Bunga) Tambah 50 Trilyun Setiap Bulan
simulasi <- data.frame(IHSG = forecast(fit_IHSG_S,h=20)$mean,
M2 = c(8350,8400,8450,8500,8550,
8600,8650,8700,8750,8800,
8900,9000,9050,9100,9150,
9200,9250,9300,9350,9400))
ts_simulasi <- ts(simulasi, start=c(2023,8),frequency = 12)
forecast(fit_M2_arimax,h=20,
xreg = ts_simulasi) %>%
autoplot() +
theme_bw() +
ylab('Indeks Harga Konsumen')
forecast(fit_M2_arimax,h=20,
xreg = ts_simulasi)- Simulasi Mengurangi Uang Beredar (Menaikkan Suku Bunga) Mengurangi 50 Trilyun Setiap Bulan
simulasi <- data.frame(IHSG = forecast(fit_IHSG_S,h=20)$mean,
M2 = c(8350,8300,8250,8200,8150,
8100,8050,8000,7950,7900,
7850,7800,7750,7700,7650,
7600,7550,7500,7450,7400))
ts_simulasi <- ts(simulasi, start=c(2023,8),frequency = 12)
forecast(fit_M2_arimax,h=20,
xreg = ts_simulasi) %>%
autoplot() +
theme_bw() +
ylab('Indeks Harga Konsumen')
forecast(fit_M2_arimax,h=20,
xreg = ts_simulasi)- Simulasi Menambah Uang Beredar (Menurunkan Suku Bunga) Ekstrim Tambah 200 Trilyun Setiap Bulan
simulasi <- data.frame(IHSG = forecast(fit_IHSG_S,h=20)$mean,
M2 = c(8350+(1:20)*200))
ts_simulasi <- ts(simulasi, start=c(2023,8),frequency = 12)
forecast(fit_M2_arimax,h=20,
xreg = ts_simulasi) %>%
autoplot() +
theme_bw() +
ylab('Uang Beredar (Trilyun Rupiah)')
forecast(fit_M2_arimax,h=20,
xreg = ts_simulasi)---
title: "RStudio for FEB Universitas Jambi"
author: M. Ammar Alwandi (BPS Kota Sungai Penuh)
output: html_notebook
---

### **RStudio untuk Penelitian Ekonomi dan Bisnis**

Data Input merupakan file excel berformat (.xlsx) yang berisi data IHK, Uang Beredar, BI Rate, dan IHSG.


### **Tahapan Analisis Data**

##### **1. Persiapan Data**
+ Install Packages 'openxlsx' agar dapat membuka data berformat .xlsx
```{r eval=F}
install.packages('openxlsx')
```
+ Panggil Packages 'openxlsx'
```{r}
library(openxlsx)
```
+ Masukkan File Data Input ke dalam R
```{r}
dt <- read.xlsx('dataset.xlsx')
```
+ Install Packages 'DT' untuk menampilkan data secara rapi
```{r eval=F}
install.packages('DT')
```
+ Tampilan Data
```{r}
library(DT)
datatable(dt)
```
##### **2. Mengubah Format Data Menjadi Time-Series dan Plotting Data**
+ Ubah format data menjadi time series
```{r}
ts_dt <- ts(dt, start=c(2018,1),frequency = 12)
```
+ Install Packages untuk plotting data
```{r eval=F}
install.packages('ggplot2')
install.packages('forecast')
```
+ Plotting Data Laju IHK
```{r}
library(ggplot2)
library(forecast)
autoplot(ts_dt[,'IHK']) +
  ggtitle('IHK Indonesia Januari 2018 - Juli 2023') +
  xlab('Tahun') +
  ylab('IHK') +
  theme_bw()
```
+ Dekomposisi IHK
```{r}
autoplot(decompose(ts_dt[,'IHK'])) +
  theme_bw()
```

+ Plotting Data M2
```{r}
autoplot(ts_dt[,'M2']) +
  ggtitle('Uang Beredar (M2) di Indonesia Januari 2018 - Juli 2023') +
  xlab('Tahun') +
  ylab('Jumlah Uang Beredar (Trilyun Rupiah)') +
  theme_bw()
```
+ Dekomposisi Data M2
```{r}
autoplot(decompose(ts_dt[,'M2'])) +
  theme_bw()
```

+ Plotting Data IHSG
```{r}
autoplot(ts_dt[,'IHSG']) +
  ggtitle('IHSG di Indonesia Januari 2018 - Juli 2023') +
  xlab('Tahun') +
  ylab('IHSG (Rupiah)') +
  theme_bw()
```
+ Dekomposisi Data IHSG
```{r}
autoplot(decompose(ts_dt[,'IHSG'])) +
  theme_bw()
```

+ Plotting Semua Grafik
```{r}
autoplot(ts_dt[,c('M2','Suku.Bunga','IHSG','IHK')],facets=T) +
  ggtitle('IHK, Uang Beredar M2, Suku Bunga, dan IHSG di Indonesia') +
  xlab('Tahun') +
  ylab(NULL) +
  theme_bw()
```

##### **3. Menampilkan Korelasi Antar Variabel**
+ Install packages menampilkan korelasi 'GGally'
```{r eval=F}
install.packages('GGally')
```

+ Menampilkan Analisis Korelasi antarvariabel
```{r}
library(GGally)
ggpairs(as.data.frame(ts_dt[,c('M2','Suku.Bunga','IHSG','IHK')])) +
  theme_bw()
```
##### **4. Cek Autokrelasi**
```{r}
ggtsdisplay(ts_dt[,'IHK']) + ggtitle('Cek Autokorelasi IHK')
```
Data IHK tidak Stasioner
```{r}
ggtsdisplay(ts_dt[,'M2']) + ggtitle('Cek Autokorelasi M2')
```
Data M2 tidak stasioner
```{r}
ggtsdisplay(ts_dt[,'Suku.Bunga']) + ggtitle('Cek Suku Bunga IHK')
```
Data suku bunga tidak stasioner
```{r}
ggtsdisplay(ts_dt[,'IHSG']) + ggtitle('Cek Autokorelasi IHSG')
```
Data IHSG tidak stasioner

##### **5. Membuat Model Autoregressive Integrated Moving Average (ARIMA)**
- Auto Arima untuk IHK
```{r}
fit <- auto.arima(ts_dt[,"IHK"], seasonal=F,trace=T,stepwise = F)
summary(fit)
checkresiduals(fit)
forecast(fit,h=10) %>% autoplot() + theme_bw() + ylab('IHK')
forecast(fit,h=10) %>% as.data.frame() %>% datatable() %>% 
  formatRound(columns=colnames(forecast(fit,h=10) %>% as.data.frame()),digits = 3)
```
- Arima Manual untuk IHK
```{r}
fit_manual <- Arima(ts_dt[,'IHK'], order=c(1,1,0))
checkresiduals(fit_manual)
forecast(fit_manual,h=10) %>% autoplot() + theme_bw() + ylab('IHK')
forecast(fit_manual,h=10) %>% as.data.frame() %>% datatable() %>% 
  formatRound(columns=colnames(forecast(fit,h=10) %>% as.data.frame()),digits = 3)
```
- Auto Seasonal Arima untuk IHK
```{r}
fit_S <- auto.arima(ts_dt[,"IHK"], seasonal=T,trace=T,stepwise = F)
summary(fit_S)
checkresiduals(fit_S)
forecast(fit_S,h=10) %>% autoplot() + theme_bw() + ylab('IHK')
forecast(fit_S,h=10) %>% as.data.frame() %>% datatable() %>% 
  formatRound(columns=colnames(forecast(fit_S,h=10) %>% as.data.frame()),digits = 3)
```

- Auto Arima untuk M2
```{r}
fit_M2 <- auto.arima(ts_dt[,"M2"], seasonal=F,trace=T,stepwise = F)
summary(fit_M2)
checkresiduals(fit_M2)
forecast(fit_M2,h=10) %>% autoplot() + theme_bw() + ylab('M2')
forecast(fit_M2,h=10) %>% as.data.frame() %>% datatable() %>% 
  formatRound(columns=colnames(forecast(fit_M2,h=10) %>% as.data.frame()),digits = 3)
```
- Auto Seasonal Arima untuk M2
```{r}
fit_M2_S <- auto.arima(ts_dt[,"M2"], seasonal=T,trace=T,stepwise = F)
summary(fit_M2_S)
checkresiduals(fit_M2_S)
forecast(fit_M2_S,h=10) %>% autoplot() + theme_bw() + ylab('M2')
forecast(fit_M2_S,h=10) %>% as.data.frame() %>% datatable() %>% 
  formatRound(columns=colnames(forecast(fit_M2_S,h=10) %>% as.data.frame()),digits = 3)
```
- Manual Sarima untuk M2
```{r}
fit_M2_manual <- Arima(ts_dt[,'M2'], order=c(1,1,0),seasonal=c(1,0,0))
summary(fit_M2_manual)
```

- Auto SArima untuk IHSG
```{r}
fit_IHSG_S <- auto.arima(ts_dt[,"IHSG"], seasonal=T,trace=T,stepwise = F)
summary(fit_IHSG_S)
checkresiduals(fit_IHSG_S)
forecast(fit_IHSG_S,h=10) %>% autoplot() + theme_bw() + ylab('IHSG')
forecast(fit_IHSG_S,h=10) %>% as.data.frame() %>% datatable() %>% 
  formatRound(columns=colnames(forecast(fit_IHSG_S,h=10) %>% as.data.frame()),digits = 3)
```

##### **6. Analisa Tematik Simulasi Forecasting IHK berdasarkan Kebijakan Moneter**

###### **Grafik Jumlah Uang Beredar dan Suku Bunga**

```{r}
autoplot(ts_dt[,c('IHK','IHSG','M2')],facets=T) + 
  ggtitle('IHK dan Jumlah Uang Beredar Jan 2018 - Jul 2023') + 
  ylab('IHK, IHSG, dan Jumlah Uang Beredar (Trilyun)') +
  xlab('Tahun') +
  theme_bw()

```

###### **Analisis Korelasi antara Jumlah Uang Beredar dan IHSG**
```{r}
ggpairs(dt[,c('IHK','M2','IHSG')]) + theme_bw()
```

###### **Membuat Model ARIMA X Jumlah Uang Beredar berdasarkan Suku Bunga**

```{r}
fit_M2_arimax <- auto.arima(ts_dt[,'IHK'],
                            xreg = ts_dt[,c('IHSG','M2')],
                            seasonal=T,trace=T,stepwise=T)
summary(fit_M2_arimax)
checkresiduals(fit_M2_arimax)
```

###### **Forecasting Indeks Harga Konsumen 12 bulan ke depan berdasarkan simulasi kebijakan yang dibuat oleh peneliti**

- Simulasi Menambah Uang Beredar (Menurunkan Suku Bunga) Tambah 50 Trilyun Setiap Bulan
```{r}
simulasi <- data.frame(IHSG = forecast(fit_IHSG_S,h=20)$mean,
                       M2 = c(8350,8400,8450,8500,8550,
                              8600,8650,8700,8750,8800,
                              8900,9000,9050,9100,9150,
                              9200,9250,9300,9350,9400))
ts_simulasi <- ts(simulasi, start=c(2023,8),frequency = 12)

forecast(fit_M2_arimax,h=20,
         xreg = ts_simulasi) %>% 
  autoplot() + 
  theme_bw() + 
  ylab('Indeks Harga Konsumen')

forecast(fit_M2_arimax,h=20,
         xreg = ts_simulasi)
```
- Simulasi Mengurangi Uang Beredar (Menaikkan Suku Bunga) Mengurangi 50 Trilyun Setiap Bulan
```{r}
simulasi <- data.frame(IHSG = forecast(fit_IHSG_S,h=20)$mean,
                       M2 = c(8350,8300,8250,8200,8150,
                              8100,8050,8000,7950,7900,
                              7850,7800,7750,7700,7650,
                              7600,7550,7500,7450,7400))
ts_simulasi <- ts(simulasi, start=c(2023,8),frequency = 12)

forecast(fit_M2_arimax,h=20,
         xreg = ts_simulasi) %>% 
  autoplot() + 
  theme_bw() + 
  ylab('Indeks Harga Konsumen')

forecast(fit_M2_arimax,h=20,
         xreg = ts_simulasi)
```
- Simulasi Menambah Uang Beredar (Menurunkan Suku Bunga) Ekstrim Tambah 200 Trilyun Setiap Bulan
```{r}
simulasi <- data.frame(IHSG = forecast(fit_IHSG_S,h=20)$mean,
                       M2 = c(8350+(1:20)*200))
ts_simulasi <- ts(simulasi, start=c(2023,8),frequency = 12)

forecast(fit_M2_arimax,h=20,
         xreg = ts_simulasi) %>% 
  autoplot() + 
  theme_bw() + 
  ylab('Uang Beredar (Trilyun Rupiah)')

forecast(fit_M2_arimax,h=20,
         xreg = ts_simulasi)
```