ARIMA Modeling
AutoRegressive Integrated Moving Average
Install Packages
library(readxl)
library(lmtest)
library(forecast)
library(FitAR)
library(fUnitRoots)
Import Data Set
table2 <- read_excel("Datum/1 SCOPUS/2022/Feb-01/Data/table2.xlsx",sheet = "Sheet2")
View(table2)
summary(table2)
avg_jual avg_beli
Min. : 8808 Min. : 8766
1st Qu.:13498 1st Qu.:13480
Median :14190 Median :14078
Mean :13979 Mean :13800
3rd Qu.:14705 3rd Qu.:14257
Max. :15753 Max. :15020
tsJual = ts(table2$avg_jual, start = c(2017,1), frequency = 12)
plot(tsJual)
tsBeli = ts(table2$avg_beli, start = c(2017,1), frequency = 12)
plot(tsBeli)
components.tsJual = decompose(tsJual)
plot(components.tsJual)
components.tsBeli = decompose(tsBeli)
plot(components.tsBeli)
urkpssTest(tsJual, type = c("tau"), lags = c("short"),use.lag = NULL, doplot = TRUE)
urkpssTest(tsBeli, type = c("tau"), lags = c("short"),use.lag = NULL, doplot = TRUE)
sstationary_Jual = diff(tsJual, differences=1)
plot(tsstationary_Jual)
tsstationary_Beli = diff(tsBeli, differences=1)
plot(tsstationary_Beli)
acf(tsJual,lag.max=34)
acf(tsBeli,lag.max=34)
Pacf(tsJual,lag.max=34)
Pacf(tsBeli,lag.max=34)
timeseriesseasonallyadjusted_Jual <- tsJual- components.tsJual$seasonal
tsstationary_Jual <- diff(timeseriesseasonallyadjusted_Jual, differences=1)
timeseriesseasonallyadjusted_Beli <- tsJual- components.tsBeli$seasonal
tsstationary_Beli <- diff(timeseriesseasonallyadjusted_Beli, differences=1)
plot(timeseriesseasonallyadjusted_Beli)
plot(timeseriesseasonallyadjusted_Jual)
acf(tsstationary_Jual, lag.max=34)
pacf(tsstationary_Jual, lag.max=34)
acf(tsstationary_Beli, lag.max=34)
pacf(tsstationary_Beli, lag.max=34)
fitARIMA_Jual <- arima(tsJual, order=c(1,1,1),seasonal = list(order = c(1,0,0), period = 12),method="ML")
fitARIMA_Beli <- arima(tsBeli, order=c(1,1,1),seasonal = list(order = c(1,0,0), period = 12),method="ML")
coeftest(fitARIMA_Jual)
z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
ar1 -0.021344 1.837953 -0.0116 0.9907
ma1 0.083561 1.842706 0.0453 0.9638
sar1 0.072859 0.274394 0.2655 0.7906
coeftest(fitARIMA_Beli)
z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
ar1 0.0032167 0.6907733 0.0047 0.9963
ma1 0.0509199 0.7058832 0.0721 0.9425
sar1 -0.0026367 0.3522116 -0.0075 0.9940
fitARIMA_Jual
Call:
arima(x = tsJual, order = c(1, 1, 1), seasonal = list(order = c(1, 0, 0), period = 12),
method = "ML")
Coefficients:
ar1 ma1 sar1
-0.0213 0.0836 0.0729
s.e. 1.8380 1.8427 0.2744
sigma^2 estimated as 472215: log likelihood = -373.76, aic = 755.51
fitARIMA_Beli
Call:
arima(x = tsBeli, order = c(1, 1, 1), seasonal = list(order = c(1, 0, 0), period = 12),
method = "ML")
Coefficients:
ar1 ma1 sar1
0.0032 0.0509 -0.0026
s.e. 0.6908 0.7059 0.3522
sigma^2 estimated as 457012: log likelihood = -372.95, aic = 753.91
confint(fitARIMA_Beli)
2.5 % 97.5 %
ar1 -1.3506740 1.3571074
ma1 -1.3325858 1.4344256
sar1 -0.6929589 0.6876854
confint(fitARIMA_Jual)
2.5 % 97.5 %
ar1 -3.6236644 3.5809772
ma1 -3.5280769 3.6951992
sar1 -0.4649435 0.6106622
acf(fitARIMA_Beli$residuals)
acf(fitARIMA_Jual$residuals)
boxplot(fitARIMA_Jual$residuals,k=2,StartLag=1)
LjungBoxTest(fitARIMA_Jual$residuals,k=2,StartLag=1)
boxplot(fitARIMA_Beli$residuals,k=2,StartLag=1)
LjungBoxTest(fitARIMA_Beli$residuals,k=2,StartLag=1)
qqnorm(fitARIMA_Jual$residuals)
qqline(fitARIMA_Jual$residuals)
qqnorm(fitARIMA_Beli$residuals)
qqline(fitARIMA_Beli$residuals)
arima(tsJual)
Call:
arima(x = tsJual)
Coefficients:
intercept
13978.5625
s.e. 177.7277
sigma^2 estimated as 1516180: log likelihood = -409.67, aic = 823.34
arima(tsBeli)
Call:
arima(x = tsBeli)
Coefficients:
intercept
13800.3958
s.e. 165.1939
sigma^2 estimated as 1309870: log likelihood = -406.16, aic = 816.32
auto.arima(tsJual, trace=TRUE)
ARIMA(2,1,2)(1,0,1)[12] with drift : Inf
ARIMA(0,1,0) with drift : 750.4713
ARIMA(1,1,0)(1,0,0)[12] with drift : 755.0944
ARIMA(0,1,1)(0,0,1)[12] with drift : 755.0899
ARIMA(0,1,0) : 749.8579
ARIMA(0,1,0)(1,0,0)[12] with drift : 752.7432
ARIMA(0,1,0)(0,0,1)[12] with drift : 752.7402
ARIMA(0,1,0)(1,0,1)[12] with drift : Inf
ARIMA(1,1,0) with drift : 752.7152
ARIMA(0,1,1) with drift : 752.7136
ARIMA(1,1,1) with drift : Inf
Best model: ARIMA(0,1,0)
Series: tsJual
ARIMA(0,1,0)
sigma^2 = 475492: log likelihood = -373.88
AIC=749.77 AICc=749.86 BIC=751.62
auto.arima(tsBeli, trace=TRUE)
ARIMA(2,1,2)(1,0,1)[12] with drift : Inf
ARIMA(0,1,0) with drift : 748.9614
ARIMA(1,1,0)(1,0,0)[12] with drift : 753.5961
ARIMA(0,1,1)(0,0,1)[12] with drift : 753.5933
ARIMA(0,1,0) : 748.1365
ARIMA(0,1,0)(1,0,0)[12] with drift : 751.2314
ARIMA(0,1,0)(0,0,1)[12] with drift : 751.2295
ARIMA(0,1,0)(1,0,1)[12] with drift : 753.6222
ARIMA(1,1,0) with drift : 751.2183
ARIMA(0,1,1) with drift : 751.2173
ARIMA(1,1,1) with drift : Inf
Best model: ARIMA(0,1,0)
Series: tsBeli
ARIMA(0,1,0)
sigma^2 = 458392: log likelihood = -373.02
AIC=748.05 AICc=748.14 BIC=749.9
fitARIMA_Jual
Call:
arima(x = tsJual, order = c(1, 1, 1), seasonal = list(order = c(1, 0, 0), period = 12),
method = "ML")
Coefficients:
ar1 ma1 sar1
-0.0213 0.0836 0.0729
s.e. 1.8380 1.8427 0.2744
sigma^2 estimated as 472215: log likelihood = -373.76, aic = 755.51
fitARIMA_Beli
all:
arima(x = tsBeli, order = c(1, 1, 1), seasonal = list(order = c(1, 0, 0), period = 12),
method = "ML")
Coefficients:
ar1 ma1 sar1
0.0032 0.0509 -0.0026
s.e. 0.6908 0.7059 0.3522
sigma^2 estimated as 457012: log likelihood = -372.95, aic = 753.91
predict(fitARIMA_Jual,n.ahead = 1)
$pred
Jan
2021 14665.9
$se
Jan
2021 687.1792
predict(fitARIMA_Beli,n.ahead = 1)
$pred
Jan
2021 14122.35
$se
Jan
2021 676.0263
futurVal_Beli <- forecast(fitARIMA_Beli,h=1, level=c(99.5))
futurVal_Jual <- forecast(fitARIMA_Jual,h=1, level=c(99.5))
plot(futurVal_Beli)
plot(futurVal_Jual)
summary(futurVal_Jual)
Forecast method: ARIMA(1,1,1)(1,0,0)[12]
Model Information:
Call:
arima(x = tsJual, order = c(1, 1, 1), seasonal = list(order = c(1, 0, 0), period = 12),
method = "ML")
Coefficients:
ar1 ma1 sar1
-0.0213 0.0836 0.0729
s.e. 1.8380 1.8427 0.2744
sigma^2 estimated as 472215: log likelihood = -373.76, aic = 755.51
Error measures:
ME RMSE MAE MPE MAPE MASE ACF1
Training set 107.4817 679.9846 237.3794 0.794616 1.695755 0.2583878 -0.02594214
Forecasts:
Point Forecast Lo 99.5 Hi 99.5
Jan 2021 14665.9 12736.97 16594.84
summary(futurVal_Beli)
Forecast method: ARIMA(1,1,1)(1,0,0)[12]
Model Information:
Call:
arima(x = tsBeli, order = c(1, 1, 1), seasonal = list(order = c(1, 0, 0), period = 12),
method = "ML")
Coefficients:
ar1 ma1 sar1
0.0032 0.0509 -0.0026
s.e. 0.6908 0.7059 0.3522
sigma^2 estimated as 457012: log likelihood = -372.95, aic = 753.91
Error measures:
ME RMSE MAE MPE MAPE MASE ACF1
Training set 106.293 668.9485 220.1657 0.7954476 1.599417 0.2807839 -0.02688605
Forecasts:
Point Forecast Lo 99.5 Hi 99.5
Jan 2021 14122.35 12224.72 16019.98
