LOAD DATA
library(readxl)
data = read_excel("C:/Users/naura/Downloads/Tekanan udara bandung.xlsx")
data
## # A tibble: 60 × 1
## `Tekanan Udara (mb)`
## <dbl>
## 1 924
## 2 924.
## 3 924.
## 4 923.
## 5 924.
## 6 924.
## 7 924.
## 8 924.
## 9 925.
## 10 925.
## # ℹ 50 more rows
MENGUBAH DATASET TERSEBUT MENJADI DATA TIME SERIES
datats <- ts(data)
#Menampilkan data teratas
head(datats)
## Tekanan Udara (mb)
## [1,] 924.0
## [2,] 923.8
## [3,] 924.1
## [4,] 923.2
## [5,] 924.1
## [6,] 923.9
#Membaca data
View(datats)
str(datats)
## Time-Series [1:60, 1] from 1 to 60: 924 924 924 923 924 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr "Tekanan Udara (mb)"
mean(datats)
## [1] 923.445
PLOT DATA TIME SERIES DATATS
plot.ts(datats)
PLOT DAN HASIL KORELASI ACF
acf(datats)
print(acf(datats))
##
## Autocorrelations of series 'datats', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 0.593 0.465 0.371 0.285 0.169 0.064 0.003 0.044 0.010 -0.030
## 11 12 13 14 15 16 17
## 0.103 0.168 0.107 0.018 0.059 -0.021 -0.038
PLOT DAN HASIL KORELASI PACF
pacf(datats)
print(pacf(datats))
##
## Partial autocorrelations of series 'datats', by lag
##
## 1 2 3 4 5 6 7 8 9 10 11
## 0.593 0.174 0.064 0.005 -0.083 -0.093 -0.040 0.117 -0.008 -0.048 0.213
## 12 13 14 15 16 17
## 0.103 -0.115 -0.166 0.066 -0.129 0.009
DIFFERENCING 1
datadiff1 <- diff(datats, differences = 1)
#Menampilkan plot time series datadiff1
plot.ts(datadiff1)
#Menampilkan plot dan hasil korelasi acf
acf(datadiff1, lag.max = 20)
acf(datadiff1, lag.max = 20, plot = FALSE)
##
## Autocorrelations of series 'datadiff1', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 -0.342 -0.049 0.004 0.024 -0.010 -0.065 -0.126 0.088 0.001 -0.186
## 11 12 13 14 15 16 17 18 19 20
## 0.074 0.149 0.042 -0.163 0.158 -0.071 0.061 -0.044 0.016 -0.007
#Menampilkan plot dan hasil korelasi pacf
pacf(datadiff1, lag.max = 20)
pacf(datadiff1, lag.max = 20, plot = FALSE)
##
## Partial autocorrelations of series 'datadiff1', by lag
##
## 1 2 3 4 5 6 7 8 9 10 11
## -0.342 -0.188 -0.094 -0.020 -0.013 -0.082 -0.219 -0.084 -0.048 -0.256 -0.153
## 12 13 14 15 16 17 18 19 20
## 0.053 0.109 -0.133 0.068 -0.062 -0.035 0.004 0.080 -0.007
PEMODELAN DENGAN AUTO.ARIMA
#Pemodelan dengan otomatis menghasilkan model terbaik
library(forecast)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
dt = auto.arima(datats, trace = TRUE)
##
## ARIMA(2,1,2) with drift : Inf
## ARIMA(0,1,0) with drift : 135.1564
## ARIMA(1,1,0) with drift : 130.1289
## ARIMA(0,1,1) with drift : 127.4932
## ARIMA(0,1,0) : 133.0202
## ARIMA(1,1,1) with drift : 128.2819
## ARIMA(0,1,2) with drift : 129.333
## ARIMA(1,1,2) with drift : Inf
## ARIMA(0,1,1) : 125.2808
## ARIMA(1,1,1) : 126.0686
## ARIMA(0,1,2) : 127.0392
## ARIMA(1,1,0) : 127.9171
## ARIMA(1,1,2) : Inf
##
## Best model: ARIMA(0,1,1)
dt
## Series: datats
## ARIMA(0,1,1)
##
## Coefficients:
## ma1
## -0.4604
## s.e. 0.1337
##
## sigma^2 = 0.4764: log likelihood = -60.53
## AIC=125.07 AICc=125.28 BIC=129.22
#MENGHITUNG NILAI AIC
dt$aic
## [1] 125.0665
#TEST DIAGNOSIS MODEL TERBAIK
#Pemodelan terbaik dengan auto.arima
tsdiag(dt)
#PERAMALAN DATA TIME SERIES
df = forecast(dt)
plot(df)
plot.ts(df$residuals)
Box.test(df$residuals)
##
## Box-Pierce test
##
## data: df$residuals
## X-squared = 0.022546, df = 1, p-value = 0.8806
hist(df$residuals)
#MEMPREDIKSI DATASET SELAMA 12 BULAN KEDEPAN
predict(dt, n.ahead = 12)
## $pred
## Time Series:
## Start = 61
## End = 72
## Frequency = 1
## [1] 923.6543 923.6543 923.6543 923.6543 923.6543 923.6543 923.6543 923.6543
## [9] 923.6543 923.6543 923.6543 923.6543
##
## $se
## Time Series:
## Start = 61
## End = 72
## Frequency = 1
## [1] 0.6902302 0.7843057 0.8682471 0.9447596 1.0155237 1.0816681 1.1439946
## [8] 1.2030965 1.2594280 1.3133455 1.3651352 1.4150307
Dataset_forecast = forecast(dt, h=12)
Dataset_forecast
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 61 923.6543 922.7697 924.5389 922.3015 925.0071
## 62 923.6543 922.6492 924.6594 922.1171 925.1915
## 63 923.6543 922.5416 924.7670 921.9526 925.3560
## 64 923.6543 922.4435 924.8651 921.8026 925.5060
## 65 923.6543 922.3529 924.9557 921.6639 925.6447
## 66 923.6543 922.2681 925.0405 921.5343 925.7743
## 67 923.6543 922.1882 925.1204 921.4121 925.8965
## 68 923.6543 922.1125 925.1961 921.2963 926.0123
## 69 923.6543 922.0403 925.2683 921.1859 926.1227
## 70 923.6543 921.9712 925.3374 921.0802 926.2284
## 71 923.6543 921.9048 925.4038 920.9787 926.3299
## 72 923.6543 921.8409 925.4677 920.8809 926.4277
PEMODELAN DATA TIME SERIES
fit1 = arima(datats, order = c(1, 1, 0))
fit2 = arima(datats, order = c(0, 1, 1))
fit3 = arima(datats, order = c(1, 1, 1))
fit4 = arima(datats, order = c(2, 1, 0))
fit5 = arima(datats, order = c(2, 1, 1))
fit6 = arima(datats, order = c(2, 1, 2))
fit7 = arima(datats, order = c(1, 1, 2))
fit8 = arima(datats, order = c(1, 1, 3))
fit9 = arima(datats, order = c(2, 1, 3))
fit10 = arima(datats, order = c(1, 1, 4))
fit11 = arima(datats, order = c(2, 1, 4))
fit12 = arima(datats, order = c(3, 1, 4))
fit13 = arima(datats, order = c(4, 1, 3))
fit14 = arima(datats, order = c(0, 1, 2))
#Menampilkan pemodelan
fit1
##
## Call:
## arima(x = datats, order = c(1, 1, 0))
##
## Coefficients:
## ar1
## -0.3374
## s.e. 0.1212
##
## sigma^2 estimated as 0.4756: log likelihood = -61.85, aic = 127.7
fit2
##
## Call:
## arima(x = datats, order = c(0, 1, 1))
##
## Coefficients:
## ma1
## -0.4604
## s.e. 0.1337
##
## sigma^2 estimated as 0.4539: log likelihood = -60.53, aic = 125.07
fit3
##
## Call:
## arima(x = datats, order = c(1, 1, 1))
##
## Coefficients:
## ar1 ma1
## 0.4360 -0.8530
## s.e. 0.2063 0.1365
##
## sigma^2 estimated as 0.4404: log likelihood = -59.82, aic = 125.63
fit4
##
## Call:
## arima(x = datats, order = c(2, 1, 0))
##
## Coefficients:
## ar1 ar2
## -0.4003 -0.1816
## s.e. 0.1271 0.1259
##
## sigma^2 estimated as 0.4589: log likelihood = -60.83, aic = 127.66
fit5
##
## Call:
## arima(x = datats, order = c(2, 1, 1))
##
## Coefficients:
## ar1 ar2 ma1
## 0.5048 0.1903 -1.0000
## s.e. 0.1283 0.1280 0.1603
##
## sigma^2 estimated as 0.4184: log likelihood = -59.2, aic = 126.4
fit6
##
## Call:
## arima(x = datats, order = c(2, 1, 2))
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 0.8010 0.0119 -1.3095 0.3095
## s.e. 0.4698 0.3231 0.4567 0.4496
##
## sigma^2 estimated as 0.4171: log likelihood = -59.02, aic = 128.04
fit7
##
## Call:
## arima(x = datats, order = c(1, 1, 2))
##
## Coefficients:
## ar1 ma1 ma2
## 0.8176 -1.3245 0.3245
## s.e. 0.1204 0.1969 0.1802
##
## sigma^2 estimated as 0.4171: log likelihood = -59.02, aic = 126.05
fit8
##
## Call:
## arima(x = datats, order = c(1, 1, 3))
##
## Coefficients:
## ar1 ma1 ma2 ma3
## 0.8148 -1.3238 0.3303 -0.0065
## s.e. 0.1392 0.1993 0.2263 0.1507
##
## sigma^2 estimated as 0.4171: log likelihood = -59.02, aic = 128.04
fit9
##
## Call:
## arima(x = datats, order = c(2, 1, 3))
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## -0.1061 0.7680 -0.3511 -1.0000 0.3511
## s.e. 0.1366 0.1158 0.1996 0.0772 0.1802
##
## sigma^2 estimated as 0.4011: log likelihood = -58.41, aic = 128.82
fit10
##
## Call:
## arima(x = datats, order = c(1, 1, 4))
##
## Coefficients:
## ar1 ma1 ma2 ma3 ma4
## -0.9147 0.4956 -0.5553 -0.1918 -0.1409
## s.e. 0.0721 0.1515 0.1488 0.1718 0.1382
##
## sigma^2 estimated as 0.4241: log likelihood = -59.29, aic = 130.57
fit11
##
## Call:
## arima(x = datats, order = c(2, 1, 4))
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3 ma4
## -0.1187 0.7446 -0.3508 -0.9546 0.3508 -0.0454
## s.e. 0.1503 0.1462 0.2117 0.1771 0.1891 0.1566
##
## sigma^2 estimated as 0.3997: log likelihood = -58.37, aic = 130.74
fit12
##
## Call:
## arima(x = datats, order = c(3, 1, 4))
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 ma3 ma4
## -0.2428 -0.1654 0.7426 -0.2270 0.0348 -1.0057 0.1980
## s.e. 0.1760 0.1426 0.1511 0.2685 0.1370 0.1098 0.2274
##
## sigma^2 estimated as 0.377: log likelihood = -57.44, aic = 130.88
fit13
##
## Call:
## arima(x = datats, order = c(4, 1, 3))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1 ma2 ma3
## -0.184 0.4036 0.2105 0.098 -0.3261 -0.5992 -0.0748
## s.e. 1.632 0.6782 0.6302 0.235 1.6370 1.2656 0.8025
##
## sigma^2 estimated as 0.4159: log likelihood = -58.94, aic = 133.89
fit14
##
## Call:
## arima(x = datats, order = c(0, 1, 2))
##
## Coefficients:
## ma1 ma2
## -0.4446 -0.1101
## s.e. 0.1308 0.1641
##
## sigma^2 estimated as 0.4498: log likelihood = -60.3, aic = 126.6
MENGHITUNG NILAI AIC
fit1$aic
## [1] 127.7028
fit2$aic
## [1] 125.0665
fit3$aic
## [1] 125.6322
fit4$aic
## [1] 127.6639
fit5$aic
## [1] 126.4048
fit6$aic
## [1] 128.0441
fit7$aic
## [1] 126.0454
fit8$aic
## [1] 128.0436
fit9$aic
## [1] 128.8193
fit10$aic
## [1] 130.5743
fit11$aic
## [1] 130.7369
fit12$aic
## [1] 130.8809
fit13$aic
## [1] 133.8881
fit14$aic
## [1] 126.6028
TEST BIC
BIC(fit1)
## [1] 131.8579
BIC(fit2)
## [1] 129.2216
BIC(fit3)
## [1] 131.8648
BIC(fit4)
## [1] 133.8965
BIC(fit5)
## [1] 134.715
BIC(fit6)
## [1] 138.4318
BIC(fit7)
## [1] 134.3556
BIC(fit8)
## [1] 138.4313
BIC(fit9)
## [1] 141.2845
BIC(fit10)
## [1] 143.0395
BIC(fit11)
## [1] 145.2797
BIC(fit12)
## [1] 147.5012
BIC(fit13)
## [1] 150.5084
BIC(fit14)
## [1] 132.8354
accuracy(fit2)
## ME RMSE MAE MPE MAPE MASE
## Training set 0.005470459 0.6786289 0.5194214 0.0005535804 0.05625969 0.8831661
## ACF1
## Training set 0.01938488
accuracy(fit3)
## ME RMSE MAE MPE MAPE MASE
## Training set -0.006550688 0.668799 0.5297182 -0.0007533817 0.05737588 0.9006736
## ACF1
## Training set -0.05958424
accuracy(fit5)
## ME RMSE MAE MPE MAPE MASE
## Training set -0.06753628 0.6524346 0.504743 -0.007357698 0.05467395 0.8582086
## ACF1
## Training set -0.04177316
accuracy(fit14)
## ME RMSE MAE MPE MAPE MASE
## Training set 0.005637226 0.6756432 0.5252431 0.0005695527 0.05689064 0.8930646
## ACF1
## Training set -0.004426878
accuracy(fit10)
## ME RMSE MAE MPE MAPE MASE
## Training set 0.001628857 0.6567257 0.5239547 0.0001341016 0.05675024 0.890874
## ACF1
## Training set -0.004135243
TEST DIAGNOSIS MODEL TERBAIK
#Pemodelan terbaik, yaitu pada fit3 karena nilai AIC nya paling kecil
tsdiag(fit2)
PERAMALAN DATA TIME SERIES
library(forecast)
df = forecast(fit2)
plot(df)
plot.ts(df$residuals)
Box.test(df$residuals)
##
## Box-Pierce test
##
## data: df$residuals
## X-squared = 0.022546, df = 1, p-value = 0.8806
hist(df$residuals)
checkresiduals(fit2)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,1)
## Q* = 7.94, df = 9, p-value = 0.5402
##
## Model df: 1. Total lags used: 10
MEMPREDIKSI DATASET SELAMA 12 BULAN KEDEPAN
predict(fit2, n.ahead = 6)
## $pred
## Time Series:
## Start = 61
## End = 66
## Frequency = 1
## [1] 923.6543 923.6543 923.6543 923.6543 923.6543 923.6543
##
## $se
## Time Series:
## Start = 61
## End = 66
## Frequency = 1
## [1] 0.6737003 0.7655228 0.8474540 0.9221341 0.9912035 1.0557639
Dataset_forecast = forecast(fit2, h=6)
Dataset_forecast
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 61 923.6543 922.7909 924.5177 922.3339 924.9747
## 62 923.6543 922.6732 924.6354 922.1539 925.1547
## 63 923.6543 922.5682 924.7404 921.9933 925.3153
## 64 923.6543 922.4725 924.8361 921.8469 925.4616
## 65 923.6543 922.3840 924.9246 921.7116 925.5970
## 66 923.6543 922.3013 925.0073 921.5850 925.7236