Analisis Runtun Waktu
X-12-ARIMA
Email         : putri.angelina@matanauniversity.ac.id
RPubs       : https://rpubs.com/putriangelinaw/
GitHub      : https://github.com/putriangelinaw/
Jurusan     : Statistika Bisnis
Address    : ARA Center, Matana University Tower
                    Jl. CBD Barat Kav, RT.1, Curug Sangereng, Kelapa Dua, Tangerang, Banten 15810.
Grafik Stock Price PT Adaro Energy Tbk. dari Tahun 2015
library(quantmod) # untuk mengambil data stock price dari yahoo finance
set.seed(345)
ADRO <- getSymbols("ADRO.JK",src = "yahoo",from = "2015-01-01")
chart_Series(ADRO.JK)
Tampilan Data Stock Price dari Tahun 2015
library(dplyr) # untuk data manipulasi
library(DT) # untuk pembuatan tabel data
ADRO <- getSymbols("ADRO.JK",src = "yahoo",
return.class = "data.frame",
from = "2015-01-01")
set.seed(345)
ADRO <- ADRO.JK %>%
select(ADRO.JK.Open, ADRO.JK.High,
ADRO.JK.Low, ADRO.JK.Close, ADRO.JK.Adjusted) %>%
tibble::rownames_to_column(var = "Date") %>%
rename("Open Price" = ADRO.JK.Open,
"High Price" = ADRO.JK.High,
"Low Price" = ADRO.JK.Low,
"Close Price" = ADRO.JK.Close,
"Adjusted Price" = ADRO.JK.Adjusted)
datatable(ADRO)X-12-ARIMA dengan R
Data Time Series
library(x12) # untuk X-12-ARIMA
# mengubah tanggal menjadi bulanan
ADRO$Date <- format(as.Date(ADRO$Date, "%Y-%m-%d"), "%m-%Y")
# time series
data <- ts(rev(ADRO$`Adjusted Price`),
start = c(2015,1),
end = c(2021,8),
frequency = 12)
data## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2015 1740 1510 1500 1415 1400 1345 1320 1335 1390 1390 1385 1340
## 2016 1350 1365 1330 1345 1365 1355 1320 1320 1260 1300 1245 1280
## 2017 1255 1260 1315 1265 1295 1340 1365 1385 1410 1340 1300 1290
## 2018 1300 1360 1350 1370 1335 1325 1270 1275 1280 1305 1335 1240
## 2019 1250 1240 1225 1220 1230 1235 1250 1220 1250 1290 1235 1260
## 2020 1205 1205 1215 1235 1285 1245 1260 1290 1285 1310 1355 1395
## 2021 1310 1325 1315 1210 1215 1210 1205 1230Mengecek nilai ekstrim Sebelum X-12-ARIMA
pacf(data, lag.max = 100)
Hasil Proses X-12-ARIMA
data_decom <- x12(data)
data_decom## An object of class "x12Output"
## Slot "a1":
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2015 1740 1510 1500 1415 1400 1345 1320 1335 1390 1390 1385 1340
## 2016 1350 1365 1330 1345 1365 1355 1320 1320 1260 1300 1245 1280
## 2017 1255 1260 1315 1265 1295 1340 1365 1385 1410 1340 1300 1290
## 2018 1300 1360 1350 1370 1335 1325 1270 1275 1280 1305 1335 1240
## 2019 1250 1240 1225 1220 1230 1235 1250 1220 1250 1290 1235 1260
## 2020 1205 1205 1215 1235 1285 1245 1260 1290 1285 1310 1355 1395
## 2021 1310 1325 1315 1210 1215 1210 1205 1230
##
## Slot "d10":
## Jan Feb Mar Apr May Jun Jul
## 2015 0.9898186 0.9987430 0.9995287 0.9938452 1.0054877 1.0050585 0.9965608
## 2016 0.9901910 0.9989522 0.9996402 0.9943330 1.0046965 1.0031799 0.9960732
## 2017 0.9908587 0.9994663 1.0001522 0.9942986 1.0025134 1.0001937 0.9942718
## 2018 0.9926072 1.0005091 1.0004397 0.9938442 0.9990859 0.9972947 0.9931082
## 2019 0.9928241 1.0005807 1.0004397 0.9938442 0.9990859 0.9972947 0.9931175
## 2020 0.9929927 1.0015545 1.0008534 0.9948956 0.9966565 0.9953733 0.9926410
## 2021 0.9934370 1.0021249 1.0010702 0.9951320 0.9945276 0.9928363 0.9910816
## 2022 0.9952827 1.0023966 1.0011109 0.9945323 0.9931409 0.9902124 0.9900524
## Aug Sep Oct Nov Dec
## 2015 1.0028317 1.0102568 1.0151785 0.9931174 0.9899754
## 2016 1.0017826 1.0087778 1.0153559 0.9957262 0.9934592
## 2017 1.0009156 1.0066973 1.0145690 1.0003951 0.9983409
## 2018 0.9999720 1.0075461 1.0154347 1.0011002 0.9987694
## 2019 0.9999685 1.0075270 1.0154064 1.0011795 0.9990592
## 2020 0.9992036 1.0047944 1.0155938 1.0041753 1.0038849
## 2021 0.9973059 1.0037255 1.0163336 1.0073802 1.0066736
## 2022 0.9959775
##
## Slot "d11":
## Jan Feb Mar Apr May Jun Jul Aug
## 2015 1757.898 1511.901 1500.707 1423.763 1392.359 1338.231 1324.555 1331.230
## 2016 1363.373 1366.432 1330.479 1352.666 1358.619 1350.705 1325.204 1317.651
## 2017 1266.578 1260.673 1314.800 1272.254 1291.753 1339.740 1372.864 1383.733
## 2018 1309.682 1359.308 1349.407 1378.486 1336.221 1328.594 1278.813 1275.036
## 2019 1259.035 1239.280 1224.462 1227.557 1231.125 1238.350 1258.663 1220.038
## 2020 1213.503 1203.130 1213.964 1241.336 1289.311 1250.787 1269.341 1291.028
## 2021 1318.654 1322.191 1313.594 1215.919 1221.685 1218.731 1215.843 1233.323
## Sep Oct Nov Dec
## 2015 1375.888 1369.217 1394.599 1353.569
## 2016 1249.036 1280.339 1250.344 1288.427
## 2017 1400.620 1320.758 1299.487 1292.144
## 2018 1270.413 1285.164 1333.533 1241.528
## 2019 1240.661 1270.427 1233.545 1261.187
## 2020 1278.869 1289.886 1349.366 1389.601
## 2021
##
## Slot "d12":
## Jan Feb Mar Apr May Jun Jul Aug
## 2015 1566.281 1527.411 1482.848 1436.167 1392.058 1358.917 1343.383 1344.050
## 2016 1364.101 1357.990 1353.974 1351.515 1348.126 1340.576 1327.761 1311.985
## 2017 1265.741 1268.079 1276.416 1292.022 1313.544 1335.805 1351.926 1355.277
## 2018 1323.279 1337.034 1347.746 1348.239 1337.511 1319.925 1300.908 1285.269
## 2019 1246.788 1238.610 1233.634 1231.729 1232.793 1235.162 1239.014 1243.640
## 2020 1226.521 1223.448 1226.172 1235.607 1247.736 1259.802 1271.547 1282.729
## 2021 1327.215 1314.511 1292.768 1267.511 1245.082 1229.256 1220.623 1219.621
## Sep Oct Nov Dec
## 2015 1353.544 1364.575 1370.490 1369.635
## 2016 1295.094 1280.772 1271.795 1267.150
## 2017 1346.760 1331.685 1318.665 1315.267
## 2018 1274.910 1268.161 1262.629 1255.613
## 2019 1246.429 1245.541 1240.315 1232.977
## 2020 1294.897 1308.466 1321.438 1329.098
## 2021
##
## Slot "d13":
## Jan Feb Mar Apr May Jun Jul
## 2015 1.1223390 0.9898450 1.0120437 0.9913631 1.0002162 0.9847769 0.9859847
## 2016 0.9994664 1.0062167 0.9826469 1.0008511 1.0077839 1.0075555 0.9980739
## 2017 1.0006614 0.9941596 1.0300713 0.9846997 0.9834110 1.0029465 1.0154879
## 2018 0.9897247 1.0166591 1.0012323 1.0224338 0.9990355 1.0065679 0.9830161
## 2019 1.0098223 1.0005412 0.9925646 0.9966125 0.9986472 1.0025808 1.0158585
## 2020 0.9893863 0.9833930 0.9900441 1.0046369 1.0333206 0.9928441 0.9982650
## 2021 0.9935496 1.0058420 1.0161101 0.9592967 0.9812086 0.9914377 0.9960842
## Aug Sep Oct Nov Dec
## 2015 0.9904623 1.0165074 1.0034018 1.0175914 0.9882697
## 2016 1.0043187 0.9644366 0.9996622 0.9831334 1.0167918
## 2017 1.0209967 1.0399920 0.9917944 0.9854565 0.9824195
## 2018 0.9920380 0.9964728 1.0134072 1.0561559 0.9887820
## 2019 0.9810223 0.9953725 1.0199808 0.9945418 1.0228794
## 2020 1.0064702 0.9876221 0.9857999 1.0211345 1.0455225
## 2021 1.0112341
##
## Slot "d16":
## Jan Feb Mar Apr May Jun Jul
## 2015 0.9898186 0.9987430 0.9995287 0.9938452 1.0054877 1.0050585 0.9965608
## 2016 0.9901910 0.9989522 0.9996402 0.9943330 1.0046965 1.0031799 0.9960732
## 2017 0.9908587 0.9994663 1.0001522 0.9942986 1.0025134 1.0001937 0.9942718
## 2018 0.9926072 1.0005091 1.0004397 0.9938442 0.9990859 0.9972947 0.9931082
## 2019 0.9928241 1.0005807 1.0004397 0.9938442 0.9990859 0.9972947 0.9931175
## 2020 0.9929927 1.0015545 1.0008534 0.9948956 0.9966565 0.9953733 0.9926410
## 2021 0.9934370 1.0021249 1.0010702 0.9951320 0.9945276 0.9928363 0.9910816
## 2022 0.9952827 1.0023966 1.0011109 0.9945323 0.9931409 0.9902124 0.9900524
## Aug Sep Oct Nov Dec
## 2015 1.0028317 1.0102568 1.0151785 0.9931174 0.9899754
## 2016 1.0017826 1.0087778 1.0153559 0.9957262 0.9934592
## 2017 1.0009156 1.0066973 1.0145690 1.0003951 0.9983409
## 2018 0.9999720 1.0075461 1.0154347 1.0011002 0.9987694
## 2019 0.9999685 1.0075270 1.0154064 1.0011795 0.9990592
## 2020 0.9992036 1.0047944 1.0155938 1.0041753 1.0038849
## 2021 0.9973059 1.0037255 1.0163336 1.0073802 1.0066736
## 2022 0.9959775
##
## Slot "c17":
## Jan Feb Mar Apr May Jun
## 2015 0.00000000 0.63275489 1.00000000 1.00000000 1.00000000 1.00000000
## 2016 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000
## 2017 1.00000000 1.00000000 0.39489903 1.00000000 1.00000000 1.00000000
## 2018 1.00000000 1.00000000 1.00000000 0.77512284 1.00000000 1.00000000
## 2019 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000
## 2020 1.00000000 1.00000000 1.00000000 1.00000000 0.51851868 1.00000000
## 2021 1.00000000 1.00000000 1.00000000 0.00000000 0.92651143 1.00000000
## Jul Aug Sep Oct Nov Dec
## 2015 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000
## 2016 1.00000000 1.00000000 0.13253662 1.00000000 1.00000000 1.00000000
## 2017 1.00000000 1.00000000 0.06028986 1.00000000 1.00000000 0.87499803
## 2018 1.00000000 1.00000000 1.00000000 1.00000000 0.00000000 1.00000000
## 2019 1.00000000 1.00000000 1.00000000 0.81875986 1.00000000 1.00000000
## 2020 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 0.00000000
## 2021 1.00000000 1.00000000
##
## Slot "d9":
## Jan Feb Mar Apr May Jun Jul
## 2015 1.0062653 0.9973328 NA NA NA NA NA
## 2016 NA NA NA NA NA NA NA
## 2017 NA NA 1.0105082 NA NA NA NA
## 2018 NA NA NA 1.0146620 NA NA NA
## 2019 NA NA NA NA NA NA NA
## 2020 NA NA NA NA 1.0112115 NA NA
## 2021 NA NA NA 0.9886937 0.9700346 NA NA
## 2022 NA NA NA NA NA NA NA
## Aug Sep Oct Nov Dec
## 2015 NA NA NA NA NA
## 2016 NA 1.0034379 NA NA NA
## 2017 NA 1.0137911 NA NA 0.9737978
## 2018 NA NA NA 1.0026726 NA
## 2019 NA NA 1.0339606 NA NA
## 2020 NA NA NA NA 1.0153398
## 2021 NA NA NA NA NA
## 2022 NA
##
## Slot "e2":
## Jan Feb Mar Apr May Jun Jul Aug
## 2015 1566.281 1511.901 1500.707 1423.763 1392.359 1338.231 1324.555 1331.230
## 2016 1363.373 1366.432 1330.479 1352.666 1358.619 1350.705 1325.204 1317.651
## 2017 1266.578 1260.673 1314.800 1272.254 1291.753 1339.740 1372.864 1383.733
## 2018 1309.682 1359.308 1349.407 1378.486 1336.221 1328.594 1278.813 1275.036
## 2019 1259.035 1239.280 1224.462 1227.557 1231.125 1238.350 1258.663 1220.038
## 2020 1213.503 1203.130 1213.964 1241.336 1289.311 1250.787 1269.341 1291.028
## 2021 1318.654 1322.191 1313.594 1267.511 1221.685 1218.731 1215.843 1233.323
## Sep Oct Nov Dec
## 2015 1375.888 1369.217 1394.599 1353.569
## 2016 1249.036 1280.339 1250.344 1288.427
## 2017 1400.620 1320.758 1299.487 1292.144
## 2018 1270.413 1285.164 1262.629 1241.528
## 2019 1240.661 1270.427 1233.545 1261.187
## 2020 1278.869 1289.886 1349.366 1329.098
## 2021
##
## Slot "d8":
## Jan Feb Mar Apr May Jun Jul
## 2015 1.1071300 0.9868898 1.0116143 0.9869534 1.0084392 0.9923221 0.9839462
## 2016 0.9862232 1.0028068 0.9823194 0.9980437 1.0178896 1.0173014 0.9998973
## 2017 0.9849663 0.9893266 1.0295769 0.9824138 0.9927357 1.0122468 1.0187486
## 2018 0.9736638 1.0119287 1.0015068 1.0204548 1.0050585 1.0113696 0.9824163
## 2019 0.9989937 0.9985007 0.9916763 0.9901250 0.9976917 0.9994931 1.0083825
## 2020 0.9852376 0.9859388 0.9897636 0.9964052 1.0249310 0.9823507 0.9850771
## 2021 0.9947746 1.0123130 1.0167516 0.9500946 0.9683811 0.9757953 0.9795265
## 2022 1.0114691 1.0054913 0.9983701 0.9924566 0.9886204 0.9864747 0.9858715
## Aug Sep Oct Nov Dec
## 2015 0.9928099 1.0247921 1.0154032 1.0069557 0.9746244
## 2016 1.0092800 0.9723826 1.0107736 0.9725132 1.0026510
## 2017 1.0283473 1.0485756 1.0022333 0.9775742 0.9707662
## 2018 0.9959093 1.0050931 1.0274726 1.0538781 0.9837219
## 2019 0.9810963 1.0042850 1.0386508 0.9994633 1.0257919
## 2020 1.0016070 0.9919639 1.0051910 1.0331730 1.0590902
## 2021 1.0034454 1.0085720 1.0121144 1.0144676 1.0145794
## 2022 0.9862745
##
## Slot "b1":
## Jan Feb Mar Apr May Jun Jul Aug
## 2015 1740.000 1510.000 1500.000 1415.000 1400.000 1345.000 1320.000 1335.000
## 2016 1350.000 1365.000 1330.000 1345.000 1365.000 1355.000 1320.000 1320.000
## 2017 1255.000 1260.000 1315.000 1265.000 1295.000 1340.000 1365.000 1385.000
## 2018 1300.000 1360.000 1350.000 1370.000 1335.000 1325.000 1270.000 1275.000
## 2019 1250.000 1240.000 1225.000 1220.000 1230.000 1235.000 1250.000 1220.000
## 2020 1205.000 1205.000 1215.000 1235.000 1285.000 1245.000 1260.000 1290.000
## 2021 1310.000 1325.000 1315.000 1210.000 1215.000 1210.000 1205.000 1230.000
## 2022 1256.609 1261.241 1265.665 1269.889 1273.922 1277.772 1281.446 1284.952
## Sep Oct Nov Dec
## 2015 1390.000 1390.000 1385.000 1340.000
## 2016 1260.000 1300.000 1245.000 1280.000
## 2017 1410.000 1340.000 1300.000 1290.000
## 2018 1280.000 1305.000 1335.000 1240.000
## 2019 1250.000 1290.000 1235.000 1260.000
## 2020 1285.000 1310.000 1355.000 1395.000
## 2021 1235.814 1241.371 1246.683 1251.759
## 2022
##
## Slot "td":
## NULL
##
## Slot "otl":
## NULL
##
## Slot "sp0":
## An object of class "spectrum"
## Slot "frequency":
## [1] 0.000000000 0.008333333 0.016666667 0.025000000 0.033333333 0.041666667
## [7] 0.050000000 0.058333333 0.066666667 0.075000000 0.083333333 0.091666667
## [13] 0.100000000 0.108333333 0.116666667 0.125000000 0.133333333 0.141666667
## [19] 0.150000000 0.158333333 0.166666667 0.175000000 0.183333333 0.191666667
## [25] 0.200000000 0.208333333 0.216666667 0.225000000 0.233333333 0.241666667
## [31] 0.250000000 0.258333333 0.266666667 0.275000000 0.283333333 0.291666667
## [37] 0.300000000 0.308333333 0.316666667 0.325000000 0.333333333 0.339866667
## [43] 0.348200000 0.356533333 0.366666667 0.375000000 0.383333333 0.391666667
## [49] 0.400000000 0.408333333 0.416666667 0.423666667 0.432000000 0.440333333
## [55] 0.450000000 0.458333333 0.466666667 0.475000000 0.483333333 0.491666667
## [61] 0.500000000
##
## Slot "spectrum":
## [1] -33.34877 -31.99640 -29.07844 -30.24639 -32.46875 -32.19305 -29.44731
## [8] -27.30013 -29.10932 -30.15924 -30.18995 -30.74409 -31.26715 -30.44925
## [15] -28.56749 -28.16352 -28.93563 -28.63125 -28.83309 -31.40575 -33.75269
## [22] -34.93161 -35.33643 -35.30044 -34.63867 -33.03218 -30.96425 -30.15094
## [29] -30.48922 -31.26457 -33.18332 -35.12019 -35.65889 -34.20963 -30.51637
## [36] -27.59620 -29.49733 -30.31313 -30.35596 -32.11050 -33.89115 -34.06234
## [43] -32.22211 -27.83534 -26.29491 -28.86339 -28.90483 -27.24610 -27.05463
## [50] -28.87426 -30.00945 -29.99495 -28.99207 -27.49204 -26.92866 -27.48527
## [57] -27.73646 -28.60607 -31.03469 -33.20998 -33.99764
##
##
## Slot "sp1":
## An object of class "spectrum"
## Slot "frequency":
## [1] 0.000000000 0.008333333 0.016666667 0.025000000 0.033333333 0.041666667
## [7] 0.050000000 0.058333333 0.066666667 0.075000000 0.083333333 0.091666667
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## [19] 0.150000000 0.158333333 0.166666667 0.175000000 0.183333333 0.191666667
## [25] 0.200000000 0.208333333 0.216666667 0.225000000 0.233333333 0.241666667
## [31] 0.250000000 0.258333333 0.266666667 0.275000000 0.283333333 0.291666667
## [37] 0.300000000 0.308333333 0.316666667 0.325000000 0.333333333 0.339866667
## [43] 0.348200000 0.356533333 0.366666667 0.375000000 0.383333333 0.391666667
## [49] 0.400000000 0.408333333 0.416666667 0.423666667 0.432000000 0.440333333
## [55] 0.450000000 0.458333333 0.466666667 0.475000000 0.483333333 0.491666667
## [61] 0.500000000
##
## Slot "spectrum":
## [1] -38.50809 -37.20118 -33.45200 -32.11200 -34.83067 -35.35480 -33.18754
## [8] -29.73089 -30.59483 -33.03631 -34.40621 -34.87956 -34.10273 -31.67381
## [15] -29.70630 -30.79323 -29.92456 -26.24008 -33.32426 -38.29651 -39.93379
## [22] -38.83550 -35.16750 -34.19622 -37.21649 -37.49259 -34.29631 -33.50844
## [29] -38.64276 -41.06175 -40.98199 -38.84100 -35.28956 -32.93217 -33.23891
## [36] -34.03102 -34.00329 -31.70454 -30.73388 -37.22361 -41.17603 -42.35083
## [43] -41.62252 -37.78049 -23.24045 -31.78237 -33.39043 -28.26048 -33.46795
## [50] -39.47863 -41.57734 -41.30034 -38.67832 -32.93873 -25.04684 -28.11987
## [57] -30.45846 -33.60272 -36.08720 -37.26439 -37.55877
##
##
## Slot "sp2":
## An object of class "spectrum"
## Slot "frequency":
## [1] 0.000000000 0.008333333 0.016666667 0.025000000 0.033333333 0.041666667
## [7] 0.050000000 0.058333333 0.066666667 0.075000000 0.083333333 0.091666667
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## [19] 0.150000000 0.158333333 0.166666667 0.175000000 0.183333333 0.191666667
## [25] 0.200000000 0.208333333 0.216666667 0.225000000 0.233333333 0.241666667
## [31] 0.250000000 0.258333333 0.266666667 0.275000000 0.283333333 0.291666667
## [37] 0.300000000 0.308333333 0.316666667 0.325000000 0.333333333 0.339866667
## [43] 0.348200000 0.356533333 0.366666667 0.375000000 0.383333333 0.391666667
## [49] 0.400000000 0.408333333 0.416666667 0.423666667 0.432000000 0.440333333
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## [61] 0.500000000
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## Slot "spectrum":
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## [15] -36.14578 -30.84440 -32.43760 -29.68567 -32.43802 -39.15101 -41.62078
## [22] -40.83442 -36.62301 -34.62842 -38.66379 -39.04392 -35.41121 -36.29610
## [29] -41.55885 -43.58057 -43.11429 -40.89111 -38.44052 -37.22175 -36.68271
## [36] -37.71010 -38.80783 -37.17321 -34.66293 -41.38326 -45.73463 -47.03066
## [43] -46.33798 -42.38687 -27.75908 -37.52892 -38.99760 -34.00985 -38.75707
## [50] -44.94043 -47.24524 -47.19070 -44.93242 -39.65955 -30.17694 -34.51044
## [57] -37.05538 -39.56201 -42.31620 -44.12042 -44.71600
##
##
## Slot "spr":
## An object of class "spectrum"
## Slot "frequency":
## [1] 0.000000000 0.008333333 0.016666667 0.025000000 0.033333333 0.041666667
## [7] 0.050000000 0.058333333 0.066666667 0.075000000 0.083333333 0.091666667
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## [37] 0.300000000 0.308333333 0.316666667 0.325000000 0.333333333 0.339866667
## [43] 0.348200000 0.356533333 0.366666667 0.375000000 0.383333333 0.391666667
## [49] 0.400000000 0.408333333 0.416666667 0.423666667 0.432000000 0.440333333
## [55] 0.450000000 0.458333333 0.466666667 0.475000000 0.483333333 0.491666667
## [61] 0.500000000
##
## Slot "spectrum":
## [1] -40.68510 -39.56890 -36.12367 -32.25390 -33.70797 -34.73288 -32.96039
## [8] -29.15431 -29.22703 -31.44618 -32.02857 -31.96217 -31.97546 -31.24355
## [15] -29.15697 -27.54044 -28.42024 -28.83956 -28.92164 -31.65727 -35.01528
## [22] -37.13182 -37.97997 -37.73918 -36.50411 -34.41564 -32.12159 -30.69364
## [29] -29.90473 -29.84584 -31.75319 -33.81143 -34.35006 -32.96817 -30.03326
## [36] -28.62546 -29.52771 -29.37989 -29.48168 -31.81329 -33.59472 -33.61456
## [43] -31.61739 -27.69769 -27.04890 -28.45875 -27.67358 -26.25829 -27.44903
## [50] -29.02225 -29.18531 -28.49084 -27.59315 -27.31500 -27.36007 -27.15537
## [57] -26.65347 -26.94138 -28.91017 -30.88471 -31.62373
##
##
## Slot "forecast":
## An object of class "fbcast"
## Slot "estimate":
## Jan Feb Mar Apr May Jun Jul Aug
## 2021
## 2022 1256.609 1261.241 1265.665 1269.889 1273.922 1277.772 1281.446 1284.952
## Sep Oct Nov Dec
## 2021 1235.814 1241.371 1246.683 1251.759
## 2022
##
## Slot "lowerci":
## Jan Feb Mar Apr May Jun Jul Aug
## 2021
## 2022 1102.976 1096.234 1090.778 1086.306 1082.608 1079.532 1076.962 1074.811
## Sep Oct Nov Dec
## 2021 1160.298 1137.482 1122.470 1111.464
## 2022
##
## Slot "upperci":
## Jan Feb Mar Apr May Jun Jul Aug
## 2021
## 2022 1431.641 1451.085 1468.592 1484.498 1499.045 1512.416 1524.756 1536.179
## Sep Oct Nov Dec
## 2021 1316.244 1354.749 1384.643 1409.764
## 2022
##
##
## Slot "backcast":
## An object of class "fbcast"
## Slot "estimate":
## Time Series:
## Start = 1
## End = 1
## Frequency = 1
## [1] NA
## attr(,".S3Class")
## [1] ts
##
## Slot "lowerci":
## Time Series:
## Start = 1
## End = 1
## Frequency = 1
## [1] NA
## attr(,".S3Class")
## [1] ts
##
## Slot "upperci":
## Time Series:
## Start = 1
## End = 1
## Frequency = 1
## [1] NA
## attr(,".S3Class")
## [1] ts
##
##
## Slot "dg":
## $x11regress
## $x11regress$x11regress
## [1] "no"
##
##
## $transform
## $transform$transform
## [1] "Automatic selection"
##
##
## $samode
## $samode$samode
## [1] "auto-mode seasonal adjustment"
##
## $samode$finalsamode
## [1] "multiplicative"
##
##
## $seasonalma
## $seasonalma$seasonalma
## [1] "MSR MSR MSR MSR MSR MSR MSR MSR MSR MSR MSR MSR"
##
## $seasonalma$finalseasonalma
## [1] "3x9"
##
##
## $trendma
## $trendma$trendma
## [1] "default"
##
## $trendma$finaltrendma
## [1] 13
##
##
## $arimamdl
## $arimamdl$arimamdl
## [1] "(1 0 0)"
##
##
## $automdl
## $automdl$automdl
## [1] "(1 0 0)"
##
##
## $regmdl
## $regmdl$regmdl
## [1] "Constant"
##
##
## $nout
## $nout$nout
## [1] 0
##
##
## $nautoout
## $nautoout$nautoout
## [1] "-"
##
##
## $nalmostout
## $nalmostout$nalmostout
## [1] "-"
##
##
## $almostoutlier
## $almostoutlier$almostoutlier
## [1] "-"
##
##
## $crit
## $crit$crit
## [1] "-"
##
##
## $outlier
## $outlier$outlier
## [1] "-"
##
##
## $userdefined
## $userdefined$userdefined
## [1] "-"
##
##
## $autooutlier
## $autooutlier$autooutlier
## [1] "-"
##
##
## $peaks.seas
## $peaks.seas$peaks.seas
## [1] "none"
##
##
## $peaks.td
## $peaks.td$peaks.td
## [1] "none"
##
##
## $id.seas
## $id.seas$id.seas
## [1] "no"
##
##
## $id.rsdseas
## $id.rsdseas$id.rsdseas
## [1] "0.32912 97.63673"
##
##
## $spcrsd
## $spcrsd$spcrsd.tukey.m
## [1] 79
##
## $spcrsd$spcrsd.median
## [1] -30.69364
##
## $spcrsd$spcrsd.range
## [1] 14.42681
##
## $spcrsd$spcrsd.t1
## [1] "nopeak"
##
## $spcrsd$spcrsd.t2
## [1] "nopeak"
##
## $spcrsd$spcrsd.t.dom
## [1] "no"
##
## $spcrsd$spcrsd.s1
## [1] "nopeak"
##
## $spcrsd$spcrsd.s2
## [1] "nopeak"
##
## $spcrsd$spcrsd.s3
## [1] "nopeak"
##
## $spcrsd$spcrsd.s4
## [1] "nopeak"
##
## $spcrsd$spcrsd.s5
## [1] "nopeak"
##
## $spcrsd$spcrsd.s.dom
## [1] "no"
##
## $spcrsd$spcrsd.dom
## [1] "no"
##
## $spcrsd$spcrsd.tukey.s1
## [1] 0.177
##
## $spcrsd$spcrsd.tukey.s2
## [1] 0.2916
##
## $spcrsd$spcrsd.tukey.s3
## [1] 0.1534
##
## $spcrsd$spcrsd.tukey.s4
## [1] 0.2593
##
## $spcrsd$spcrsd.tukey.s5
## [1] 0.5105
##
## $spcrsd$spcrsd.tukey.s6
## [1] 0.3118
##
## $spcrsd$spcrsd.tukey.td
## [1] 0.5022
##
##
## $spcori
## $spcori$spcori.median
## [1] -30.31313
##
## $spcori$spcori.range
## [1] 9.363977
##
## $spcori$spcori.t1
## [1] "nopeak"
##
## $spcori$spcori.t2
## [1] "nopeak"
##
## $spcori$spcori.t.dom
## [1] "no"
##
## $spcori$spcori.s1
## [1] "nopeak"
##
## $spcori$spcori.s2
## [1] "nopeak"
##
## $spcori$spcori.s3
## [1] "nopeak"
##
## $spcori$spcori.s4
## [1] "nopeak"
##
## $spcori$spcori.s5
## [1] "nopeak"
##
## $spcori$spcori.s.dom
## [1] "no"
##
## $spcori$spcori.dom
## [1] "no"
##
##
## $spcsa
## $spcsa$spcsa.median
## [1] -34.19622
##
## $spcsa$spcsa.range
## [1] 19.11038
##
## $spcsa$spcsa.t1
## [1] "nopeak"
##
## $spcsa$spcsa.t2
## [1] "nopeak"
##
## $spcsa$spcsa.t.dom
## [1] "no"
##
## $spcsa$spcsa.s1
## [1] "nopeak"
##
## $spcsa$spcsa.s2
## [1] "nopeak"
##
## $spcsa$spcsa.s3
## [1] "nopeak"
##
## $spcsa$spcsa.s4
## [1] "nopeak"
##
## $spcsa$spcsa.s5
## [1] "nopeak"
##
## $spcsa$spcsa.s.dom
## [1] "no"
##
## $spcsa$spcsa.dom
## [1] "no"
##
##
## $spcirr
## $spcirr$spcirr.median
## [1] -40.83442
##
## $spcirr$spcirr.range
## [1] 20.20899
##
## $spcirr$spcirr.t1
## [1] "nopeak"
##
## $spcirr$spcirr.t2
## [1] "nopeak"
##
## $spcirr$spcirr.t.dom
## [1] "no"
##
## $spcirr$spcirr.s1
## [1] "nopeak"
##
## $spcirr$spcirr.s2
## [1] "nopeak"
##
## $spcirr$spcirr.s3
## [1] "nopeak"
##
## $spcirr$spcirr.s4
## [1] "nopeak"
##
## $spcirr$spcirr.s5
## [1] "nopeak"
##
## $spcirr$spcirr.s.dom
## [1] "no"
##
## $spcirr$spcirr.dom
## [1] "no"
##
##
## $m1
## $m1$m1
## [1] 3
##
##
## $m2
## $m2$m2
## [1] 1.222
##
##
## $m3
## $m3$m3
## [1] 0.563
##
##
## $m4
## $m4$m4
## [1] 0.52
##
##
## $m5
## $m5$m5
## [1] 0.463
##
##
## $m6
## $m6$m6
## [1] 0.931
##
##
## $m7
## $m7$m7
## [1] 2.625
##
##
## $m8
## $m8$m8
## [1] 1.822
##
##
## $m9
## $m9$m9
## [1] 1.761
##
##
## $m10
## $m10$m10
## [1] 1.95
##
##
## $m11
## $m11$m11
## [1] 1.807
##
##
## $q
## $q$q
## [1] 1.62
##
##
## $q2
## $q2$q2
## [1] 1.67
##
##
## $nmfail
## $nmfail$nmfail
## [1] 7
##
##
## $loglikelihood
## $loglikelihood$loglikelihood
## [1] 160.5755
##
##
## $aic
## $aic$aic
## [1] 832.8236
##
##
## $aicc
## $aicc$aicc
## [1] 833.1394
##
##
## $bic
## $bic$bic
## [1] 839.9697
##
##
## $hq
## $hq$hq
## [1] 835.6887
##
##
## $aape
## $aape$aape.mode
## [1] "withinsample"
##
## $aape$aape.0
## [1] 3.813905
##
## $aape$aape.1
## [1] 4.712368
##
## $aape$aape.2
## [1] 2.248731
##
## $aape$aape.3
## [1] 4.480615
##
##
## $autotransform
## $autotransform$autotransform
## [1] "Log(y)"
##
##
## $Constant
## $Constant$Constant
## $Constant$Constant[[1]]
## coef stderr tval
## 7.21220237 0.06059945 119.01432298
##
##
##
## $ifout
## [1] "No outlier detection performed"
##
## $rsd.acf
## lag sample.acf stderr.acf Ljung-Box.q df.q pval
## 1 1 -0.249746541 0.1118034 5.179355 0 0.00000000
## 2 2 0.112705953 0.1185721 6.247679 1 0.01243561
## 3 3 -0.032125263 0.1199037 6.335603 2 0.04209604
## 4 4 -0.133105908 0.1200112 7.864876 3 0.04888844
## 5 5 -0.038507643 0.1218426 7.994575 4 0.09177713
## 6 6 -0.090116998 0.1219947 8.714497 5 0.12100827
## 7 7 0.046355728 0.1228240 8.907599 6 0.17884170
## 8 8 0.052317349 0.1230425 9.156980 7 0.24158122
## 9 9 0.001125123 0.1233202 9.157097 8 0.32921738
## 10 10 -0.064689688 0.1233203 9.549268 9 0.38818988
## 11 11 -0.034617973 0.1237438 9.663204 10 0.47052161
## 12 12 -0.152814198 0.1238648 11.916002 11 0.36999012
## 13 13 0.129723317 0.1261994 13.563653 12 0.32943550
## 14 14 0.017905849 0.1278554 13.595520 13 0.40293299
## 15 15 0.001591354 0.1278867 13.595776 14 0.48023928
## 16 16 0.031192801 0.1278870 13.695507 15 0.54873660
## 17 17 0.057465592 0.1279820 14.039365 16 0.59578109
## 18 18 -0.040285053 0.1283042 14.211077 17 0.65210833
## 19 19 -0.017458758 0.1284622 14.243856 18 0.71306178
## 20 20 -0.016363275 0.1284918 14.273131 19 0.76754264
## 21 21 -0.008381181 0.1285179 14.280941 20 0.81597062
## 22 22 -0.023479697 0.1285247 14.343295 21 0.85440654
## 23 23 -0.005173698 0.1285783 14.346375 22 0.88873113
## 24 24 -0.060303474 0.1285809 14.772367 23 0.90260604
##
## $rsd.pacf
## lag sample.pacf stderr.pacf
## 1 1 -0.249746541 0.1118034
## 2 2 0.053680874 0.1118034
## 3 3 0.008469416 0.1118034
## 4 4 -0.154968549 0.1118034
## 5 5 -0.113224993 0.1118034
## 6 6 -0.111251333 0.1118034
## 7 7 0.003853965 0.1118034
## 8 8 0.059643659 0.1118034
## 9 9 -0.004986112 0.1118034
## 10 10 -0.122654859 0.1118034
## 11 11 -0.096511770 0.1118034
## 12 12 -0.179488142 0.1118034
## 13 13 0.075602662 0.1118034
## 14 14 0.091248842 0.1118034
## 15 15 -0.042053813 0.1118034
## 16 16 -0.083975437 0.1118034
## 17 17 0.049197578 0.1118034
## 18 18 0.013139131 0.1118034
## 19 19 0.011767379 0.1118034
## 20 20 -0.009372913 0.1118034
## 21 21 -0.044903837 0.1118034
## 22 22 -0.080833437 0.1118034
## 23 23 -0.018850477 0.1118034
## 24 24 -0.075832949 0.1118034
##
## $tsName
## [1] "Rout"
##
## $frequency
## [1] 12
##
## $span
## [1] "span: 1st month,2015 to 8th month,2021"
## [2] "modelspan: 1st month,2015 to 8th month,2021"
## [3] "nobsmodelspan: 80"
##
##
## Slot "file":
## [1] "Rout"
##
## Slot "tblnames":
## [1] "a1" "d10" "d11" "d12" "d13" "d16" "c17" "d9" "e2" "d8" "b1" "td"
## [13] "otl"
##
## Slot "Rtblnames":
## [1] "Original series"
## [2] "Final seasonal factors"
## [3] "Final seasonally adjusted data"
## [4] "Final trend cycle"
## [5] "Final irregular components"
## [6] "Combined adjustment factors"
## [7] "Final weights for irregular component"
## [8] "Final replacements for SI ratios"
## [9] "Differenced, transformed, seasonally adjusted data"
## [10] "Final unmodified SI Ratios"
## [11] "Orig2"
## [12] "Trading day component"
## [13] "regressor"Plot data setelah X-12-ARIMA
plot(data_decom, original=T, trend=T, sa=T)
Hasil dekomposisi
data_decom2 <- stl(data, t.window = 15, s.window="periodic", robust=TRUE)
plot(data_decom2)
Mengecek nilai ekstrim setelah X-12-ARIMA
data_diff <- diff(data)
pacf(data_diff, lag.max = 100)
Forecasting
plot(data_decom, original=T, trend=T, sa=T, forecast = T)