Data Tidak Stasioner
2023-09-23
library(ggplot2)
library(tsibble)## Warning: package 'tsibble' was built under R version 4.3.1##
## Attaching package: 'tsibble'## The following objects are masked from 'package:base':
##
## intersect, setdiff, unionlibrary(tseries)## Warning: package 'tseries' was built under R version 4.3.1## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(MASS)## Warning: package 'MASS' was built under R version 4.3.1library(tseries)
library(forecast)## Warning: package 'forecast' was built under R version 4.3.1library(TTR)## Warning: package 'TTR' was built under R version 4.3.1library(TSA)## Warning: package 'TSA' was built under R version 4.3.1## Registered S3 methods overwritten by 'TSA':
## method from
## fitted.Arima forecast
## plot.Arima forecast##
## Attaching package: 'TSA'## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tarlibrary(imputeTS)## Warning: package 'imputeTS' was built under R version 4.3.1##
## Attaching package: 'imputeTS'## The following object is masked from 'package:tseries':
##
## na.removelibrary(ggplot2)
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following object is masked from 'package:imputeTS':
##
## na.locf## The following object is masked from 'package:tsibble':
##
## index## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericset.seed(1002)IMPORT DATA
library(rio)## Warning: package 'rio' was built under R version 4.3.1data <- import ("https://raw.githubusercontent.com/divanm/mpdw/main/Data/DATA%20IDX%20COMPOSITE%20JKSE.csv")
x <- data$Open
y <- data$CloseStasioner dalam Rataan dan Ragam
Pada dasarnya, pembangkitan data ARIMA akan menghasilkan data yang
stasioner dalam rataan dan ragam karena akan mengikuti fungsi
default-nya yang mengikuti pembangkitan bilangan acak normal
dengan mean=0 dan ragam=1 .
Cek apakah ada missing value:
data[which(is.na(data$Close)),]## Date Open High Low Close Adj Close Volume
## 109 2022-05-02 NA NA NA NA NA NAMenduga missing value
data <- na_interpolation(data, option = "spline")
data## Date Open High Low Close Adj Close Volume
## 1 2020-04-06 4623.429 4975.536 4562.902 4649.079 4649.079 255758500
## 2 2020-04-13 4649.079 4747.725 4480.607 4634.821 4634.821 218419900
## 3 2020-04-20 4634.821 4669.542 4441.090 4496.064 4496.064 238397200
## 4 2020-04-27 4496.064 4726.774 4474.893 4716.403 4716.403 183906700
## 5 2020-05-04 4716.403 4716.403 4576.228 4597.430 4597.430 179791700
## 6 2020-05-11 4597.430 4659.862 4460.273 4507.607 4507.607 231060000
## 7 2020-05-18 4507.607 4609.042 4487.179 4545.952 4545.952 139287000
## 8 2020-05-25 4545.952 4755.957 4541.834 4753.612 4753.612 288083800
## 9 2020-06-01 4753.612 5014.764 4753.612 4947.782 4947.782 372565600
## 10 2020-06-08 4947.782 5139.406 4712.073 4880.359 4880.359 490084700
## 11 2020-06-15 4880.359 5018.985 4809.619 4942.275 4942.275 336775500
## 12 2020-06-22 4942.275 4977.651 4879.133 4904.088 4904.088 260206800
## 13 2020-06-29 4904.088 4997.482 4862.041 4973.794 4973.794 249816600
## 14 2020-07-06 4973.794 5111.564 4973.490 5031.256 5031.256 358094500
## 15 2020-07-13 5031.256 5116.464 5024.934 5079.585 5079.585 349862400
## 16 2020-07-20 5079.585 5162.980 5031.888 5082.991 5082.991 427056800
## 17 2020-07-27 5082.991 5149.630 5080.121 5149.627 5149.627 356913600
## 18 2020-08-03 5149.627 5187.964 4928.468 5143.893 5143.893 423927900
## 19 2020-08-10 5157.834 5279.349 5157.834 5247.690 5247.690 340206700
## 20 2020-08-17 5247.690 5327.316 5243.995 5272.810 5272.810 188318800
## 21 2020-08-24 5272.810 5381.948 5261.408 5346.659 5346.659 665155800
## 22 2020-08-31 5346.659 5369.447 5188.609 5239.851 5239.851 568186400
## 23 2020-09-07 5235.010 5256.305 4754.799 5016.712 5016.712 492882200
## 24 2020-09-14 5060.024 5187.279 5013.186 5059.223 5059.223 503336800
## 25 2020-09-21 5058.990 5075.819 4820.331 4945.791 4945.791 406370800
## 26 2020-09-28 4962.953 4991.762 4841.362 4926.734 4926.734 440809400
## 27 2020-10-05 4947.040 5057.836 4915.685 5053.663 5053.663 421591900
## 28 2020-10-12 5078.129 5182.531 5064.171 5103.414 5103.414 525143900
## 29 2020-10-19 5116.758 5135.078 5063.697 5112.188 5112.188 522912300
## 30 2020-10-26 5113.149 5158.265 5110.618 5128.225 5128.225 210436500
## 31 2020-11-02 5108.029 5335.529 5073.500 5335.529 5335.529 516535700
## 32 2020-11-09 5371.971 5520.908 5319.420 5461.058 5461.058 669558400
## 33 2020-11-16 5500.034 5628.442 5462.460 5571.656 5571.656 789934400
## 34 2020-11-23 5583.330 5795.836 5583.330 5783.335 5783.335 1255563200
## 35 2020-11-30 5779.671 5853.156 5563.862 5810.483 5810.483 1160743700
## 36 2020-12-07 5854.303 6004.423 5854.303 5938.329 5938.329 1003237500
## 37 2020-12-14 5959.275 6160.977 5959.275 6104.324 6104.324 1292048600
## 38 2020-12-21 6131.623 6195.154 5853.261 6008.709 6008.709 692226400
## 39 2020-12-28 6067.000 6143.870 5962.010 5979.073 5979.073 526030000
## 40 2021-01-04 5997.830 6275.742 5929.048 6257.835 6257.835 1007037000
## 41 2021-01-11 6278.413 6472.312 6278.374 6373.412 6373.412 1527600500
## 42 2021-01-18 6365.026 6504.992 6283.313 6307.127 6307.127 1081229300
## 43 2021-01-25 6322.519 6322.727 5825.292 5862.352 5862.352 813369600
## 44 2021-02-01 5856.777 6179.368 5735.469 6151.729 6151.729 872980000
## 45 2021-02-08 6193.551 6286.291 6157.135 6222.521 6222.521 563483000
## 46 2021-02-15 6244.385 6314.555 6173.594 6231.932 6231.932 739117700
## 47 2021-02-22 6267.025 6312.873 6184.517 6241.796 6241.796 880483600
## 48 2021-03-01 6281.857 6394.452 6245.308 6258.749 6258.749 987879800
## 49 2021-03-08 6304.000 6364.357 6167.718 6358.209 6358.209 652024500
## 50 2021-03-15 6374.762 6387.736 6268.839 6356.160 6356.160 742809300
## 51 2021-03-22 6346.795 6354.939 6058.843 6195.562 6195.562 712370600
## 52 2021-03-29 6205.569 6230.990 5892.645 6011.456 6011.456 462735200
## 53 2021-04-05 6040.055 6113.156 5944.421 6070.209 6070.209 720785500
## 54 2021-04-12 6080.792 6115.620 5883.524 6086.258 6086.258 669695000
## 55 2021-04-19 6084.785 6096.995 5973.247 6016.864 6016.864 675194300
## 56 2021-04-26 6018.340 6033.900 5950.868 5995.616 5995.616 641211400
## 57 2021-05-03 5999.661 6005.088 5922.493 5928.309 5928.309 667078400
## 58 2021-05-10 5942.106 5985.372 5911.376 5938.351 5938.351 240955800
## 59 2021-05-17 5950.137 5958.793 5742.038 5773.120 5773.120 696962000
## 60 2021-05-24 5793.067 5904.838 5759.340 5848.616 5848.616 679387300
## 61 2021-05-31 5869.218 6103.859 5860.536 6065.166 6065.166 687508700
## 62 2021-06-07 6075.507 6134.882 5972.449 6095.497 6095.497 1116799300
## 63 2021-06-14 6110.797 6124.872 5944.053 6007.120 6007.120 955804200
## 64 2021-06-21 5959.965 6130.096 5884.918 6022.399 6022.399 851733600
## 65 2021-06-28 6015.279 6043.432 5913.591 6023.008 6023.008 825550700
## 66 2021-07-05 6024.165 6080.222 5985.354 6039.844 6039.844 754205300
## 67 2021-07-12 6060.054 6114.286 5947.618 6072.510 6072.510 716924100
## 68 2021-07-19 6062.966 6166.305 6015.149 6101.690 6101.690 597748400
## 69 2021-07-26 6109.031 6160.463 6068.512 6070.039 6070.039 869133600
## 70 2021-08-02 6098.008 6263.539 6048.101 6203.431 6203.431 1228093800
## 71 2021-08-09 6203.747 6239.015 6042.475 6139.492 6139.492 869347300
## 72 2021-08-16 6144.943 6147.304 5938.407 6030.772 6030.772 796085900
## 73 2021-08-23 6037.700 6138.497 6021.954 6041.366 6041.366 977033500
## 74 2021-08-30 6062.113 6169.056 6054.281 6126.921 6126.921 893890700
## 75 2021-09-06 6137.126 6150.358 5982.766 6094.873 6094.873 958513400
## 76 2021-09-13 6080.062 6137.669 6052.970 6133.246 6133.246 992844400
## 77 2021-09-20 6132.034 6163.884 5996.407 6144.815 6144.815 950159400
## 78 2021-09-27 6141.470 6286.943 6086.263 6228.845 6228.845 1102928200
## 79 2021-10-04 6234.799 6497.656 6234.799 6481.769 6481.769 1172175100
## 80 2021-10-11 6482.957 6680.009 6451.678 6633.338 6633.338 941178200
## 81 2021-10-18 6649.281 6687.134 6585.557 6643.738 6643.738 757917300
## 82 2021-10-25 6626.367 6680.117 6509.878 6591.346 6591.346 899190300
## 83 2021-11-01 6618.122 6627.851 6480.010 6581.785 6581.785 828841100
## 84 2021-11-08 6599.405 6714.158 6592.055 6651.054 6651.054 921099300
## 85 2021-11-15 6661.849 6720.988 6592.228 6720.263 6720.263 1134263700
## 86 2021-11-22 6731.515 6754.464 6544.896 6561.553 6561.553 1087199900
## 87 2021-11-29 6552.803 6647.477 6484.578 6538.506 6538.506 795330100
## 88 2021-12-06 6552.816 6652.922 6525.985 6652.922 6652.922 1078695000
## 89 2021-12-13 6663.739 6688.379 6559.303 6601.932 6601.932 1011838100
## 90 2021-12-20 6571.345 6592.167 6529.593 6562.900 6562.900 941359400
## 91 2021-12-27 6570.558 6621.579 6562.554 6581.482 6581.482 763376600
## 92 2022-01-03 6586.260 6738.110 6586.133 6701.316 6701.316 884588500
## 93 2022-01-10 6697.376 6727.767 6625.757 6693.401 6693.401 854569300
## 94 2022-01-17 6711.406 6726.373 6534.270 6726.373 6726.373 805658500
## 95 2022-01-24 6700.822 6712.262 6523.929 6645.511 6645.511 986322200
## 96 2022-01-31 6656.707 6731.391 6626.656 6731.391 6731.391 777116900
## 97 2022-02-07 6751.349 6874.351 6748.909 6815.607 6815.607 1238259600
## 98 2022-02-14 6791.316 6899.410 6698.509 6892.818 6892.818 1092845600
## 99 2022-02-21 6896.752 6929.911 6758.861 6888.171 6888.171 1127214800
## 100 2022-02-28 6964.697 6996.935 6861.959 6928.328 6928.328 769293800
## 101 2022-03-07 6905.324 6929.863 6814.183 6922.602 6922.602 1085654100
## 102 2022-03-14 6949.206 7032.702 6894.921 6954.965 6954.965 949839000
## 103 2022-03-21 6945.893 7055.341 6929.934 7002.532 7002.532 1086012100
## 104 2022-03-28 6996.318 7099.497 6987.223 7078.760 7078.760 890142300
## 105 2022-04-04 7082.247 7216.494 7060.214 7210.835 7210.835 986772300
## 106 2022-04-11 7212.003 7355.300 7146.586 7235.532 7235.532 1073108900
## 107 2022-04-18 7245.504 7297.394 7174.810 7225.606 7225.606 1118782600
## 108 2022-04-25 7204.161 7267.112 7121.860 7228.914 7228.914 805992800
## 109 2022-05-02 7324.780 7258.343 6799.028 6840.217 6840.217 697324161
## 110 2022-05-09 7154.917 7156.484 6509.879 6597.993 6597.993 778348200
## 111 2022-05-16 6603.893 6965.106 6574.136 6918.144 6918.144 816107000
## 112 2022-05-23 6930.939 7032.822 6802.713 7026.256 7026.256 750357000
## 113 2022-05-30 7052.173 7233.995 6974.616 7182.961 7182.961 949041500
## 114 2022-06-06 7163.174 7257.997 7051.223 7086.648 7086.648 1281571500
## 115 2022-06-13 6992.230 7138.496 6882.644 6936.967 6936.967 1322143900
## 116 2022-06-20 6937.008 7067.747 6859.599 7042.937 7042.937 1133599100
## 117 2022-06-27 7043.018 7070.519 6777.317 6794.328 6794.328 840889500
## 118 2022-07-04 6794.368 6796.519 6559.637 6740.219 6740.219 810131700
## 119 2022-07-11 6740.019 6757.087 6607.702 6651.905 6651.905 794121300
## 120 2022-07-18 6652.065 6901.720 6611.926 6886.962 6886.962 853012300
## 121 2022-07-25 6887.042 7032.353 6857.801 6951.123 6951.123 1387470600
## 122 2022-08-01 6951.123 7090.767 6902.630 7084.655 7084.655 1102623400
## 123 2022-08-08 7084.655 7181.100 7021.673 7129.277 7129.277 1169007600
## 124 2022-08-15 7129.277 7230.111 7080.753 7172.434 7172.434 931624200
## 125 2022-08-22 7172.434 7210.163 7064.501 7135.248 7135.248 1241361100
## 126 2022-08-29 7135.088 7223.126 7015.347 7177.179 7177.179 1359158600
## 127 2022-09-05 7177.139 7287.700 7147.976 7242.656 7242.656 1535050500
## 128 2022-09-12 7242.696 7377.495 7163.073 7168.870 7168.870 1462367300
## 129 2022-09-19 7168.950 7252.186 7127.457 7178.583 7178.583 1266925400
## 130 2022-09-26 7178.503 7178.503 6926.860 7040.798 7040.798 1036700200
## 131 2022-10-03 7040.798 7135.908 6995.062 7026.783 7026.783 1020558200
## 132 2022-10-10 7026.663 7026.663 6814.530 6814.530 6814.530 1046699200
## 133 2022-10-17 6814.530 7058.911 6747.380 7017.771 7017.771 995211200
## 134 2022-10-24 7017.811 7108.816 7016.702 7056.040 7056.040 989950000
## 135 2022-10-31 7056.040 7128.136 6962.853 7045.527 7045.527 907843500
## 136 2022-11-07 7045.527 7111.440 6956.288 7089.206 7089.206 989493100
## 137 2022-11-14 7089.206 7104.764 6955.529 7082.181 7082.181 831349300
## 138 2022-11-21 7082.181 7108.831 7013.221 7053.150 7053.150 816522900
## 139 2022-11-28 7053.110 7090.277 6967.950 7019.639 7019.639 932257000
## 140 2022-12-05 7019.639 7053.903 6683.629 6715.118 6715.118 763168800
## 141 2022-12-12 6715.118 6854.098 6641.810 6812.193 6812.193 1047258100
## 142 2022-12-19 6812.154 6844.121 6715.045 6800.673 6800.673 668236600
## 143 2022-12-26 6800.713 6858.147 6796.167 6835.808 6835.808 117543200data[109,]## Date Open High Low Close Adj Close Volume
## 109 2022-05-02 7324.78 7258.343 6799.028 6840.217 6840.217 697324161stas <- ts(data$Close)Plot Time Series
plot_stas <- stas |> as_tsibble() |>
ggplot(aes(x = index, y = value)) + geom_line() + theme_bw() +
xlab("Obs") + ylab("Nilai")
plot_stas
mean(stas)## [1] 6200.346Plot deret waktu di atas menunjukkan bahwa data tidak stasioner dalam rataan, ditandai dengan data yang memiliki pola tren.
Plot ACF
acf(stas)
Berdasarkan plot ACF, terlihat bahwa plot ACF pada data tersebut cenderung tails off slowlysehingga berdasarkan plot ACF data tidak stasioner.
Uji ADF
tseries::adf.test(stas)##
## Augmented Dickey-Fuller Test
##
## data: stas
## Dickey-Fuller = -2.291, Lag order = 5, p-value = 0.4553
## alternative hypothesis: stationary\(H_0\) : Data tidak stasioner dalam rataan
\(H_1\) : Data stasioner dalam rataan
Berdasarkan uji ADF tersebut, didapat p-value sebesar 0.4553 yang lebih besar dari taraf nyata 5% sehingga tak tolak \(H_0\) dan menandakan bahwa data tidak stasioner dalam rataan. Hal ini sesuai dengan hasil eksplorasi menggunakan plot time series dan plot ACF.
Plot Box-Cox
index <- seq(1:143)
bc = boxcox(stas~index, lambda = seq(-2,10,by=0.01))
#Nilai Rounded Lambda
lambda <- bc$x[which.max(bc$y)]
lambda## [1] 3.49#SK
bc$x[bc$y > max(bc$y) - 1/2 * qchisq(.95,1)]## [1] 2.67 2.68 2.69 2.70 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81
## [16] 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96
## [31] 2.97 2.98 2.99 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11
## [46] 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26
## [61] 3.27 3.28 3.29 3.30 3.31 3.32 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.40 3.41
## [76] 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49 3.50 3.51 3.52 3.53 3.54 3.55 3.56
## [91] 3.57 3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71
## [106] 3.72 3.73 3.74 3.75 3.76 3.77 3.78 3.79 3.80 3.81 3.82 3.83 3.84 3.85 3.86
## [121] 3.87 3.88 3.89 3.90 3.91 3.92 3.93 3.94 3.95 3.96 3.97 3.98 3.99 4.00 4.01
## [136] 4.02 4.03 4.04 4.05 4.06 4.07 4.08 4.09 4.10 4.11 4.12 4.13 4.14 4.15 4.16
## [151] 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28 4.29 4.30 4.31
## [166] 4.32Gambar di atas menunjukkan nilai rounded value (\(\lambda\)) optimum sebesar 3,49 dan pada selang kepercayaan 95% nilai memiliki batas bawah 2.67 dan batas atas 4,00. Selang tersebut tidak memuat nilai satu sehingga dapat dikatakan bahwa data tidak stasioner dalam ragam.
Partisi Data
Bagian 1
dt_stas1 <- stas[1:90] |> ts()
mean(dt_stas1)## [1] 5753.671var(dt_stas1)## [1] 402891.1Plot Time Series
dt_stas1 |> as_tsibble() |>
ggplot(aes(x = index, y = value)) +
geom_line() + theme_bw() +
xlab("Obs") + ylab("Nilai")
Plot deret waktu di atas menunjukkan bahwa data tidak stasioner dalam rataan, ditandai dengan data berpola tren naik.
Plot ACF
acf(dt_stas1)
Berdasarkan plot ACF, terlihat bahwa plot ACF pada data tersebut cenderung tails off slowly sehingga berdasarkan plot ACF data tidak stasioner. #### Uji ADF
tseries::adf.test(dt_stas1)##
## Augmented Dickey-Fuller Test
##
## data: dt_stas1
## Dickey-Fuller = -2.3111, Lag order = 4, p-value = 0.4481
## alternative hypothesis: stationary\(H_0\) : Data tidak stasioner dalam rataan
\(H_1\) : Data stasioner dalam rataan
Berdasarkan uji ADF tersebut, didapat p-value sebesar 0.4481 yang lebih besar dari taraf nyata 5% sehingga tak tolak \(H_0\) dan menandakan bahwa data tidak stasioner dalam rataan. Hal ini sesuai dengan hasil eksplorasi menggunakan plot time series dan plot ACF.
Plot Boxcox
index <- seq(1:90)
bc = boxcox(dt_stas1~index, lambda = seq(-4,10,by=1))
#Nilai Rounded Lambda
lambda <- bc$x[which.max(bc$y)]
lambda## [1] 2.787879#SK
bc$x[bc$y > max(bc$y) - 1/2 * qchisq(.95,1)]## [1] 1.373737 1.515152 1.656566 1.797980 1.939394 2.080808 2.222222 2.363636
## [9] 2.505051 2.646465 2.787879 2.929293 3.070707 3.212121 3.353535 3.494949
## [17] 3.636364 3.777778 3.919192 4.060606 4.202020Gambar di atas menunjukkan nilai rounded value (\(\lambda\)) optimum sebesar 2.787879 dan pada selang kepercayaan 95% nilai memiliki batas bawah 1.373737 dan batas atas 4.202020. Selang tersebuttidak memuat nilai satu sehingga dapat dikatakan bahwa data tidak stasioner dalam ragam.
Bagian 2
dt_stas2 <- stas[1:130] |> ts()
mean(dt_stas2)## [1] 6125.238var(dt_stas2)## [1] 603129.4Plot Time Series
dt_stas2 |> as_tsibble() |>
ggplot(aes(x = index, y = value)) +
geom_line() + theme_bw() +
xlab("Obs") + ylab("Nilai")
Plot deret waktu di atas menunjukkan bahwa data tidak stasioner dalam rataan, ditandai dengan data yang berpola tren naik.
Plot ACF
acf(dt_stas2)
Berdasarkan plot ACF, terlihat bahwa plot ACF pada data tersebut cenderung tails off slowly
Uji ADF
adf.test(dt_stas2)##
## Augmented Dickey-Fuller Test
##
## data: dt_stas2
## Dickey-Fuller = -2.8358, Lag order = 5, p-value = 0.229
## alternative hypothesis: stationary\(H_0\) : Data tidak stasioner dalam rataan
\(H_1\) : Data stasioner dalam rataan
Berdasarkan uji ADF tersebut, didapat p-value sebesar 0.229 yang lebih besar dari taraf nyata 5% sehingga tak tolak \(H_0\) dan menandakan bahwa data tidak stasioner dalam rataan. Hal ini sesuai dengan hasil eksplorasi menggunakan plot time series dan plot ACF.
Plot Boxcox
index <- seq(1:130)
bc = boxcox(dt_stas2~index, lambda = seq(-5,12,by=1))
#Nilai Rounded Lambda
lambda <- bc$x[which.max(bc$y)]
lambda## [1] 3.070707#SK
bc$x[bc$y > max(bc$y) - 1/2 * qchisq(.95,1)]## [1] 2.383838 2.555556 2.727273 2.898990 3.070707 3.242424 3.414141 3.585859
## [9] 3.757576Gambar di atas menunjukkan nilai rounded value (\(\lambda\)) optimum sebesar 3.070707 dan pada selang kepercayaan 95% nilai memiliki batas bawah 2.383838 dan batas atas 3.757576. Selang tersebut tidak memuat nilai satu sehingga dapat dikatakan bahwa data tidak stasioner dalam ragam.