G1401221060_Tugas5_P2

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.3.2

library(tsibble)

## Warning: package 'tsibble' was built under R version 4.3.3

## Registered S3 method overwritten by 'tsibble':
##   method               from 
##   as_tibble.grouped_df dplyr

## 
## Attaching package: 'tsibble'

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, union

library(tseries)

## Warning: package 'tseries' was built under R version 4.3.2

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

library(MASS)

Data

data <- read.csv ("C:/Users/Muhammad Rizqa Salas/Downloads/Semester 5/MPDW/Project/Data Air MPDW.csv")

View(data)
str(data)

## 'data.frame':    100 obs. of  2 variables:
##  $ Periode: int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Air    : int  185 194 192 198 210 208 214 220 225 219 ...

dim(data)

## [1] 100   2

Eksplorasi Data

data.ts<-ts(data$Air)
summary(data.ts)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   133.0   161.8   189.0   185.8   210.8   230.0

Plot Time Series

ts.plot(data.ts, xlab="Time Periode ", ylab="Tinggi Air", 
        main = "Time Series Plot")
points(data.ts)

lattice :: densityplot(as.vector(data.ts))

mean(density(data.ts)$x)

## [1] 181.5

Plot deret waktu di atas menunjukkan bahwa data stasioner dalam rataan, ditandai dengan data yang menyebar di sekitar nilai tengahnya (181.5) dan stasioner dalam ragam, ditandai dengan lebar pita yang cenderung sama.

Plot ACF

acf(data.ts)

Berdasarkan plot ACF, terlihat bahwa plot ACF pada data tersebut cenderung tails off dan membentuk gelombang sinus.

Uji ADF

tseries::adf.test(data.ts)

## Warning in tseries::adf.test(data.ts): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  data.ts
## Dickey-Fuller = -5.313, Lag order = 4, p-value = 0.01
## alternative hypothesis: stationary

\(H_0\) : Data tidak stasioner dalam rataan

\(H_1\) : Data stasioner dalam rataan

Berdasarkan uji ADF tersebut, didapat p-value sebesar 0.01 yang lebih kecil dari taraf nyata 5% sehingga tolak \(H_0\) dan menandakan bahwa data stasioner dalam rataan. Hal ini sesuai dengan hasil eksplorasi menggunakan plot time series dan plot ACF.

Plot Box-Cox

indeks <- seq(1:100)
bc = boxcox(data.ts~indeks, lambda = seq (-1, 2, by = 0.001))

#Nilai Rounded Lambda
lambda <- bc$x[which.max(bc$y)]
lambda

## [1] 1.653

#SK
bc$x[bc$y > max(bc$y) - 1/2 * qchisq(.95,1)]

##    [1] 0.317 0.318 0.319 0.320 0.321 0.322 0.323 0.324 0.325 0.326 0.327 0.328
##   [13] 0.329 0.330 0.331 0.332 0.333 0.334 0.335 0.336 0.337 0.338 0.339 0.340
##   [25] 0.341 0.342 0.343 0.344 0.345 0.346 0.347 0.348 0.349 0.350 0.351 0.352
##   [37] 0.353 0.354 0.355 0.356 0.357 0.358 0.359 0.360 0.361 0.362 0.363 0.364
##   [49] 0.365 0.366 0.367 0.368 0.369 0.370 0.371 0.372 0.373 0.374 0.375 0.376
##   [61] 0.377 0.378 0.379 0.380 0.381 0.382 0.383 0.384 0.385 0.386 0.387 0.388
##   [73] 0.389 0.390 0.391 0.392 0.393 0.394 0.395 0.396 0.397 0.398 0.399 0.400
##   [85] 0.401 0.402 0.403 0.404 0.405 0.406 0.407 0.408 0.409 0.410 0.411 0.412
##   [97] 0.413 0.414 0.415 0.416 0.417 0.418 0.419 0.420 0.421 0.422 0.423 0.424
##  [109] 0.425 0.426 0.427 0.428 0.429 0.430 0.431 0.432 0.433 0.434 0.435 0.436
##  [121] 0.437 0.438 0.439 0.440 0.441 0.442 0.443 0.444 0.445 0.446 0.447 0.448
##  [133] 0.449 0.450 0.451 0.452 0.453 0.454 0.455 0.456 0.457 0.458 0.459 0.460
##  [145] 0.461 0.462 0.463 0.464 0.465 0.466 0.467 0.468 0.469 0.470 0.471 0.472
##  [157] 0.473 0.474 0.475 0.476 0.477 0.478 0.479 0.480 0.481 0.482 0.483 0.484
##  [169] 0.485 0.486 0.487 0.488 0.489 0.490 0.491 0.492 0.493 0.494 0.495 0.496
##  [181] 0.497 0.498 0.499 0.500 0.501 0.502 0.503 0.504 0.505 0.506 0.507 0.508
##  [193] 0.509 0.510 0.511 0.512 0.513 0.514 0.515 0.516 0.517 0.518 0.519 0.520
##  [205] 0.521 0.522 0.523 0.524 0.525 0.526 0.527 0.528 0.529 0.530 0.531 0.532
##  [217] 0.533 0.534 0.535 0.536 0.537 0.538 0.539 0.540 0.541 0.542 0.543 0.544
##  [229] 0.545 0.546 0.547 0.548 0.549 0.550 0.551 0.552 0.553 0.554 0.555 0.556
##  [241] 0.557 0.558 0.559 0.560 0.561 0.562 0.563 0.564 0.565 0.566 0.567 0.568
##  [253] 0.569 0.570 0.571 0.572 0.573 0.574 0.575 0.576 0.577 0.578 0.579 0.580
##  [265] 0.581 0.582 0.583 0.584 0.585 0.586 0.587 0.588 0.589 0.590 0.591 0.592
##  [277] 0.593 0.594 0.595 0.596 0.597 0.598 0.599 0.600 0.601 0.602 0.603 0.604
##  [289] 0.605 0.606 0.607 0.608 0.609 0.610 0.611 0.612 0.613 0.614 0.615 0.616
##  [301] 0.617 0.618 0.619 0.620 0.621 0.622 0.623 0.624 0.625 0.626 0.627 0.628
##  [313] 0.629 0.630 0.631 0.632 0.633 0.634 0.635 0.636 0.637 0.638 0.639 0.640
##  [325] 0.641 0.642 0.643 0.644 0.645 0.646 0.647 0.648 0.649 0.650 0.651 0.652
##  [337] 0.653 0.654 0.655 0.656 0.657 0.658 0.659 0.660 0.661 0.662 0.663 0.664
##  [349] 0.665 0.666 0.667 0.668 0.669 0.670 0.671 0.672 0.673 0.674 0.675 0.676
##  [361] 0.677 0.678 0.679 0.680 0.681 0.682 0.683 0.684 0.685 0.686 0.687 0.688
##  [373] 0.689 0.690 0.691 0.692 0.693 0.694 0.695 0.696 0.697 0.698 0.699 0.700
##  [385] 0.701 0.702 0.703 0.704 0.705 0.706 0.707 0.708 0.709 0.710 0.711 0.712
##  [397] 0.713 0.714 0.715 0.716 0.717 0.718 0.719 0.720 0.721 0.722 0.723 0.724
##  [409] 0.725 0.726 0.727 0.728 0.729 0.730 0.731 0.732 0.733 0.734 0.735 0.736
##  [421] 0.737 0.738 0.739 0.740 0.741 0.742 0.743 0.744 0.745 0.746 0.747 0.748
##  [433] 0.749 0.750 0.751 0.752 0.753 0.754 0.755 0.756 0.757 0.758 0.759 0.760
##  [445] 0.761 0.762 0.763 0.764 0.765 0.766 0.767 0.768 0.769 0.770 0.771 0.772
##  [457] 0.773 0.774 0.775 0.776 0.777 0.778 0.779 0.780 0.781 0.782 0.783 0.784
##  [469] 0.785 0.786 0.787 0.788 0.789 0.790 0.791 0.792 0.793 0.794 0.795 0.796
##  [481] 0.797 0.798 0.799 0.800 0.801 0.802 0.803 0.804 0.805 0.806 0.807 0.808
##  [493] 0.809 0.810 0.811 0.812 0.813 0.814 0.815 0.816 0.817 0.818 0.819 0.820
##  [505] 0.821 0.822 0.823 0.824 0.825 0.826 0.827 0.828 0.829 0.830 0.831 0.832
##  [517] 0.833 0.834 0.835 0.836 0.837 0.838 0.839 0.840 0.841 0.842 0.843 0.844
##  [529] 0.845 0.846 0.847 0.848 0.849 0.850 0.851 0.852 0.853 0.854 0.855 0.856
##  [541] 0.857 0.858 0.859 0.860 0.861 0.862 0.863 0.864 0.865 0.866 0.867 0.868
##  [553] 0.869 0.870 0.871 0.872 0.873 0.874 0.875 0.876 0.877 0.878 0.879 0.880
##  [565] 0.881 0.882 0.883 0.884 0.885 0.886 0.887 0.888 0.889 0.890 0.891 0.892
##  [577] 0.893 0.894 0.895 0.896 0.897 0.898 0.899 0.900 0.901 0.902 0.903 0.904
##  [589] 0.905 0.906 0.907 0.908 0.909 0.910 0.911 0.912 0.913 0.914 0.915 0.916
##  [601] 0.917 0.918 0.919 0.920 0.921 0.922 0.923 0.924 0.925 0.926 0.927 0.928
##  [613] 0.929 0.930 0.931 0.932 0.933 0.934 0.935 0.936 0.937 0.938 0.939 0.940
##  [625] 0.941 0.942 0.943 0.944 0.945 0.946 0.947 0.948 0.949 0.950 0.951 0.952
##  [637] 0.953 0.954 0.955 0.956 0.957 0.958 0.959 0.960 0.961 0.962 0.963 0.964
##  [649] 0.965 0.966 0.967 0.968 0.969 0.970 0.971 0.972 0.973 0.974 0.975 0.976
##  [661] 0.977 0.978 0.979 0.980 0.981 0.982 0.983 0.984 0.985 0.986 0.987 0.988
##  [673] 0.989 0.990 0.991 0.992 0.993 0.994 0.995 0.996 0.997 0.998 0.999 1.000
##  [685] 1.001 1.002 1.003 1.004 1.005 1.006 1.007 1.008 1.009 1.010 1.011 1.012
##  [697] 1.013 1.014 1.015 1.016 1.017 1.018 1.019 1.020 1.021 1.022 1.023 1.024
##  [709] 1.025 1.026 1.027 1.028 1.029 1.030 1.031 1.032 1.033 1.034 1.035 1.036
##  [721] 1.037 1.038 1.039 1.040 1.041 1.042 1.043 1.044 1.045 1.046 1.047 1.048
##  [733] 1.049 1.050 1.051 1.052 1.053 1.054 1.055 1.056 1.057 1.058 1.059 1.060
##  [745] 1.061 1.062 1.063 1.064 1.065 1.066 1.067 1.068 1.069 1.070 1.071 1.072
##  [757] 1.073 1.074 1.075 1.076 1.077 1.078 1.079 1.080 1.081 1.082 1.083 1.084
##  [769] 1.085 1.086 1.087 1.088 1.089 1.090 1.091 1.092 1.093 1.094 1.095 1.096
##  [781] 1.097 1.098 1.099 1.100 1.101 1.102 1.103 1.104 1.105 1.106 1.107 1.108
##  [793] 1.109 1.110 1.111 1.112 1.113 1.114 1.115 1.116 1.117 1.118 1.119 1.120
##  [805] 1.121 1.122 1.123 1.124 1.125 1.126 1.127 1.128 1.129 1.130 1.131 1.132
##  [817] 1.133 1.134 1.135 1.136 1.137 1.138 1.139 1.140 1.141 1.142 1.143 1.144
##  [829] 1.145 1.146 1.147 1.148 1.149 1.150 1.151 1.152 1.153 1.154 1.155 1.156
##  [841] 1.157 1.158 1.159 1.160 1.161 1.162 1.163 1.164 1.165 1.166 1.167 1.168
##  [853] 1.169 1.170 1.171 1.172 1.173 1.174 1.175 1.176 1.177 1.178 1.179 1.180
##  [865] 1.181 1.182 1.183 1.184 1.185 1.186 1.187 1.188 1.189 1.190 1.191 1.192
##  [877] 1.193 1.194 1.195 1.196 1.197 1.198 1.199 1.200 1.201 1.202 1.203 1.204
##  [889] 1.205 1.206 1.207 1.208 1.209 1.210 1.211 1.212 1.213 1.214 1.215 1.216
##  [901] 1.217 1.218 1.219 1.220 1.221 1.222 1.223 1.224 1.225 1.226 1.227 1.228
##  [913] 1.229 1.230 1.231 1.232 1.233 1.234 1.235 1.236 1.237 1.238 1.239 1.240
##  [925] 1.241 1.242 1.243 1.244 1.245 1.246 1.247 1.248 1.249 1.250 1.251 1.252
##  [937] 1.253 1.254 1.255 1.256 1.257 1.258 1.259 1.260 1.261 1.262 1.263 1.264
##  [949] 1.265 1.266 1.267 1.268 1.269 1.270 1.271 1.272 1.273 1.274 1.275 1.276
##  [961] 1.277 1.278 1.279 1.280 1.281 1.282 1.283 1.284 1.285 1.286 1.287 1.288
##  [973] 1.289 1.290 1.291 1.292 1.293 1.294 1.295 1.296 1.297 1.298 1.299 1.300
##  [985] 1.301 1.302 1.303 1.304 1.305 1.306 1.307 1.308 1.309 1.310 1.311 1.312
##  [997] 1.313 1.314 1.315 1.316 1.317 1.318 1.319 1.320 1.321 1.322 1.323 1.324
## [1009] 1.325 1.326 1.327 1.328 1.329 1.330 1.331 1.332 1.333 1.334 1.335 1.336
## [1021] 1.337 1.338 1.339 1.340 1.341 1.342 1.343 1.344 1.345 1.346 1.347 1.348
## [1033] 1.349 1.350 1.351 1.352 1.353 1.354 1.355 1.356 1.357 1.358 1.359 1.360
## [1045] 1.361 1.362 1.363 1.364 1.365 1.366 1.367 1.368 1.369 1.370 1.371 1.372
## [1057] 1.373 1.374 1.375 1.376 1.377 1.378 1.379 1.380 1.381 1.382 1.383 1.384
## [1069] 1.385 1.386 1.387 1.388 1.389 1.390 1.391 1.392 1.393 1.394 1.395 1.396
## [1081] 1.397 1.398 1.399 1.400 1.401 1.402 1.403 1.404 1.405 1.406 1.407 1.408
## [1093] 1.409 1.410 1.411 1.412 1.413 1.414 1.415 1.416 1.417 1.418 1.419 1.420
## [1105] 1.421 1.422 1.423 1.424 1.425 1.426 1.427 1.428 1.429 1.430 1.431 1.432
## [1117] 1.433 1.434 1.435 1.436 1.437 1.438 1.439 1.440 1.441 1.442 1.443 1.444
## [1129] 1.445 1.446 1.447 1.448 1.449 1.450 1.451 1.452 1.453 1.454 1.455 1.456
## [1141] 1.457 1.458 1.459 1.460 1.461 1.462 1.463 1.464 1.465 1.466 1.467 1.468
## [1153] 1.469 1.470 1.471 1.472 1.473 1.474 1.475 1.476 1.477 1.478 1.479 1.480
## [1165] 1.481 1.482 1.483 1.484 1.485 1.486 1.487 1.488 1.489 1.490 1.491 1.492
## [1177] 1.493 1.494 1.495 1.496 1.497 1.498 1.499 1.500 1.501 1.502 1.503 1.504
## [1189] 1.505 1.506 1.507 1.508 1.509 1.510 1.511 1.512 1.513 1.514 1.515 1.516
## [1201] 1.517 1.518 1.519 1.520 1.521 1.522 1.523 1.524 1.525 1.526 1.527 1.528
## [1213] 1.529 1.530 1.531 1.532 1.533 1.534 1.535 1.536 1.537 1.538 1.539 1.540
## [1225] 1.541 1.542 1.543 1.544 1.545 1.546 1.547 1.548 1.549 1.550 1.551 1.552
## [1237] 1.553 1.554 1.555 1.556 1.557 1.558 1.559 1.560 1.561 1.562 1.563 1.564
## [1249] 1.565 1.566 1.567 1.568 1.569 1.570 1.571 1.572 1.573 1.574 1.575 1.576
## [1261] 1.577 1.578 1.579 1.580 1.581 1.582 1.583 1.584 1.585 1.586 1.587 1.588
## [1273] 1.589 1.590 1.591 1.592 1.593 1.594 1.595 1.596 1.597 1.598 1.599 1.600
## [1285] 1.601 1.602 1.603 1.604 1.605 1.606 1.607 1.608 1.609 1.610 1.611 1.612
## [1297] 1.613 1.614 1.615 1.616 1.617 1.618 1.619 1.620 1.621 1.622 1.623 1.624
## [1309] 1.625 1.626 1.627 1.628 1.629 1.630 1.631 1.632 1.633 1.634 1.635 1.636
## [1321] 1.637 1.638 1.639 1.640 1.641 1.642 1.643 1.644 1.645 1.646 1.647 1.648
## [1333] 1.649 1.650 1.651 1.652 1.653 1.654 1.655 1.656 1.657 1.658 1.659 1.660
## [1345] 1.661 1.662 1.663 1.664 1.665 1.666 1.667 1.668 1.669 1.670 1.671 1.672
## [1357] 1.673 1.674 1.675 1.676 1.677 1.678 1.679 1.680 1.681 1.682 1.683 1.684
## [1369] 1.685 1.686 1.687 1.688 1.689 1.690 1.691 1.692 1.693 1.694 1.695 1.696
## [1381] 1.697 1.698 1.699 1.700 1.701 1.702 1.703 1.704 1.705 1.706 1.707 1.708
## [1393] 1.709 1.710 1.711 1.712 1.713 1.714 1.715 1.716 1.717 1.718 1.719 1.720
## [1405] 1.721 1.722 1.723 1.724 1.725 1.726 1.727 1.728 1.729 1.730 1.731 1.732
## [1417] 1.733 1.734 1.735 1.736 1.737 1.738 1.739 1.740 1.741 1.742 1.743 1.744
## [1429] 1.745 1.746 1.747 1.748 1.749 1.750 1.751 1.752 1.753 1.754 1.755 1.756
## [1441] 1.757 1.758 1.759 1.760 1.761 1.762 1.763 1.764 1.765 1.766 1.767 1.768
## [1453] 1.769 1.770 1.771 1.772 1.773 1.774 1.775 1.776 1.777 1.778 1.779 1.780
## [1465] 1.781 1.782 1.783 1.784 1.785 1.786 1.787 1.788 1.789 1.790 1.791 1.792
## [1477] 1.793 1.794 1.795 1.796 1.797 1.798 1.799 1.800 1.801 1.802 1.803 1.804
## [1489] 1.805 1.806 1.807 1.808 1.809 1.810 1.811 1.812 1.813 1.814 1.815 1.816
## [1501] 1.817 1.818 1.819 1.820 1.821 1.822 1.823 1.824 1.825 1.826 1.827 1.828
## [1513] 1.829 1.830 1.831 1.832 1.833 1.834 1.835 1.836 1.837 1.838 1.839 1.840
## [1525] 1.841 1.842 1.843 1.844 1.845 1.846 1.847 1.848 1.849 1.850 1.851 1.852
## [1537] 1.853 1.854 1.855 1.856 1.857 1.858 1.859 1.860 1.861 1.862 1.863 1.864
## [1549] 1.865 1.866 1.867 1.868 1.869 1.870 1.871 1.872 1.873 1.874 1.875 1.876
## [1561] 1.877 1.878 1.879 1.880 1.881 1.882 1.883 1.884 1.885 1.886 1.887 1.888
## [1573] 1.889 1.890 1.891 1.892 1.893 1.894 1.895 1.896 1.897 1.898 1.899 1.900
## [1585] 1.901 1.902 1.903 1.904 1.905 1.906 1.907 1.908 1.909 1.910 1.911 1.912
## [1597] 1.913 1.914 1.915 1.916 1.917 1.918 1.919 1.920 1.921 1.922 1.923 1.924
## [1609] 1.925 1.926 1.927 1.928 1.929 1.930 1.931 1.932 1.933 1.934 1.935 1.936
## [1621] 1.937 1.938 1.939 1.940 1.941 1.942 1.943 1.944 1.945 1.946 1.947 1.948
## [1633] 1.949 1.950 1.951 1.952 1.953 1.954 1.955 1.956 1.957 1.958 1.959 1.960
## [1645] 1.961 1.962 1.963 1.964 1.965 1.966 1.967 1.968 1.969 1.970 1.971 1.972
## [1657] 1.973 1.974 1.975 1.976 1.977 1.978 1.979 1.980 1.981 1.982 1.983 1.984
## [1669] 1.985 1.986 1.987 1.988 1.989 1.990 1.991 1.992 1.993 1.994 1.995 1.996
## [1681] 1.997 1.998 1.999 2.000

Gambar di atas menunjukkan nilai rounded value (\(\lambda\)) optimum sebesar 1.653 dan pada selang kepercayaan 95% nilai memiliki batas bawah 0,317 dan batas atas 1,316. Selang tersebut memuat nilai satu sehingga dapat dikatakan bahwa data bangkitan stasioner dalam ragam.

Summary Eksplorasi

pada data keseluruhan 100 periode dapat di identifikasi stasionernya dengan melakukan uji ACF dengan hasil Tail off lalu dilakukan uji stasioner bagi rataan Menggunakan uji ADF.hasil p-value 0.01 yang lebih kecil dari taraf nyata 5% sehingga tolak \(H_0\) dan menandakan bahwa data stasioner dalam rataan. lalu dilakukan uji stasioner bagi ragam Menggunakan Box-Cox dengan hasil lambda 1.653 dan pada selang kepercayaan 95% nilai memiliki batas bawah 0,317 dan batas atas 1,316.

Partisi Data

Bagian 1

data_training <- data[1:80,]
data_training.ts <- ts(data_training$Air)

mean(data_training.ts)

## [1] 187.6625

var(data_training.ts)

## [1] 841.8973

Plot Time Series

ts.plot(data_training.ts, xlab="Time Periode ", ylab="Air", 
        main = "Time Series Plot")

Plot ACF

acf(data_training.ts)

Berdasarkan plot ACF, terlihat bahwa plot ACF pada data tersebut cenderung tails off dan membentuk gelombang sinus.

Uji ADF

tseries::adf.test(data_training.ts)

## 
##  Augmented Dickey-Fuller Test
## 
## data:  data_training.ts
## Dickey-Fuller = -4.0619, Lag order = 4, p-value = 0.01112
## alternative hypothesis: stationary

\(H_0\) : Data tidak stasioner dalam rataan

\(H_1\) : Data stasioner dalam rataan

Berdasarkan uji ADF tersebut, didapat p-value sebesar \(0.01112\) yang lebih kecil dari taraf nyata 5% sehingga tolak \(H_0\) dan menandakan bahwa data stasioner dalam rataan. Hal ini sesuai dengan hasil eksplorasi menggunakan plot time series dan plot ACF.

Plot Boxcox

index_2 <- seq(1:80)
bc = boxcox(data_training.ts~index_2, lambda = seq(-1,2,by=0.001))

#Nilai Rounded Lambda
lambda <- bc$x[which.max(bc$y)]
lambda

## [1] 2

#SK
bc$x[bc$y > max(bc$y) - 1/2 * qchisq(.95,1)]

##    [1] 0.489 0.490 0.491 0.492 0.493 0.494 0.495 0.496 0.497 0.498 0.499 0.500
##   [13] 0.501 0.502 0.503 0.504 0.505 0.506 0.507 0.508 0.509 0.510 0.511 0.512
##   [25] 0.513 0.514 0.515 0.516 0.517 0.518 0.519 0.520 0.521 0.522 0.523 0.524
##   [37] 0.525 0.526 0.527 0.528 0.529 0.530 0.531 0.532 0.533 0.534 0.535 0.536
##   [49] 0.537 0.538 0.539 0.540 0.541 0.542 0.543 0.544 0.545 0.546 0.547 0.548
##   [61] 0.549 0.550 0.551 0.552 0.553 0.554 0.555 0.556 0.557 0.558 0.559 0.560
##   [73] 0.561 0.562 0.563 0.564 0.565 0.566 0.567 0.568 0.569 0.570 0.571 0.572
##   [85] 0.573 0.574 0.575 0.576 0.577 0.578 0.579 0.580 0.581 0.582 0.583 0.584
##   [97] 0.585 0.586 0.587 0.588 0.589 0.590 0.591 0.592 0.593 0.594 0.595 0.596
##  [109] 0.597 0.598 0.599 0.600 0.601 0.602 0.603 0.604 0.605 0.606 0.607 0.608
##  [121] 0.609 0.610 0.611 0.612 0.613 0.614 0.615 0.616 0.617 0.618 0.619 0.620
##  [133] 0.621 0.622 0.623 0.624 0.625 0.626 0.627 0.628 0.629 0.630 0.631 0.632
##  [145] 0.633 0.634 0.635 0.636 0.637 0.638 0.639 0.640 0.641 0.642 0.643 0.644
##  [157] 0.645 0.646 0.647 0.648 0.649 0.650 0.651 0.652 0.653 0.654 0.655 0.656
##  [169] 0.657 0.658 0.659 0.660 0.661 0.662 0.663 0.664 0.665 0.666 0.667 0.668
##  [181] 0.669 0.670 0.671 0.672 0.673 0.674 0.675 0.676 0.677 0.678 0.679 0.680
##  [193] 0.681 0.682 0.683 0.684 0.685 0.686 0.687 0.688 0.689 0.690 0.691 0.692
##  [205] 0.693 0.694 0.695 0.696 0.697 0.698 0.699 0.700 0.701 0.702 0.703 0.704
##  [217] 0.705 0.706 0.707 0.708 0.709 0.710 0.711 0.712 0.713 0.714 0.715 0.716
##  [229] 0.717 0.718 0.719 0.720 0.721 0.722 0.723 0.724 0.725 0.726 0.727 0.728
##  [241] 0.729 0.730 0.731 0.732 0.733 0.734 0.735 0.736 0.737 0.738 0.739 0.740
##  [253] 0.741 0.742 0.743 0.744 0.745 0.746 0.747 0.748 0.749 0.750 0.751 0.752
##  [265] 0.753 0.754 0.755 0.756 0.757 0.758 0.759 0.760 0.761 0.762 0.763 0.764
##  [277] 0.765 0.766 0.767 0.768 0.769 0.770 0.771 0.772 0.773 0.774 0.775 0.776
##  [289] 0.777 0.778 0.779 0.780 0.781 0.782 0.783 0.784 0.785 0.786 0.787 0.788
##  [301] 0.789 0.790 0.791 0.792 0.793 0.794 0.795 0.796 0.797 0.798 0.799 0.800
##  [313] 0.801 0.802 0.803 0.804 0.805 0.806 0.807 0.808 0.809 0.810 0.811 0.812
##  [325] 0.813 0.814 0.815 0.816 0.817 0.818 0.819 0.820 0.821 0.822 0.823 0.824
##  [337] 0.825 0.826 0.827 0.828 0.829 0.830 0.831 0.832 0.833 0.834 0.835 0.836
##  [349] 0.837 0.838 0.839 0.840 0.841 0.842 0.843 0.844 0.845 0.846 0.847 0.848
##  [361] 0.849 0.850 0.851 0.852 0.853 0.854 0.855 0.856 0.857 0.858 0.859 0.860
##  [373] 0.861 0.862 0.863 0.864 0.865 0.866 0.867 0.868 0.869 0.870 0.871 0.872
##  [385] 0.873 0.874 0.875 0.876 0.877 0.878 0.879 0.880 0.881 0.882 0.883 0.884
##  [397] 0.885 0.886 0.887 0.888 0.889 0.890 0.891 0.892 0.893 0.894 0.895 0.896
##  [409] 0.897 0.898 0.899 0.900 0.901 0.902 0.903 0.904 0.905 0.906 0.907 0.908
##  [421] 0.909 0.910 0.911 0.912 0.913 0.914 0.915 0.916 0.917 0.918 0.919 0.920
##  [433] 0.921 0.922 0.923 0.924 0.925 0.926 0.927 0.928 0.929 0.930 0.931 0.932
##  [445] 0.933 0.934 0.935 0.936 0.937 0.938 0.939 0.940 0.941 0.942 0.943 0.944
##  [457] 0.945 0.946 0.947 0.948 0.949 0.950 0.951 0.952 0.953 0.954 0.955 0.956
##  [469] 0.957 0.958 0.959 0.960 0.961 0.962 0.963 0.964 0.965 0.966 0.967 0.968
##  [481] 0.969 0.970 0.971 0.972 0.973 0.974 0.975 0.976 0.977 0.978 0.979 0.980
##  [493] 0.981 0.982 0.983 0.984 0.985 0.986 0.987 0.988 0.989 0.990 0.991 0.992
##  [505] 0.993 0.994 0.995 0.996 0.997 0.998 0.999 1.000 1.001 1.002 1.003 1.004
##  [517] 1.005 1.006 1.007 1.008 1.009 1.010 1.011 1.012 1.013 1.014 1.015 1.016
##  [529] 1.017 1.018 1.019 1.020 1.021 1.022 1.023 1.024 1.025 1.026 1.027 1.028
##  [541] 1.029 1.030 1.031 1.032 1.033 1.034 1.035 1.036 1.037 1.038 1.039 1.040
##  [553] 1.041 1.042 1.043 1.044 1.045 1.046 1.047 1.048 1.049 1.050 1.051 1.052
##  [565] 1.053 1.054 1.055 1.056 1.057 1.058 1.059 1.060 1.061 1.062 1.063 1.064
##  [577] 1.065 1.066 1.067 1.068 1.069 1.070 1.071 1.072 1.073 1.074 1.075 1.076
##  [589] 1.077 1.078 1.079 1.080 1.081 1.082 1.083 1.084 1.085 1.086 1.087 1.088
##  [601] 1.089 1.090 1.091 1.092 1.093 1.094 1.095 1.096 1.097 1.098 1.099 1.100
##  [613] 1.101 1.102 1.103 1.104 1.105 1.106 1.107 1.108 1.109 1.110 1.111 1.112
##  [625] 1.113 1.114 1.115 1.116 1.117 1.118 1.119 1.120 1.121 1.122 1.123 1.124
##  [637] 1.125 1.126 1.127 1.128 1.129 1.130 1.131 1.132 1.133 1.134 1.135 1.136
##  [649] 1.137 1.138 1.139 1.140 1.141 1.142 1.143 1.144 1.145 1.146 1.147 1.148
##  [661] 1.149 1.150 1.151 1.152 1.153 1.154 1.155 1.156 1.157 1.158 1.159 1.160
##  [673] 1.161 1.162 1.163 1.164 1.165 1.166 1.167 1.168 1.169 1.170 1.171 1.172
##  [685] 1.173 1.174 1.175 1.176 1.177 1.178 1.179 1.180 1.181 1.182 1.183 1.184
##  [697] 1.185 1.186 1.187 1.188 1.189 1.190 1.191 1.192 1.193 1.194 1.195 1.196
##  [709] 1.197 1.198 1.199 1.200 1.201 1.202 1.203 1.204 1.205 1.206 1.207 1.208
##  [721] 1.209 1.210 1.211 1.212 1.213 1.214 1.215 1.216 1.217 1.218 1.219 1.220
##  [733] 1.221 1.222 1.223 1.224 1.225 1.226 1.227 1.228 1.229 1.230 1.231 1.232
##  [745] 1.233 1.234 1.235 1.236 1.237 1.238 1.239 1.240 1.241 1.242 1.243 1.244
##  [757] 1.245 1.246 1.247 1.248 1.249 1.250 1.251 1.252 1.253 1.254 1.255 1.256
##  [769] 1.257 1.258 1.259 1.260 1.261 1.262 1.263 1.264 1.265 1.266 1.267 1.268
##  [781] 1.269 1.270 1.271 1.272 1.273 1.274 1.275 1.276 1.277 1.278 1.279 1.280
##  [793] 1.281 1.282 1.283 1.284 1.285 1.286 1.287 1.288 1.289 1.290 1.291 1.292
##  [805] 1.293 1.294 1.295 1.296 1.297 1.298 1.299 1.300 1.301 1.302 1.303 1.304
##  [817] 1.305 1.306 1.307 1.308 1.309 1.310 1.311 1.312 1.313 1.314 1.315 1.316
##  [829] 1.317 1.318 1.319 1.320 1.321 1.322 1.323 1.324 1.325 1.326 1.327 1.328
##  [841] 1.329 1.330 1.331 1.332 1.333 1.334 1.335 1.336 1.337 1.338 1.339 1.340
##  [853] 1.341 1.342 1.343 1.344 1.345 1.346 1.347 1.348 1.349 1.350 1.351 1.352
##  [865] 1.353 1.354 1.355 1.356 1.357 1.358 1.359 1.360 1.361 1.362 1.363 1.364
##  [877] 1.365 1.366 1.367 1.368 1.369 1.370 1.371 1.372 1.373 1.374 1.375 1.376
##  [889] 1.377 1.378 1.379 1.380 1.381 1.382 1.383 1.384 1.385 1.386 1.387 1.388
##  [901] 1.389 1.390 1.391 1.392 1.393 1.394 1.395 1.396 1.397 1.398 1.399 1.400
##  [913] 1.401 1.402 1.403 1.404 1.405 1.406 1.407 1.408 1.409 1.410 1.411 1.412
##  [925] 1.413 1.414 1.415 1.416 1.417 1.418 1.419 1.420 1.421 1.422 1.423 1.424
##  [937] 1.425 1.426 1.427 1.428 1.429 1.430 1.431 1.432 1.433 1.434 1.435 1.436
##  [949] 1.437 1.438 1.439 1.440 1.441 1.442 1.443 1.444 1.445 1.446 1.447 1.448
##  [961] 1.449 1.450 1.451 1.452 1.453 1.454 1.455 1.456 1.457 1.458 1.459 1.460
##  [973] 1.461 1.462 1.463 1.464 1.465 1.466 1.467 1.468 1.469 1.470 1.471 1.472
##  [985] 1.473 1.474 1.475 1.476 1.477 1.478 1.479 1.480 1.481 1.482 1.483 1.484
##  [997] 1.485 1.486 1.487 1.488 1.489 1.490 1.491 1.492 1.493 1.494 1.495 1.496
## [1009] 1.497 1.498 1.499 1.500 1.501 1.502 1.503 1.504 1.505 1.506 1.507 1.508
## [1021] 1.509 1.510 1.511 1.512 1.513 1.514 1.515 1.516 1.517 1.518 1.519 1.520
## [1033] 1.521 1.522 1.523 1.524 1.525 1.526 1.527 1.528 1.529 1.530 1.531 1.532
## [1045] 1.533 1.534 1.535 1.536 1.537 1.538 1.539 1.540 1.541 1.542 1.543 1.544
## [1057] 1.545 1.546 1.547 1.548 1.549 1.550 1.551 1.552 1.553 1.554 1.555 1.556
## [1069] 1.557 1.558 1.559 1.560 1.561 1.562 1.563 1.564 1.565 1.566 1.567 1.568
## [1081] 1.569 1.570 1.571 1.572 1.573 1.574 1.575 1.576 1.577 1.578 1.579 1.580
## [1093] 1.581 1.582 1.583 1.584 1.585 1.586 1.587 1.588 1.589 1.590 1.591 1.592
## [1105] 1.593 1.594 1.595 1.596 1.597 1.598 1.599 1.600 1.601 1.602 1.603 1.604
## [1117] 1.605 1.606 1.607 1.608 1.609 1.610 1.611 1.612 1.613 1.614 1.615 1.616
## [1129] 1.617 1.618 1.619 1.620 1.621 1.622 1.623 1.624 1.625 1.626 1.627 1.628
## [1141] 1.629 1.630 1.631 1.632 1.633 1.634 1.635 1.636 1.637 1.638 1.639 1.640
## [1153] 1.641 1.642 1.643 1.644 1.645 1.646 1.647 1.648 1.649 1.650 1.651 1.652
## [1165] 1.653 1.654 1.655 1.656 1.657 1.658 1.659 1.660 1.661 1.662 1.663 1.664
## [1177] 1.665 1.666 1.667 1.668 1.669 1.670 1.671 1.672 1.673 1.674 1.675 1.676
## [1189] 1.677 1.678 1.679 1.680 1.681 1.682 1.683 1.684 1.685 1.686 1.687 1.688
## [1201] 1.689 1.690 1.691 1.692 1.693 1.694 1.695 1.696 1.697 1.698 1.699 1.700
## [1213] 1.701 1.702 1.703 1.704 1.705 1.706 1.707 1.708 1.709 1.710 1.711 1.712
## [1225] 1.713 1.714 1.715 1.716 1.717 1.718 1.719 1.720 1.721 1.722 1.723 1.724
## [1237] 1.725 1.726 1.727 1.728 1.729 1.730 1.731 1.732 1.733 1.734 1.735 1.736
## [1249] 1.737 1.738 1.739 1.740 1.741 1.742 1.743 1.744 1.745 1.746 1.747 1.748
## [1261] 1.749 1.750 1.751 1.752 1.753 1.754 1.755 1.756 1.757 1.758 1.759 1.760
## [1273] 1.761 1.762 1.763 1.764 1.765 1.766 1.767 1.768 1.769 1.770 1.771 1.772
## [1285] 1.773 1.774 1.775 1.776 1.777 1.778 1.779 1.780 1.781 1.782 1.783 1.784
## [1297] 1.785 1.786 1.787 1.788 1.789 1.790 1.791 1.792 1.793 1.794 1.795 1.796
## [1309] 1.797 1.798 1.799 1.800 1.801 1.802 1.803 1.804 1.805 1.806 1.807 1.808
## [1321] 1.809 1.810 1.811 1.812 1.813 1.814 1.815 1.816 1.817 1.818 1.819 1.820
## [1333] 1.821 1.822 1.823 1.824 1.825 1.826 1.827 1.828 1.829 1.830 1.831 1.832
## [1345] 1.833 1.834 1.835 1.836 1.837 1.838 1.839 1.840 1.841 1.842 1.843 1.844
## [1357] 1.845 1.846 1.847 1.848 1.849 1.850 1.851 1.852 1.853 1.854 1.855 1.856
## [1369] 1.857 1.858 1.859 1.860 1.861 1.862 1.863 1.864 1.865 1.866 1.867 1.868
## [1381] 1.869 1.870 1.871 1.872 1.873 1.874 1.875 1.876 1.877 1.878 1.879 1.880
## [1393] 1.881 1.882 1.883 1.884 1.885 1.886 1.887 1.888 1.889 1.890 1.891 1.892
## [1405] 1.893 1.894 1.895 1.896 1.897 1.898 1.899 1.900 1.901 1.902 1.903 1.904
## [1417] 1.905 1.906 1.907 1.908 1.909 1.910 1.911 1.912 1.913 1.914 1.915 1.916
## [1429] 1.917 1.918 1.919 1.920 1.921 1.922 1.923 1.924 1.925 1.926 1.927 1.928
## [1441] 1.929 1.930 1.931 1.932 1.933 1.934 1.935 1.936 1.937 1.938 1.939 1.940
## [1453] 1.941 1.942 1.943 1.944 1.945 1.946 1.947 1.948 1.949 1.950 1.951 1.952
## [1465] 1.953 1.954 1.955 1.956 1.957 1.958 1.959 1.960 1.961 1.962 1.963 1.964
## [1477] 1.965 1.966 1.967 1.968 1.969 1.970 1.971 1.972 1.973 1.974 1.975 1.976
## [1489] 1.977 1.978 1.979 1.980 1.981 1.982 1.983 1.984 1.985 1.986 1.987 1.988
## [1501] 1.989 1.990 1.991 1.992 1.993 1.994 1.995 1.996 1.997 1.998 1.999 2.000

Gambar di atas menunjukkan nilai rounded value (\(\lambda\)) optimum sebesar 2 dan pada selang kepercayaan 95% nilai memiliki batas bawah 0.489 dan batas atas 1,488. Selang tersebut memuat nilai satu sehingga dapat dikatakan bahwa data bangkitan stasioner dalam ragam.

Summary Data Training

Pada data ini terdapat 80 periode, dapat di identifikasi stasionernya dengan melakukan uji ACF dengan hasil Tails off lalu dilakukan uji stasioner bagi rataan Menggunakan uji ADF. Hasil p-value \(0,01112\) yang lebih kecil dari taraf nyata 5% sehingga tolak \(H_0\) dan menandakan bahwa data stasioner dalam rataan. Lalu dilakukan uji stasioner bagi ragam Menggunakan Box-Cox dengan hasil lambda \(2\) dan pada selang kepercayaan 95% nilai memiliki batas bawah \(0,489\) dan batas atas \(1,488\).

Dari seluruh uji dapat di identifikasi bahwa data training 80 periode termasuk dalam model dan rataan yang stasioner.

Bagian 2

data_testing <- data[81:100,]
data_testing.ts <- ts(data_testing$Air)

mean(data_testing.ts)

## [1] 178.6

var(data_testing.ts)

## [1] 886.4632

Plot Time Series

ts.plot(data_testing.ts, xlab="Time Periode ", ylab="Air", 
        main = "Time Series Plot")

Plot ACF

acf(data_testing.ts)

Berdasarkan plot ACF, terlihat bahwa plot ACF pada data tersebut cenderung tails off dan membentuk gelombang sinus.

Uji ADF

adf.test(data_testing.ts)

## 
##  Augmented Dickey-Fuller Test
## 
## data:  data_testing.ts
## Dickey-Fuller = -1.4264, Lag order = 2, p-value = 0.7909
## alternative hypothesis: stationary

\(H_0\) : Data tidak stasioner dalam rataan

\(H_1\) : Data stasioner dalam rataan

Berdasarkan uji ADF tersebut, didapat p-value sebesar \(0.7909\) yang lebih besar dari taraf nyata 5% sehingga tak tolak \(H_0\) dan menandakan bahwa data tidak stasioner dalam rataan.

Plot Boxcox

index_3 <- seq(81:100)
bc = boxcox(data_testing.ts~index_3, lambda = seq(-1,2,by=0.001))

#Nilai Rounded Lambda
lambda <- bc$x[which.max(bc$y)]
lambda

## [1] 1.51

#SK
bc$x[bc$y > max(bc$y) - 1/2 * qchisq(.95,1)]

##    [1] -1.000 -0.999 -0.998 -0.997 -0.996 -0.995 -0.994 -0.993 -0.992 -0.991
##   [11] -0.990 -0.989 -0.988 -0.987 -0.986 -0.985 -0.984 -0.983 -0.982 -0.981
##   [21] -0.980 -0.979 -0.978 -0.977 -0.976 -0.975 -0.974 -0.973 -0.972 -0.971
##   [31] -0.970 -0.969 -0.968 -0.967 -0.966 -0.965 -0.964 -0.963 -0.962 -0.961
##   [41] -0.960 -0.959 -0.958 -0.957 -0.956 -0.955 -0.954 -0.953 -0.952 -0.951
##   [51] -0.950 -0.949 -0.948 -0.947 -0.946 -0.945 -0.944 -0.943 -0.942 -0.941
##   [61] -0.940 -0.939 -0.938 -0.937 -0.936 -0.935 -0.934 -0.933 -0.932 -0.931
##   [71] -0.930 -0.929 -0.928 -0.927 -0.926 -0.925 -0.924 -0.923 -0.922 -0.921
##   [81] -0.920 -0.919 -0.918 -0.917 -0.916 -0.915 -0.914 -0.913 -0.912 -0.911
##   [91] -0.910 -0.909 -0.908 -0.907 -0.906 -0.905 -0.904 -0.903 -0.902 -0.901
##  [101] -0.900 -0.899 -0.898 -0.897 -0.896 -0.895 -0.894 -0.893 -0.892 -0.891
##  [111] -0.890 -0.889 -0.888 -0.887 -0.886 -0.885 -0.884 -0.883 -0.882 -0.881
##  [121] -0.880 -0.879 -0.878 -0.877 -0.876 -0.875 -0.874 -0.873 -0.872 -0.871
##  [131] -0.870 -0.869 -0.868 -0.867 -0.866 -0.865 -0.864 -0.863 -0.862 -0.861
##  [141] -0.860 -0.859 -0.858 -0.857 -0.856 -0.855 -0.854 -0.853 -0.852 -0.851
##  [151] -0.850 -0.849 -0.848 -0.847 -0.846 -0.845 -0.844 -0.843 -0.842 -0.841
##  [161] -0.840 -0.839 -0.838 -0.837 -0.836 -0.835 -0.834 -0.833 -0.832 -0.831
##  [171] -0.830 -0.829 -0.828 -0.827 -0.826 -0.825 -0.824 -0.823 -0.822 -0.821
##  [181] -0.820 -0.819 -0.818 -0.817 -0.816 -0.815 -0.814 -0.813 -0.812 -0.811
##  [191] -0.810 -0.809 -0.808 -0.807 -0.806 -0.805 -0.804 -0.803 -0.802 -0.801
##  [201] -0.800 -0.799 -0.798 -0.797 -0.796 -0.795 -0.794 -0.793 -0.792 -0.791
##  [211] -0.790 -0.789 -0.788 -0.787 -0.786 -0.785 -0.784 -0.783 -0.782 -0.781
##  [221] -0.780 -0.779 -0.778 -0.777 -0.776 -0.775 -0.774 -0.773 -0.772 -0.771
##  [231] -0.770 -0.769 -0.768 -0.767 -0.766 -0.765 -0.764 -0.763 -0.762 -0.761
##  [241] -0.760 -0.759 -0.758 -0.757 -0.756 -0.755 -0.754 -0.753 -0.752 -0.751
##  [251] -0.750 -0.749 -0.748 -0.747 -0.746 -0.745 -0.744 -0.743 -0.742 -0.741
##  [261] -0.740 -0.739 -0.738 -0.737 -0.736 -0.735 -0.734 -0.733 -0.732 -0.731
##  [271] -0.730 -0.729 -0.728 -0.727 -0.726 -0.725 -0.724 -0.723 -0.722 -0.721
##  [281] -0.720 -0.719 -0.718 -0.717 -0.716 -0.715 -0.714 -0.713 -0.712 -0.711
##  [291] -0.710 -0.709 -0.708 -0.707 -0.706 -0.705 -0.704 -0.703 -0.702 -0.701
##  [301] -0.700 -0.699 -0.698 -0.697 -0.696 -0.695 -0.694 -0.693 -0.692 -0.691
##  [311] -0.690 -0.689 -0.688 -0.687 -0.686 -0.685 -0.684 -0.683 -0.682 -0.681
##  [321] -0.680 -0.679 -0.678 -0.677 -0.676 -0.675 -0.674 -0.673 -0.672 -0.671
##  [331] -0.670 -0.669 -0.668 -0.667 -0.666 -0.665 -0.664 -0.663 -0.662 -0.661
##  [341] -0.660 -0.659 -0.658 -0.657 -0.656 -0.655 -0.654 -0.653 -0.652 -0.651
##  [351] -0.650 -0.649 -0.648 -0.647 -0.646 -0.645 -0.644 -0.643 -0.642 -0.641
##  [361] -0.640 -0.639 -0.638 -0.637 -0.636 -0.635 -0.634 -0.633 -0.632 -0.631
##  [371] -0.630 -0.629 -0.628 -0.627 -0.626 -0.625 -0.624 -0.623 -0.622 -0.621
##  [381] -0.620 -0.619 -0.618 -0.617 -0.616 -0.615 -0.614 -0.613 -0.612 -0.611
##  [391] -0.610 -0.609 -0.608 -0.607 -0.606 -0.605 -0.604 -0.603 -0.602 -0.601
##  [401] -0.600 -0.599 -0.598 -0.597 -0.596 -0.595 -0.594 -0.593 -0.592 -0.591
##  [411] -0.590 -0.589 -0.588 -0.587 -0.586 -0.585 -0.584 -0.583 -0.582 -0.581
##  [421] -0.580 -0.579 -0.578 -0.577 -0.576 -0.575 -0.574 -0.573 -0.572 -0.571
##  [431] -0.570 -0.569 -0.568 -0.567 -0.566 -0.565 -0.564 -0.563 -0.562 -0.561
##  [441] -0.560 -0.559 -0.558 -0.557 -0.556 -0.555 -0.554 -0.553 -0.552 -0.551
##  [451] -0.550 -0.549 -0.548 -0.547 -0.546 -0.545 -0.544 -0.543 -0.542 -0.541
##  [461] -0.540 -0.539 -0.538 -0.537 -0.536 -0.535 -0.534 -0.533 -0.532 -0.531
##  [471] -0.530 -0.529 -0.528 -0.527 -0.526 -0.525 -0.524 -0.523 -0.522 -0.521
##  [481] -0.520 -0.519 -0.518 -0.517 -0.516 -0.515 -0.514 -0.513 -0.512 -0.511
##  [491] -0.510 -0.509 -0.508 -0.507 -0.506 -0.505 -0.504 -0.503 -0.502 -0.501
##  [501] -0.500 -0.499 -0.498 -0.497 -0.496 -0.495 -0.494 -0.493 -0.492 -0.491
##  [511] -0.490 -0.489 -0.488 -0.487 -0.486 -0.485 -0.484 -0.483 -0.482 -0.481
##  [521] -0.480 -0.479 -0.478 -0.477 -0.476 -0.475 -0.474 -0.473 -0.472 -0.471
##  [531] -0.470 -0.469 -0.468 -0.467 -0.466 -0.465 -0.464 -0.463 -0.462 -0.461
##  [541] -0.460 -0.459 -0.458 -0.457 -0.456 -0.455 -0.454 -0.453 -0.452 -0.451
##  [551] -0.450 -0.449 -0.448 -0.447 -0.446 -0.445 -0.444 -0.443 -0.442 -0.441
##  [561] -0.440 -0.439 -0.438 -0.437 -0.436 -0.435 -0.434 -0.433 -0.432 -0.431
##  [571] -0.430 -0.429 -0.428 -0.427 -0.426 -0.425 -0.424 -0.423 -0.422 -0.421
##  [581] -0.420 -0.419 -0.418 -0.417 -0.416 -0.415 -0.414 -0.413 -0.412 -0.411
##  [591] -0.410 -0.409 -0.408 -0.407 -0.406 -0.405 -0.404 -0.403 -0.402 -0.401
##  [601] -0.400 -0.399 -0.398 -0.397 -0.396 -0.395 -0.394 -0.393 -0.392 -0.391
##  [611] -0.390 -0.389 -0.388 -0.387 -0.386 -0.385 -0.384 -0.383 -0.382 -0.381
##  [621] -0.380 -0.379 -0.378 -0.377 -0.376 -0.375 -0.374 -0.373 -0.372 -0.371
##  [631] -0.370 -0.369 -0.368 -0.367 -0.366 -0.365 -0.364 -0.363 -0.362 -0.361
##  [641] -0.360 -0.359 -0.358 -0.357 -0.356 -0.355 -0.354 -0.353 -0.352 -0.351
##  [651] -0.350 -0.349 -0.348 -0.347 -0.346 -0.345 -0.344 -0.343 -0.342 -0.341
##  [661] -0.340 -0.339 -0.338 -0.337 -0.336 -0.335 -0.334 -0.333 -0.332 -0.331
##  [671] -0.330 -0.329 -0.328 -0.327 -0.326 -0.325 -0.324 -0.323 -0.322 -0.321
##  [681] -0.320 -0.319 -0.318 -0.317 -0.316 -0.315 -0.314 -0.313 -0.312 -0.311
##  [691] -0.310 -0.309 -0.308 -0.307 -0.306 -0.305 -0.304 -0.303 -0.302 -0.301
##  [701] -0.300 -0.299 -0.298 -0.297 -0.296 -0.295 -0.294 -0.293 -0.292 -0.291
##  [711] -0.290 -0.289 -0.288 -0.287 -0.286 -0.285 -0.284 -0.283 -0.282 -0.281
##  [721] -0.280 -0.279 -0.278 -0.277 -0.276 -0.275 -0.274 -0.273 -0.272 -0.271
##  [731] -0.270 -0.269 -0.268 -0.267 -0.266 -0.265 -0.264 -0.263 -0.262 -0.261
##  [741] -0.260 -0.259 -0.258 -0.257 -0.256 -0.255 -0.254 -0.253 -0.252 -0.251
##  [751] -0.250 -0.249 -0.248 -0.247 -0.246 -0.245 -0.244 -0.243 -0.242 -0.241
##  [761] -0.240 -0.239 -0.238 -0.237 -0.236 -0.235 -0.234 -0.233 -0.232 -0.231
##  [771] -0.230 -0.229 -0.228 -0.227 -0.226 -0.225 -0.224 -0.223 -0.222 -0.221
##  [781] -0.220 -0.219 -0.218 -0.217 -0.216 -0.215 -0.214 -0.213 -0.212 -0.211
##  [791] -0.210 -0.209 -0.208 -0.207 -0.206 -0.205 -0.204 -0.203 -0.202 -0.201
##  [801] -0.200 -0.199 -0.198 -0.197 -0.196 -0.195 -0.194 -0.193 -0.192 -0.191
##  [811] -0.190 -0.189 -0.188 -0.187 -0.186 -0.185 -0.184 -0.183 -0.182 -0.181
##  [821] -0.180 -0.179 -0.178 -0.177 -0.176 -0.175 -0.174 -0.173 -0.172 -0.171
##  [831] -0.170 -0.169 -0.168 -0.167 -0.166 -0.165 -0.164 -0.163 -0.162 -0.161
##  [841] -0.160 -0.159 -0.158 -0.157 -0.156 -0.155 -0.154 -0.153 -0.152 -0.151
##  [851] -0.150 -0.149 -0.148 -0.147 -0.146 -0.145 -0.144 -0.143 -0.142 -0.141
##  [861] -0.140 -0.139 -0.138 -0.137 -0.136 -0.135 -0.134 -0.133 -0.132 -0.131
##  [871] -0.130 -0.129 -0.128 -0.127 -0.126 -0.125 -0.124 -0.123 -0.122 -0.121
##  [881] -0.120 -0.119 -0.118 -0.117 -0.116 -0.115 -0.114 -0.113 -0.112 -0.111
##  [891] -0.110 -0.109 -0.108 -0.107 -0.106 -0.105 -0.104 -0.103 -0.102 -0.101
##  [901] -0.100 -0.099 -0.098 -0.097 -0.096 -0.095 -0.094 -0.093 -0.092 -0.091
##  [911] -0.090 -0.089 -0.088 -0.087 -0.086 -0.085 -0.084 -0.083 -0.082 -0.081
##  [921] -0.080 -0.079 -0.078 -0.077 -0.076 -0.075 -0.074 -0.073 -0.072 -0.071
##  [931] -0.070 -0.069 -0.068 -0.067 -0.066 -0.065 -0.064 -0.063 -0.062 -0.061
##  [941] -0.060 -0.059 -0.058 -0.057 -0.056 -0.055 -0.054 -0.053 -0.052 -0.051
##  [951] -0.050 -0.049 -0.048 -0.047 -0.046 -0.045 -0.044 -0.043 -0.042 -0.041
##  [961] -0.040 -0.039 -0.038 -0.037 -0.036 -0.035 -0.034 -0.033 -0.032 -0.031
##  [971] -0.030 -0.029 -0.028 -0.027 -0.026 -0.025 -0.024 -0.023 -0.022 -0.021
##  [981] -0.020 -0.019 -0.018 -0.017 -0.016 -0.015 -0.014 -0.013 -0.012 -0.011
##  [991] -0.010 -0.009 -0.008 -0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001
## [1001]  0.000  0.001  0.002  0.003  0.004  0.005  0.006  0.007  0.008  0.009
## [1011]  0.010  0.011  0.012  0.013  0.014  0.015  0.016  0.017  0.018  0.019
## [1021]  0.020  0.021  0.022  0.023  0.024  0.025  0.026  0.027  0.028  0.029
## [1031]  0.030  0.031  0.032  0.033  0.034  0.035  0.036  0.037  0.038  0.039
## [1041]  0.040  0.041  0.042  0.043  0.044  0.045  0.046  0.047  0.048  0.049
## [1051]  0.050  0.051  0.052  0.053  0.054  0.055  0.056  0.057  0.058  0.059
## [1061]  0.060  0.061  0.062  0.063  0.064  0.065  0.066  0.067  0.068  0.069
## [1071]  0.070  0.071  0.072  0.073  0.074  0.075  0.076  0.077  0.078  0.079
## [1081]  0.080  0.081  0.082  0.083  0.084  0.085  0.086  0.087  0.088  0.089
## [1091]  0.090  0.091  0.092  0.093  0.094  0.095  0.096  0.097  0.098  0.099
## [1101]  0.100  0.101  0.102  0.103  0.104  0.105  0.106  0.107  0.108  0.109
## [1111]  0.110  0.111  0.112  0.113  0.114  0.115  0.116  0.117  0.118  0.119
## [1121]  0.120  0.121  0.122  0.123  0.124  0.125  0.126  0.127  0.128  0.129
## [1131]  0.130  0.131  0.132  0.133  0.134  0.135  0.136  0.137  0.138  0.139
## [1141]  0.140  0.141  0.142  0.143  0.144  0.145  0.146  0.147  0.148  0.149
## [1151]  0.150  0.151  0.152  0.153  0.154  0.155  0.156  0.157  0.158  0.159
## [1161]  0.160  0.161  0.162  0.163  0.164  0.165  0.166  0.167  0.168  0.169
## [1171]  0.170  0.171  0.172  0.173  0.174  0.175  0.176  0.177  0.178  0.179
## [1181]  0.180  0.181  0.182  0.183  0.184  0.185  0.186  0.187  0.188  0.189
## [1191]  0.190  0.191  0.192  0.193  0.194  0.195  0.196  0.197  0.198  0.199
## [1201]  0.200  0.201  0.202  0.203  0.204  0.205  0.206  0.207  0.208  0.209
## [1211]  0.210  0.211  0.212  0.213  0.214  0.215  0.216  0.217  0.218  0.219
## [1221]  0.220  0.221  0.222  0.223  0.224  0.225  0.226  0.227  0.228  0.229
## [1231]  0.230  0.231  0.232  0.233  0.234  0.235  0.236  0.237  0.238  0.239
## [1241]  0.240  0.241  0.242  0.243  0.244  0.245  0.246  0.247  0.248  0.249
## [1251]  0.250  0.251  0.252  0.253  0.254  0.255  0.256  0.257  0.258  0.259
## [1261]  0.260  0.261  0.262  0.263  0.264  0.265  0.266  0.267  0.268  0.269
## [1271]  0.270  0.271  0.272  0.273  0.274  0.275  0.276  0.277  0.278  0.279
## [1281]  0.280  0.281  0.282  0.283  0.284  0.285  0.286  0.287  0.288  0.289
## [1291]  0.290  0.291  0.292  0.293  0.294  0.295  0.296  0.297  0.298  0.299
## [1301]  0.300  0.301  0.302  0.303  0.304  0.305  0.306  0.307  0.308  0.309
## [1311]  0.310  0.311  0.312  0.313  0.314  0.315  0.316  0.317  0.318  0.319
## [1321]  0.320  0.321  0.322  0.323  0.324  0.325  0.326  0.327  0.328  0.329
## [1331]  0.330  0.331  0.332  0.333  0.334  0.335  0.336  0.337  0.338  0.339
## [1341]  0.340  0.341  0.342  0.343  0.344  0.345  0.346  0.347  0.348  0.349
## [1351]  0.350  0.351  0.352  0.353  0.354  0.355  0.356  0.357  0.358  0.359
## [1361]  0.360  0.361  0.362  0.363  0.364  0.365  0.366  0.367  0.368  0.369
## [1371]  0.370  0.371  0.372  0.373  0.374  0.375  0.376  0.377  0.378  0.379
## [1381]  0.380  0.381  0.382  0.383  0.384  0.385  0.386  0.387  0.388  0.389
## [1391]  0.390  0.391  0.392  0.393  0.394  0.395  0.396  0.397  0.398  0.399
## [1401]  0.400  0.401  0.402  0.403  0.404  0.405  0.406  0.407  0.408  0.409
## [1411]  0.410  0.411  0.412  0.413  0.414  0.415  0.416  0.417  0.418  0.419
## [1421]  0.420  0.421  0.422  0.423  0.424  0.425  0.426  0.427  0.428  0.429
## [1431]  0.430  0.431  0.432  0.433  0.434  0.435  0.436  0.437  0.438  0.439
## [1441]  0.440  0.441  0.442  0.443  0.444  0.445  0.446  0.447  0.448  0.449
## [1451]  0.450  0.451  0.452  0.453  0.454  0.455  0.456  0.457  0.458  0.459
## [1461]  0.460  0.461  0.462  0.463  0.464  0.465  0.466  0.467  0.468  0.469
## [1471]  0.470  0.471  0.472  0.473  0.474  0.475  0.476  0.477  0.478  0.479
## [1481]  0.480  0.481  0.482  0.483  0.484  0.485  0.486  0.487  0.488  0.489
## [1491]  0.490  0.491  0.492  0.493  0.494  0.495  0.496  0.497  0.498  0.499
## [1501]  0.500  0.501  0.502  0.503  0.504  0.505  0.506  0.507  0.508  0.509
## [1511]  0.510  0.511  0.512  0.513  0.514  0.515  0.516  0.517  0.518  0.519
## [1521]  0.520  0.521  0.522  0.523  0.524  0.525  0.526  0.527  0.528  0.529
## [1531]  0.530  0.531  0.532  0.533  0.534  0.535  0.536  0.537  0.538  0.539
## [1541]  0.540  0.541  0.542  0.543  0.544  0.545  0.546  0.547  0.548  0.549
## [1551]  0.550  0.551  0.552  0.553  0.554  0.555  0.556  0.557  0.558  0.559
## [1561]  0.560  0.561  0.562  0.563  0.564  0.565  0.566  0.567  0.568  0.569
## [1571]  0.570  0.571  0.572  0.573  0.574  0.575  0.576  0.577  0.578  0.579
## [1581]  0.580  0.581  0.582  0.583  0.584  0.585  0.586  0.587  0.588  0.589
## [1591]  0.590  0.591  0.592  0.593  0.594  0.595  0.596  0.597  0.598  0.599
## [1601]  0.600  0.601  0.602  0.603  0.604  0.605  0.606  0.607  0.608  0.609
## [1611]  0.610  0.611  0.612  0.613  0.614  0.615  0.616  0.617  0.618  0.619
## [1621]  0.620  0.621  0.622  0.623  0.624  0.625  0.626  0.627  0.628  0.629
## [1631]  0.630  0.631  0.632  0.633  0.634  0.635  0.636  0.637  0.638  0.639
## [1641]  0.640  0.641  0.642  0.643  0.644  0.645  0.646  0.647  0.648  0.649
## [1651]  0.650  0.651  0.652  0.653  0.654  0.655  0.656  0.657  0.658  0.659
## [1661]  0.660  0.661  0.662  0.663  0.664  0.665  0.666  0.667  0.668  0.669
## [1671]  0.670  0.671  0.672  0.673  0.674  0.675  0.676  0.677  0.678  0.679
## [1681]  0.680  0.681  0.682  0.683  0.684  0.685  0.686  0.687  0.688  0.689
## [1691]  0.690  0.691  0.692  0.693  0.694  0.695  0.696  0.697  0.698  0.699
## [1701]  0.700  0.701  0.702  0.703  0.704  0.705  0.706  0.707  0.708  0.709
## [1711]  0.710  0.711  0.712  0.713  0.714  0.715  0.716  0.717  0.718  0.719
## [1721]  0.720  0.721  0.722  0.723  0.724  0.725  0.726  0.727  0.728  0.729
## [1731]  0.730  0.731  0.732  0.733  0.734  0.735  0.736  0.737  0.738  0.739
## [1741]  0.740  0.741  0.742  0.743  0.744  0.745  0.746  0.747  0.748  0.749
## [1751]  0.750  0.751  0.752  0.753  0.754  0.755  0.756  0.757  0.758  0.759
## [1761]  0.760  0.761  0.762  0.763  0.764  0.765  0.766  0.767  0.768  0.769
## [1771]  0.770  0.771  0.772  0.773  0.774  0.775  0.776  0.777  0.778  0.779
## [1781]  0.780  0.781  0.782  0.783  0.784  0.785  0.786  0.787  0.788  0.789
## [1791]  0.790  0.791  0.792  0.793  0.794  0.795  0.796  0.797  0.798  0.799
## [1801]  0.800  0.801  0.802  0.803  0.804  0.805  0.806  0.807  0.808  0.809
## [1811]  0.810  0.811  0.812  0.813  0.814  0.815  0.816  0.817  0.818  0.819
## [1821]  0.820  0.821  0.822  0.823  0.824  0.825  0.826  0.827  0.828  0.829
## [1831]  0.830  0.831  0.832  0.833  0.834  0.835  0.836  0.837  0.838  0.839
## [1841]  0.840  0.841  0.842  0.843  0.844  0.845  0.846  0.847  0.848  0.849
## [1851]  0.850  0.851  0.852  0.853  0.854  0.855  0.856  0.857  0.858  0.859
## [1861]  0.860  0.861  0.862  0.863  0.864  0.865  0.866  0.867  0.868  0.869
## [1871]  0.870  0.871  0.872  0.873  0.874  0.875  0.876  0.877  0.878  0.879
## [1881]  0.880  0.881  0.882  0.883  0.884  0.885  0.886  0.887  0.888  0.889
## [1891]  0.890  0.891  0.892  0.893  0.894  0.895  0.896  0.897  0.898  0.899
## [1901]  0.900  0.901  0.902  0.903  0.904  0.905  0.906  0.907  0.908  0.909
## [1911]  0.910  0.911  0.912  0.913  0.914  0.915  0.916  0.917  0.918  0.919
## [1921]  0.920  0.921  0.922  0.923  0.924  0.925  0.926  0.927  0.928  0.929
## [1931]  0.930  0.931  0.932  0.933  0.934  0.935  0.936  0.937  0.938  0.939
## [1941]  0.940  0.941  0.942  0.943  0.944  0.945  0.946  0.947  0.948  0.949
## [1951]  0.950  0.951  0.952  0.953  0.954  0.955  0.956  0.957  0.958  0.959
## [1961]  0.960  0.961  0.962  0.963  0.964  0.965  0.966  0.967  0.968  0.969
## [1971]  0.970  0.971  0.972  0.973  0.974  0.975  0.976  0.977  0.978  0.979
## [1981]  0.980  0.981  0.982  0.983  0.984  0.985  0.986  0.987  0.988  0.989
## [1991]  0.990  0.991  0.992  0.993  0.994  0.995  0.996  0.997  0.998  0.999
## [2001]  1.000  1.001  1.002  1.003  1.004  1.005  1.006  1.007  1.008  1.009
## [2011]  1.010  1.011  1.012  1.013  1.014  1.015  1.016  1.017  1.018  1.019
## [2021]  1.020  1.021  1.022  1.023  1.024  1.025  1.026  1.027  1.028  1.029
## [2031]  1.030  1.031  1.032  1.033  1.034  1.035  1.036  1.037  1.038  1.039
## [2041]  1.040  1.041  1.042  1.043  1.044  1.045  1.046  1.047  1.048  1.049
## [2051]  1.050  1.051  1.052  1.053  1.054  1.055  1.056  1.057  1.058  1.059
## [2061]  1.060  1.061  1.062  1.063  1.064  1.065  1.066  1.067  1.068  1.069
## [2071]  1.070  1.071  1.072  1.073  1.074  1.075  1.076  1.077  1.078  1.079
## [2081]  1.080  1.081  1.082  1.083  1.084  1.085  1.086  1.087  1.088  1.089
## [2091]  1.090  1.091  1.092  1.093  1.094  1.095  1.096  1.097  1.098  1.099
## [2101]  1.100  1.101  1.102  1.103  1.104  1.105  1.106  1.107  1.108  1.109
## [2111]  1.110  1.111  1.112  1.113  1.114  1.115  1.116  1.117  1.118  1.119
## [2121]  1.120  1.121  1.122  1.123  1.124  1.125  1.126  1.127  1.128  1.129
## [2131]  1.130  1.131  1.132  1.133  1.134  1.135  1.136  1.137  1.138  1.139
## [2141]  1.140  1.141  1.142  1.143  1.144  1.145  1.146  1.147  1.148  1.149
## [2151]  1.150  1.151  1.152  1.153  1.154  1.155  1.156  1.157  1.158  1.159
## [2161]  1.160  1.161  1.162  1.163  1.164  1.165  1.166  1.167  1.168  1.169
## [2171]  1.170  1.171  1.172  1.173  1.174  1.175  1.176  1.177  1.178  1.179
## [2181]  1.180  1.181  1.182  1.183  1.184  1.185  1.186  1.187  1.188  1.189
## [2191]  1.190  1.191  1.192  1.193  1.194  1.195  1.196  1.197  1.198  1.199
## [2201]  1.200  1.201  1.202  1.203  1.204  1.205  1.206  1.207  1.208  1.209
## [2211]  1.210  1.211  1.212  1.213  1.214  1.215  1.216  1.217  1.218  1.219
## [2221]  1.220  1.221  1.222  1.223  1.224  1.225  1.226  1.227  1.228  1.229
## [2231]  1.230  1.231  1.232  1.233  1.234  1.235  1.236  1.237  1.238  1.239
## [2241]  1.240  1.241  1.242  1.243  1.244  1.245  1.246  1.247  1.248  1.249
## [2251]  1.250  1.251  1.252  1.253  1.254  1.255  1.256  1.257  1.258  1.259
## [2261]  1.260  1.261  1.262  1.263  1.264  1.265  1.266  1.267  1.268  1.269
## [2271]  1.270  1.271  1.272  1.273  1.274  1.275  1.276  1.277  1.278  1.279
## [2281]  1.280  1.281  1.282  1.283  1.284  1.285  1.286  1.287  1.288  1.289
## [2291]  1.290  1.291  1.292  1.293  1.294  1.295  1.296  1.297  1.298  1.299
## [2301]  1.300  1.301  1.302  1.303  1.304  1.305  1.306  1.307  1.308  1.309
## [2311]  1.310  1.311  1.312  1.313  1.314  1.315  1.316  1.317  1.318  1.319
## [2321]  1.320  1.321  1.322  1.323  1.324  1.325  1.326  1.327  1.328  1.329
## [2331]  1.330  1.331  1.332  1.333  1.334  1.335  1.336  1.337  1.338  1.339
## [2341]  1.340  1.341  1.342  1.343  1.344  1.345  1.346  1.347  1.348  1.349
## [2351]  1.350  1.351  1.352  1.353  1.354  1.355  1.356  1.357  1.358  1.359
## [2361]  1.360  1.361  1.362  1.363  1.364  1.365  1.366  1.367  1.368  1.369
## [2371]  1.370  1.371  1.372  1.373  1.374  1.375  1.376  1.377  1.378  1.379
## [2381]  1.380  1.381  1.382  1.383  1.384  1.385  1.386  1.387  1.388  1.389
## [2391]  1.390  1.391  1.392  1.393  1.394  1.395  1.396  1.397  1.398  1.399
## [2401]  1.400  1.401  1.402  1.403  1.404  1.405  1.406  1.407  1.408  1.409
## [2411]  1.410  1.411  1.412  1.413  1.414  1.415  1.416  1.417  1.418  1.419
## [2421]  1.420  1.421  1.422  1.423  1.424  1.425  1.426  1.427  1.428  1.429
## [2431]  1.430  1.431  1.432  1.433  1.434  1.435  1.436  1.437  1.438  1.439
## [2441]  1.440  1.441  1.442  1.443  1.444  1.445  1.446  1.447  1.448  1.449
## [2451]  1.450  1.451  1.452  1.453  1.454  1.455  1.456  1.457  1.458  1.459
## [2461]  1.460  1.461  1.462  1.463  1.464  1.465  1.466  1.467  1.468  1.469
## [2471]  1.470  1.471  1.472  1.473  1.474  1.475  1.476  1.477  1.478  1.479
## [2481]  1.480  1.481  1.482  1.483  1.484  1.485  1.486  1.487  1.488  1.489
## [2491]  1.490  1.491  1.492  1.493  1.494  1.495  1.496  1.497  1.498  1.499
## [2501]  1.500  1.501  1.502  1.503  1.504  1.505  1.506  1.507  1.508  1.509
## [2511]  1.510  1.511  1.512  1.513  1.514  1.515  1.516  1.517  1.518  1.519
## [2521]  1.520  1.521  1.522  1.523  1.524  1.525  1.526  1.527  1.528  1.529
## [2531]  1.530  1.531  1.532  1.533  1.534  1.535  1.536  1.537  1.538  1.539
## [2541]  1.540  1.541  1.542  1.543  1.544  1.545  1.546  1.547  1.548  1.549
## [2551]  1.550  1.551  1.552  1.553  1.554  1.555  1.556  1.557  1.558  1.559
## [2561]  1.560  1.561  1.562  1.563  1.564  1.565  1.566  1.567  1.568  1.569
## [2571]  1.570  1.571  1.572  1.573  1.574  1.575  1.576  1.577  1.578  1.579
## [2581]  1.580  1.581  1.582  1.583  1.584  1.585  1.586  1.587  1.588  1.589
## [2591]  1.590  1.591  1.592  1.593  1.594  1.595  1.596  1.597  1.598  1.599
## [2601]  1.600  1.601  1.602  1.603  1.604  1.605  1.606  1.607  1.608  1.609
## [2611]  1.610  1.611  1.612  1.613  1.614  1.615  1.616  1.617  1.618  1.619
## [2621]  1.620  1.621  1.622  1.623  1.624  1.625  1.626  1.627  1.628  1.629
## [2631]  1.630  1.631  1.632  1.633  1.634  1.635  1.636  1.637  1.638  1.639
## [2641]  1.640  1.641  1.642  1.643  1.644  1.645  1.646  1.647  1.648  1.649
## [2651]  1.650  1.651  1.652  1.653  1.654  1.655  1.656  1.657  1.658  1.659
## [2661]  1.660  1.661  1.662  1.663  1.664  1.665  1.666  1.667  1.668  1.669
## [2671]  1.670  1.671  1.672  1.673  1.674  1.675  1.676  1.677  1.678  1.679
## [2681]  1.680  1.681  1.682  1.683  1.684  1.685  1.686  1.687  1.688  1.689
## [2691]  1.690  1.691  1.692  1.693  1.694  1.695  1.696  1.697  1.698  1.699
## [2701]  1.700  1.701  1.702  1.703  1.704  1.705  1.706  1.707  1.708  1.709
## [2711]  1.710  1.711  1.712  1.713  1.714  1.715  1.716  1.717  1.718  1.719
## [2721]  1.720  1.721  1.722  1.723  1.724  1.725  1.726  1.727  1.728  1.729
## [2731]  1.730  1.731  1.732  1.733  1.734  1.735  1.736  1.737  1.738  1.739
## [2741]  1.740  1.741  1.742  1.743  1.744  1.745  1.746  1.747  1.748  1.749
## [2751]  1.750  1.751  1.752  1.753  1.754  1.755  1.756  1.757  1.758  1.759
## [2761]  1.760  1.761  1.762  1.763  1.764  1.765  1.766  1.767  1.768  1.769
## [2771]  1.770  1.771  1.772  1.773  1.774  1.775  1.776  1.777  1.778  1.779
## [2781]  1.780  1.781  1.782  1.783  1.784  1.785  1.786  1.787  1.788  1.789
## [2791]  1.790  1.791  1.792  1.793  1.794  1.795  1.796  1.797  1.798  1.799
## [2801]  1.800  1.801  1.802  1.803  1.804  1.805  1.806  1.807  1.808  1.809
## [2811]  1.810  1.811  1.812  1.813  1.814  1.815  1.816  1.817  1.818  1.819
## [2821]  1.820  1.821  1.822  1.823  1.824  1.825  1.826  1.827  1.828  1.829
## [2831]  1.830  1.831  1.832  1.833  1.834  1.835  1.836  1.837  1.838  1.839
## [2841]  1.840  1.841  1.842  1.843  1.844  1.845  1.846  1.847  1.848  1.849
## [2851]  1.850  1.851  1.852  1.853  1.854  1.855  1.856  1.857  1.858  1.859
## [2861]  1.860  1.861  1.862  1.863  1.864  1.865  1.866  1.867  1.868  1.869
## [2871]  1.870  1.871  1.872  1.873  1.874  1.875  1.876  1.877  1.878  1.879
## [2881]  1.880  1.881  1.882  1.883  1.884  1.885  1.886  1.887  1.888  1.889
## [2891]  1.890  1.891  1.892  1.893  1.894  1.895  1.896  1.897  1.898  1.899
## [2901]  1.900  1.901  1.902  1.903  1.904  1.905  1.906  1.907  1.908  1.909
## [2911]  1.910  1.911  1.912  1.913  1.914  1.915  1.916  1.917  1.918  1.919
## [2921]  1.920  1.921  1.922  1.923  1.924  1.925  1.926  1.927  1.928  1.929
## [2931]  1.930  1.931  1.932  1.933  1.934  1.935  1.936  1.937  1.938  1.939
## [2941]  1.940  1.941  1.942  1.943  1.944  1.945  1.946  1.947  1.948  1.949
## [2951]  1.950  1.951  1.952  1.953  1.954  1.955  1.956  1.957  1.958  1.959
## [2961]  1.960  1.961  1.962  1.963  1.964  1.965  1.966  1.967  1.968  1.969
## [2971]  1.970  1.971  1.972  1.973  1.974  1.975  1.976  1.977  1.978  1.979
## [2981]  1.980  1.981  1.982  1.983  1.984  1.985  1.986  1.987  1.988  1.989
## [2991]  1.990  1.991  1.992  1.993  1.994  1.995  1.996  1.997  1.998  1.999
## [3001]  2.000

Gambar di atas menunjukkan nilai rounded value (\(\lambda\)) optimum sebesar 1,51 dan pada selang kepercayaan 95% nilai memiliki batas bawah -1,000 dan batas atas -0,001. Selang tersebut memuat nilai satu sehingga dapat dikatakan bahwa data bangkitan stasioner dalam ragam.

Summary Data Testing

Pada data ini terdapat 80 periode, dapat di identifikasi stasionernya dengan melakukan uji ACF dengan hasil Tails off lalu dilakukan uji stasioner bagi rataan Menggunakan uji ADF. Hasil p-value \(0,7909\) yang lebih besar dari taraf nyata 5% sehingga tak tolak \(H_0\) dan menandakan bahwa data tidak stasioner dalam rataan. Lalu dilakukan uji stasioner bagi ragam Menggunakan Box-Cox dengan hasil lambda \(1,51\) dan pada selang kepercayaan 95% nilai memiliki batas bawah \(-1,000\) dan batas atas \(0,001\).

Dari seluruh uji dapat di identifikasi bahwa data testing 20 periode termasuk dalam model yang stasioner akan tetapi tidak stasioner terhadap rataannya.