Tugas Praktikum 5 MPDW

Memanggil Library

library(ggplot2)
library(tsibble)

## 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)

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

library(MASS)
library(readxl)
library(rio)

Data Penuh

Input Data

data <- read_excel("C:/Users/luthf/Downloads/Data MPDW.xlsx")
data_ts <- ts(data$Kurs)
data_ts

## Time Series:
## Start = 1 
## End = 100 
## Frequency = 1 
##   [1] 15285 15462 15522 15549 15610 15474 15629 15675 15362 15582 15616 15566
##  [13] 15509 15602 15115 15056 14970 15079 15182 15159 15258 15255 15473 15369
##  [25] 15165 14969 14934 14783 14929 14666 14668 14843 14929 15008 14875 14886
##  [37] 14954 15043 15036 15158 14996 15041 15095 15139 15324 15314 15291 15194
##  [49] 15379 15360 15346 15487 15636 15696 15864 15904 15582 15683 15399 15447
##  [61] 15399 15560 15283 15409 15383 15478 15503 15601 15768 15727 15598 15629
##  [73] 15586 15692 15536 15639 15803 15873 15883 16112 16210 16232 15951 16047
##  [85] 15920 16038 16244 16268 16480 16470 16343 16239 16067 16208 16284 16135
##  [97] 15934 15672 15484 15649

Time Series Plot

ts.plot(data_ts)

Dapat dilihat pada eksplorasi plot diatas data tidak stasioner dalam rataan.

PLot ACF

acf(data_ts,lag.max = 20)

Plot ACF menunjukkan pola Tails-off slowly yang menunjukkan data tersebut tidak stasioner dalam rataan.

ADF Test

adf.test(data_ts)

## 
##  Augmented Dickey-Fuller Test
## 
## data:  data_ts
## Dickey-Fuller = -2.4683, Lag order = 4, p-value = 0.3827
## alternative hypothesis: stationary

Dari tes ADF yang dilakukan didapat \(p-value =0.3827\) dimana \(p-value<0.05\) maka data tersebut tidak stasioner dalam rataan.

Boxcox dan Lambda Optimum

index <- seq(1:100)
bc = boxcox(data$Kurs~index, lambda = seq(-10,10,by=0.01))

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

## [1] 0.22

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

##    [1] -5.83 -5.82 -5.81 -5.80 -5.79 -5.78 -5.77 -5.76 -5.75 -5.74 -5.73 -5.72
##   [13] -5.71 -5.70 -5.69 -5.68 -5.67 -5.66 -5.65 -5.64 -5.63 -5.62 -5.61 -5.60
##   [25] -5.59 -5.58 -5.57 -5.56 -5.55 -5.54 -5.53 -5.52 -5.51 -5.50 -5.49 -5.48
##   [37] -5.47 -5.46 -5.45 -5.44 -5.43 -5.42 -5.41 -5.40 -5.39 -5.38 -5.37 -5.36
##   [49] -5.35 -5.34 -5.33 -5.32 -5.31 -5.30 -5.29 -5.28 -5.27 -5.26 -5.25 -5.24
##   [61] -5.23 -5.22 -5.21 -5.20 -5.19 -5.18 -5.17 -5.16 -5.15 -5.14 -5.13 -5.12
##   [73] -5.11 -5.10 -5.09 -5.08 -5.07 -5.06 -5.05 -5.04 -5.03 -5.02 -5.01 -5.00
##   [85] -4.99 -4.98 -4.97 -4.96 -4.95 -4.94 -4.93 -4.92 -4.91 -4.90 -4.89 -4.88
##   [97] -4.87 -4.86 -4.85 -4.84 -4.83 -4.82 -4.81 -4.80 -4.79 -4.78 -4.77 -4.76
##  [109] -4.75 -4.74 -4.73 -4.72 -4.71 -4.70 -4.69 -4.68 -4.67 -4.66 -4.65 -4.64
##  [121] -4.63 -4.62 -4.61 -4.60 -4.59 -4.58 -4.57 -4.56 -4.55 -4.54 -4.53 -4.52
##  [133] -4.51 -4.50 -4.49 -4.48 -4.47 -4.46 -4.45 -4.44 -4.43 -4.42 -4.41 -4.40
##  [145] -4.39 -4.38 -4.37 -4.36 -4.35 -4.34 -4.33 -4.32 -4.31 -4.30 -4.29 -4.28
##  [157] -4.27 -4.26 -4.25 -4.24 -4.23 -4.22 -4.21 -4.20 -4.19 -4.18 -4.17 -4.16
##  [169] -4.15 -4.14 -4.13 -4.12 -4.11 -4.10 -4.09 -4.08 -4.07 -4.06 -4.05 -4.04
##  [181] -4.03 -4.02 -4.01 -4.00 -3.99 -3.98 -3.97 -3.96 -3.95 -3.94 -3.93 -3.92
##  [193] -3.91 -3.90 -3.89 -3.88 -3.87 -3.86 -3.85 -3.84 -3.83 -3.82 -3.81 -3.80
##  [205] -3.79 -3.78 -3.77 -3.76 -3.75 -3.74 -3.73 -3.72 -3.71 -3.70 -3.69 -3.68
##  [217] -3.67 -3.66 -3.65 -3.64 -3.63 -3.62 -3.61 -3.60 -3.59 -3.58 -3.57 -3.56
##  [229] -3.55 -3.54 -3.53 -3.52 -3.51 -3.50 -3.49 -3.48 -3.47 -3.46 -3.45 -3.44
##  [241] -3.43 -3.42 -3.41 -3.40 -3.39 -3.38 -3.37 -3.36 -3.35 -3.34 -3.33 -3.32
##  [253] -3.31 -3.30 -3.29 -3.28 -3.27 -3.26 -3.25 -3.24 -3.23 -3.22 -3.21 -3.20
##  [265] -3.19 -3.18 -3.17 -3.16 -3.15 -3.14 -3.13 -3.12 -3.11 -3.10 -3.09 -3.08
##  [277] -3.07 -3.06 -3.05 -3.04 -3.03 -3.02 -3.01 -3.00 -2.99 -2.98 -2.97 -2.96
##  [289] -2.95 -2.94 -2.93 -2.92 -2.91 -2.90 -2.89 -2.88 -2.87 -2.86 -2.85 -2.84
##  [301] -2.83 -2.82 -2.81 -2.80 -2.79 -2.78 -2.77 -2.76 -2.75 -2.74 -2.73 -2.72
##  [313] -2.71 -2.70 -2.69 -2.68 -2.67 -2.66 -2.65 -2.64 -2.63 -2.62 -2.61 -2.60
##  [325] -2.59 -2.58 -2.57 -2.56 -2.55 -2.54 -2.53 -2.52 -2.51 -2.50 -2.49 -2.48
##  [337] -2.47 -2.46 -2.45 -2.44 -2.43 -2.42 -2.41 -2.40 -2.39 -2.38 -2.37 -2.36
##  [349] -2.35 -2.34 -2.33 -2.32 -2.31 -2.30 -2.29 -2.28 -2.27 -2.26 -2.25 -2.24
##  [361] -2.23 -2.22 -2.21 -2.20 -2.19 -2.18 -2.17 -2.16 -2.15 -2.14 -2.13 -2.12
##  [373] -2.11 -2.10 -2.09 -2.08 -2.07 -2.06 -2.05 -2.04 -2.03 -2.02 -2.01 -2.00
##  [385] -1.99 -1.98 -1.97 -1.96 -1.95 -1.94 -1.93 -1.92 -1.91 -1.90 -1.89 -1.88
##  [397] -1.87 -1.86 -1.85 -1.84 -1.83 -1.82 -1.81 -1.80 -1.79 -1.78 -1.77 -1.76
##  [409] -1.75 -1.74 -1.73 -1.72 -1.71 -1.70 -1.69 -1.68 -1.67 -1.66 -1.65 -1.64
##  [421] -1.63 -1.62 -1.61 -1.60 -1.59 -1.58 -1.57 -1.56 -1.55 -1.54 -1.53 -1.52
##  [433] -1.51 -1.50 -1.49 -1.48 -1.47 -1.46 -1.45 -1.44 -1.43 -1.42 -1.41 -1.40
##  [445] -1.39 -1.38 -1.37 -1.36 -1.35 -1.34 -1.33 -1.32 -1.31 -1.30 -1.29 -1.28
##  [457] -1.27 -1.26 -1.25 -1.24 -1.23 -1.22 -1.21 -1.20 -1.19 -1.18 -1.17 -1.16
##  [469] -1.15 -1.14 -1.13 -1.12 -1.11 -1.10 -1.09 -1.08 -1.07 -1.06 -1.05 -1.04
##  [481] -1.03 -1.02 -1.01 -1.00 -0.99 -0.98 -0.97 -0.96 -0.95 -0.94 -0.93 -0.92
##  [493] -0.91 -0.90 -0.89 -0.88 -0.87 -0.86 -0.85 -0.84 -0.83 -0.82 -0.81 -0.80
##  [505] -0.79 -0.78 -0.77 -0.76 -0.75 -0.74 -0.73 -0.72 -0.71 -0.70 -0.69 -0.68
##  [517] -0.67 -0.66 -0.65 -0.64 -0.63 -0.62 -0.61 -0.60 -0.59 -0.58 -0.57 -0.56
##  [529] -0.55 -0.54 -0.53 -0.52 -0.51 -0.50 -0.49 -0.48 -0.47 -0.46 -0.45 -0.44
##  [541] -0.43 -0.42 -0.41 -0.40 -0.39 -0.38 -0.37 -0.36 -0.35 -0.34 -0.33 -0.32
##  [553] -0.31 -0.30 -0.29 -0.28 -0.27 -0.26 -0.25 -0.24 -0.23 -0.22 -0.21 -0.20
##  [565] -0.19 -0.18 -0.17 -0.16 -0.15 -0.14 -0.13 -0.12 -0.11 -0.10 -0.09 -0.08
##  [577] -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01  0.00  0.01  0.02  0.03  0.04
##  [589]  0.05  0.06  0.07  0.08  0.09  0.10  0.11  0.12  0.13  0.14  0.15  0.16
##  [601]  0.17  0.18  0.19  0.20  0.21  0.22  0.23  0.24  0.25  0.26  0.27  0.28
##  [613]  0.29  0.30  0.31  0.32  0.33  0.34  0.35  0.36  0.37  0.38  0.39  0.40
##  [625]  0.41  0.42  0.43  0.44  0.45  0.46  0.47  0.48  0.49  0.50  0.51  0.52
##  [637]  0.53  0.54  0.55  0.56  0.57  0.58  0.59  0.60  0.61  0.62  0.63  0.64
##  [649]  0.65  0.66  0.67  0.68  0.69  0.70  0.71  0.72  0.73  0.74  0.75  0.76
##  [661]  0.77  0.78  0.79  0.80  0.81  0.82  0.83  0.84  0.85  0.86  0.87  0.88
##  [673]  0.89  0.90  0.91  0.92  0.93  0.94  0.95  0.96  0.97  0.98  0.99  1.00
##  [685]  1.01  1.02  1.03  1.04  1.05  1.06  1.07  1.08  1.09  1.10  1.11  1.12
##  [697]  1.13  1.14  1.15  1.16  1.17  1.18  1.19  1.20  1.21  1.22  1.23  1.24
##  [709]  1.25  1.26  1.27  1.28  1.29  1.30  1.31  1.32  1.33  1.34  1.35  1.36
##  [721]  1.37  1.38  1.39  1.40  1.41  1.42  1.43  1.44  1.45  1.46  1.47  1.48
##  [733]  1.49  1.50  1.51  1.52  1.53  1.54  1.55  1.56  1.57  1.58  1.59  1.60
##  [745]  1.61  1.62  1.63  1.64  1.65  1.66  1.67  1.68  1.69  1.70  1.71  1.72
##  [757]  1.73  1.74  1.75  1.76  1.77  1.78  1.79  1.80  1.81  1.82  1.83  1.84
##  [769]  1.85  1.86  1.87  1.88  1.89  1.90  1.91  1.92  1.93  1.94  1.95  1.96
##  [781]  1.97  1.98  1.99  2.00  2.01  2.02  2.03  2.04  2.05  2.06  2.07  2.08
##  [793]  2.09  2.10  2.11  2.12  2.13  2.14  2.15  2.16  2.17  2.18  2.19  2.20
##  [805]  2.21  2.22  2.23  2.24  2.25  2.26  2.27  2.28  2.29  2.30  2.31  2.32
##  [817]  2.33  2.34  2.35  2.36  2.37  2.38  2.39  2.40  2.41  2.42  2.43  2.44
##  [829]  2.45  2.46  2.47  2.48  2.49  2.50  2.51  2.52  2.53  2.54  2.55  2.56
##  [841]  2.57  2.58  2.59  2.60  2.61  2.62  2.63  2.64  2.65  2.66  2.67  2.68
##  [853]  2.69  2.70  2.71  2.72  2.73  2.74  2.75  2.76  2.77  2.78  2.79  2.80
##  [865]  2.81  2.82  2.83  2.84  2.85  2.86  2.87  2.88  2.89  2.90  2.91  2.92
##  [877]  2.93  2.94  2.95  2.96  2.97  2.98  2.99  3.00  3.01  3.02  3.03  3.04
##  [889]  3.05  3.06  3.07  3.08  3.09  3.10  3.11  3.12  3.13  3.14  3.15  3.16
##  [901]  3.17  3.18  3.19  3.20  3.21  3.22  3.23  3.24  3.25  3.26  3.27  3.28
##  [913]  3.29  3.30  3.31  3.32  3.33  3.34  3.35  3.36  3.37  3.38  3.39  3.40
##  [925]  3.41  3.42  3.43  3.44  3.45  3.46  3.47  3.48  3.49  3.50  3.51  3.52
##  [937]  3.53  3.54  3.55  3.56  3.57  3.58  3.59  3.60  3.61  3.62  3.63  3.64
##  [949]  3.65  3.66  3.67  3.68  3.69  3.70  3.71  3.72  3.73  3.74  3.75  3.76
##  [961]  3.77  3.78  3.79  3.80  3.81  3.82  3.83  3.84  3.85  3.86  3.87  3.88
##  [973]  3.89  3.90  3.91  3.92  3.93  3.94  3.95  3.96  3.97  3.98  3.99  4.00
##  [985]  4.01  4.02  4.03  4.04  4.05  4.06  4.07  4.08  4.09  4.10  4.11  4.12
##  [997]  4.13  4.14  4.15  4.16  4.17  4.18  4.19  4.20  4.21  4.22  4.23  4.24
## [1009]  4.25  4.26  4.27  4.28  4.29  4.30  4.31  4.32  4.33  4.34  4.35  4.36
## [1021]  4.37  4.38  4.39  4.40  4.41  4.42  4.43  4.44  4.45  4.46  4.47  4.48
## [1033]  4.49  4.50  4.51  4.52  4.53  4.54  4.55  4.56  4.57  4.58  4.59  4.60
## [1045]  4.61  4.62  4.63  4.64  4.65  4.66  4.67  4.68  4.69  4.70  4.71  4.72
## [1057]  4.73  4.74  4.75  4.76  4.77  4.78  4.79  4.80  4.81  4.82  4.83  4.84
## [1069]  4.85  4.86  4.87  4.88  4.89  4.90  4.91  4.92  4.93  4.94  4.95  4.96
## [1081]  4.97  4.98  4.99  5.00  5.01  5.02  5.03  5.04  5.05  5.06  5.07  5.08
## [1093]  5.09  5.10  5.11  5.12  5.13  5.14  5.15  5.16  5.17  5.18  5.19  5.20
## [1105]  5.21  5.22  5.23  5.24  5.25  5.26  5.27  5.28  5.29  5.30  5.31  5.32
## [1117]  5.33  5.34  5.35  5.36  5.37  5.38  5.39  5.40  5.41  5.42  5.43  5.44
## [1129]  5.45  5.46  5.47  5.48  5.49  5.50  5.51  5.52  5.53  5.54  5.55  5.56
## [1141]  5.57  5.58  5.59  5.60  5.61  5.62  5.63  5.64  5.65  5.66  5.67  5.68
## [1153]  5.69  5.70  5.71  5.72  5.73  5.74  5.75  5.76  5.77  5.78  5.79  5.80
## [1165]  5.81  5.82  5.83  5.84  5.85  5.86  5.87  5.88  5.89  5.90  5.91  5.92
## [1177]  5.93  5.94  5.95  5.96  5.97  5.98  5.99  6.00  6.01  6.02  6.03  6.04
## [1189]  6.05  6.06  6.07  6.08  6.09  6.10  6.11  6.12  6.13  6.14

Dari kurva boxcox dapat dilihat kurva melewati \(\lambda=1\) yang menunjukkan data stasioner dalam ragam. Dan juga didapat \(\lambda\) optimum \(0.22\)

Partisi 1 : Data 1-50

Input Data

data2_s<-data[1:50,]
data2 <-data_ts[1:50]
data2

##  [1] 15285 15462 15522 15549 15610 15474 15629 15675 15362 15582 15616 15566
## [13] 15509 15602 15115 15056 14970 15079 15182 15159 15258 15255 15473 15369
## [25] 15165 14969 14934 14783 14929 14666 14668 14843 14929 15008 14875 14886
## [37] 14954 15043 15036 15158 14996 15041 15095 15139 15324 15314 15291 15194
## [49] 15379 15360

Time Series Plot

ts.plot(data2)

Dapat dilihat pada eksplorasi plot diatas data tidak stasioner dalam rataan.

Plot ACF

acf(data2,lag.max = 20)

Plot ACF menunjukkan pola Tails-off slowly yang menunjukkan data tersebut tidak stasioner dalam rataan.

ADF Test

adf.test(data2)

## 
##  Augmented Dickey-Fuller Test
## 
## data:  data2
## Dickey-Fuller = -1.4698, Lag order = 3, p-value = 0.7869
## alternative hypothesis: stationary

Dari tes ADF yang dilakukan didapat \(p-value =0.7869\) dimana \(p-value<0.05\) maka data tersebut tidak stasioner dalam rataan.

Boxcox dan Lambda Optimum

index <- seq(1:50)
bc = boxcox(data2_s$Kurs~index, lambda = seq(-10,10,by=0.01))

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

## [1] 7.59

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

##    [1] -8.27 -8.26 -8.25 -8.24 -8.23 -8.22 -8.21 -8.20 -8.19 -8.18 -8.17 -8.16
##   [13] -8.15 -8.14 -8.13 -8.12 -8.11 -8.10 -8.09 -8.08 -8.07 -8.06 -8.05 -8.04
##   [25] -8.03 -8.02 -8.01 -8.00 -7.99 -7.98 -7.97 -7.96 -7.95 -7.94 -7.93 -7.92
##   [37] -7.91 -7.90 -7.89 -7.88 -7.87 -7.86 -7.85 -7.84 -7.83 -7.82 -7.81 -7.80
##   [49] -7.79 -7.78 -7.77 -7.76 -7.75 -7.74 -7.73 -7.72 -7.71 -7.70 -7.69 -7.68
##   [61] -7.67 -7.66 -7.65 -7.64 -7.63 -7.62 -7.61 -7.60 -7.59 -7.58 -7.57 -7.56
##   [73] -7.55 -7.54 -7.53 -7.52 -7.51 -7.50 -7.49 -7.48 -7.47 -7.46 -7.45 -7.44
##   [85] -7.43 -7.42 -7.41 -7.40 -7.39 -7.38 -7.37 -7.36 -7.35 -7.34 -7.33 -7.32
##   [97] -7.31 -7.30 -7.29 -7.28 -7.27 -7.26 -7.25 -7.24 -7.23 -7.22 -7.21 -7.20
##  [109] -7.19 -7.18 -7.17 -7.16 -7.15 -7.14 -7.13 -7.12 -7.11 -7.10 -7.09 -7.08
##  [121] -7.07 -7.06 -7.05 -7.04 -7.03 -7.02 -7.01 -7.00 -6.99 -6.98 -6.97 -6.96
##  [133] -6.95 -6.94 -6.93 -6.92 -6.91 -6.90 -6.89 -6.88 -6.87 -6.86 -6.85 -6.84
##  [145] -6.83 -6.82 -6.81 -6.80 -6.79 -6.78 -6.77 -6.76 -6.75 -6.74 -6.73 -6.72
##  [157] -6.71 -6.70 -6.69 -6.68 -6.67 -6.66 -6.65 -6.64 -6.63 -6.62 -6.61 -6.60
##  [169] -6.59 -6.58 -6.57 -6.56 -6.55 -6.54 -6.53 -6.52 -6.51 -6.50 -6.49 -6.48
##  [181] -6.47 -6.46 -6.45 -6.44 -6.43 -6.42 -6.41 -6.40 -6.39 -6.38 -6.37 -6.36
##  [193] -6.35 -6.34 -6.33 -6.32 -6.31 -6.30 -6.29 -6.28 -6.27 -6.26 -6.25 -6.24
##  [205] -6.23 -6.22 -6.21 -6.20 -6.19 -6.18 -6.17 -6.16 -6.15 -6.14 -6.13 -6.12
##  [217] -6.11 -6.10 -6.09 -6.08 -6.07 -6.06 -6.05 -6.04 -6.03 -6.02 -6.01 -6.00
##  [229] -5.99 -5.98 -5.97 -5.96 -5.95 -5.94 -5.93 -5.92 -5.91 -5.90 -5.89 -5.88
##  [241] -5.87 -5.86 -5.85 -5.84 -5.83 -5.82 -5.81 -5.80 -5.79 -5.78 -5.77 -5.76
##  [253] -5.75 -5.74 -5.73 -5.72 -5.71 -5.70 -5.69 -5.68 -5.67 -5.66 -5.65 -5.64
##  [265] -5.63 -5.62 -5.61 -5.60 -5.59 -5.58 -5.57 -5.56 -5.55 -5.54 -5.53 -5.52
##  [277] -5.51 -5.50 -5.49 -5.48 -5.47 -5.46 -5.45 -5.44 -5.43 -5.42 -5.41 -5.40
##  [289] -5.39 -5.38 -5.37 -5.36 -5.35 -5.34 -5.33 -5.32 -5.31 -5.30 -5.29 -5.28
##  [301] -5.27 -5.26 -5.25 -5.24 -5.23 -5.22 -5.21 -5.20 -5.19 -5.18 -5.17 -5.16
##  [313] -5.15 -5.14 -5.13 -5.12 -5.11 -5.10 -5.09 -5.08 -5.07 -5.06 -5.05 -5.04
##  [325] -5.03 -5.02 -5.01 -5.00 -4.99 -4.98 -4.97 -4.96 -4.95 -4.94 -4.93 -4.92
##  [337] -4.91 -4.90 -4.89 -4.88 -4.87 -4.86 -4.85 -4.84 -4.83 -4.82 -4.81 -4.80
##  [349] -4.79 -4.78 -4.77 -4.76 -4.75 -4.74 -4.73 -4.72 -4.71 -4.70 -4.69 -4.68
##  [361] -4.67 -4.66 -4.65 -4.64 -4.63 -4.62 -4.61 -4.60 -4.59 -4.58 -4.57 -4.56
##  [373] -4.55 -4.54 -4.53 -4.52 -4.51 -4.50 -4.49 -4.48 -4.47 -4.46 -4.45 -4.44
##  [385] -4.43 -4.42 -4.41 -4.40 -4.39 -4.38 -4.37 -4.36 -4.35 -4.34 -4.33 -4.32
##  [397] -4.31 -4.30 -4.29 -4.28 -4.27 -4.26 -4.25 -4.24 -4.23 -4.22 -4.21 -4.20
##  [409] -4.19 -4.18 -4.17 -4.16 -4.15 -4.14 -4.13 -4.12 -4.11 -4.10 -4.09 -4.08
##  [421] -4.07 -4.06 -4.05 -4.04 -4.03 -4.02 -4.01 -4.00 -3.99 -3.98 -3.97 -3.96
##  [433] -3.95 -3.94 -3.93 -3.92 -3.91 -3.90 -3.89 -3.88 -3.87 -3.86 -3.85 -3.84
##  [445] -3.83 -3.82 -3.81 -3.80 -3.79 -3.78 -3.77 -3.76 -3.75 -3.74 -3.73 -3.72
##  [457] -3.71 -3.70 -3.69 -3.68 -3.67 -3.66 -3.65 -3.64 -3.63 -3.62 -3.61 -3.60
##  [469] -3.59 -3.58 -3.57 -3.56 -3.55 -3.54 -3.53 -3.52 -3.51 -3.50 -3.49 -3.48
##  [481] -3.47 -3.46 -3.45 -3.44 -3.43 -3.42 -3.41 -3.40 -3.39 -3.38 -3.37 -3.36
##  [493] -3.35 -3.34 -3.33 -3.32 -3.31 -3.30 -3.29 -3.28 -3.27 -3.26 -3.25 -3.24
##  [505] -3.23 -3.22 -3.21 -3.20 -3.19 -3.18 -3.17 -3.16 -3.15 -3.14 -3.13 -3.12
##  [517] -3.11 -3.10 -3.09 -3.08 -3.07 -3.06 -3.05 -3.04 -3.03 -3.02 -3.01 -3.00
##  [529] -2.99 -2.98 -2.97 -2.96 -2.95 -2.94 -2.93 -2.92 -2.91 -2.90 -2.89 -2.88
##  [541] -2.87 -2.86 -2.85 -2.84 -2.83 -2.82 -2.81 -2.80 -2.79 -2.78 -2.77 -2.76
##  [553] -2.75 -2.74 -2.73 -2.72 -2.71 -2.70 -2.69 -2.68 -2.67 -2.66 -2.65 -2.64
##  [565] -2.63 -2.62 -2.61 -2.60 -2.59 -2.58 -2.57 -2.56 -2.55 -2.54 -2.53 -2.52
##  [577] -2.51 -2.50 -2.49 -2.48 -2.47 -2.46 -2.45 -2.44 -2.43 -2.42 -2.41 -2.40
##  [589] -2.39 -2.38 -2.37 -2.36 -2.35 -2.34 -2.33 -2.32 -2.31 -2.30 -2.29 -2.28
##  [601] -2.27 -2.26 -2.25 -2.24 -2.23 -2.22 -2.21 -2.20 -2.19 -2.18 -2.17 -2.16
##  [613] -2.15 -2.14 -2.13 -2.12 -2.11 -2.10 -2.09 -2.08 -2.07 -2.06 -2.05 -2.04
##  [625] -2.03 -2.02 -2.01 -2.00 -1.99 -1.98 -1.97 -1.96 -1.95 -1.94 -1.93 -1.92
##  [637] -1.91 -1.90 -1.89 -1.88 -1.87 -1.86 -1.85 -1.84 -1.83 -1.82 -1.81 -1.80
##  [649] -1.79 -1.78 -1.77 -1.76 -1.75 -1.74 -1.73 -1.72 -1.71 -1.70 -1.69 -1.68
##  [661] -1.67 -1.66 -1.65 -1.64 -1.63 -1.62 -1.61 -1.60 -1.59 -1.58 -1.57 -1.56
##  [673] -1.55 -1.54 -1.53 -1.52 -1.51 -1.50 -1.49 -1.48 -1.47 -1.46 -1.45 -1.44
##  [685] -1.43 -1.42 -1.41 -1.40 -1.39 -1.38 -1.37 -1.36 -1.35 -1.34 -1.33 -1.32
##  [697] -1.31 -1.30 -1.29 -1.28 -1.27 -1.26 -1.25 -1.24 -1.23 -1.22 -1.21 -1.20
##  [709] -1.19 -1.18 -1.17 -1.16 -1.15 -1.14 -1.13 -1.12 -1.11 -1.10 -1.09 -1.08
##  [721] -1.07 -1.06 -1.05 -1.04 -1.03 -1.02 -1.01 -1.00 -0.99 -0.98 -0.97 -0.96
##  [733] -0.95 -0.94 -0.93 -0.92 -0.91 -0.90 -0.89 -0.88 -0.87 -0.86 -0.85 -0.84
##  [745] -0.83 -0.82 -0.81 -0.80 -0.79 -0.78 -0.77 -0.76 -0.75 -0.74 -0.73 -0.72
##  [757] -0.71 -0.70 -0.69 -0.68 -0.67 -0.66 -0.65 -0.64 -0.63 -0.62 -0.61 -0.60
##  [769] -0.59 -0.58 -0.57 -0.56 -0.55 -0.54 -0.53 -0.52 -0.51 -0.50 -0.49 -0.48
##  [781] -0.47 -0.46 -0.45 -0.44 -0.43 -0.42 -0.41 -0.40 -0.39 -0.38 -0.37 -0.36
##  [793] -0.35 -0.34 -0.33 -0.32 -0.31 -0.30 -0.29 -0.28 -0.27 -0.26 -0.25 -0.24
##  [805] -0.23 -0.22 -0.21 -0.20 -0.19 -0.18 -0.17 -0.16 -0.15 -0.14 -0.13 -0.12
##  [817] -0.11 -0.10 -0.09 -0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01  0.00
##  [829]  0.01  0.02  0.03  0.04  0.05  0.06  0.07  0.08  0.09  0.10  0.11  0.12
##  [841]  0.13  0.14  0.15  0.16  0.17  0.18  0.19  0.20  0.21  0.22  0.23  0.24
##  [853]  0.25  0.26  0.27  0.28  0.29  0.30  0.31  0.32  0.33  0.34  0.35  0.36
##  [865]  0.37  0.38  0.39  0.40  0.41  0.42  0.43  0.44  0.45  0.46  0.47  0.48
##  [877]  0.49  0.50  0.51  0.52  0.53  0.54  0.55  0.56  0.57  0.58  0.59  0.60
##  [889]  0.61  0.62  0.63  0.64  0.65  0.66  0.67  0.68  0.69  0.70  0.71  0.72
##  [901]  0.73  0.74  0.75  0.76  0.77  0.78  0.79  0.80  0.81  0.82  0.83  0.84
##  [913]  0.85  0.86  0.87  0.88  0.89  0.90  0.91  0.92  0.93  0.94  0.95  0.96
##  [925]  0.97  0.98  0.99  1.00  1.01  1.02  1.03  1.04  1.05  1.06  1.07  1.08
##  [937]  1.09  1.10  1.11  1.12  1.13  1.14  1.15  1.16  1.17  1.18  1.19  1.20
##  [949]  1.21  1.22  1.23  1.24  1.25  1.26  1.27  1.28  1.29  1.30  1.31  1.32
##  [961]  1.33  1.34  1.35  1.36  1.37  1.38  1.39  1.40  1.41  1.42  1.43  1.44
##  [973]  1.45  1.46  1.47  1.48  1.49  1.50  1.51  1.52  1.53  1.54  1.55  1.56
##  [985]  1.57  1.58  1.59  1.60  1.61  1.62  1.63  1.64  1.65  1.66  1.67  1.68
##  [997]  1.69  1.70  1.71  1.72  1.73  1.74  1.75  1.76  1.77  1.78  1.79  1.80
## [1009]  1.81  1.82  1.83  1.84  1.85  1.86  1.87  1.88  1.89  1.90  1.91  1.92
## [1021]  1.93  1.94  1.95  1.96  1.97  1.98  1.99  2.00  2.01  2.02  2.03  2.04
## [1033]  2.05  2.06  2.07  2.08  2.09  2.10  2.11  2.12  2.13  2.14  2.15  2.16
## [1045]  2.17  2.18  2.19  2.20  2.21  2.22  2.23  2.24  2.25  2.26  2.27  2.28
## [1057]  2.29  2.30  2.31  2.32  2.33  2.34  2.35  2.36  2.37  2.38  2.39  2.40
## [1069]  2.41  2.42  2.43  2.44  2.45  2.46  2.47  2.48  2.49  2.50  2.51  2.52
## [1081]  2.53  2.54  2.55  2.56  2.57  2.58  2.59  2.60  2.61  2.62  2.63  2.64
## [1093]  2.65  2.66  2.67  2.68  2.69  2.70  2.71  2.72  2.73  2.74  2.75  2.76
## [1105]  2.77  2.78  2.79  2.80  2.81  2.82  2.83  2.84  2.85  2.86  2.87  2.88
## [1117]  2.89  2.90  2.91  2.92  2.93  2.94  2.95  2.96  2.97  2.98  2.99  3.00
## [1129]  3.01  3.02  3.03  3.04  3.05  3.06  3.07  3.08  3.09  3.10  3.11  3.12
## [1141]  3.13  3.14  3.15  3.16  3.17  3.18  3.19  3.20  3.21  3.22  3.23  3.24
## [1153]  3.25  3.26  3.27  3.28  3.29  3.30  3.31  3.32  3.33  3.34  3.35  3.36
## [1165]  3.37  3.38  3.39  3.40  3.41  3.42  3.43  3.44  3.45  3.46  3.47  3.48
## [1177]  3.49  3.50  3.51  3.52  3.53  3.54  3.55  3.56  3.57  3.58  3.59  3.60
## [1189]  3.61  3.62  3.63  3.64  3.65  3.66  3.67  3.68  3.69  3.70  3.71  3.72
## [1201]  3.73  3.74  3.75  3.76  3.77  3.78  3.79  3.80  3.81  3.82  3.83  3.84
## [1213]  3.85  3.86  3.87  3.88  3.89  3.90  3.91  3.92  3.93  3.94  3.95  3.96
## [1225]  3.97  3.98  3.99  4.00  4.01  4.02  4.03  4.04  4.05  4.06  4.07  4.08
## [1237]  4.09  4.10  4.11  4.12  4.13  4.14  4.15  4.16  4.17  4.18  4.19  4.20
## [1249]  4.21  4.22  4.23  4.24  4.25  4.26  4.27  4.28  4.29  4.30  4.31  4.32
## [1261]  4.33  4.34  4.35  4.36  4.37  4.38  4.39  4.40  4.41  4.42  4.43  4.44
## [1273]  4.45  4.46  4.47  4.48  4.49  4.50  4.51  4.52  4.53  4.54  4.55  4.56
## [1285]  4.57  4.58  4.59  4.60  4.61  4.62  4.63  4.64  4.65  4.66  4.67  4.68
## [1297]  4.69  4.70  4.71  4.72  4.73  4.74  4.75  4.76  4.77  4.78  4.79  4.80
## [1309]  4.81  4.82  4.83  4.84  4.85  4.86  4.87  4.88  4.89  4.90  4.91  4.92
## [1321]  4.93  4.94  4.95  4.96  4.97  4.98  4.99  5.00  5.01  5.02  5.03  5.04
## [1333]  5.05  5.06  5.07  5.08  5.09  5.10  5.11  5.12  5.13  5.14  5.15  5.16
## [1345]  5.17  5.18  5.19  5.20  5.21  5.22  5.23  5.24  5.25  5.26  5.27  5.28
## [1357]  5.29  5.30  5.31  5.32  5.33  5.34  5.35  5.36  5.37  5.38  5.39  5.40
## [1369]  5.41  5.42  5.43  5.44  5.45  5.46  5.47  5.48  5.49  5.50  5.51  5.52
## [1381]  5.53  5.54  5.55  5.56  5.57  5.58  5.59  5.60  5.61  5.62  5.63  5.64
## [1393]  5.65  5.66  5.67  5.68  5.69  5.70  5.71  5.72  5.73  5.74  5.75  5.76
## [1405]  5.77  5.78  5.79  5.80  5.81  5.82  5.83  5.84  5.85  5.86  5.87  5.88
## [1417]  5.89  5.90  5.91  5.92  5.93  5.94  5.95  5.96  5.97  5.98  5.99  6.00
## [1429]  6.01  6.02  6.03  6.04  6.05  6.06  6.07  6.08  6.09  6.10  6.11  6.12
## [1441]  6.13  6.14  6.15  6.16  6.17  6.18  6.19  6.20  6.21  6.22  6.23  6.24
## [1453]  6.25  6.26  6.27  6.28  6.29  6.30  6.31  6.32  6.33  6.34  6.35  6.36
## [1465]  6.37  6.38  6.39  6.40  6.41  6.42  6.43  6.44  6.45  6.46  6.47  6.48
## [1477]  6.49  6.50  6.51  6.52  6.53  6.54  6.55  6.56  6.57  6.58  6.59  6.60
## [1489]  6.61  6.62  6.63  6.64  6.65  6.66  6.67  6.68  6.69  6.70  6.71  6.72
## [1501]  6.73  6.74  6.75  6.76  6.77  6.78  6.79  6.80  6.81  6.82  6.83  6.84
## [1513]  6.85  6.86  6.87  6.88  6.89  6.90  6.91  6.92  6.93  6.94  6.95  6.96
## [1525]  6.97  6.98  6.99  7.00  7.01  7.02  7.03  7.04  7.05  7.06  7.07  7.08
## [1537]  7.09  7.10  7.11  7.12  7.13  7.14  7.15  7.16  7.17  7.18  7.19  7.20
## [1549]  7.21  7.22  7.23  7.24  7.25  7.26  7.27  7.28  7.29  7.30  7.31  7.32
## [1561]  7.33  7.34  7.35  7.36  7.37  7.38  7.39  7.40  7.41  7.42  7.43  7.44
## [1573]  7.45  7.46  7.47  7.48  7.49  7.50  7.51  7.52  7.53  7.54  7.55  7.56
## [1585]  7.57  7.58  7.59  7.60  7.61  7.62  7.63  7.64  7.65  7.66  7.67  7.68
## [1597]  7.69  7.70  7.71  7.72  7.73  7.74  7.75  7.76  7.77  7.78  7.79  7.80
## [1609]  7.81  7.82  7.83  7.84  7.85  7.86  7.87  7.88  7.89  7.90  7.91  7.92
## [1621]  7.93  7.94  7.95  7.96  7.97  7.98  7.99  8.00  8.01  8.02  8.03  8.04
## [1633]  8.05  8.06  8.07  8.08  8.09  8.10  8.11  8.12  8.13  8.14  8.15  8.16
## [1645]  8.17  8.18  8.19  8.20  8.21  8.22  8.23  8.24  8.25  8.26  8.27  8.28
## [1657]  8.29  8.30  8.31  8.32  8.33  8.34  8.35  8.36  8.37  8.38  8.39  8.40
## [1669]  8.41  8.42  8.43  8.44  8.45  8.46  8.47  8.48  8.49  8.50  8.51  8.52
## [1681]  8.53  8.54  8.55  8.56  8.57  8.58  8.59  8.60  8.61  8.62  8.63  8.64
## [1693]  8.65  8.66  8.67  8.68  8.69  8.70  8.71  8.72  8.73  8.74  8.75  8.76
## [1705]  8.77  8.78  8.79  8.80  8.81  8.82  8.83  8.84  8.85  8.86  8.87  8.88
## [1717]  8.89  8.90  8.91  8.92  8.93  8.94  8.95  8.96  8.97  8.98  8.99  9.00
## [1729]  9.01  9.02  9.03  9.04  9.05  9.06  9.07  9.08  9.09  9.10  9.11  9.12
## [1741]  9.13  9.14  9.15  9.16  9.17  9.18  9.19  9.20  9.21  9.22  9.23  9.24
## [1753]  9.25  9.26  9.27  9.28  9.29  9.30  9.31  9.32  9.33  9.34  9.35  9.36
## [1765]  9.37  9.38  9.39  9.40  9.41  9.42  9.43  9.44  9.45  9.46  9.47  9.48
## [1777]  9.49  9.50  9.51  9.52  9.53  9.54  9.55  9.56  9.57  9.58  9.59  9.60
## [1789]  9.61  9.62  9.63  9.64  9.65  9.66  9.67  9.68  9.69  9.70  9.71  9.72
## [1801]  9.73  9.74  9.75  9.76  9.77  9.78  9.79  9.80  9.81  9.82  9.83  9.84
## [1813]  9.85  9.86  9.87  9.88  9.89  9.90  9.91  9.92  9.93  9.94  9.95  9.96
## [1825]  9.97  9.98  9.99 10.00

Dari kurva boxcox dapat dilihat kurva melewati \(\lambda=1\) yang menunjukkan data stasioner dalam ragam. Dan juga didapat \(\lambda\) optimum \(7.59\)

Partisi 2 : Data 51-100

Input Data

data3_s<-data[51:100,]
data3 <-data_ts[51:100]
data3

##  [1] 15346 15487 15636 15696 15864 15904 15582 15683 15399 15447 15399 15560
## [13] 15283 15409 15383 15478 15503 15601 15768 15727 15598 15629 15586 15692
## [25] 15536 15639 15803 15873 15883 16112 16210 16232 15951 16047 15920 16038
## [37] 16244 16268 16480 16470 16343 16239 16067 16208 16284 16135 15934 15672
## [49] 15484 15649

Time Series Plot

ts.plot(data3)

Dapat dilihat pada eksplorasi plot diatas data tidak stasioner dalam rataan.

Plot ACF

acf(data3,lag.max = 20)

Plot ACF menunjukkan pola Tails-off slowly yang menunjukkan data tersebut tidak stasioner dalam rataan.

ADF Test

adf.test(data3)

## 
##  Augmented Dickey-Fuller Test
## 
## data:  data3
## Dickey-Fuller = -2.0266, Lag order = 3, p-value = 0.5636
## alternative hypothesis: stationary

Dari tes ADF yang dilakukan didapat \(p-value =0.5636\) dimana \(p-value<0.05\) maka data tersebut tidak stasioner dalam rataan.

Boxcox dan Lambda Optimum

index <- seq(51:100)
bc = boxcox(data3_s$Kurs~index, lambda = seq(-20,10,by=0.01))

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

## [1] -9.66

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

##    [1] -20.00 -19.99 -19.98 -19.97 -19.96 -19.95 -19.94 -19.93 -19.92 -19.91
##   [11] -19.90 -19.89 -19.88 -19.87 -19.86 -19.85 -19.84 -19.83 -19.82 -19.81
##   [21] -19.80 -19.79 -19.78 -19.77 -19.76 -19.75 -19.74 -19.73 -19.72 -19.71
##   [31] -19.70 -19.69 -19.68 -19.67 -19.66 -19.65 -19.64 -19.63 -19.62 -19.61
##   [41] -19.60 -19.59 -19.58 -19.57 -19.56 -19.55 -19.54 -19.53 -19.52 -19.51
##   [51] -19.50 -19.49 -19.48 -19.47 -19.46 -19.45 -19.44 -19.43 -19.42 -19.41
##   [61] -19.40 -19.39 -19.38 -19.37 -19.36 -19.35 -19.34 -19.33 -19.32 -19.31
##   [71] -19.30 -19.29 -19.28 -19.27 -19.26 -19.25 -19.24 -19.23 -19.22 -19.21
##   [81] -19.20 -19.19 -19.18 -19.17 -19.16 -19.15 -19.14 -19.13 -19.12 -19.11
##   [91] -19.10 -19.09 -19.08 -19.07 -19.06 -19.05 -19.04 -19.03 -19.02 -19.01
##  [101] -19.00 -18.99 -18.98 -18.97 -18.96 -18.95 -18.94 -18.93 -18.92 -18.91
##  [111] -18.90 -18.89 -18.88 -18.87 -18.86 -18.85 -18.84 -18.83 -18.82 -18.81
##  [121] -18.80 -18.79 -18.78 -18.77 -18.76 -18.75 -18.74 -18.73 -18.72 -18.71
##  [131] -18.70 -18.69 -18.68 -18.67 -18.66 -18.65 -18.64 -18.63 -18.62 -18.61
##  [141] -18.60 -18.59 -18.58 -18.57 -18.56 -18.55 -18.54 -18.53 -18.52 -18.51
##  [151] -18.50 -18.49 -18.48 -18.47 -18.46 -18.45 -18.44 -18.43 -18.42 -18.41
##  [161] -18.40 -18.39 -18.38 -18.37 -18.36 -18.35 -18.34 -18.33 -18.32 -18.31
##  [171] -18.30 -18.29 -18.28 -18.27 -18.26 -18.25 -18.24 -18.23 -18.22 -18.21
##  [181] -18.20 -18.19 -18.18 -18.17 -18.16 -18.15 -18.14 -18.13 -18.12 -18.11
##  [191] -18.10 -18.09 -18.08 -18.07 -18.06 -18.05 -18.04 -18.03 -18.02 -18.01
##  [201] -18.00 -17.99 -17.98 -17.97 -17.96 -17.95 -17.94 -17.93 -17.92 -17.91
##  [211] -17.90 -17.89 -17.88 -17.87 -17.86 -17.85 -17.84 -17.83 -17.82 -17.81
##  [221] -17.80 -17.79 -17.78 -17.77 -17.76 -17.75 -17.74 -17.73 -17.72 -17.71
##  [231] -17.70 -17.69 -17.68 -17.67 -17.66 -17.65 -17.64 -17.63 -17.62 -17.61
##  [241] -17.60 -17.59 -17.58 -17.57 -17.56 -17.55 -17.54 -17.53 -17.52 -17.51
##  [251] -17.50 -17.49 -17.48 -17.47 -17.46 -17.45 -17.44 -17.43 -17.42 -17.41
##  [261] -17.40 -17.39 -17.38 -17.37 -17.36 -17.35 -17.34 -17.33 -17.32 -17.31
##  [271] -17.30 -17.29 -17.28 -17.27 -17.26 -17.25 -17.24 -17.23 -17.22 -17.21
##  [281] -17.20 -17.19 -17.18 -17.17 -17.16 -17.15 -17.14 -17.13 -17.12 -17.11
##  [291] -17.10 -17.09 -17.08 -17.07 -17.06 -17.05 -17.04 -17.03 -17.02 -17.01
##  [301] -17.00 -16.99 -16.98 -16.97 -16.96 -16.95 -16.94 -16.93 -16.92 -16.91
##  [311] -16.90 -16.89 -16.88 -16.87 -16.86 -16.85 -16.84 -16.83 -16.82 -16.81
##  [321] -16.80 -16.79 -16.78 -16.77 -16.76 -16.75 -16.74 -16.73 -16.72 -16.71
##  [331] -16.70 -16.69 -16.68 -16.67 -16.66 -16.65 -16.64 -16.63 -16.62 -16.61
##  [341] -16.60 -16.59 -16.58 -16.57 -16.56 -16.55 -16.54 -16.53 -16.52 -16.51
##  [351] -16.50 -16.49 -16.48 -16.47 -16.46 -16.45 -16.44 -16.43 -16.42 -16.41
##  [361] -16.40 -16.39 -16.38 -16.37 -16.36 -16.35 -16.34 -16.33 -16.32 -16.31
##  [371] -16.30 -16.29 -16.28 -16.27 -16.26 -16.25 -16.24 -16.23 -16.22 -16.21
##  [381] -16.20 -16.19 -16.18 -16.17 -16.16 -16.15 -16.14 -16.13 -16.12 -16.11
##  [391] -16.10 -16.09 -16.08 -16.07 -16.06 -16.05 -16.04 -16.03 -16.02 -16.01
##  [401] -16.00 -15.99 -15.98 -15.97 -15.96 -15.95 -15.94 -15.93 -15.92 -15.91
##  [411] -15.90 -15.89 -15.88 -15.87 -15.86 -15.85 -15.84 -15.83 -15.82 -15.81
##  [421] -15.80 -15.79 -15.78 -15.77 -15.76 -15.75 -15.74 -15.73 -15.72 -15.71
##  [431] -15.70 -15.69 -15.68 -15.67 -15.66 -15.65 -15.64 -15.63 -15.62 -15.61
##  [441] -15.60 -15.59 -15.58 -15.57 -15.56 -15.55 -15.54 -15.53 -15.52 -15.51
##  [451] -15.50 -15.49 -15.48 -15.47 -15.46 -15.45 -15.44 -15.43 -15.42 -15.41
##  [461] -15.40 -15.39 -15.38 -15.37 -15.36 -15.35 -15.34 -15.33 -15.32 -15.31
##  [471] -15.30 -15.29 -15.28 -15.27 -15.26 -15.25 -15.24 -15.23 -15.22 -15.21
##  [481] -15.20 -15.19 -15.18 -15.17 -15.16 -15.15 -15.14 -15.13 -15.12 -15.11
##  [491] -15.10 -15.09 -15.08 -15.07 -15.06 -15.05 -15.04 -15.03 -15.02 -15.01
##  [501] -15.00 -14.99 -14.98 -14.97 -14.96 -14.95 -14.94 -14.93 -14.92 -14.91
##  [511] -14.90 -14.89 -14.88 -14.87 -14.86 -14.85 -14.84 -14.83 -14.82 -14.81
##  [521] -14.80 -14.79 -14.78 -14.77 -14.76 -14.75 -14.74 -14.73 -14.72 -14.71
##  [531] -14.70 -14.69 -14.68 -14.67 -14.66 -14.65 -14.64 -14.63 -14.62 -14.61
##  [541] -14.60 -14.59 -14.58 -14.57 -14.56 -14.55 -14.54 -14.53 -14.52 -14.51
##  [551] -14.50 -14.49 -14.48 -14.47 -14.46 -14.45 -14.44 -14.43 -14.42 -14.41
##  [561] -14.40 -14.39 -14.38 -14.37 -14.36 -14.35 -14.34 -14.33 -14.32 -14.31
##  [571] -14.30 -14.29 -14.28 -14.27 -14.26 -14.25 -14.24 -14.23 -14.22 -14.21
##  [581] -14.20 -14.19 -14.18 -14.17 -14.16 -14.15 -14.14 -14.13 -14.12 -14.11
##  [591] -14.10 -14.09 -14.08 -14.07 -14.06 -14.05 -14.04 -14.03 -14.02 -14.01
##  [601] -14.00 -13.99 -13.98 -13.97 -13.96 -13.95 -13.94 -13.93 -13.92 -13.91
##  [611] -13.90 -13.89 -13.88 -13.87 -13.86 -13.85 -13.84 -13.83 -13.82 -13.81
##  [621] -13.80 -13.79 -13.78 -13.77 -13.76 -13.75 -13.74 -13.73 -13.72 -13.71
##  [631] -13.70 -13.69 -13.68 -13.67 -13.66 -13.65 -13.64 -13.63 -13.62 -13.61
##  [641] -13.60 -13.59 -13.58 -13.57 -13.56 -13.55 -13.54 -13.53 -13.52 -13.51
##  [651] -13.50 -13.49 -13.48 -13.47 -13.46 -13.45 -13.44 -13.43 -13.42 -13.41
##  [661] -13.40 -13.39 -13.38 -13.37 -13.36 -13.35 -13.34 -13.33 -13.32 -13.31
##  [671] -13.30 -13.29 -13.28 -13.27 -13.26 -13.25 -13.24 -13.23 -13.22 -13.21
##  [681] -13.20 -13.19 -13.18 -13.17 -13.16 -13.15 -13.14 -13.13 -13.12 -13.11
##  [691] -13.10 -13.09 -13.08 -13.07 -13.06 -13.05 -13.04 -13.03 -13.02 -13.01
##  [701] -13.00 -12.99 -12.98 -12.97 -12.96 -12.95 -12.94 -12.93 -12.92 -12.91
##  [711] -12.90 -12.89 -12.88 -12.87 -12.86 -12.85 -12.84 -12.83 -12.82 -12.81
##  [721] -12.80 -12.79 -12.78 -12.77 -12.76 -12.75 -12.74 -12.73 -12.72 -12.71
##  [731] -12.70 -12.69 -12.68 -12.67 -12.66 -12.65 -12.64 -12.63 -12.62 -12.61
##  [741] -12.60 -12.59 -12.58 -12.57 -12.56 -12.55 -12.54 -12.53 -12.52 -12.51
##  [751] -12.50 -12.49 -12.48 -12.47 -12.46 -12.45 -12.44 -12.43 -12.42 -12.41
##  [761] -12.40 -12.39 -12.38 -12.37 -12.36 -12.35 -12.34 -12.33 -12.32 -12.31
##  [771] -12.30 -12.29 -12.28 -12.27 -12.26 -12.25 -12.24 -12.23 -12.22 -12.21
##  [781] -12.20 -12.19 -12.18 -12.17 -12.16 -12.15 -12.14 -12.13 -12.12 -12.11
##  [791] -12.10 -12.09 -12.08 -12.07 -12.06 -12.05 -12.04 -12.03 -12.02 -12.01
##  [801] -12.00 -11.99 -11.98 -11.97 -11.96 -11.95 -11.94 -11.93 -11.92 -11.91
##  [811] -11.90 -11.89 -11.88 -11.87 -11.86 -11.85 -11.84 -11.83 -11.82 -11.81
##  [821] -11.80 -11.79 -11.78 -11.77 -11.76 -11.75 -11.74 -11.73 -11.72 -11.71
##  [831] -11.70 -11.69 -11.68 -11.67 -11.66 -11.65 -11.64 -11.63 -11.62 -11.61
##  [841] -11.60 -11.59 -11.58 -11.57 -11.56 -11.55 -11.54 -11.53 -11.52 -11.51
##  [851] -11.50 -11.49 -11.48 -11.47 -11.46 -11.45 -11.44 -11.43 -11.42 -11.41
##  [861] -11.40 -11.39 -11.38 -11.37 -11.36 -11.35 -11.34 -11.33 -11.32 -11.31
##  [871] -11.30 -11.29 -11.28 -11.27 -11.26 -11.25 -11.24 -11.23 -11.22 -11.21
##  [881] -11.20 -11.19 -11.18 -11.17 -11.16 -11.15 -11.14 -11.13 -11.12 -11.11
##  [891] -11.10 -11.09 -11.08 -11.07 -11.06 -11.05 -11.04 -11.03 -11.02 -11.01
##  [901] -11.00 -10.99 -10.98 -10.97 -10.96 -10.95 -10.94 -10.93 -10.92 -10.91
##  [911] -10.90 -10.89 -10.88 -10.87 -10.86 -10.85 -10.84 -10.83 -10.82 -10.81
##  [921] -10.80 -10.79 -10.78 -10.77 -10.76 -10.75 -10.74 -10.73 -10.72 -10.71
##  [931] -10.70 -10.69 -10.68 -10.67 -10.66 -10.65 -10.64 -10.63 -10.62 -10.61
##  [941] -10.60 -10.59 -10.58 -10.57 -10.56 -10.55 -10.54 -10.53 -10.52 -10.51
##  [951] -10.50 -10.49 -10.48 -10.47 -10.46 -10.45 -10.44 -10.43 -10.42 -10.41
##  [961] -10.40 -10.39 -10.38 -10.37 -10.36 -10.35 -10.34 -10.33 -10.32 -10.31
##  [971] -10.30 -10.29 -10.28 -10.27 -10.26 -10.25 -10.24 -10.23 -10.22 -10.21
##  [981] -10.20 -10.19 -10.18 -10.17 -10.16 -10.15 -10.14 -10.13 -10.12 -10.11
##  [991] -10.10 -10.09 -10.08 -10.07 -10.06 -10.05 -10.04 -10.03 -10.02 -10.01
## [1001] -10.00  -9.99  -9.98  -9.97  -9.96  -9.95  -9.94  -9.93  -9.92  -9.91
## [1011]  -9.90  -9.89  -9.88  -9.87  -9.86  -9.85  -9.84  -9.83  -9.82  -9.81
## [1021]  -9.80  -9.79  -9.78  -9.77  -9.76  -9.75  -9.74  -9.73  -9.72  -9.71
## [1031]  -9.70  -9.69  -9.68  -9.67  -9.66  -9.65  -9.64  -9.63  -9.62  -9.61
## [1041]  -9.60  -9.59  -9.58  -9.57  -9.56  -9.55  -9.54  -9.53  -9.52  -9.51
## [1051]  -9.50  -9.49  -9.48  -9.47  -9.46  -9.45  -9.44  -9.43  -9.42  -9.41
## [1061]  -9.40  -9.39  -9.38  -9.37  -9.36  -9.35  -9.34  -9.33  -9.32  -9.31
## [1071]  -9.30  -9.29  -9.28  -9.27  -9.26  -9.25  -9.24  -9.23  -9.22  -9.21
## [1081]  -9.20  -9.19  -9.18  -9.17  -9.16  -9.15  -9.14  -9.13  -9.12  -9.11
## [1091]  -9.10  -9.09  -9.08  -9.07  -9.06  -9.05  -9.04  -9.03  -9.02  -9.01
## [1101]  -9.00  -8.99  -8.98  -8.97  -8.96  -8.95  -8.94  -8.93  -8.92  -8.91
## [1111]  -8.90  -8.89  -8.88  -8.87  -8.86  -8.85  -8.84  -8.83  -8.82  -8.81
## [1121]  -8.80  -8.79  -8.78  -8.77  -8.76  -8.75  -8.74  -8.73  -8.72  -8.71
## [1131]  -8.70  -8.69  -8.68  -8.67  -8.66  -8.65  -8.64  -8.63  -8.62  -8.61
## [1141]  -8.60  -8.59  -8.58  -8.57  -8.56  -8.55  -8.54  -8.53  -8.52  -8.51
## [1151]  -8.50  -8.49  -8.48  -8.47  -8.46  -8.45  -8.44  -8.43  -8.42  -8.41
## [1161]  -8.40  -8.39  -8.38  -8.37  -8.36  -8.35  -8.34  -8.33  -8.32  -8.31
## [1171]  -8.30  -8.29  -8.28  -8.27  -8.26  -8.25  -8.24  -8.23  -8.22  -8.21
## [1181]  -8.20  -8.19  -8.18  -8.17  -8.16  -8.15  -8.14  -8.13  -8.12  -8.11
## [1191]  -8.10  -8.09  -8.08  -8.07  -8.06  -8.05  -8.04  -8.03  -8.02  -8.01
## [1201]  -8.00  -7.99  -7.98  -7.97  -7.96  -7.95  -7.94  -7.93  -7.92  -7.91
## [1211]  -7.90  -7.89  -7.88  -7.87  -7.86  -7.85  -7.84  -7.83  -7.82  -7.81
## [1221]  -7.80  -7.79  -7.78  -7.77  -7.76  -7.75  -7.74  -7.73  -7.72  -7.71
## [1231]  -7.70  -7.69  -7.68  -7.67  -7.66  -7.65  -7.64  -7.63  -7.62  -7.61
## [1241]  -7.60  -7.59  -7.58  -7.57  -7.56  -7.55  -7.54  -7.53  -7.52  -7.51
## [1251]  -7.50  -7.49  -7.48  -7.47  -7.46  -7.45  -7.44  -7.43  -7.42  -7.41
## [1261]  -7.40  -7.39  -7.38  -7.37  -7.36  -7.35  -7.34  -7.33  -7.32  -7.31
## [1271]  -7.30  -7.29  -7.28  -7.27  -7.26  -7.25  -7.24  -7.23  -7.22  -7.21
## [1281]  -7.20  -7.19  -7.18  -7.17  -7.16  -7.15  -7.14  -7.13  -7.12  -7.11
## [1291]  -7.10  -7.09  -7.08  -7.07  -7.06  -7.05  -7.04  -7.03  -7.02  -7.01
## [1301]  -7.00  -6.99  -6.98  -6.97  -6.96  -6.95  -6.94  -6.93  -6.92  -6.91
## [1311]  -6.90  -6.89  -6.88  -6.87  -6.86  -6.85  -6.84  -6.83  -6.82  -6.81
## [1321]  -6.80  -6.79  -6.78  -6.77  -6.76  -6.75  -6.74  -6.73  -6.72  -6.71
## [1331]  -6.70  -6.69  -6.68  -6.67  -6.66  -6.65  -6.64  -6.63  -6.62  -6.61
## [1341]  -6.60  -6.59  -6.58  -6.57  -6.56  -6.55  -6.54  -6.53  -6.52  -6.51
## [1351]  -6.50  -6.49  -6.48  -6.47  -6.46  -6.45  -6.44  -6.43  -6.42  -6.41
## [1361]  -6.40  -6.39  -6.38  -6.37  -6.36  -6.35  -6.34  -6.33  -6.32  -6.31
## [1371]  -6.30  -6.29  -6.28  -6.27  -6.26  -6.25  -6.24  -6.23  -6.22  -6.21
## [1381]  -6.20  -6.19  -6.18  -6.17  -6.16  -6.15  -6.14  -6.13  -6.12  -6.11
## [1391]  -6.10  -6.09  -6.08  -6.07  -6.06  -6.05  -6.04  -6.03  -6.02  -6.01
## [1401]  -6.00  -5.99  -5.98  -5.97  -5.96  -5.95  -5.94  -5.93  -5.92  -5.91
## [1411]  -5.90  -5.89  -5.88  -5.87  -5.86  -5.85  -5.84  -5.83  -5.82  -5.81
## [1421]  -5.80  -5.79  -5.78  -5.77  -5.76  -5.75  -5.74  -5.73  -5.72  -5.71
## [1431]  -5.70  -5.69  -5.68  -5.67  -5.66  -5.65  -5.64  -5.63  -5.62  -5.61
## [1441]  -5.60  -5.59  -5.58  -5.57  -5.56  -5.55  -5.54  -5.53  -5.52  -5.51
## [1451]  -5.50  -5.49  -5.48  -5.47  -5.46  -5.45  -5.44  -5.43  -5.42  -5.41
## [1461]  -5.40  -5.39  -5.38  -5.37  -5.36  -5.35  -5.34  -5.33  -5.32  -5.31
## [1471]  -5.30  -5.29  -5.28  -5.27  -5.26  -5.25  -5.24  -5.23  -5.22  -5.21
## [1481]  -5.20  -5.19  -5.18  -5.17  -5.16  -5.15  -5.14  -5.13  -5.12  -5.11
## [1491]  -5.10  -5.09  -5.08  -5.07  -5.06  -5.05  -5.04  -5.03  -5.02  -5.01
## [1501]  -5.00  -4.99  -4.98  -4.97  -4.96  -4.95  -4.94  -4.93  -4.92  -4.91
## [1511]  -4.90  -4.89  -4.88  -4.87  -4.86  -4.85  -4.84  -4.83  -4.82  -4.81
## [1521]  -4.80  -4.79  -4.78  -4.77  -4.76  -4.75  -4.74  -4.73  -4.72  -4.71
## [1531]  -4.70  -4.69  -4.68  -4.67  -4.66  -4.65  -4.64  -4.63  -4.62  -4.61
## [1541]  -4.60  -4.59  -4.58  -4.57  -4.56  -4.55  -4.54  -4.53  -4.52  -4.51
## [1551]  -4.50  -4.49  -4.48  -4.47  -4.46  -4.45  -4.44  -4.43  -4.42  -4.41
## [1561]  -4.40  -4.39  -4.38  -4.37  -4.36  -4.35  -4.34  -4.33  -4.32  -4.31
## [1571]  -4.30  -4.29  -4.28  -4.27  -4.26  -4.25  -4.24  -4.23  -4.22  -4.21
## [1581]  -4.20  -4.19  -4.18  -4.17  -4.16  -4.15  -4.14  -4.13  -4.12  -4.11
## [1591]  -4.10  -4.09  -4.08  -4.07  -4.06  -4.05  -4.04  -4.03  -4.02  -4.01
## [1601]  -4.00  -3.99  -3.98  -3.97  -3.96  -3.95  -3.94  -3.93  -3.92  -3.91
## [1611]  -3.90  -3.89  -3.88  -3.87  -3.86  -3.85  -3.84  -3.83  -3.82  -3.81
## [1621]  -3.80  -3.79  -3.78  -3.77  -3.76  -3.75  -3.74  -3.73  -3.72  -3.71
## [1631]  -3.70  -3.69  -3.68  -3.67  -3.66  -3.65  -3.64  -3.63  -3.62  -3.61
## [1641]  -3.60  -3.59  -3.58  -3.57  -3.56  -3.55  -3.54  -3.53  -3.52  -3.51
## [1651]  -3.50  -3.49  -3.48  -3.47  -3.46  -3.45  -3.44  -3.43  -3.42  -3.41
## [1661]  -3.40  -3.39  -3.38  -3.37  -3.36  -3.35  -3.34  -3.33  -3.32  -3.31
## [1671]  -3.30  -3.29  -3.28  -3.27  -3.26  -3.25  -3.24  -3.23  -3.22  -3.21
## [1681]  -3.20  -3.19  -3.18  -3.17  -3.16  -3.15  -3.14  -3.13  -3.12  -3.11
## [1691]  -3.10  -3.09  -3.08  -3.07  -3.06  -3.05  -3.04  -3.03  -3.02  -3.01
## [1701]  -3.00  -2.99  -2.98  -2.97  -2.96  -2.95  -2.94  -2.93  -2.92  -2.91
## [1711]  -2.90  -2.89  -2.88  -2.87  -2.86  -2.85  -2.84  -2.83  -2.82  -2.81
## [1721]  -2.80  -2.79  -2.78  -2.77  -2.76  -2.75  -2.74  -2.73  -2.72  -2.71
## [1731]  -2.70  -2.69  -2.68  -2.67  -2.66  -2.65  -2.64  -2.63  -2.62  -2.61
## [1741]  -2.60  -2.59  -2.58  -2.57  -2.56  -2.55  -2.54  -2.53  -2.52  -2.51
## [1751]  -2.50  -2.49  -2.48  -2.47  -2.46  -2.45  -2.44  -2.43  -2.42  -2.41
## [1761]  -2.40  -2.39  -2.38  -2.37  -2.36  -2.35  -2.34  -2.33  -2.32  -2.31
## [1771]  -2.30  -2.29  -2.28  -2.27  -2.26  -2.25  -2.24  -2.23  -2.22  -2.21
## [1781]  -2.20  -2.19  -2.18  -2.17  -2.16  -2.15  -2.14  -2.13  -2.12  -2.11
## [1791]  -2.10  -2.09  -2.08  -2.07  -2.06  -2.05  -2.04  -2.03  -2.02  -2.01
## [1801]  -2.00  -1.99  -1.98  -1.97  -1.96  -1.95  -1.94  -1.93  -1.92  -1.91
## [1811]  -1.90  -1.89  -1.88  -1.87  -1.86  -1.85  -1.84  -1.83  -1.82  -1.81
## [1821]  -1.80  -1.79  -1.78  -1.77  -1.76  -1.75  -1.74  -1.73  -1.72  -1.71
## [1831]  -1.70  -1.69  -1.68  -1.67  -1.66  -1.65  -1.64  -1.63  -1.62  -1.61
## [1841]  -1.60  -1.59  -1.58  -1.57  -1.56  -1.55  -1.54  -1.53  -1.52  -1.51
## [1851]  -1.50  -1.49  -1.48  -1.47  -1.46  -1.45  -1.44  -1.43  -1.42  -1.41
## [1861]  -1.40  -1.39  -1.38  -1.37  -1.36  -1.35  -1.34  -1.33  -1.32  -1.31
## [1871]  -1.30  -1.29  -1.28  -1.27  -1.26  -1.25  -1.24  -1.23  -1.22  -1.21
## [1881]  -1.20  -1.19  -1.18  -1.17  -1.16  -1.15  -1.14  -1.13  -1.12  -1.11
## [1891]  -1.10  -1.09  -1.08  -1.07  -1.06  -1.05  -1.04  -1.03  -1.02  -1.01
## [1901]  -1.00  -0.99  -0.98  -0.97  -0.96  -0.95  -0.94  -0.93  -0.92  -0.91
## [1911]  -0.90  -0.89  -0.88  -0.87  -0.86  -0.85  -0.84  -0.83  -0.82  -0.81
## [1921]  -0.80  -0.79  -0.78  -0.77  -0.76  -0.75  -0.74  -0.73  -0.72  -0.71
## [1931]  -0.70  -0.69  -0.68  -0.67  -0.66  -0.65  -0.64  -0.63  -0.62  -0.61
## [1941]  -0.60  -0.59  -0.58  -0.57  -0.56  -0.55  -0.54  -0.53  -0.52  -0.51
## [1951]  -0.50  -0.49  -0.48  -0.47  -0.46  -0.45  -0.44  -0.43  -0.42  -0.41
## [1961]  -0.40  -0.39  -0.38  -0.37  -0.36  -0.35  -0.34  -0.33  -0.32  -0.31
## [1971]  -0.30  -0.29  -0.28  -0.27  -0.26  -0.25  -0.24  -0.23  -0.22  -0.21
## [1981]  -0.20  -0.19  -0.18  -0.17  -0.16  -0.15  -0.14  -0.13  -0.12  -0.11
## [1991]  -0.10  -0.09  -0.08  -0.07  -0.06  -0.05  -0.04  -0.03  -0.02  -0.01
## [2001]   0.00   0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09
## [2011]   0.10   0.11   0.12   0.13   0.14   0.15   0.16   0.17   0.18   0.19
## [2021]   0.20   0.21   0.22   0.23   0.24   0.25   0.26   0.27   0.28   0.29
## [2031]   0.30   0.31   0.32   0.33   0.34   0.35   0.36   0.37   0.38   0.39
## [2041]   0.40   0.41   0.42   0.43   0.44   0.45   0.46   0.47   0.48   0.49
## [2051]   0.50   0.51   0.52   0.53   0.54   0.55   0.56   0.57   0.58   0.59
## [2061]   0.60   0.61   0.62   0.63   0.64   0.65   0.66   0.67   0.68   0.69
## [2071]   0.70   0.71   0.72   0.73   0.74   0.75   0.76   0.77   0.78   0.79
## [2081]   0.80   0.81   0.82   0.83   0.84   0.85   0.86   0.87   0.88   0.89
## [2091]   0.90   0.91   0.92   0.93   0.94   0.95   0.96   0.97   0.98   0.99
## [2101]   1.00   1.01   1.02   1.03   1.04   1.05   1.06   1.07   1.08   1.09
## [2111]   1.10   1.11   1.12   1.13   1.14   1.15   1.16   1.17   1.18   1.19
## [2121]   1.20   1.21   1.22   1.23   1.24   1.25   1.26   1.27   1.28   1.29
## [2131]   1.30   1.31   1.32   1.33   1.34   1.35   1.36   1.37   1.38   1.39
## [2141]   1.40   1.41   1.42   1.43   1.44   1.45   1.46   1.47   1.48   1.49
## [2151]   1.50   1.51   1.52   1.53   1.54   1.55   1.56   1.57   1.58   1.59
## [2161]   1.60   1.61   1.62   1.63   1.64   1.65   1.66   1.67   1.68   1.69
## [2171]   1.70   1.71   1.72   1.73   1.74   1.75   1.76   1.77   1.78   1.79
## [2181]   1.80   1.81   1.82   1.83   1.84   1.85   1.86   1.87   1.88   1.89
## [2191]   1.90   1.91   1.92   1.93   1.94   1.95   1.96   1.97   1.98   1.99
## [2201]   2.00   2.01   2.02   2.03   2.04   2.05   2.06   2.07   2.08   2.09
## [2211]   2.10   2.11   2.12   2.13   2.14   2.15   2.16   2.17   2.18   2.19
## [2221]   2.20   2.21   2.22   2.23   2.24   2.25   2.26   2.27   2.28   2.29
## [2231]   2.30   2.31   2.32   2.33   2.34   2.35   2.36   2.37   2.38   2.39
## [2241]   2.40   2.41   2.42   2.43   2.44   2.45   2.46   2.47   2.48   2.49
## [2251]   2.50   2.51   2.52   2.53   2.54   2.55   2.56   2.57   2.58   2.59
## [2261]   2.60   2.61   2.62   2.63   2.64   2.65   2.66   2.67   2.68   2.69
## [2271]   2.70   2.71   2.72   2.73   2.74   2.75   2.76   2.77   2.78   2.79
## [2281]   2.80   2.81   2.82   2.83   2.84   2.85   2.86   2.87   2.88   2.89
## [2291]   2.90   2.91   2.92   2.93   2.94   2.95   2.96   2.97   2.98   2.99
## [2301]   3.00   3.01   3.02   3.03   3.04   3.05   3.06   3.07   3.08   3.09
## [2311]   3.10   3.11   3.12   3.13   3.14   3.15   3.16   3.17   3.18   3.19
## [2321]   3.20   3.21   3.22   3.23   3.24   3.25   3.26   3.27   3.28   3.29
## [2331]   3.30   3.31   3.32   3.33   3.34   3.35   3.36   3.37   3.38   3.39
## [2341]   3.40   3.41   3.42   3.43   3.44   3.45   3.46   3.47   3.48   3.49
## [2351]   3.50   3.51   3.52   3.53   3.54   3.55   3.56   3.57   3.58   3.59
## [2361]   3.60   3.61   3.62   3.63   3.64   3.65   3.66   3.67   3.68   3.69
## [2371]   3.70   3.71   3.72   3.73   3.74   3.75   3.76   3.77   3.78   3.79
## [2381]   3.80   3.81   3.82   3.83   3.84   3.85   3.86   3.87   3.88   3.89

Dari kurva boxcox dapat dilihat kurva melewati \(\lambda=1\) yang menunjukkan data stasioner dalam ragam. Dan juga didapat \(\lambda\) optimum \(-9.66\)