LBB Time Series
BUdiman
April 27, 2023
library(TTR)## Warning: package 'TTR' was built under R version 4.2.3library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionSeri Waktu Penjualan Properti Rumah Rata-Rata Pergerakan Harga Median yang dikelompokkan berdasarkan interval triwulan per jenis properti dan jumlah kamar tidur.
1 Baca Data
properti <- read.csv("data_input/ma_lga_12345.csv")
properti- Deskripsi Tabel
- Saledate = tanggal penjualan properti berdasrkan Triwulan
- MA = Pergerakan rata rata Harga per triwulan
- type = tyepe properti
- bedrooms = Jumlah kamar
2 Data Pre-processing
properti_ts <- ts(data = properti$MA,
start = 2007,
#end = 2009,
frequency = 3)
properti_ts## Time Series:
## Start = c(2007, 1)
## End = c(2122, 2)
## Frequency = 3
## [1] 441854 441854 441854 441854 451583 440256 442566 446113 440123
## [10] 442131 459222 456822 457806 459109 460758 464788 467546 470333
## [19] 470365 469149 465919 463090 451077 451516 454270 456548 469920
## [28] 472726 475326 478413 478398 477238 477330 479010 482440 486436
## [37] 489104 491152 494544 498846 504592 506578 507248 506116 504318
## [46] 506001 496133 500158 510712 421291 421291 421291 421291 416031
## [55] 419628 423811 426488 437724 444351 449742 457394 466433 474590
## [64] 483176 491715 498022 503891 507090 507744 507449 507014 506615
## [73] 506615 506380 505739 505823 506406 508499 512374 516618 522103
## [82] 528926 534927 542051 549278 556586 564267 572582 581485 590949
## [91] 601041 609355 615743 619638 622466 624602 626608 628423 630814
## [100] 631875 548969 548969 548969 548969 552484 559580 561852 565467
## [109] 569682 574680 579369 588379 599614 608528 615603 623105 628969
## [118] 634155 636582 637421 635411 633695 634803 633875 634229 635515
## [127] 636687 641125 648174 655757 664635 673762 684006 694800 706711
## [136] 718261 727736 737159 745430 755683 771216 789732 810694 828058
## [145] 836056 837295 830727 820924 811121 803925 791446 735904 735904
## [154] 735904 735904 758340 764025 770046 765555 765515 771280 773355
## [163] 776325 772699 775199 778470 789627 789614 790965 794533 792171
## [172] 800432 804474 807826 812224 805066 805682 811908 820368 843904
## [181] 855039 866489 880625 891981 909131 923594 933589 952327 968331
## [190] 980953 995349 1004117 1010848 1015529 1017752 1007114 1002323 998136
## [199] 995363 970268 326076 326076 326076 326076 327321 324712 323556
## [208] 318922 316914 316751 317711 318695 324778 329856 333049 337144
## [217] 337400 339125 341807 344793 347754 348491 348512 347962 345573
## [226] 343298 341289 338293 336520 334488 332703 330278 328300 326476
## [235] 324725 325127 325521 327870 330319 332481 334804 336637 338105
## [244] 339220 339350 337838 336551 335449 368817 368817 368817 368817
## [253] 373482 377481 382010 380810 385791 391161 396448 402898 408608
## [262] 412509 415991 417970 419777 421158 423144 424673 424249 425453
## [271] 425922 425751 426621 428398 428365 429283 429361 428911 429832
## [280] 431567 432730 432791 432801 431418 430880 430654 430308 429897
## [289] 429059 428878 428532 427856 427623 426970 426936 426669 425659
## [298] 424412 518911 518911 518911 518911 518911 518911 518911 518911
## [307] 523285 522862 524008 535063 538694 555117 550851 547981 539828
## [316] 530987 540344 537592 548326 555644 566706 580696 581428 586470
## [325] 583883 583370 598512 598812 599507 602877 603343 612295 617363
## [334] 622045 616198 610618 606935 605273 606850 604413 604293 603434
## [343] 603281 601167 605637 599339 5978843 EDA
3.1 Visualisasi autoplot()
library(fpp)## Warning: package 'fpp' was built under R version 4.2.3## Loading required package: forecast## Warning: package 'forecast' was built under R version 4.2.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Loading required package: fma## Warning: package 'fma' was built under R version 4.2.3## Loading required package: expsmooth## Warning: package 'expsmooth' was built under R version 4.2.3## Loading required package: lmtest## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: tseries## Warning: package 'tseries' was built under R version 4.2.3properti_ts %>%
autoplot()
properti_decom1 <- properti_ts %>%
decompose()
properti_decom1 %>%
autoplot()
properti_ts## Time Series:
## Start = c(2007, 1)
## End = c(2122, 2)
## Frequency = 3
## [1] 441854 441854 441854 441854 451583 440256 442566 446113 440123
## [10] 442131 459222 456822 457806 459109 460758 464788 467546 470333
## [19] 470365 469149 465919 463090 451077 451516 454270 456548 469920
## [28] 472726 475326 478413 478398 477238 477330 479010 482440 486436
## [37] 489104 491152 494544 498846 504592 506578 507248 506116 504318
## [46] 506001 496133 500158 510712 421291 421291 421291 421291 416031
## [55] 419628 423811 426488 437724 444351 449742 457394 466433 474590
## [64] 483176 491715 498022 503891 507090 507744 507449 507014 506615
## [73] 506615 506380 505739 505823 506406 508499 512374 516618 522103
## [82] 528926 534927 542051 549278 556586 564267 572582 581485 590949
## [91] 601041 609355 615743 619638 622466 624602 626608 628423 630814
## [100] 631875 548969 548969 548969 548969 552484 559580 561852 565467
## [109] 569682 574680 579369 588379 599614 608528 615603 623105 628969
## [118] 634155 636582 637421 635411 633695 634803 633875 634229 635515
## [127] 636687 641125 648174 655757 664635 673762 684006 694800 706711
## [136] 718261 727736 737159 745430 755683 771216 789732 810694 828058
## [145] 836056 837295 830727 820924 811121 803925 791446 735904 735904
## [154] 735904 735904 758340 764025 770046 765555 765515 771280 773355
## [163] 776325 772699 775199 778470 789627 789614 790965 794533 792171
## [172] 800432 804474 807826 812224 805066 805682 811908 820368 843904
## [181] 855039 866489 880625 891981 909131 923594 933589 952327 968331
## [190] 980953 995349 1004117 1010848 1015529 1017752 1007114 1002323 998136
## [199] 995363 970268 326076 326076 326076 326076 327321 324712 323556
## [208] 318922 316914 316751 317711 318695 324778 329856 333049 337144
## [217] 337400 339125 341807 344793 347754 348491 348512 347962 345573
## [226] 343298 341289 338293 336520 334488 332703 330278 328300 326476
## [235] 324725 325127 325521 327870 330319 332481 334804 336637 338105
## [244] 339220 339350 337838 336551 335449 368817 368817 368817 368817
## [253] 373482 377481 382010 380810 385791 391161 396448 402898 408608
## [262] 412509 415991 417970 419777 421158 423144 424673 424249 425453
## [271] 425922 425751 426621 428398 428365 429283 429361 428911 429832
## [280] 431567 432730 432791 432801 431418 430880 430654 430308 429897
## [289] 429059 428878 428532 427856 427623 426970 426936 426669 425659
## [298] 424412 518911 518911 518911 518911 518911 518911 518911 518911
## [307] 523285 522862 524008 535063 538694 555117 550851 547981 539828
## [316] 530987 540344 537592 548326 555644 566706 580696 581428 586470
## [325] 583883 583370 598512 598812 599507 602877 603343 612295 617363
## [334] 622045 616198 610618 606935 605273 606850 604413 604293 603434
## [343] 603281 601167 605637 599339 5978844 Build Model ARIMA
properti_holts <- HoltWinters(x = properti_ts,
gamma = T)
properti_holts## Holt-Winters exponential smoothing with trend and additive seasonal component.
##
## Call:
## HoltWinters(x = properti_ts, gamma = T)
##
## Smoothing parameters:
## alpha: 0.996756
## beta : 0
## gamma: TRUE
##
## Coefficients:
## [,1]
## a 596176.6635
## b 1137.4000
## s1 -528.7849
## s2 -1945.2835
## s3 1707.3365properti_holts2 <- HoltWinters(x = properti_ts,
alpha = 0.8,
beta = 0.2,
gamma = T)properti_holts3 <- HoltWinters(x = properti_ts,
alpha = 0.7,
beta = 0.05,
gamma = T)#Model Evaluation
properti_holts$fitted %>%
head()## Time Series:
## Start = c(2008, 1)
## End = c(2009, 3)
## Frequency = 3
## xhat level trend season
## 2008.000 438304.5 440498.8 1137.4 -3331.77778
## 2008.333 449732.2 445174.3 1137.4 3420.55556
## 2008.667 449205.1 448156.4 1137.4 -88.77778
## 2009.000 438190.9 440373.8 1137.4 -3320.26309
## 2009.333 450436.0 445872.1 1137.4 3426.55947
## 2009.667 443720.1 442700.5 1137.4 -117.80846Nilai hasil prediksi hanya tertampung pada variabel
xhat, maka dari itu kita hanya akan mengambil nilai pada
variabel tersebut saja.
properti_holts2$fitted[,1] %>%
head()## Time Series:
## Start = c(2008, 1)
## End = c(2009, 3)
## Frequency = 3
## [1] 438304.5 449601.8 449699.7 440123.0 449418.3 441353.1accuracy(properti_holts$fitted[,1], properti_ts)## ME RMSE MAE MPE MAPE ACF1 Theil's U
## Test set -687.077 36628.84 8087.364 -0.4175741 1.714465 0.05037177 1.015088accuracy(properti_holts2$fitted[,1], properti_ts)## ME RMSE MAE MPE MAPE ACF1 Theil's U
## Test set -37.46197 41087.86 10516.06 0.02278259 2.496971 0.09806313 1.70262accuracy(properti_holts3$fitted[,1], properti_ts)## ME RMSE MAE MPE MAPE ACF1 Theil's U
## Test set 17.50677 41653.45 11704.52 -0.06116779 2.751971 0.2357503 1.699795properti_ts %>%
autoplot() +
autolayer(properti_holts$fitted[,1]) +
autolayer(properti_holts2$fitted[,1]) +
autolayer(properti_holts3$fitted[,1]) 
5 Holt’s Winter Exponential
merupakan metode forecasting yang tepat digunakan untuk data yang memiliki efek trend dan seasonal
5.1 cross Validation
# Data Train
properti_train <- head(properti_ts, -24)
# Data Test
properti_test <- tail(properti_ts, 24)5.2 Membuat Model
membuat model dengan data properti train dan seasenal multiplikatif
properti_hw <- HoltWinters(x = properti_train,
seasonal = "multiplicative")
properti_hw## Holt-Winters exponential smoothing with trend and multiplicative seasonal component.
##
## Call:
## HoltWinters(x = properti_train, seasonal = "multiplicative")
##
## Smoothing parameters:
## alpha: 0.9986851
## beta : 0
## gamma: 1
##
## Coefficients:
## [,1]
## a 5.780988e+05
## b 1.137400e+03
## s1 9.986007e-01
## s2 9.937442e-01
## s3 1.005759e+005.3 Melakukan forecast masa depan
properti_forecast <- forecast(object = properti_hw,
h = 50) # nilai prediksi yang akan di tentukan dalam bulan hari atau tahun
properti_forecast## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2114.667 578425.7 529657.8 627193.6 503841.6 653009.8
## 2115.000 576742.9 507987.2 645498.7 471590.1 681895.8
## 2115.333 584859.9 515318.8 654400.9 478506.0 691213.7
## 2115.667 581833.1 497264.1 666402.2 452495.9 711170.3
## 2116.000 580133.8 482898.4 677369.1 431425.2 728842.4
## 2116.333 588291.7 489945.8 686637.6 437884.7 738698.7
## 2116.667 585240.5 476036.4 694444.7 418227.3 752253.8
## 2117.000 583524.6 464436.2 702613.1 401394.5 765654.7
## 2117.333 591723.6 471275.0 712172.1 407513.3 775933.8
## 2117.667 588648.0 459422.8 717873.2 391015.1 786280.8
## 2118.000 586915.5 449404.0 724427.0 376609.7 797221.2
## 2118.333 595155.4 456073.3 734237.5 382447.8 807863.0
## 2118.667 592055.4 445519.5 738591.3 367948.1 816162.7
## 2119.000 590306.3 436563.8 744048.9 355177.4 825435.3
## 2119.333 598587.3 443088.8 754085.7 360772.9 836401.6
## 2119.667 595462.8 433455.5 757470.2 347694.0 843231.7
## 2120.000 593697.2 425280.6 762113.7 336126.3 851268.1
## 2120.333 602019.1 431679.1 772359.1 341506.5 862531.7
## 2120.667 598870.2 422745.3 774995.2 329510.4 868230.1
## 2121.000 597088.0 415177.4 778998.7 318879.7 875296.4
## 2121.333 605451.0 421462.7 789439.2 324065.2 886836.7
## 2121.667 602277.7 413085.7 791469.6 312933.5 891621.8
## 2122.000 600478.9 406008.2 794949.6 303061.7 897896.1
## 2122.333 608882.8 412191.1 805574.5 308068.8 909696.8
## 2122.667 605685.1 404272.1 807098.1 297650.4 913719.8
## 2123.000 603869.8 397602.5 810137.0 288411.1 919328.4
## 2123.333 612314.7 403691.6 820937.7 293253.2 931376.1
## 2123.667 609092.5 396158.7 822026.4 283438.3 934746.8
## 2124.000 607260.6 389835.8 824685.4 274738.0 939783.2
## 2124.333 615746.5 395838.5 835654.5 279426.2 952066.8
## 2124.667 612499.9 388637.4 836362.5 270131.7 954868.2
## 2125.000 610651.5 382614.4 838688.5 261898.8 959404.1
## 2125.333 619178.4 388536.9 849819.8 266442.6 971914.1
## 2125.667 615907.4 381625.4 850189.4 257604.0 974210.8
## 2126.000 614042.3 375865.4 852219.3 249782.1 978302.5
## 2126.333 622610.2 381713.0 863507.4 254189.8 991030.6
## 2126.667 619314.8 375057.4 863572.2 245755.4 992874.2
## 2127.000 617433.2 369530.7 865335.6 238299.1 996567.2
## 2127.333 626042.1 375308.3 876775.8 242577.9 1009506.2
## 2127.667 622722.2 368881.2 876563.3 234505.8 1010938.6
## 2128.000 620824.0 363563.5 878084.5 227378.0 1014270.0
## 2128.333 629473.9 369275.2 889672.6 231534.3 1027413.5
## 2128.667 626129.7 363053.8 889205.5 223789.9 1028469.4
## 2129.000 624214.9 357924.9 890504.8 216959.6 1031470.2
## 2129.333 632905.8 363574.5 902237.0 220999.2 1044812.3
## 2129.667 629537.1 357539.8 901534.3 213553.2 1045521.0
## 2130.000 627605.7 352582.7 902628.8 206994.2 1048217.2
## 2130.333 636337.6 358173.5 914501.7 210922.3 1061752.9
## 2130.667 632944.5 352309.3 913579.7 203750.0 1062139.0
## 2131.000 630996.6 347509.3 914483.9 197440.2 1064553.05.4 Evaluasi Hasil Forecast
accuracy(properti_forecast$mean, properti_test)## ME RMSE MAE MPE MAPE ACF1 Theil's U
## Test set 11130.32 15310.29 12623.03 1.829348 2.079165 0.6582717 3.170081- Dari Hasil evaluasi berdasrkan akurasi pada data test di dapatkan hasil MAE = 12623.03
6 Model SARIMA*
auto_arima <- auto.arima(y = properti_ts)accuracy(auto_arima)## ME RMSE MAE MPE MAPE MASE
## Training set 450.9275 36269.57 7122.507 -0.1888173 1.498312 0.3587781
## ACF1
## Training set 0.052900926.1 No-autocorrelation residual
yang diinginkan p-value > 0.05 (alpha), no-autocorrelation dengan mengguakan Ljung-Box test
# menggunakan Ljung-Box test
Box.test(x = auto_arima$residuals, type = "Ljung-Box")##
## Box-Ljung test
##
## data: auto_arima$residuals
## X-squared = 0.9795, df = 1, p-value = 0.3223hasil test tersebut masih terdapat autokorelasi, maka kita akan melakukan tuning kembali terhadap model
6.2 Normality of residual
Untuk mengecek normality residual pada hasil forecasting time series
kita bisa melakukan uji normality (shapiro test) dengan menggunakan
fungsi shapiro.test(residual model). Hipotesis yang
digunakan yaitu:
H_0: residual menyebar normal H_1: residual tidak menyebar normal yang diinginkan p-value > 0.05 (alpha), residual menyebar normal
shapiro.test(auto_arima$residuals)##
## Shapiro-Wilk normality test
##
## data: auto_arima$residuals
## W = 0.14208, p-value < 2.2e-16Dari uji Shapiro menunjukan hasil = 1.923 berarti residual menyebar normal