Kütüphaneler
library(ggplot2)
library(forecast)
library(lmtest)
library(readxl)
library(tseries)
library(stats)
library(readxl)
- İstihdam edilen çalışanların aylık olarak ortalama çalışma
süreleri.
- Bu veriler, Türkiye İstatistik Kurumu’nun (TÜİK) resmi internet
sitesinden elde edilmiştir.
- Veriler, 2014 yılından başlayarak 2023 yılının Şubat ayına kadar
olan süreci kapsamaktadır.
Veri <- read_excel("ZamanSerisi_Veri.xlsx")
data=ts(Veri, start = 2014, frequency=12)
Zaman Serisi Grafiği
- Azalan Trend.
- Düzensiz Hareket.
- Mevsimsellik etkisi çok düşük.
autoplot(data)
Bileşenlere Ayırma
autoplot(data)
Components <- decompose(data)
plot(Components)
plot(Components$trend)
Components$seasonal
## Jan Feb Mar Apr May Jun
## 2014 -0.93623167 -0.38258584 -0.25810667 -0.88102334 -1.36071084 0.40230999
## 2015 -0.93623167 -0.38258584 -0.25810667 -0.88102334 -1.36071084 0.40230999
## 2016 -0.93623167 -0.38258584 -0.25810667 -0.88102334 -1.36071084 0.40230999
## 2017 -0.93623167 -0.38258584 -0.25810667 -0.88102334 -1.36071084 0.40230999
## 2018 -0.93623167 -0.38258584 -0.25810667 -0.88102334 -1.36071084 0.40230999
## 2019 -0.93623167 -0.38258584 -0.25810667 -0.88102334 -1.36071084 0.40230999
## 2020 -0.93623167 -0.38258584 -0.25810667 -0.88102334 -1.36071084 0.40230999
## 2021 -0.93623167 -0.38258584 -0.25810667 -0.88102334 -1.36071084 0.40230999
## 2022 -0.93623167 -0.38258584 -0.25810667 -0.88102334 -1.36071084 0.40230999
## 2023 -0.93623167 -0.38258584
## Jul Aug Sep Oct Nov Dec
## 2014 0.89704379 1.08037712 0.77783083 0.41845583 0.31637249 -0.07373167
## 2015 0.89704379 1.08037712 0.77783083 0.41845583 0.31637249 -0.07373167
## 2016 0.89704379 1.08037712 0.77783083 0.41845583 0.31637249 -0.07373167
## 2017 0.89704379 1.08037712 0.77783083 0.41845583 0.31637249 -0.07373167
## 2018 0.89704379 1.08037712 0.77783083 0.41845583 0.31637249 -0.07373167
## 2019 0.89704379 1.08037712 0.77783083 0.41845583 0.31637249 -0.07373167
## 2020 0.89704379 1.08037712 0.77783083 0.41845583 0.31637249 -0.07373167
## 2021 0.89704379 1.08037712 0.77783083 0.41845583 0.31637249 -0.07373167
## 2022 0.89704379 1.08037712 0.77783083 0.41845583 0.31637249 -0.07373167
## 2023
Üssel Düzeltme Yöntemi
- Mevsimsellik çok düşük ve azalan trend var.
- Holt Trend üssel düzeltme yöntemi kullanılmıştır.
- Gamma “false” olarak seçilmiştir.
- Alpha değerine bakıldığında yakın ve uzak gözlemlere eşit etki
vermiştir.
- Beta değerine bakılarak trendin etkisi görülmektedir.
HWData <- HoltWinters(data, gamma = FALSE)
HWData
## Holt-Winters exponential smoothing with trend and without seasonal component.
##
## Call:
## HoltWinters(x = data, gamma = FALSE)
##
## Smoothing parameters:
## alpha: 0.4385627
## beta : 0.02431247
## gamma: FALSE
##
## Coefficients:
## [,1]
## a 44.17129385
## b 0.00184244
plot(HWData)
HWData$fitted
## xhat level trend
## Mar 2014 47.40000 47.20000 0.2000000000
## Apr 2014 47.28554 47.09301 0.1925362195
## May 2014 47.43965 47.24803 0.1916241204
## Jun 2014 47.74823 47.55383 0.1944001052
## Jul 2014 48.23542 48.03407 0.2013496276
## Aug 2014 48.82516 48.61459 0.2105682303
## Sep 2014 48.39551 48.20014 0.1953723810
## Oct 2014 48.59290 48.39748 0.1954202409
## Nov 2014 46.68015 46.53477 0.1453819882
## Dec 2014 46.78953 46.64500 0.1445273710
## Jan 2015 46.93876 46.79412 0.1446390363
## Feb 2015 46.25738 46.13235 0.1250331852
## Mar 2015 46.31171 46.18836 0.1233551003
## Apr 2015 46.33996 46.21886 0.1210976816
## May 2015 46.84741 46.71714 0.1302678711
## Jun 2015 47.09115 46.95819 0.1329611167
## Jul 2015 47.49762 47.35817 0.1394530277
## Aug 2015 47.05415 46.92853 0.1256170896
## Sep 2015 48.05389 47.90753 0.1463648017
## Oct 2015 47.14283 47.02156 0.1212663270
## Nov 2015 47.73900 47.60646 0.1325384577
## Dec 2015 47.22511 47.10791 0.1171950228
## Jan 2016 46.79195 46.68782 0.1041322856
## Feb 2016 46.58524 46.48849 0.0967543165
## Mar 2016 46.46401 46.37243 0.0915804021
## Apr 2016 46.25730 46.17280 0.0845003303
## May 2016 46.40591 46.31988 0.0860218513
## Jun 2016 46.62404 46.53488 0.0891576414
## Jul 2016 47.10670 47.00820 0.0984975787
## Aug 2016 46.93265 46.84063 0.0920285898
## Sep 2016 47.54908 47.44461 0.1044754688
## Oct 2016 46.50845 46.43115 0.0772957521
## Nov 2016 46.58195 46.50474 0.0772056904
## Dec 2016 46.62234 46.54601 0.0763319174
## Jan 2017 46.10464 46.04241 0.0622324039
## Feb 2017 45.85033 45.79561 0.0547191092
## Mar 2017 45.79260 45.74055 0.0520499290
## Apr 2017 45.80305 45.75199 0.0510626212
## May 2017 45.94259 45.88942 0.0531626155
## Jun 2017 46.15631 46.09934 0.0569735450
## Jul 2017 45.60399 45.56148 0.0425118448
## Aug 2017 46.49824 46.43551 0.0627280897
## Sep 2017 46.51684 46.45516 0.0616806054
## Oct 2017 46.39126 46.33403 0.0572360734
## Nov 2017 46.45242 46.39509 0.0573292282
## Dec 2017 46.35144 46.29786 0.0535714902
## Jan 2018 46.02252 45.97803 0.0444930214
## Feb 2018 45.33814 45.31094 0.0271928233
## Mar 2018 45.30327 45.27756 0.0257199364
## Apr 2018 45.19276 45.17027 0.0224862541
## May 2018 45.30834 45.28365 0.0246960009
## Jun 2018 45.41914 45.39240 0.0267395674
## Jul 2018 44.89821 44.88447 0.0137404834
## Aug 2018 45.85613 45.81998 0.0361509260
## Sep 2018 45.73230 45.69994 0.0323537089
## Oct 2018 45.97475 45.93741 0.0373406171
## Nov 2018 45.88867 45.85426 0.0344110358
## Dec 2018 45.34418 45.32351 0.0206705524
## Jan 2019 45.03054 45.01781 0.0127357313
## Feb 2019 44.49049 44.49087 -0.0003850036
## Mar 2019 44.49438 44.49466 -0.0002835884
## Apr 2019 44.49662 44.49684 -0.0002236264
## May 2019 44.58776 44.58581 0.0019449317
## Jun 2019 44.68505 44.68084 0.0042079576
## Jul 2019 44.47136 44.47232 -0.0009638888
## Aug 2019 45.47156 45.44876 0.0227990800
## Sep 2019 44.87822 44.87004 0.0081747883
## Oct 2019 45.43525 45.41405 0.0212020881
## Nov 2019 45.44062 45.41979 0.0208262519
## Dec 2019 45.12874 45.11581 0.0129294021
## Jan 2020 45.08384 45.07228 0.0115567185
## Feb 2020 44.33897 44.34537 -0.0063972510
## Mar 2020 44.22522 44.23417 -0.0089452884
## Apr 2020 43.93541 43.95102 -0.0156117439
## May 2020 41.20854 41.28851 -0.0799645785
## Jun 2020 38.96846 39.09969 -0.1312358520
## Jul 2020 41.05260 41.13125 -0.0786530741
## Aug 2020 42.70229 42.73992 -0.0376299540
## Sep 2020 42.79840 42.83286 -0.0344556447
## Oct 2020 43.79788 43.80780 -0.0099147426
## Nov 2020 44.10338 44.10580 -0.0024283737
## Dec 2020 44.14435 44.14575 -0.0013981172
## Jan 2021 43.44919 43.46706 -0.0178648550
## Feb 2021 42.37601 42.41892 -0.0429132269
## Mar 2021 41.84973 41.90411 -0.0543862452
## Apr 2021 42.35699 42.39805 -0.0410551518
## May 2021 41.79619 41.84958 -0.0533916588
## Jun 2021 41.29528 41.35930 -0.0640135609
## Jul 2021 42.98537 43.00775 -0.0223793541
## Aug 2021 43.64340 43.64963 -0.0062295157
## Sep 2021 44.92043 44.89620 0.0242291161
## Oct 2021 45.29486 45.26232 0.0325413503
## Nov 2021 45.01525 44.99012 0.0251323774
## Dec 2021 45.03353 45.00856 0.0249697457
## Jan 2022 44.90867 44.88726 0.0214134342
## Feb 2022 44.47696 44.46631 0.0106584316
## Mar 2022 44.45305 44.44321 0.0098377974
## Apr 2022 44.39413 44.38593 0.0082059124
## May 2022 44.31513 44.30899 0.0061359610
## Jun 2022 43.05664 43.08052 -0.0238804797
## Jul 2022 44.13038 44.12821 0.0021719710
## Aug 2022 43.35522 43.37150 -0.0162782545
## Sep 2022 44.61689 44.60283 0.0140543334
## Oct 2022 44.75812 44.74105 0.0170730190
## Nov 2022 44.70416 44.68878 0.0153870169
## Dec 2022 44.58291 44.57077 0.0121438590
## Jan 2023 44.37812 44.37113 0.0069947815
## Feb 2023 44.30510 44.30000 0.0050955694
HWData$SSE
## [1] 261.7672
HWForecasts<-forecast(HWData, h=12)
HWForecasts
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Mar 2023 44.17314 42.18094 46.16533 41.12633 47.21994
## Apr 2023 44.17498 41.99100 46.35896 40.83486 47.51509
## May 2023 44.17682 41.80845 46.54519 40.55471 47.79893
## Jun 2023 44.17866 41.63152 46.72581 40.28314 48.07419
## Jul 2023 44.18051 41.45892 46.90209 40.01821 48.34281
## Aug 2023 44.18235 41.28973 47.07497 39.75847 48.60623
## Sep 2023 44.18419 41.12322 47.24516 39.50284 48.86554
## Oct 2023 44.18603 40.95883 47.41324 39.25045 49.12162
## Nov 2023 44.18788 40.79612 47.57963 39.00063 49.37512
## Dec 2023 44.18972 40.63472 47.74471 38.75282 49.62662
## Jan 2024 44.19156 40.47435 47.90877 38.50658 49.87655
## Feb 2024 44.19340 40.31475 48.07205 38.26152 50.12529
plot(HWForecasts)
