White noise

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Rob J. Hyndman

Professor of Statistics at Monash University

White noise

set.seed(3)          # Reproducibility
wn <- ts(rnorm(36))  # White noise
autoplot(wn)         # Plot!

"White noise" hanyalah deret waktu dari data iid

ACF white noise

ggAcf(wn) +
    ggtitle("Sample ACF for white noise")

ch1_vid3_slides.008.png

ACF white noise

ggAcf(wn) +
    ggtitle("Sample ACF for white noise")

ch1_vid3_slides.009.png

ACF white noise

ggAcf(wn) +
    ggtitle("Sample ACF for white noise")

ch1_vid3_slides.010.png

ACF white noise

ggAcf(wn) +
    ggtitle("Sample ACF for white noise")

ch1_vid3_slides.011.png

Contoh: Babi disembelih

pigs <- window(pigs, start=1990)
autoplot(pigs/1000) +
  xlab("Year") +
  ylab("thousands") +
  ggtitle("Monthly number of pigs slaughtered in Victoria")

Contoh: Babi disembelih

ggAcf(pigs) +
  ggtitle("ACF of monthly pigs slaughtered
          in Victoria")

ch1_vid3_slides.017.png

Contoh: Babi disembelih

ggAcf(pigs) +
  ggtitle("ACF of monthly pigs slaughtered
          in Victoria")

ch1_vid3_slides.018.png

Contoh: Babi disembelih

ggAcf(pigs) +
  ggtitle("ACF of monthly pigs slaughtered
          in Victoria")

ch1_vid3_slides.019.png

Uji Ljung-Box

Uji Ljung-Box mempertimbangkan h nilai autokorelasi pertama secara bersama.

Uji signifikan (p-value kecil) menunjukkan data kemungkinan bukan white noise.

Box.test(pigs, lag = 24, fitdf = 0, type = "Lj")

Box-Ljung test
data:  pigs
X-squared = 634.15, df = 24, p-value < 2.2e-16

Ringkasan white noise

White noise adalah deret waktu yang murni acak
Kita dapat menguji white noise dengan melihat plot ACF atau melakukan uji Ljung-Box

Ayo berlatih!

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