Metode pemulusan eksponensial dengan tren

Peramalan di R

Rob J. Hyndman

Professor of Statistics at Monash University

Tren linear Holt

	Pemulusan eksponensial sederhana
Ramalan	$\hat{y}_{t+h \mid t} = \ell_t$
Level	$\ell_t = \alpha y_t + (1-\alpha)\ell_{t-1}$

	Tren linear Holt
Ramalan	$\hat{y}_{t+h \mid t} = \ell_t + hb_t$
Level	$\ell_t = \alpha y_t + (1-\alpha)(\ell_{t-1} + b_{t-1})$
Tren	$b_t = \beta^(\ell_t = \ell_{t-1}) + (1 - \beta^) b_{t-1}$

Tren linear Holt

	Tren linear Holt
Ramalan	$\hat{y}_{t+h \mid t} = \ell_t + hb_t$
Level	$\ell_t = \alpha y_t + (1-\alpha)(\ell_{t-1} + b_{t-1})$
Tren	$b_t = \beta^(\ell_t = \ell_{t-1}) + (1 - \beta^) b_{t-1}$

Dua parameter pemulusan $\alpha$ dan $\beta^*$ dengan $0 \leq \alpha$ dan $\beta^* \leq 1$
Pilih $\alpha, \beta^*, \ell_0, b_0$ untuk meminimalkan SSE

Metode Holt di R

airpassengers %>% holt(h = 5) %>% autoplot

Metode tren teredam

Bentuk komponen
$\hat{y}_{t+h \mid t} = \ell_t + (\phi + \phi^2 + ... + \phi^h)b_t$
$\ell_t = \alpha y_t + (1-\alpha)(\ell_{t-1} + \phi b_{t-1})$
$b_t = \beta^(\ell_t = \ell_{t-1}) + (1 - \beta^) \phi b_{t-1}$

Parameter redaman $\ 0 < \phi < 1$
Jika $\ \phi = 1$, sama dengan tren linear Holt
Ramalan jangka pendek bertren, jangka panjang konstan

Contoh: penumpang pesawat

fc1 <- holt(airpassengers, h = 15, PI = FALSE)
fc2 <- holt(airpassengers, damped = TRUE, h = 15, PI = FALSE)
autoplot(airpassengers) + xlab("Year") + ylab("millions") +
  autolayer(fc1, series="Linear trend") +
  autolayer(fc2, series="Damped trend")

Ayo berlatih!

Peramalan di R