Pengantar model AR, MA, dan ARMA

Model ARIMA di Python

James Fulton

Climate informatics researcher

Model AR

Model autoregresif (AR)

Model AR(1): $$y_t = a_1 y_{t-1} + \epsilon_t$$

Model AR

Model autoregresif (AR)

Model AR(1): $$y_t = a_1 y_{t-1} + \epsilon_t$$

Model AR(2): $$y_t = a_1 y_{t-1} + a_2 y_{t-2} + \epsilon_t$$

Model AR(p): $$y_t = a_1 y_{t-1} + a_2 y_{t-2} + ... + a_p y_{t-p} + \epsilon_t$$

Model MA

Model rataan bergerak (MA)

Model MA(1): $$y_t = m_1 \epsilon_{t-1} + \epsilon_t$$

Model MA(2): $$y_t = m_1 \epsilon_{t-1} + m_2 \epsilon_{t-2} + \epsilon_t$$

Model MA(q): $$y_t = m_1 \epsilon_{t-1} + m_2 \epsilon_{t-2} + ... + m_q \epsilon_{t-q} + \epsilon_t$$

Model ARMA

Model autoregresif rataan bergerak (ARMA)

ARMA = AR + MA

Model ARMA(1,1): $$y_t = a_1 y_{t-1} + m_1 \epsilon_{t-1} + \epsilon_t$$

ARMA(p, q)

p adalah orde bagian AR
q adalah orde bagian MA

Membuat data ARMA

$$y_t = a_1 y_{t-1} + m_1 \epsilon_{t-1} + \epsilon_t$$

Membuat data ARMA

$$y_t = 0.5 y_{t-1} + 0.2 \epsilon_{t-1} + \epsilon_t$$

from statsmodels.tsa.arima_process import arma_generate_sample

ar_coefs = [1, -0.5]
ma_coefs = [1, 0.2]

y = arma_generate_sample(ar_coefs, ma_coefs, nsample=100, scale=0.5)

Membuat data ARMA

$$y_t = 0.5 y_{t-1} + 0.2 \epsilon_{t-1} + \epsilon_t$$

Memasang model ARMA

from statsmodels.tsa.arima.model import ARIMA

# Instantiate model object
model = ARIMA(y, order=(1,0,1))

# Fit model
results = model.fit()

Ayo berlatih!

Model ARIMA di Python