Autoregressive moving average model

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Dina statistik, model autoregressive moving average (ARMA) nyaeta aplikasi tipikal nu dipake dina data deret waktu.

Anggap urang boga dua deret waktu , x1, x2, x3, ..., jeung y1, y2, y3, .... Deret x sacara konvensional teu bisa "sacara pasti" di-prediksi ku pangaruh atawa parobahan y. Urang dihareokeun keur ngira-ngira yt. Lamun model prediksi ngan miboga watesan x, model disebut model moving average (MA). Lamun model prediksi ngan miboga watesan y, model disebut model autoregressive (AR). Lamun prediski miboga duanana watesan boh x sarta y terms, model disebut model autoregressive moving average (ARMA).

Model moving average[édit | sunting sumber]

Lambang MA(q) hartina model moving average mibanda watesan q. Model MA(q) bisa dituliskeun

 y_t = x_t + \theta_1 x_{t-1} + \cdots + \theta_q x_{t-q}

keur sababraha koefisien θ1, ..., θq. Model moving average model ngarupakeun hal penting dina finite impulse response filter nu mibanda sawangan tambahan dina eta tempat.

Model Autoregressive[édit | sunting sumber]

Lambang AR(p) hartina model autoregressive mibanda watesa p. Model AR(p) bisa dituliskeun

 y_t = \phi_1 y_{t-1} + \cdots + \phi_p y_{t-p}

keur sababaraha koefisien φ1, ..., φp. Model autoregressive model ngarupakeun hal penting dina infinite impulse response filter nu mibanda sawangan tambahan dina eta tempat.

Model Autoregressive moving average[édit | sunting sumber]

Lambang ARMA(p, q) hartina model mibanda watesan p autoregressive sarta watesan q moving average. Ieu model ngarupakeun jumlah tina model AR jeung MA,

 y_t = \phi_1 y_{t-1} + \cdots + \phi_p y_{t-p} 
   + x_t + \theta_1 x_{t-1} + \cdots + \theta_q x_{t-q}

Generalisasi[édit | sunting sumber]

Kawengku kana yt dina nilai x atawa y samemehna dianggap bakal linier iwal dina kasus husus. Lamun dependen nonlinear, model sacara husus disebut nonlinear moving average (NMA), nonlinear autoregressive (NAR), atawa model nonlinear autoregressive moving average (NARMA) .

Model autoregressive moving average models bisa digeneralisir make cara sejen. Tempo oge model autoregressive conditional heteroskedasticity (ARCH) sarta model autoregressive integrated moving average (ARIMA).

Rujukan[édit | sunting sumber]

  • George E.P. Box and F.M. Jenkins. Time Series Analysis: Forecasting and Control, second edition. Oakland, CA: Holden-Day, 1976.