Autoregressive moving average model

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Dina statistik, model autoregressive moving average (ARMA) nyaéta aplikasi tipikal nu dipaké 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 diharéokeun 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 | édit sumber]

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

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

Model Autoregressive[édit | édit sumber]

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

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

Model Autoregressive moving average[édit | édit sumber]

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

Generalisasi[édit | édit sumber]

Kawengku kana yt dina nilai x atawa y samemehna dianggap bakal linier iwal dina kasus husus. Lamun dependen nonlinéar, 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 maké cara sejen. Tempo ogé model autoregressive conditional heteroskedasticity (ARCH) sarta model autoregressive integrated moving average (ARIMA).

Rujukan[édit | édit sumber]

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