Autoregressive moving average model Details, Meaning Autoregressive moving average model Article and Explanation Guide

Autoregressive moving average model Guide, Meaning , Facts, Information and Description

In statistics, autoregressive moving average (ARMA) models are typically applied to time series data.

Suppose we have at hand two time series, x₁, x₂, x₃, ..., and y₁, y₂, y₃, .... The series x is conventionally assumed to be unpredictable "shocks" which affect or modify y. We wish to predict y_t. If the prediction model contains only x terms, the model is called a moving average (MA) model. If the prediction model contains only y terms, the model is called an autoregressive (AR) model. If the prediction model contains both x and y terms, the model is called an autoregressive moving average (ARMA) model.

Table of contents

1 Moving average model
2 Autoregressive model
3 Autoregressive moving average model
4 Generalizations
5 References

Moving average model

The notation MA(q) means a moving average model with q terms. An MA(q) model can be written

for some coefficients θ₁, ..., θ_q. A moving average model is essentially a finite impulse response filter with some additional interpretation placed on it.

Autoregressive model

The notation AR(p) means an autoregressive model with p terms. An AR(p) model can be written

for some coefficients φ₁, ..., φ_p. An autoregressive model is essentially an infinite impulse response filter with some additional interpretation placed on it.