C46. AR, MA and ARMA orders

Topic: Dependence along a series · more questions on this topic
‹ C45 C48 ›

What are AR(p), MA(q) and ARMA(p,q) models? What do their orders count?

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Definitions/notation. An ARMA(p,q) representation combines p lagged responses with the current and q lagged white-noise innovations: X_t=c+\sum_{j=1}^p a_jX_{t-j}+\varepsilon_t+ \sum_{k=1}^q b_k\varepsilon_{t-k}, with intercept c. AR(p) sets q=0, MA(q) sets p=0, and the orders are the largest included lags, not the number of observations.