Time Series Models
Time series models come in three kinds (Box and Jenkins 1976):
- Moving average (MA) models where
- autoregressive (AR) models where
- autoregressive moving average (ARMA) models where
A moving average of order q averages the random variation over the last q time periods. An autoregressive model of order p computes Xt as a function of the last p values of X, so, for a second-order process, we would use
Typically, we would use the partial autocorrelation plot (above) to determine the order. So, for the lynx data (p. 717) we would use order 2 or 4, depending on taste. Other things being equal, parsimony suggests the use of order 2. The fundamental difference is that a set of random components (
t–j) influences the current value of a MA process, whereas only the current random effect (t) affects an AR process. Both kinds of effects are at work in an ARMA processes. Ecological ...
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