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Order determination is related to the problem of finding the subset of nonzero coefficients of an ARMA model with sufficiently high ARMA orders. A subset ARMA(p,q) model is an ARMA(p,q) model with a subset of its coefficients known to be zero. For example, the model
Yt = 0.8Yt−12 + et + 0.7et−12 (6.5.4)
is a subset ARMA(12,12) model useful for modeling some monthly seasonal time series. For ARMA models of very high orders, such as the preceding ARMA(12,12) model, finding a subset ARMA model that adequately approximates the underlying process is more important from a practical standpoint than simply determining the ARMA orders. The method of Hannan and Rissanen (1982) for estimating the ARMA orders can be extended to solving the problem of finding an optimal subset ARMA model
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