A useful reparameterization for second?order autoregressive processes

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Abstract
In time series analysis, autoregressive (a.r.) models are often fitted successfully to data, and such models are usually among the first to be taught. It is therefore important to understand why such models are useful in practice. An alternative parameterization for second order a.r. models, which assists understanding and interpretation, is discussed. The models are most plausible if certain restrictions are placed on the autoregressive parameters, which in turn lead to restrictions on the autocorrelation coefficients. Fitting the reparameterized model is straightforward, and the reparameterization may be extended, less usefully, to higher order a.r. models. The second‐order model is fitted to some meteorological data.

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