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Theory & Methods: Non‐Gaussian Conditional Linear AR(1) Models
Author(s) -
Grunwald Gary K.,
Hyndman Rob J.,
Tedesco Leanna,
Tweedie Richard L.
Publication year - 2000
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00143
Subject(s) - autoregressive model , mathematics , gaussian , linear model , conditional variance , range (aeronautics) , gaussian process , model selection , variance (accounting) , conditional expectation , series (stratigraphy) , econometrics , statistics , autoregressive conditional heteroskedasticity , quantum mechanics , volatility (finance) , paleontology , physics , materials science , accounting , biology , business , composite material
This paper gives a general formulation of a non‐Gaussian conditional linear AR(1) model subsuming most of the non‐Gaussian AR(1) models that have appeared in the literature. It derives some general results giving properties for the stationary process mean, variance and correlation structure, and conditions for stationarity. These results highlight similarities with and differences from the Gaussian AR(1) model, and unify many separate results appearing in the literature. Examples illustrate the wide range of properties that can appear under the conditional linear autoregressive assumption. These results are used in analysing three real datasets, illustrating general methods of estimation, model diagnostics and model selection. In particular, the theoretical results can be used to develop diagnostics for deciding if a time series can be modelled by some linear autoregressive model, and for selecting among several candidate models.