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Pogány, Tibor K.; Nadarajah, Saralees

Explicit expressions for the variogram of first-order intrinsic autoregressions. (English) Zbl 1326.62192

Electron. J. Stat. 3, 376-383 (2009).
Summary: Exact and explicit expressions for the variogram of first-order intrinsic autoregressions have not been known. Various asymptotic expansions and approximations have been used to compute the variogram. In this note, an exact and explicit expression applicable for all parameter values is derived. The expression involves Appell’s hypergeometric function of the fourth kind. Various particular cases of the expression are also derived.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
33C65 Appell, Horn and Lauricella functions
33C90 Applications of hypergeometric functions
62M20 Inference from stochastic processes and prediction

Keywords:

Appell’s hypergeometric functions \(F_2, F_4\); first-order intrinsic autoregression; hypergeometric \(_3F_2\) and \(_4F_3\); variogram

Software:

F1
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References:

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