Electronic Journal of Statistics

Explicit expressions for the variogram of first-order intrinsic autoregressions

Tibor K. Pogány and Saralees Nadarajah

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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.

Article information

Electron. J. Statist., Volume 3 (2009), 376-383.

First available in Project Euclid: 17 April 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 33C65: Appell, Horn and Lauricella functions 33C90: Applications 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

Appell’s hypergeometric functions $F_2$, $F_4$ first-order intrinsic autoregression hypergeometric $_3F_2$, $_4F_3$ variogram


Pogány, Tibor K.; Nadarajah, Saralees. Explicit expressions for the variogram of first-order intrinsic autoregressions. Electron. J. Statist. 3 (2009), 376--383. doi:10.1214/09-EJS380. https://projecteuclid.org/euclid.ejs/1239974320

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