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Biometrika 1987 74(4):771-779; doi:10.1093/biomet/74.4.771
© 1987 by Biometrika Trust
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Estimation of the interpolation error variance and an index of linear determinism

F. BATTAGLIA and R. J. BHANSALI

Departimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma ‘La Sapienza’ 00185 Rome, Italy
Department of Statistics and Computational Mathematics, University of Liverpool Liverpool L69 3BX, U.K.

The autoregressive and window estimators of the inverse variance, Ri (0), say, are adopted for estimating the interpolation error variance, {Ri (0)}–1, and an index of linear determinism, A, of a stationary process {Xt}. The index A is defined as 1 –{R(0) Ri (0)}–1, where R(0) denotes the variance of Xt; A measures the proportion of total variance explained by the interpolator when interpolating Xt, say, from {Xs, S != t}. Some uses of A and {Ri (0)}–1 are discussed. The asymptotic distributions of the estimators are derived; the order of consistency of the autoregressive and window estimators of A is different when A = 0 than when 0 < A < 1. The finite sample behaviour of the estimators is examined by means of a simulation study.

Key Words: Bilateral autoregressive process • Conditional autoregressive process • Inverse correlation function • Linear interpolation • Outlier detection • Simultaneous autoregressive process • Time series


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