The Annals of Statistics

On Unequally Spaced Time Points in Time Series

William Clinger and John W. Van Ness

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This article discusses the sampling of stationary discrete-time stochastic processes at fixed but unequally spaced time points. The pattern of the sampling times is periodic with a cycle of $p$ time units. One of the major problems is to determine given $p$ the minimum number of sampling points required per cycle in order to estimate the covariances at all lags. The second problem is to find a pattern of distribution for the sampling points within the cycle which will allow the estimation of all covariances. A discussion of the references which describe the statistical properties of the estimates of covariances and spectra in this sampling situation is given.

Article information

Ann. Statist. Volume 4, Number 4 (1976), 736-745.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62M15: Spectral analysis
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Time series spectral analysis missing observations autocorrelation autocovariance covariance sequence unequally spaced samples


Clinger, William; Ness, John W. Van. On Unequally Spaced Time Points in Time Series. Ann. Statist. 4 (1976), no. 4, 736--745. doi:10.1214/aos/1176343545.

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