On Unequally Spaced Time Points in Time Series

Abstract

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.