The main purpose of this paper is the development of an asymptotic theory of systematic sampling from a stochastic population. The superpopulation model assumed is that the population arises from a second-order stationary process. A comparison among the multiple random start systematic sampling schemes is made in terms of the limiting expected variance of the sample mean. Asymptotic normality of the systematic sampling mean is obtained, both unconditionally and conditionally on the given population. Finally, the asymptotic behavior of confidence intervals based on two distinct variance estimators is studied.
"Asymptotic Theory of Systematic Sampling." Ann. Statist. 11 (3) 959 - 969, September, 1983. https://doi.org/10.1214/aos/1176346261