Abstract
This chapter discusses periodogram testing based on spacings. The duality between periodogram testing in time series analysis and coverage probability calculation in geometrical probability was discovered by Fisher. Fisher's test for periodicity is based on the ratio of the largest value to the sum of all the periodogram values; its null distribution corresponds to the probability that a collection of randomly-placed arcs covers a circle. Siegel's test for periodicity generalizes this by summing the amount by which each strong period exceeds a threshold; the null distribution corresponds to the distribution of the vacancy, that is, that portion of a circle not covered by a collection of randomly-placed arcs.
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