  This paper examines the problem of testing whether a discrete time-series
vector contains a periodic signal or is merely noise. To do this we examine the
stochastic behaviour of the maximum intensity of the observed time-series
vector and formulate a simple hypothesis test that rejects the null hypothesis
of exchangeability if the maximum intensity spike in the Fourier domain is "too
big" relative to its null distribution. This comparison is undertaken by
simulating the null distribution of the maximum intensity using random
permutations of the time-series vector. We show that this test has a p-value
that is uniformly distributed for an exchangeable time-series vector, and that
the p-value increases when there is a periodic signal present in the observed
vector. We compare our test to Fisher's spectrum test, which assumes normality
of the underlying noise terms. We show that our test is more robust than this
test, and accommodates noise vectors with fat tails.
