In order that a time series be stationary, a sufficient condition is the time invariance of all statistical parameters. Hence, a necessary condition is the time invariance of an arbitrary selection of statistical parameters. The object of this section is the derivation of a significance test of invariance; and in line with general principles governing the construction of statistical tests, the aim is to find nontrivial functions of the variates having two properties: 1. Sample values of the test function can be determined uniquely from observations of the initial variates; that is, no unknown constants are involved in the test. 2. The probability distribution of the test variate is fully determinate; that is, the mathematical derivation can actually be carried out, and the result is free from unknown constants. The test here presented assumes knowledge of the autocorrelation function, whereas it is usually necessary to estimate this function empirically. Hence, to this extent it has been necessary to compromise on the second property.

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