Abstract
In a recent publication (ref. 11) the author developed statistical tests for discriminating between certain types of hypotheses involved in time series analysis. Since the results were intended to be of at least as much practical as theoretical interest they were presented in a direct expository manner rather than as theorems. This was almost necessitated by the border nature of the subject. However, a connected logical presentation has much to recommend it, and the present article is an attempt in this direction. The original material has been considerably revised and extended, although much of the extension is little more than the formulation of that which was before implicit. It is hoped, however, that the article contains sufficient new matter to justify its independent existence.

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