Abstract
This paper attempts to give a mathematically precise version of recent tests on an observed time series { a t } for the presence of low dimensional deterministic chaos. Three practical tests for chaos are discussed: (a) the correlation dimension of { a t } must be low, (b) the estimated largest Lyapunov exponent must be positive, (c) the residuals { a t } of an estimated linear time (or nonlinear) series model (for a large class of such models) must have the same dimension and largest Lyapunov exponent as { a t }. Based on (a)-(c) evidence for chaos in post war II, U.S. quarterly real GNP is weak.
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