A discrete weakly stationary
Gaussian stochastic process {x(t)}, is completely nondeterministic if no non-trivial
set from the σ-algebra generated by {x(t) : t > 0} lies in the σ-algebra generated
by {x(t) : t ≤ 0}. In [8] Levinson and McKean essentially showed that a
necessary and sufficient condition for complete nondeterminism is that the
spectrum of the process is given by |h|2 where h is an outer function in the
Hardy space, H2, of the unit circle in C with the property that h∕h uniquely
determines the outer function h up to an arbitrary constant. In this paper we
consider several characterizations of complete nondeterminism in terms of the
geometry of the unit ball of the Hardy space H1 and in terms of Hankel
operators.
