  We use the exact calculation of the quantum mechanical, temporal
characteristic function $\chi(\eta)$ and the degree of second-order coherence
$g^{(2)}(\tau)$ for a single-mode, degenerate parametric amplifier for a system
in the Gaussian state, viz., a displaced-squeezed thermal state, to study the
different criteria for nonclassicality. In particular, we contrast criteria
that involve only one-time functions of the dynamical system, for instance, the
quasiprobability distribution $P(\beta)$ of the Glauber-Sudarshan coherent or
P-representation of the density of state and the Mandel $Q_{M}(\tau)$
parameter, versus the criteria associated with the two-time correlation
function $g^{(2)}(\tau)$.
