  Shot-noise of electrons that are transmitted with probability $T$ through a
quantum point contact (biased at a voltage $V_0$) leads to a fluctuating
current that in turn emits radiation in the microwave regime. By calculating
the Fano factor $F$ for the case where only a single channel contributes to the
transport, it has been shown that the radiation produced at finite frequency
$\omega_0$ close to $e V_0/\hbar$ and at low temperatures is nonclassical with
sub-Poissonian statistics ($F<1$). The origin of this effect is the fermionic
nature of the electrons producing the radiation, which reduces the probability
of simultaneous emission of two or more photons. However, the Fano factor,
being a time-averaged quantity, offers only limited information about the
system. Here, we calculate the second-order coherence $g^{(2)}(\tau)$ for this
source of radiation. We show that due to the interference of two contributions,
two photon processes (leading to bunching) are completely absent at zero
temperature for $T=50\,\%$. At low temperatures, we find a competition of the
contribution due to Gaussian current-current fluctuations (leading to bunching)
with the one due to non-Gaussian fluctuations (leading to antibunching). At
slightly elevated temperatures, the non-Gaussian contribution becomes
suppressed whereas the Gaussian contributions remain largely independent of
temperature. We show that the competition of the two contributions leads to a
nonmonotonic behavior of the second-order coherence as a function of time. As a
result, $g^{(2)}(\tau)$ obtains a minimal value for times $\tau^* \simeq
\omega_0^{-1}$. Close to this time, the second-order coherence remains below 1
at temperatures where the Fano factor is already above 1. We identify realistic
experimental parameters that can be used to test the sub-Poissonian nature of
the radiation.
