  The quest for an integrated light source that promises high energy efficiency
and fast modulation for high-performance photonic circuits has led to the
development of room-temperature telecom-wavelength nanoscale laser with high
spontaneous emission factors, \beta. The coherence characterization of this
type of lasers is inherently difficult with the conventional measurement of
output light intensity versus input pump intensity due to the diminishing kink
in the measurement curve. We demonstrate the transition from chaotic to
coherent emission of a high-{\beta} pulse-pump metallo-dielectric nanolaser can
be determined by examining the width of a second order intensity correlation
peak, which shrinks below and broadens above threshold. Photon fluctuation
study, first one ever reported for this type of nanolaser, confirms the
validity of this measurement technique. Additionally, we show that the width
variation above threshold results from the delayed threshold phenomenon,
providing the first indirect observation of dynamical hysteresis in a
nanolaser.
