  In this work, the photometric data from the American Association of Variable
Star Observers are collected and analyzed on the SX Phoenicis star DY Pegasi
(DY Peg). From the frequency analysis, we get three independent frequencies:
$f_0 = 13.71249\ \rm{c\ days^{-1}}$, $f_1 = 17.7000\ \rm{c\ days^{-1}}$, and
$f_2 =18.138\ \rm{c\ days^{-1}}$, in which $f_0$ and $f_1$ are the radial
fundamental and first overtone mode, respectively, while $f_2$ is detected for
the first time and should belong to a nonradial mode. The $O-C$ diagram of the
times of maximum light shows that DY Peg has a period change rate
$(1/P_0)(\mathrm{d} P_0/\mathrm{d} t) = -(5.87 \pm 0.03) \times 10^{-8} \
\mathrm{yr^{-1}}$ for its fundamental pulsation mode, and should belong to a
binary system that has an orbital period $P_{\mathrm{orb}} = 15425.0 \pm 205.7
\ \mathrm{days}$. Based on the spectroscopic information, single star
evolutionary models are constructed to fit the observed frequencies. However,
some important parameters of the fitted models are not consistent with that
from observations. Combing with the information from observation and
theoretical calculation, we conclude that DY Peg should be an SX Phoenicis star
in a binary system and accreting mass from a dust disk, which was the residue
of its evolved companion (most probably a hot white dwarf at the present stage)
produced in the asymptotic giant branch phase. Further observations are needed
to confirm this inference, and it might be potentially a universal formation
mechanism and evolutionary history for SX Phoenicis stars.
