We analyse the power spectra and structure functions (SFs) of the temperature and radial velocity fields, calculated in the radial and azimuthal directions, in annular centrifugal Rayleigh-B\'{e}nard convection (ACRBC) for Rayleigh number Ra $ \in [{10^8},{10^{11}}]$, Prandtl number Pr = 10.7, and inverse Rossby number $\rm{Ro}^{-1} = 16$ using the spatial data obtained by quasi-two-dimensional direct numerical simulation. Bolgiano and Obukhov-like (BO59-like) scalings for the energy spectrum in both the azimuthal and radial directions and thermal spectrum in the azimuthal direction are observed. The range of BO59-like scaling becomes wider as Ra increases. At $\rm{Ra} = 10^{11}$, it is found that BO59-like scaling ${E_u}({k_r}) \sim {k_r}^{ - 11/5}$ spans nearly two decades for the energy spectrum calculated in the radial direction. Power-law fittings in the range larger than the Bolgiano scales, the scaling exponents of transverse and longitudinal velocity SFs versus the order coincide with the theoretical prediction of BO59 scaling $\zeta _p^u = 3p/5$ basically. The second-order temperature SFs exhibit a gradual transition from the Obukhov-Corrsin behaviour at scales smaller than the Bolgiano scales to the BO59 behaviour at scales larger than the Bolgiano scales. The slopes from the 3rd to 6th-order temperature SFs are similar, which is similar to classical Rayleigh-B\'{e}nard convection and Rayleigh-Taylor turbulence. The probability density functions (p.d.f.) of temperature fluctuations $\delta T/{\sigma _T}$ reveal the cold plumes are strong and the p.d.f. in different regions at high Ra are similar. The stronger turbulent-mixing and larger centrifugal buoyancy in ACRBC may result in the BO59-like scaling.