I. INTRODUCTION The convincing fact that our universe is experiencing accelerated expansion [1, 2] has become one of the most important and mysterious issues of modern cosmology. In the framework of general relativity, the cosmic acceleration is attributed to an exotic energy called dark energy (DE). The simplest candidate of the DE is the cosmological constant with equation of state (EOS) w = − 1. Despite some severe problems such as the cosmolog- ical constant problem and the coincidence problem, the cosmological constant is favored by current astronomical observations. Besides, there are some other DE models with EOS vary- ing with cosmic time either above − 1 or below − 1. Interestingly, some current observations even give the hint that EOS of DE has crossed − 1 at least once [3, 4]. To narrow down the DE candidates, one has to examine the EOS carefully by confronting different observational data sets including the type Ia supernova (SNIa) luminosity distance, the cosmic microwave background (CMB) temperature anisotropy and the baryon acoustic oscillations (BAO) in the galaxy power spectrum, and this could be the best what we can do to approach the truth of DE. In addition to the EOS, a new diagnostic of DE was introduced in [5] which is called Om diagnostic. It is a combination of the Hubble parameter and the cosmological redshift, which depends upon the first derivative of the luminosity distance and is less sensitive to observational errors than the EOS. If the value of Om is the same at different redshifts, then the DE is the cosmological constant. The slope of Om can differentiate between different DE models with w > − 1 or w < − 1 even if the value of the matter density is not accurately known. Analyzing the Constitution SNIa sample [6] together with the BAO data [7, 8] by using the popular Chevallier-Polarski-Linder (CPL) parametrization [9, 10], it was revealed that there appears the increase of Om and w at redshifts z < 0 . 3 [11]. This suggests that the cosmic acceleration may have already been over the peak and now the acceleration is slowing down. However, including the CMB shift parameter which is another independent observable at high redshift, it was found that the result changes dramatically and the value of Om becomes un-evolving which is consistent with the ΛCDM model. Further check shows that the CPL ansatz is unable to fit the data simultaneously at low and high redshifts. It was argued that this could either due to the systematics in some of the data sets which is not 2