w$_{de}$ at the divided points in our LS method. In the LS method, w$_{de}$ is continuous, but not smooth at the divided points, i.e., its derivative is not continuous at those points. In fact, w$_{de}$ in LS method can be made smooth at the divided points, such as by the relation where w ′ i is the slope of linear expansion in the i th bin ( i ≥ 1 and w ′ 0 = 0), and Δ is related to the smoothed extent at the divided points. With this parameterization, one can still find out the turning positions of w$_{de}$ that are favored by observational data, and perturbations of DE can be calculated. Furthermore our results are also dependent on the data set we have used [32]. For example, although there is still a 2 σ deviation at z = 0 . 9 by using the widely-used data set SnIa + CMB-shift R + BAO parameter A [33], now the best-fitted turning point in z ∈ (0 , 0 . 9) changes to z = 0 . 39. Whatever, from the observational data we have used, a big deviation of w$_{de}$ from − 1 around z = 0 . 9 is found. Unlike the deviations around z = 0 and z = 0 . 45, this deviation around z = 0 . 9 does not to be reduced in the uncorrelated estimate. At least, our result shows that if DE is dynamical it is more possible to find the deviation of w$_{de}$ from − 1 around this redshift value. If the EoS of DE is indeed of an oscillating behavior around − 1, it is then not surprising that the cosmological constant always fits well with observational data because the oscillating behavior could be smeared in the luminosity distance. However, if the oscillation region of w$_{de}$ is wide enough (like the case of our best-fitted w$_{de}$ in Model I), DE may be distinguished confidently from the cosmological constant by more precise astronomical observations in the next generation. In addition, let us mention that an oscillating behavior of w$_{de}$ is also possibly due to some systematic errors in observational data, or due to some interactions between DE and dark matter [34]. RGC thanks Y.G. Gong and B. Wang for some relevant discussions. This work was partially supported by NNSF of China (No. 10821504 and No. 10975168) and the National 14 Acknowledgments w$_{de}$ ( z ) = w$_{0}$ + m ∑ i =1 w ′ i − w ′ i − 1 2 ( z + Δ ln cosh( z − z i − 1 Δ ) cosh( z$_{i}$$_{−}$$_{1}$/ Δ) ) , (28)