Is the Newton exploration polynomial a trustworthy and noiseproof filter?

The Newton extrapolation polynomial (NEP) is often used in the interpolation and extrapolation of sampled-data signals. In this correspondence, it is presented under a form which allows, when white noise is present 1) the easy computation of the error variance due to measurement errors, and 2) the choice of the degree of this NEP for signals which are closely polynomials in a given interval.