“…This class generalizes the well-known Musgrave's asymmetric approximation of the Henderson filters [Musgrave (1964), see also Doherty (2001), Gray and Thomson (2002) and Quenneville, Ladiray and Lefrancois (2003)], which is implemented in the seasonal adjustment filter X-11, developed by the US Census Bureau [see Findley et al (1998) and Ladiray and Quenneville (2001)]. The class of filters depends on the properties of the true underlying signal, namely, its level, slope, curvature and so forth, which can be estimated from the data.…”