  Singular spectrum analysis (SSA) is considered for decomposition of time
series into identifiable components. The Basic SSA method is nonparametric and
constructs an adaptive expansion based on singular value decomposition. The
investigated modification is able to take into consideration a structure given
in advance and therefore can be called semi-nonparametric. The approach called
SSA with projection includes preliminary projections of rows and columns of the
series trajectory matrix to given subspaces. One application of SSA with
projection is the extraction of polynomial trends, e.g., a linear trend. It is
shown that SSA with projection can extract polynomial trends much better than
Basic SSA, especially for linear trends. Numerical examples including
comparison with the least-square approach to polynomial regression are
presented.
