A Symmetric Linear Filter for Non Stationary Mean Prediction of Seasonally Adjusted Time Series

A symmetric linear filter for short-term trend-cycle estimation of seasonally adjusted time series is introduced and analysed. The filter is a derived as a linear approximation of the symmetric part of the non linear Dagum estimator. The main advantages of a linear approximation are easiness of application and feasibility of studying the filter statistical properties independently of the data characteristics. Furthermore, a linear transformation to the original series does not destroy the relationship among the seasonally adjusted variables. The symmetric linear filter then obtained is analysed here in terms of its theoretical properties of fitting and smoothing as well as applying it to a large sample of real time series, representative of different degrees of variability. The results are evaluated in terms of empirical fitting and smoothing measures and compared with those of other widely applied non parametric estimators such as loess of degree 1 and 2 (L1, L2), the Gaussian kernel (GK) and the Cubic smoothing spline (CSS), all constrained to be linear by a priori fixing their length equal to 13 terms as that of our benchmark, H13.