Enhancements of moving trend based filters aimed at time series prediction

Abstract

One of the techniques recommended for calculating the nonparametric trend (nonstationary, low-frequency time series component) is the moving trend based smoothing 10, 3, 4 typically based on linear Least Square (LS) approximates of the series in a moving window. Such algorithm splits input time series into three sections, starting, central, final ones. The procedures used in each section may be viewed as Moving Trend based Filters (MTF). In the paper MTFs properties in frequency domain are considered, from seasonal time series decomposition, smoothing and prediction efficiency perspectives. A number of MTFs enhancements is proposed, involving different approximating polynomials and final section signal corrections. In particular, a compression of the final section MTF output signal is proposed to reduce the filter delay, and then reconstruction of the missing signal by a special multiple LS approximation. It improves significantly the final section signal shape evaluation, which are essential for further prediction purposes.