ABSTRACT
A new method for filtering and forecasting univariate time series is proposed, which is based on a particular type of a causal filter with functional, time-varying coefficients. The main novelty of the proposed method is the nature of the filtering coefficients, which are data-dependent and local in character. The filtering and forecasting procedures can incorporate two different delay parameters, one applied to the functional coefficients and the other to the data used in the filter; a data-dependent methodology is also presented for selecting these delays and the order of the filter. Various simpler cases of the general method are presented and the potential of the method is illustrated using simulated and real-world time series.
