In general, a time series may be viewed as an aggregate of various parts: for example trend plus seasonal plus noise component. Since users are often interested in particular components only (for example the trend or the seasonally adjusted time series), filters are used to ‘remove ’ the undesirable ones. In practice, signal extraction is based on finite samples X1,..., XT and, very often,
... [Show full abstract] current estimates of the interesting components (t = T) import: a socalled ‘concurrent ’ or ‘real-time ’ estimate of the trend or of its turning-points has a strong prospective content, since the future evolution of the time series is likely to be conditioned by this component. Whereas forecasting tools generally emphasize the one-step ahead perspective (at least this is true for model-based approaches such as ARIMA), real-time signal extraction may be used to infer future mid-term dynamics. The following package proposes real-time signal extraction algorithms based on Wildi [1]. In the following, references to the book are marked by an asterisk in the text. The main difference between traditional model-based approaches (such as ARIMA) and the direct filter approach (dfa) is that the latter optimization criteria emphasize specifically two important estimation problems: the estimation of the current level (of the interesting signal) and the early detection of turning-points (of a trend component). Since both criteria are incongruent, different algorithms are available which match user preferences (level or turningpoints) and time series characteristics (trending or non-trending series). Also, important filter characteristics at frequency zero can be imposed or relaxed such as the local level restriction 1 or the instantaneous level restriction 2. This document provides a ‘step-by-step ’ introduction to the dfa real-time signal extraction package and demonstrates its functionalities based on a leading indicator application (the so-called KOF-Economic Barometer). More generally, the text emphasizes topics that are specific to real-time signal extraction. 1 A(0) = 1, where A(ω) is the amplitude function. 2 A(0) = 1 and the time delay of the filter vanishes in frequency zero. 1 2