Notes on time serie analysis, ARIMA models and signal extraction

Present practice in applied time series work, mostly at economic policy or data producing agencies, relies heavily on using moving average filters to estimate unobserved components (or signals) in time series, such as the seasonally adjusted series, the trend, or the cycle. The purpose of the present paper is to provide an informal introduction to the time series analysis tools and concepts required by the user or analyst to understand the basic methodology behind the application of filters. The paper is aimed at economists, statisticians, and analysts in general, that do applied work in the field, but have not had an advanced course in applied time series analysis. Although the presentation is informal, we hope that careful reading of the paper will provide them with an important tool to understand and improve their work, in an autonomous manner. Emphasis is put on the model-based approach, although much of the material applies to ad-hoc filtering. The basic structure consists of modelling the series as a linear stochastic process, and estimating the components by means of"signal extraction", i.e., by optimal estimation ofwell-defined components.