Seasonal adjustment of some economic indicators (Q1286326)

The purpose of this article is to identify the underlying long-term trend in the evolution of some indicator over time and to find its periodic (seasonal) variations. The notion of evolutionary trend is quite imprecise. In the statistical literature trend usually signifies a general direction of change, long-term evolution. Trend is represented by some curve that corresponds to a particular function of time. This trend curve captures the main regularities of motion over time and to a certain extent (although not completely) is free from random factors affecting the particular indicator. The trend curve describes some ``averaged'' evolution as observed over a sufficiently long period. Sometimes the trend is represented as a deterministic component of the observed variable (while the variation of this component is not necessarily related with time). Deviation from the trend is regarded as a random variable. We will try to explain the generating mechanism of the observed time series and identify its various components. This is often the basis for statistical forecasting, which in most cases reduces to extrapolation of the detected trend. This approach to forecasting relies on the following assumptions: (1) the evolution of a phenomenon can be adequately characterized by its trend representing the evolutionary path; (2) the general conditions that determine the past trend will remain essentially unchanged in the future. Extrapolation thus provides a description of some general future development of the observed system in cases when there is reason to expect a certain inertial behavior and the hypotheses about future development may be largely based on an analysis of the past.