Time Series Components

An important objective in time series analysis is the decomposition of a series into a set of unobservable (latent) components that can be associated with different types of temporal variations. This chapter introduces the definitions and assumptions made on these unobservable components that are: (1) a long-term tendency or secular trend, (2) cyclical movements superimposed upon the long-term trend. These cycles appear to reach their peaks during periods of economic prosperity and their troughs during periods of depressions, their rise and fall constituting the business cycle, (3) seasonal variations that represent the composite effect of climatic and institutional events which repeat more or less regularly each year, and (4) the irregular component. When the series result from the daily accumulation of activities, they can also be affected by other variations associated with the composition of the calendar. The two most important are trading day variations, due to the fact that the activity in some days of the week is more important than others, and moving holidays the date of which change in consecutive months from year to year, e.g., Easter.