Secular variation

The secular variation of a time series is its long-term, non-periodic variation (see decomposition of time series). Whether a variation is perceived as secular or not depends on the available timescale: a variation that is secular over a timescale of centuries may be a segment of what is, over a timescale of millions of years, a periodic variation. Natural quantities often have both periodic and secular variations. Secular variation is sometimes called secular trend or secular drift when the emphasis is on a linear long-term trend. The term is used wherever time series are applicable in history, economics, operations research, biological anthropology, and astronomy (particularly celestial mechanics) such as VSOP (planets). The word secular, from the Latin root saecularis ("of an age, occurring once in an age"), has two basic meanings: I. Of or pertaining to the world (from which secularity is derived), and II. Of or belonging to an age or long period. The latter use appeared in the 18th century in the sense of "living or lasting for an age or ages". In the 19th century terms like secular acceleration and secular variation appeared in astronomy, and similar language was used in economics by 1895. In astronomy, secular variations are distinguished from periodic phenomena. In particular, astronomical ephemerides use secular to label the longest duration or non-oscillatory perturbations in the motion of planets, contrasted with periodic perturbations which exhibit repetition over the course of a given time frame. In this context it is referred to as secular motion. Solar System ephemerides are essential for the navigation of spacecraft and for all kinds of space observations of the planets, their natural satellites, stars and galaxies. Most of the known perturbations to motion in stable, regular, and well-determined dynamical systems tend to be periodic at some level, but in many-body systems, chaotic dynamics result in some effects which are unidirectional (for example, planetary migration).