The secular variation of a time series is its long-term non-periodic variation. Whether something is perceived as a secular variation or not depends on the available timescale: a secular variation over a time scale of centuries may be part of a periodic variation over a time scale of millions of years. 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 secular variation is used wherever time series are applicable in history, economics, operations research, biological anthropology, astronomy such as VSOP etc.
Etymology
The word secular, from the Latin rootsaecularis, has two basic meanings: I. Of or pertaining to the world, 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.
Astronomy
In astronomy, secular variations are contrasted with periodic phenomena. In particular, astronomical ephemerides use secular to label the longest-lasting or non-oscillatory perturbations in the motion of planets, as opposed to periodic perturbations which exhibit repetition over the course of a time frame of interest. 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 one-way.
Depending on what time frames are considered, perturbations can appear secular even if they are actually periodic. An example of this is the precession of the Earth's axis considered over the time frame of a few hundred or thousand years. When viewed in this time frame the so-called "precession of the equinoxes" can appear to mimic a secular phenomenon since the axial precession takes 25,771.5 years and monitoring it over a much smaller timeframe appears to simply result in a "drift" of the position of the equinox in the plane of the ecliptic of approximately one degree every 71.6 years, influencing the Milankovitch cycles.
The planets
Secular variation also refers to long-term trends in the orbits of the planets Mercury to Neptune. Several attempts have from time to time been undertaken to analyze and predict such gravitational deviations from ordinary satellite orbits. Others are often referred to as post keplerian effects. Variations Séculaires des Orbites Planétaires is a modern numerical model that tries to address the problem.
Market trends
are classified as secular, primary and secondary for long, medium and short time frames. Some traders identify market trends using technical analysis.
A secular trend has been observed in the age of onset of puberty of girls around the world beginning roughly 4 months earlier each decade. This is largely believed to be caused by nutritional changes in children over time.
