View source for Secular variation

{{short description|Long-term non-periodic variation}}
The '''secular variation''' of a [[Time series|time series]] is its long-term, non-periodic variation (see [[Decomposition of time series|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 [[Physics:Century|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:History|history]], [[Finance:Economics|economics]], [[Operations research|operations research]], [[Biology:Biological anthropology|biological anthropology]], and [[Astronomy:Astronomy|astronomy]] (particularly [[Physics:Celestial mechanics|celestial mechanics]]) such as [[Astronomy:VSOP (planets)|VSOP (planets)]].

==Etymology==
The word ''secular'', from the Latin root ''saecularis'' ("of an age, occurring once in an age"),<ref>{{cite encyclopedia |title=secular (adj.) |encyclopedia=Etymology Online |url=https://www.etymonline.com/word/secular#etymonline_v_23091}}</ref> has two basic meanings: I. Of or pertaining to the world (from which [[Philosophy:Secularity|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.<ref>{{cite encyclopedia |title=secular, adj. and n. |encyclopedia=Oxford English Dictionary |url=http://www.oed.com/view/Entry/174620?redirectedFrom=secular}}</ref>
=={{Anchor|secular motion}}Astronomy==
In [[Astronomy:Astronomy|astronomy]], secular variations are distinguished from periodic phenomena. In particular, astronomical [[Astronomy:Ephemeris|ephemerides]] use ''secular'' to label the longest duration or non-oscillatory [[Physics:Perturbation theory|perturbation]]s 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. [[Astronomy:Solar System|Solar System]] ephemerides are essential for the navigation of [[Engineering:Spacecraft|spacecraft]] and for all kinds of space observations of the planets, their [[Astronomy:Natural satellite|natural satellite]]s, [[Astronomy:Star|star]]s and galaxies.
 
Most of the known perturbations to motion in stable, regular, and well-determined [[Dynamical system|dynamical system]]s tend to be periodic at some level, but in many-body systems, [[Chaos theory|chaotic dynamics]] result in some effects which are unidirectional (for example, [[Astronomy:Planetary migration|planetary migration]]).

===Solar System===
Secular phenomena create variations in the orbits of the Moon and the planets. The [[Astronomy:Sun|solar]] [[Physics:Emission spectrum|emission spectrum]] and the [[Astronomy:Solar wind|solar wind]] follow [[Astronomy:Sun#Possible long-term cycle|secular trends]] due to  [[Astronomy:Galactic habitable zone|migration]] through the [[Astronomy:Galactic plane|galactic plane]]. Consensus has determined these to have been [[Astronomy:Sun#Motion and location|among the smallest of factors]] to influence [[Earth:Climate|climate]] and [[Biology:Extinction event|extinction]] during human evolution, dwarfed by complex [[Astronomy:Solar cycle|solar cycles]] and magnetic cycles.

====Moon====
The secular acceleration of the Moon depends on [[Physics:Tidal force|tidal force]]s. It was discovered early but it was some time before it was correctly explained.<ref>Jyri B. Kolesnik; [http://adsabs.harvard.edu/abs/2001jsrs.meet..231K ''Revision of the tidal acceleration of the Moon and the tidal deceleration of the Earth's rotation from historical optical observations of planets''], in {{isbn|2-901057-45-4}} (2001) pp. 231 - 234.</ref>

====Earth====
Depending on the time frame, 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 timeframe the so-called "precession of the equinoxes" can appear to be a secular phenomenon since the axial precession takes 25,771.5 years. Thus monitoring it over a much smaller timeframe appears to simply result in a "drift" of the position of the [[Astronomy:Equinox (celestial coordinates)|equinox]] in the plane of the ecliptic of approximately one degree per 71.6 years,<ref>{{cite book
|last = Lowrie
|first = William
|title = Fundamentals of Geophysics
|publisher = {{wipe|Cambridge University Press}}
|year = 2004
|isbn=978-0-521-46164-1
}}</ref> influencing the [[Earth:Milankovitch cycles|Milankovitch cycles]].<ref>Jurij B. Kolesnik; [http://adsabs.harvard.edu/abs/2001jsrs.meet..119K ''A new approach to interpretation of the non-precessional equinox motion''], in Journées 2000 - systèmes de référence spatio-temporels. J2000, a fundamental epoch for origins of reference systems and astronomical models, Paris, Septembre 2000, edited by N. Capitaine,  Observatoire de Paris (2001),  pp. 119 – 120. {{isbn|2-901057-45-4}}</ref>

====Planets====
Secular variation also refers to long-term trends in the orbits of all of the planets. Several attempts have from time to time been undertaken to analyze and predict such gravitational deviations for planets, observing ordinary satellite orbits. Others are referred to as post-[[Kepler's laws of planetary motion|keplerian]] effects.

''Variations Séculaires des Orbites Planétaires'' (VSOP) is a modern numerical model<ref>{{cite journal | last1 = Bretagnon | first1 = P. | year = 1982 | title = Théorie du mouvement de l'ensemble des planètes. Solution VSOP82 | bibcode = 1982A&A...114..278B | journal = Astronomy & Astrophysics | volume = 114 | pages = 278–288 }}</ref> that tries to address the problem.

==Market trends==
Market trends are classified as ''secular'', ''primary'' and ''secondary'' for long, medium and short time frames.<ref>{{cite book|last=Edwards|first=R.|last2=McGee|first2=J.|last3=Bessetti|first3=W. H. C. |title=Technical Analysis of Stock Trends|publisher= CRC Press|year= 2007|isbn=978-0-8493-3772-7 |page=17}}
</ref> Some traders identify market trends using [[Finance:Technical analysis|technical analysis]].

==Geomagnetic secular variation==
[[Physics:Geomagnetic secular variation|Geomagnetic secular variation]] refers to some changes in the [[Earth:Earth's magnetic field|Earth's magnetic field]]. The field has variations on timescales from milliseconds to millions of years &ndash; its rapid ones mostly come from currents in the [[Astronomy:Ionosphere|ionosphere]] and [[Astronomy:Magnetosphere|magnetosphere]]. The secular variations are those over periods of a year or more, reflecting changes in the [[Physics:Outer core|Earth's core]]. Phenomena associated with these include [[Physics:Geomagnetic jerk|geomagnetic jerk]], westward drift and geomagnetic reversals.<ref>{{cite book   |last1 = Merrill   |first1 = Ronald T.   |last2 = McElhinny   |first2 = Michael W.   |last3 = McFadden   |first3 = Phillip L.   |title = The Magnetic Field of the Earth: Paleomagnetism, the Core, and the Deep Mantle   |series = International Geophysics Series   |volume = 63   |publisher = [[Company:Academic Press|Academic Press]]   |year = 1996   |isbn = 9780124912458 }}</ref>

==Biological anthropology==
A secular trend, widely tapered off and in some places ended, in which case a discrete developmental shift, has been found to apply across the continents in the average age of onset of puberty ([[Biology:Menarche|menarche]]/first menstruation and beginning of breast development) of girls from the 1940s to 2010s: beginning roughly 4 months earlier per decade. This is largely believed to be caused by nutritional changes in children over time.<ref>{{Cite journal | last1 = Okasha | first1 = M | last2 = McCarron | first2 = P | last3 = McEwen | first3 = J | last4 = Smith | first4 = GD | title = Age at menarche: secular trends and association with adult anthropometric measures | journal = Annals of Human Biology | volume = 28 | issue = 1 | pages = 68–78 | year = 2001 | doi=10.1080/03014460150201896 | pmid=11201332}}</ref><ref>{{Cite journal | last1 = Wattigney | first1 = WA | last2 = Srinivasan | first2 = SR | last3 = Chen | first3 = W | last4 = Greenlund | first4 = KJ | last5 = Berenson | first5 = GS | title = Secular trend of earlier onset of menarche with increasing obesity in black and white girls: the Bogalusa Heart Study | journal = Ethnicity & Disease | volume = 9 | issue = 2 | pages = 181–189 | year = 1999 | pmid=10421080}}</ref><ref>{{Cite journal | last1 = Prentice | first1 = S | last2 = Fulford | first2 = AJ | last3 = Jarjou | first3 = LM | last4 = Goldberg | first4 = GR | last5 = Prentice | first5 = A | title = Evidence for a downward secular trend in age of menarche in a rural Gambian population | journal = Annals of Human Biology | volume = 37 | issue = 5 | pages = 717–721 | year = 2010 | doi=10.3109/03014461003727606 | pmid=20465526 | pmc=3575631}}</ref><ref>{{Citation | last1 = Biro | first1 = Frank | last2 = Galvez | first2 = MP | last3 = Greenspan | first3 = LC | last4 = Succop | first4 = PA | last5 = Vangeepuram | first5 = N | title = Pubertal assessment method and baseline characteristics in a mixed longitudinal study of girls | journal = Pediatrics | volume = 126 | issue = 3 |date=Sep 2010 | pmid=20696727 | doi=10.1542/peds.2009-3079 | pages=e583–90 | pmc=4460992}}</ref><ref>{{Cite journal | last1 = Euling | first1 = Susan | last2 = Herman-Giddens | first2 = Marcia | last3 = Lee | first3 = Peter | last4 = Selevan | first4 = Sherry | title = Examination of US Puberty-Timing Data from 1940 to 1994 for Secular Trends: Panel Findings | journal = Pediatrics | volume = 121 | issue = 3 |date=February 2008 | url = http://pediatrics.aappublications.org/content/121/Supplement_3/S172.abstract }}</ref>

==References==
{{Reflist|30em}}

{{DEFAULTSORT:Secular Variation}}
[[Category:Geomagnetism]]
[[Category:Time series]]

{{Sourceattribution|Secular variation}}