# Trend (statistics)

A trend is a systematic increase or systematic decrease in a time series that also exhibits fluctuations or periodic fluctuations . A trend in a short time series can be fundamental or a temporary tendency .

## General

There are trends wherever a reference value can change and a development direction arises from this change. In particular, natural sciences , technology and economics deal with trends in the form of time series . Trends are intended to provide the analyst with information about developments in a reference value within a certain period and / or location in order to be able to gain knowledge about certain processes. The starting point is initially a trend-free observation within a period / location. Then the mean value and variance of a time series remain constant over the entire observation period, one speaks of stationarity. Only non-stationary time series are subject to a trend development and therefore do not have a fixed mean. A distinction is made between stationary time series with a deterministic trend and stationary time series with purely random stochastic trends.

The easiest way to determine a trend in a series of measurements is to display it graphically over time or the measurement location. The more precisely the line is horizontal (or the point cloud is round if there is a large scatter ), the lower the trend. A linear regression is usually the next step in the analysis.

With deterministic trends, a distinction is made between the following trend models :

• Linear trend :
${\ displaystyle \ y = a + b \ cdot t}$
This denotes the reference value of the trend, the axis intercept of the trend and the increase in the trend function in the time series .${\ displaystyle y}$${\ displaystyle a}$${\ displaystyle b}$${\ displaystyle t}$
• Parabolic trend :
The general function of a parabola should be used for :${\ displaystyle y}$
${\ displaystyle \ y = a + b \ cdot t + c \ cdot t ^ {2}}$
• Exponential trend :
${\ displaystyle \ y = a \ cdot b ^ {t}}$.
• Logistic trend :
${\ displaystyle \ y = {\ frac {S} {1 + e ^ {ab \ cdot t}}}}$
${\ displaystyle S}$is the degree of saturation of the reference value of a trend (see logistic function ).

Trends can be exposed to discontinuities, whereby unpredictable events can cause a structural break, an interruption or a change of direction of the trend ( trend reversal ). Then the regression parameters do not remain constant over the entire time series.

## physics

In physics , the trend is a linear regression coefficient in the temporal development of the diagonally arranged recurrence points away from the identical recurrence diagonal and thus a measure of the stationarity of the time series. Disturbed measurement series can be corrected ( trend-adjusted ) by trend analyzes or improved by more precise modeling of the physical environment, by expanding the measurement series to include further parameters or by removing systematic sources of error .

A trend often caused by changes in external circumstances - such as in physics by rise in temperature , or GPS - surveying by solar activity and the ionosphere .

## Secular Trends in Astronomy

In astronomy , a long-term trend is called secular (from the Latin saeculum for century, age ). Such effects are e.g. B.

These changes are mainly caused by deviations from the spherically symmetrical gravitational field of the sun (due to the existence of the planets, see three-body problem ) and the planets (due to their flattening ). The general theory of relativity and the light pressure of the sun cause minor effects .

## Economics

With regard to the duration of the effect and the scope, a distinction can be made between fashion trends , consumer trends, socio-cultural trends, megatrends and metatrends . Fashion trends last a maximum of 5 years, satisfy the need for fashion variety and have regional short-term effects. Consumer trends take place between 5 and 8 years and affect consumer behavior . Sociocultural trends operate between 5 and 10 years of age and relate to significant national changes in attitudes , needs and behaviors that influence lifestyle . Megatrends span periods of 25 years and more and have profound, global long-term effects. The term megatrend was coined in 1982 by trend researcher John Naisbitt . Finally, metatrends are far-reaching developments with a lasting character such as the Roman Empire , Christianity or colonization .

While business trends affect the entire economy , market trends are limited to a specific market. Here the market development can be determined with the help of the market analysis of market data . Trends can change the market behavior of market participants , such as in the case of commoditization .

## economy

Product lifecycle trends

There are trends in the economy in particular . All prices , stock prices , yields or indices ( price index , stock index ) and the level of prices and interest rates make time series and are constantly changing, so that financial analysts for these time series trend analysis can be used. The product life cycle is characterized by characteristic trend phases. After market maturity , a progressive growth trend begins with increasing sales and marginal profit , followed by a saturation phase without a growth rate and finally a degeneration phase begins, in which losses can even occur. Also, economic indicators , economic indicators or corporate data from a single company can be combined into trends and analyzed.

In the economy, one speaks of an unbroken trend when the direction of movement of the oscillators is convergent to the price trend. The following principle applies: " Chart technology defines the trend, market technology assesses its quality".

Trends are reported frequently in the mass media and especially in the specialist media . The economic subjects use identified trends in their decisions and in their planning in order to assess future developments and to be able to base decisions on them. Trends then often function as indicators of future developments, although there is uncertainty as to whether a trend - always related to the past - will continue in the future. For this purpose, is the instrument of trend extrapolation that help in a time series analysis future trend developments with a certain probability can be predicted.

If trends are subject to seasonal effects (such as the winter with unemployment ), these effects must be eliminated in the context of seasonal adjustment for a better comparison in order to be able to represent the trend without seasonal influences.

## Demarcation from tendency

Labeling a current significant change as a " trend " expresses the expectation that it will prove to be a short-term fluctuation, not a change in the longer-term trend.

## literature

• Manfred Schneider : Celestial Mechanics , Volume 4, Theory of Satellite Movement, Orbit Determination . Spektrum-Verlag Heidelberg 1999, ISBN 3-8274-0484-3
• Karl Stumpff , H.-H. Vogt: The Fischer Lexicon Astronomy . Revised 8th edition, Fischer Taschenbuch Verlag, Frankfurt / Main 1972

## Individual evidence

1. Sönke Albers (Ed.), Methodik der empirischen Forschung , 2006, p. 369
2. Gabler Wirtschaftslexikon, keyword: Trend , Volume 5, 1984, Col. 1646
3. Norbert Marwan, Investigation of Climate Variability in Northwest Argentina , 1999, p. 37
4. Jörn Fontius, Megatrends and their implications for logistics , 2014, p. 16 f.
5. Walter Simon, Gabals great methods suitcase future: Fundamentals and Trends , 2011, p 191
6. Uwe Bergold, Bernt Mayer: Market and Opinion: Belonging to the winners with behavioral finance and technical analysis. FinanzBook Verlag, Munich 2005, ISBN 978-3-89879-105-2 , pp. 100 .
7. Ulrich Becker, Lexikon Terminhandel , 1994, p. 97