Overview
Trends in an asset's price series have been used successfully to create trade strategies that follow the trend. A trend is a general upward or downward movement in the price of the asset.
The fact that one can identify trends in a chart does not necessarily mean that following the trend will earn more money than a market index fund would do. In fact, the efficient market Hypothesis postulates that such visible price trends convey no useful information.
From a statistical perspective, stochastic trends are expected to develop within random walks, and do not convey any information.
However, there is a behavioural component to market trends which may justify some expectation of
Modeling Price Trends Quantitatively
The standard quantitative model of asset prices is based on the theory of Brownian Motion and Ito Processes.
{% dX(t,B(t)) = u(t) dt + \sigma(t) dB(t) %}
Within this framework, a trend is usually interpreted to mean some value for {% u(t) %}
When there is a known long term return, (some average annual return over a long time frame), the Ito model can be extended by using a Brownian Bridge
Trend Following
A common way to implement a trend following strategy is through the use of Moving Averages.