Random walk hypothesis

The random walk theory and the theory of symmetric random walk describes the time course of market prices ( particularly in equity and other securities prices) mathematically. It is also called Irrflugstatistik. The term random walk or Symmetric random walk is an immediate consequence of market efficiency theory.

Description

According to the random walk theory, the price signal can be decomposed according to the teachings of the signal theory in the trend and the Threshold:

This means the signal, so the course, the drift component, the periodic component and an independent noise component.

The drift component and the periodic component are combined with the trend, which can be described through moving averages. It is due to the instantaneous manifestation of all information is equal to the information input function, ie the real information content of the course. This is a random function, since there is no way to predict the future course.

The threshold here is equivalent with U ( t), the independent noise component. It is assumed in the random walk theory as informationslos. It is postulated here is a Brownian motion.

Criticism of the random walk theory

The signal analysis using time series analysis of the indices such as DAX or Dow Jones shows that the threshold is not white noise.

Time Series Analysis of the Threshold

The threshold is not normally distributed, but has so-called "fat - tails", ie there is a leptokurtosis. In addition, he has no quasi- constant amplitude: There are large amplitude fluctuations of the threshold, form the so-called volatility clusters. The threshold is a function of the noise with heteroscedasticity.

A good approximation of the threshold, however, is given by the GARCH models. However, this applies only to the past, the forecast skills are not very good.

Compared with general approaches

ARMA models by Box and Jenkins demonstrate Otto Loistl on best-fit approximation approaches for most DAX values ​​that do not correspond to the random walk theory, since these approaches have nonvanishing p, q.

Other approaches

As an alternative to the random walk theory of price movements can be approximated with Markov chains. ( So the approach of a function with complete forgetfulness).