Variation Index shows if a trend or a flat movement is prevailing in the time series or random behaviour.
Nowadays, the most popular representatives of the fractal time functions are the financial time series. The fractal structure of these series is well-known and aсcording to Mandelbrot is a “theoretical reformulation of a down-to-earth bit of market folklore-namely, that movements of a stock or currency all look alike when a market chart is enlarged or reduced so that it 5ts the same time and price scale” [1].
Usually, to determine the fractal dimension the Hurst’s exponent is calculated [2]. However, for the reliable calculation of this exponent a huge amount of data is necesary (~ 10^3) and that is too much comparing to the duration of the trends of trading.
The authors [1] interpose the fractal characteristics – the variation index (m) that is closely related to the common fractal dimension. In distinct from the Hurst’s exponent, the amount of information that is necessary for index determination is less by a factor of 2. It leads to use it as a local characteristics for determination of the dynamics of the price series. If m < 0.5, it can be interpretated as a trend and m > 0.5 – as a flat.
The suggested indicator calculates the variation index on a previous interval which is 2^n long. The “n” parameter is specified by the user.
The common rules of the indicator application are the following:
- If the value of the indicator is lower than 0.5, it means the trend state of the market.
- The extremely low value is often precedes the end (correction) of the current trend.
- If the value of the indicator is higher than 0.5, it means the flat state of the market.
- The extremely high value is often precedes the beginning of the considerable trends.
- If the value of the indicator is close to 0.5, it means an undefined state of the market.
This indicator was first implemented in MQL4 and published in CodeBase at mql4.com 06.10.2008.
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