What do most of indicators of Technical Analysis represent?
«What The Thinker thinks,
The Prover proves...»
Orr law
Most of indicators of technical analysis are linear digital filters (DF). One part of filters values the velocity of price change and another part values averaged price that is used also for measuring velocity.
The rest of indicators are nonlinear DF working similarly. Moreover, there are indicators valuating not first derivative (velocity of price change) but second derivative (velocity of velocity change or in other words acceleration).
Other complicated methods like neural networks for measuring velocity also can be counted as linear or nonlinear DF, destined for valuation of velocity or sign of velocity.
Most of Trading Systems are built on valuation of velocity and consist from small number of enter/exit types (that have hundreds of different names).
Example
Such famous indicators like Momentum, Trix and all types of moving averages
(MA) and prices value first derivative. For example, systems applying two moving averages from
example for Genetic Optimizer – it is signal on valuation of velocity sign.
Momentum is difference between two prices, today and K bars back – velocity of moving average K length.
Indicator MACD – zone filter, difference between two moving averages or in other words aligned valuation of velocity. Signaling line in
MACD – it is additional alignment of velocity. Calculation of signaling line from basic line
MACD is valuation of second derivative - acceleration or powers impacting price.
Well known oscillators RSI and Stochastic – valuation of velocity and crossover of their levels inside. It is signal on valuation of sign of second derivative.
Velocity is preemptive indicator for price. If price goes up (velocity is positive), but acceleration (second derivative) is negative, it means that velocity decreases and there is possibility of zero velocity and price reversal. Therefore acceleration can be assumed as preemptive indicator.
What do most trading systems use?
Almost all trade systems, possibly excepting systems based on trend identification, are based on valuation of velocity of price change or valuation of price acceleration.
For example, disruptions of several levels (it seems there are no average or derivative) – it is difference between current price and some average (or maximal) for period – ie., it is also valuation of derivative.
A bit of History
Charles Dow in his famous theory determined that prices changes as directional trends until direction will change to opposite. But classical economy at that time declared that prices changes according to Brownian motion (L. Bachelier). Truth rather is somewhere in the middle. There are both directional trends and random Brownian motion in price behavior.
In the second half of XX century it was discovered that a lot of natural phenomena (clouds, trees, length of coastline etc.) and price changes can be described by fractal structures (B.Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman, San Francisco,1982.).
What is fractal?
Fractals are forms or structures, which look equally on different scales. For price series it is well known from times of Charles Dow (end of XIX century). Looking at diagram it is difficult to say of what scale are data – day or week. Price behaviors on different time frames are similar outwardly, although there are several differences also. Only actual fractals shouldn’t be mistaken for those “fractals” described by big specialist on “crocodiles” and “butterflies” Bill Williams.
Formally as fractal can be termed set with Hausdorff dimension bigger than topological dimension. Practically it arises in fractional dimension of the set. For example, it is length of coastline or price diagram. If we measure their length on one scale (time frame), than on more detailed scale (time frame) the length would be bigger than if it would be usual line.
Fractal dimension – numerical characteristic of trend
Popular measure of fractal dimension is Hirst parameter H (Edgar E. Peters, Fractal Market Analysis. Applying Chaos Theory to Investment and Economics, John Wiley & Sons, 2003.). Problem of this method applied on price series is that for correct calculation of Hirst parameter it is necessary to have thousands of bars, what is too much in comparison to duration of traded trends. Random walk has Hirst parameter of 0,5 value. Other values show difference between time series and random walk. Hirst parameter shows what dominates in time series – trend or contra – trend component, or series behave randomly.
Can it be used in practice?
It can be used in practice, if use variation index offered by M.M. Dubovikov and N.V. Starchenko (Ì.Ì. Dubovikov, N.V. Starchenko, Variation index and its application to analysis of fractal structures. scientific almanac "Gordon", Moscow 2005). Variation index analogical to Hirst parameter allows using data by two lines less than in calculation of Hirts parameter itself. In other words we can calculate Hirst parameter by using several tens of bars instead of several thousands.
Implementation in practice
Modification idea of variation index lies in a base of algorithm realized in module Dll TS Trendiness. For correct calculation of the index it is enough with several tens of bars (recommended 30-40), what is quite comparable to duration of trends. Given indicator can be applied on any time frames and different trade platforms (TradeStation,
eSignal, MultiCharts).
General rules for applying the indicator are as follows:
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Indicator value less than 0,5 means contra – trend market situation.
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Extremely low value often precedes beginning of significant trends.
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Indicator value more than 0,5 means trend market situation.
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Extremely high value often precedes end of significant trends.
Indicator value around the 0,5 means uncertain market situation, what corresponds to Brownian
motion.
Given function can be used in other systems and indicators, for example, to create adaptive filters or systems, what will be automatically adapting to current market situation.
You can see examples how function works on different
markets >>>
Indicators Examples >>>
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