Overview: Wavelet Transform

The complete indicator-based technical analysis without magic and profanation.

Babylonian does not decline to speculative operations.
He honours verdicts of a case, consigns them his life, hope and panic fear.
However he does not consider an investigation neither the confusing
laws of a case nor the movement of rotating spheres which open it to him.
Borches

There are thousand indicators which to an essence are, in fact, the same as minimal variations. They are often different only by theirs names. New "magic" indicators are created for two reasons: 1) poor knowledge of the underlying subject which can lead to the second invention; 2) the intentional profanation. The majority of indicator users accept them like the absolute and do not think of their physical meanings and properties. Moreover, popular books give the indicators such properties which they don’t have. Looking inside the indicators the curious can discover that it is nothing but elementary digital filters. Its theory and methods exists more than hundred years and they are used in engineering everywhere. For example, a simple moving average is a low frequencies filter with the finite impulse characteristic, an exponential moving average is a low frequencies filter with the infinite impulse characteristic, MACD is a band pass filter. Stochastic and CCI are the same as price normalized by different ways etc. the filtration can be prodused either in the state space like moving average or in frequency domain where one operates by Fourier transformed initial data etc. All filters have attributes such as smoothing degree of an input signal and delay degree of the smoothed signal in relation to an input signal. Classical indicators were created before computer age when the main requirement to the indicator was easy computing it “by hands", and smoothing and delay quality were estimated later. The classical indicators under these characteristics are varied from bad up to worse. For example, 200-day's moving average that popular among technical analytics delays neither much nor a little for a half of a window of averaging, or for 100 days, at very poor quality of smoothing.

From the point of view of the filtration theory oscillators are band pass filters or differentiating filters. Their physical analogue is a velocity of prices. Take a look to the popular technical analysis tool "divergence" meaning that the price and an oscillator have different directions. It is the analog of necessary extremum condition of a smooth function. It is good to emphasize that sufficient extremum condition does not follow from anywhere, i.e. extremum of a smooth function should be followed by divergence, but it does not follow from divergence that extremum is reached there. Use of this approach of the technical analysis, as well as many others, is based on a logic mistake of substitution of a sufficient condition by necessary one. The turn of the prices follows by divergence is similar to the fact that eating of cucumbers before death follows that the cucumbers are the reason of death.