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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.

The computerization and digital signal processing development let improve classical indicators essentially due to application of modern methods of information processing to prices. Indicators began to smooth better and to delay less. However Holy Grail has failed. First, the prices are non stationary, i.e. the characteristics of filters are varied during the time. Second, as different from technical problems, the kind of a signal and noise distributions for the price are unknown, i.e. nobody know what to filter actually. Third, being filtered by means of Fourier and similar methods prices change the previous values to the addition of the new data: we receive ideal trends under a history data but we can only trade them from right hand to left hand.

Fourier transformation is based on representation of initial series by the infinite sum of sinusoids with a various phase, amplitude and frequency. Recently wavelet transformations was widely adopted in various areas of data processing in which initial series are represented as the sum of some locally defined functions named wavelets. They are constructed by shifting and vertical and horizontal scaling of certain the prototype function. Wavelet transformation, in essence, is fractal that allows the effective using it in the technical analysis. First, it allows to carry out the multiscale analysis of prices, objectively identify trends on various scales by duration and amplitude, separate traders to various groups: scalpers, day traders, swing traders, position traders and long-term investors. The multiscale analysis can be interpreted as the analysis on various time frames. Second, it allows determine noise as the insufficient for reception of the profit amplitude and frequency movement of the prices that effectively allows filter the price series simply subtracting the lowest scale wavelets from it. Third, the additional filtration of white noise without delay is possible. Fourth, long-term trends are defined objectively. Fifth, wavelets do not contain optimized parameters in construct to standard indicators. Sixth, the used wavelets type is adapted to deal with the time ordered data and does not distorted on the last price values. Seventh, the used wavelet transformation is very effective computationally that allows use it in real time for the large massives of tick data. Eighth, it is effective to use wavelets as input data for neural networks and other methods of forecasting and recognition.

We use Redundant Haar wavelet transformation that represents an initial price series by the sum of the band pass filters named wavelets, and the residual low-frequency filter:

Price = + Residual,

Where N – - number of examined scales. It is necessary to say that the number of the used data values (i.e. the lookback period),on which wavelets compute is equal , therefore the greatest possible scale . 512 previous price values are more than enough for any practical problems. Wavelet_i i are similar to oscillators with consistently growing lookback periods while Residual term is similar to moving average. It is possible to read about Redundant Haar wavelets at http://www.multiresolution.comin more details.

The white noise filtration is made as follows. A signal or noise is defined on every scale. If noise is identified then the appropriate wavelet has zero value. If the signal is identified then the appropriate wavelet remains without change. Then we make inverse wavelet transformation and we receive the filtered signal.

Trend is determined as a significant movement on the considered scale, i.e. the signal / noise ratio for trend identification should be more than the given threshold of sensitivity. As noise is Gaussian by supposition, it is possible to apply statistical " Sigma rule " by setting a threshold in a range of 2 to 3.

The Application is realized as the dynamic library dll. The interaction with the library is carried out by means of two functions: