RAOS and RAOSQ quadrature indicators - more information for your trading strategy

 This publication is a continuation of a previously published article Digital Signal Processing for Trading Strategy.

An earlier article noted:

  • The quotation signal on average consists of a set of rhythms with different periods and scales (amplitudes), superimposed on each other, and the rhythms are not constant - they appear and disappear in the course of their evolution over time,
  • if it is possible to separate these rhythms from each other and by their correlation between them, you can make trading decisions, that is to form trading signals,
  • to divide (stratify) a complex quote signal into simpler components (rhythms with different periods and different
  • The following table lists the types of digital filters, such as digital low-pass filters (LPFs), that can be used for this purpose,)
  • the task of the LPF is to smooth (average) all oscillations with periods smaller than the specified averaging period and leave (pass) all oscillations with periods larger than the specified averaging period. At the same time it is possible to flexibly change the ratio of passed (not smoothed) rhythms among themselves (i.e., to change the desired response of the smoothed curve at the LPF (indicator) output to the change in the quotation signal in time).

Note that the function of the change in the ratio of the passing (not smoothed) rhythms among themselves is called frequency response digital filter (digital indicator). By forming the required frequency response you can get an indicator with the necessary reaction to the change of the quotation signal.

Trade strategy using RAOS and RAOSQ indicators

Construction of a trading strategy and formation of trading signals using quadrature digital indicators RAOS and RAOSQ is based precisely on division (stratification) of a complex quotation signal into simpler components (rhythms with different periods and different amplitude scales). RAOS and RAOSQ indicators together reflect the dynamics of these rhythms in sufficient detail.

The term "digital" means that indicators are digital filters. And the term "quadrature" means that indicators are applied in a pair, and their mutual dynamic change in time in relation to each other occurs in quadrature, for example, mutual dynamic change in time of mathematical functions SIN and COS in relation to each other also occurs in quadrature.

At present, the design of RAOS and RAOSQ indicator algorithms requires special software for the calculation (synthesis) of digital filters. An extensive literature is currently available on various calculation (synthesis) techniques. The resulting RAOS and RAOSQ indicator algorithms are executed sequentially in real time, that is, they are not redrawn.

Results of RAOS and RAOSQ indicators

Figure 1 shows the moving average RAMA with a smoothing period of 20 (red line) (for more information about the indicator, see the article "Improved modification of the moving average - indicator RAMA vs SMA"), also shows the RAOS(20) indicator (solid and dashed black lines), matched in its frequency response (in the design) with the moving average RAMA(20). The frequency response was chosen so that the RAOS reflects the rate of change of the RAMA.

From Figure 1 shows that if the line indicator RAOS (20) above the line indicator RAMA (20), the line indicator RAMA (20) moves "up", if the line indicator RAOS (20) below the line indicator RAMA (20), the line indicator RAMA (20) moves "down".

The RAOS indicator is displayed in the quotation field in absolute units relative to the RAMA moving average line, rather than in a footnote "below" relative to the zero line. Also, the RAOS indicator interacts with the quote signal as a reference line.

The RAOS indicator characterizes the value of the rate (first derivative) of change of the RAMA moving average line, with which it is matched by its frequency response.

Fig. 1. Moving average RAMA(20) with a smoothing period of 20 (red line) and the RAOS(20) indicator (solid and dashed black lines), consistent in its frequency response with the moving average RAMA(20).
Fig. 1. Moving average RAMA(20) with a smoothing period of 20 (red line) and the RAOS(20) indicator (solid and dashed black lines), consistent in its frequency response with the moving average RAMA(20).

Figure 2 shows a moving average RAMA (20) with a smoothing period of 20 (red line), it also shows the RAOSQ (20) indicator (solid and dashed red lines). The RAOSQ indicator (20) is a quadrature with respect to the RAOS indicator (20). In this case, while RAOS indicator reflects the speed (first derivative) of change of the moving average line of RAMA, the RAOSQ quadrature indicator reflects the acceleration (second derivative) of change of the moving average line of RAMA. That is, the frequency response (when designing) of the RAOSQ indicator has been chosen so that the RAOSQ indicator reflects the acceleration of the changing of the RAMA moving average

Fig. 2. Moving average RAMA(20) with a smoothing period of 20 (red line) and the RAOSQ(20) indicator (solid and dashed red lines), consistent in its frequency response with the moving average RAMA(20).
Fig. 2. Moving average RAMA(20) with a smoothing period of 20 (red line) and the RAOSQ(20) indicator (solid and dashed red lines), consistent in its frequency response with the moving average RAMA(20).

Figure 2 shows that the quadrature indicator RAOSQ is located relative to the moving average line RAMA in accordance with change the rate of increase (or deceleration) of change of the RAMA moving average line.

It can also be seen that if the movement "down" moving average line RAMA slows down, the indicator RAOSQ goes to "above" moving average line RAMA, and vice versa, if the movement "up" moving average line RAMA slows down, the indicator RAOSQ goes to "below" moving average line RAMA.

The RAOSQ indicator characterizes the magnitude of acceleration (or deceleration) (i.e., the second derivative) of the change in the RAMA moving average line, with which it is matched by its frequency response.

Figure 3 combines Figures 1 and 2. From it we can see that the quadrature indicators RAOS and RAOSQ together describe the dynamics of the moving average RAMA quite completely.

It is possible to determine "reversals" of the moving average RAMA line or "resumptions" of the continuation of the directional movement of the moving average RAMA line.

RAOSQ indicator is more "reactive" than the RAOS indicator, that is, it reacts with "anticipation" to dynamic changes in the dynamics of the moving average line RAMA, with which it is consistent in its frequency response, that is, it gives additional information for more accurate identification of "reversals" and "continuation.

Indicators RAOS и RAOSQ can be considered as oscillatorsif we consider them as changing (oscillating) relative to the line, consistent with the moving average RAMA.

Fig. 3. The result of combining Figures 1 and 2.
Fig. 3. The result of combining Figures 1 and 2.
Fig. 4. Moving average RAMA with a smoothing period of 40 (black line), also shown quadrature indicators RAOS (40) (solid and dashed black lines), RAOSQ (40) (solid and dashed red lines), matched in their frequency response with a moving average RAMA (40).
Fig. 4. Moving average RAMA with a smoothing period of 40 (black line), also shown quadrature indicators RAOS (40) (solid and dashed black lines), RAOSQ (40) (solid and dashed red lines), matched in their frequency response with a moving average RAMA (40).

Two-period and three-period systems of technical analysis

Figure 5 combines Figures 3 and 4 and shows a two-period (20 and 40) technical analysis system with two moving averages RAMA (20), RAMA (40) and two pairs of digital quadrature indicators RAOS (20), RAOSQ (20), RAOS (40), RAOSQ (40). Based on the joint dynamics of the indicator lines it is possible to form trading signals.

Fig. 5. The result of combining Figures 3 and 4. Two-period (20 and 40) technical analysis system.
Fig. 5. The result of combining Figures 3 and 4. Two-period (20 and 40) technical analysis system.

Further, Figures 6 and 7 show the resulting two-period technical analysis system (Figure 5) for other sections of the quote signal.

Fig. 6. Two-period (periods 20 and 40) technical analysis system, the second quotation section.
Fig. 6. Two-period (periods 20 and 40) technical analysis system, the second quotation section.
Fig. 7. Two-period (periods 20 and 40) technical analysis system, the third quotation section.
Fig. 7. Two-period (periods 20 and 40) technical analysis system, the third quotation section.
Fig. 8. Moving average RAMA with a smoothing period of 9, quadrature indicators RAOS(9) and RAOSQ(9) (blue - lines of the RAOS(9) indicator), coordinated in their frequency response with the moving average RAMA(9).
Fig. 8. Moving average RAMA with a smoothing period of 9, quadrature indicators RAOS(9) and RAOSQ(9) (blue - lines of the RAOS(9) indicator), coordinated in their frequency response with the moving average RAMA(9).

Figure 9 combines Figures 3 and 8.

Figure 9 shows a two-period (periods 9 and 20) technical analysis system using two moving averages RAMA (9), RAMA (20) and two pairs of digital quadrature indicators RAOS (9), RAOSQ (9), RAOS (20), RAOSQ (20) coordinated with them.

Fig. 9. The result of combining Figures 3 and 8. A two-period (periods 9 and 20) system of technical analysis.
Fig. 9. The result of combining Figures 3 and 8. A two-period (periods 9 and 20) system of technical analysis.

Figure 10 combines Figures 4 and 9.

Figure 10 shows a three-period (periods 9, 20 and 40) system of technical analysis with three moving averages RAMA (9), RAMA (20), RAMA (40) and three pairs of digital quadrature indicators RAOS (9), RAOSQ (9), RAOS (20), RAOSQ (20), RAOS (40) and RAOSQ (40) coordinated with them.

Fig. 10. The result of combining Figures 4 and 9. Three-period (periods 9, 20 and 40) system of technical analysis.
Fig. 10. The result of combining Figures 4 and 9. Three-period (periods 9, 20 and 40) system of technical analysis.

Figures 11. 12 shows a three-period technical analysis system with periods 9, 20, 40 for other parts of the quotation signal.

Fig. 11. Three-period (periods 9, 20 and 40) technical analysis system, the second quotation section.
Fig. 11. Three-period (periods 9, 20 and 40) technical analysis system, the second quotation section.
Fig. 12. Three-period (periods 9, 20 and 40) technical analysis system, the third quotes section.
Fig. 12. Three-period (periods 9, 20 and 40) technical analysis system, the third quotes section.

The considered multi-period system of technical analysis is built from a given number of moving averages RAMA with given smoothing periods. Each moving average RAMA, adjusted to its own smoothing period, is accompanied by a pair of quadrature indicators RAOS and RAOSQ, coordinated with it by their frequency response.

The trio of coordinated indicators (RAMA, RAOS, RAOSQ, (moving average, its speed and acceleration)) is considered a basic component in building a multi-period technical analysis system.

Jointly quadrature indicators RAOS and RAOSQ quite fully reflect the dynamics of change of the line of moving average RAMA. RAOS indicator reflects the speed of change (first derivative) of the line over time of the RAMA moving average, RAOSQ indicator reflects the acceleration of change (second derivative) of the line over time of the RAMA moving average.

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