All moving averages smooth the input data, and they all suffer from one shortcoming - lagging behind. The greater the smoothing, the greater the lag. Such is life. However, some MA have unique characteristics. For example, a weighted moving average is similar in its delay Bessel filter. That is, with a large range of cycle they have a similar lag. This minimizes the distortion of filtered output data. Lag moving average is calculated as the "center of gravity" (cg) of its function of weighing. Since the weight function of the traditional triangular weighted moving average, then the estimated gap is about 1 / 3 the length.
Simple moving averages are more interesting to use the cycles as they can be used to remove the dominant cyclical component. The reaction of the moving average Sin (X) / X, which is the Fourier transform of a rectangular weighting function. X is p times with respect to frequency filtering cycle length, which represents a moving average. Imagine a long moving average, which fully corresponds to the length of one cycle. In the construction of the moving average the same number of points above and below the center. The result is a zero mean, the loop in this window will be completely removed by averaging. We can make the length of the moving average equal to the length of the dominant cycle in every day. This leads to the fact that the filter output dominant cycle is ignored. If we repeat this every day and correlate data on the output, together, we obtain an adaptive moving average, which completely ignores the dominant cycle. This moving average is converted into an instantaneous trendline because we have adopted the model market can be located only in the two states' cyclic phase "and" Phase trend. " Since the cyclical components ignored, then the remainder is the instantaneous trendline. The ability to create an instantaneous trend line is an important result of our technical analysis.
If we use a Kalman filter with zero lag, the line will cross the filter Instantaneous Trendline every half cycle, when the market is in a "cyclic phase." If the Kalman filter will not cross trendliniyu, as indicated above, this would mean that the market has entered a state of "Phases of the trend." "Phase trend" is completed when the Kalman filter with zero lag again crossing instant trendliniyu.
After analyzing the swings Kalman filter with zero lag from peak to peak, we can predict the swings of the dominant cycle. If you swing from peak to peak Kalman filter is more than double the average price range of the bar, then a cyclic amplitude is quite enough to trade on short-term cycle. If the swing is less than twice the average height of the bar, the amplitude is small. In this case it is better to take no action.
Trading strategies and tactics.
Trading strategy. Figure 1 shows a screen MESA2000 to the theoretical cycle of 24 bars. On display are four main segments.
1. In one window we see the price bars with a Kalman filter and instantaneous trend line. It also forecast a 10 bars forward. Color bars determined by the phase of the market.
2. Forex indicator of harmonic oscillations. It consists of a sine of the measured phase advance of the sinus, transferred forward by 45 degrees.
3. Phase meter (0 to 360 degrees).
4. The dominant series of spectral lines.
picture 1
Because our series is conditional, in the lower window the spectral line is centered exactly a straight line corresponding to the length of the cycle in 24 bars. Accordingly, the phase of the cycle completely changed from 0 to 360 at the end of the cycle. These two windows are not interesting from a theoretical point of view, they only confirm the correctness of the data cycle.
Forex indicator of harmonic oscillations. The dark line represents the sine of the measured phase. Its motion is fully consistent with the movement of prices. Red Line - advanced sinus. With her help, we can determine entry and exit points on the peaks and bases.
At the top box price movement in the theoretical cycle of 24 bars, with a swing + / -5 centered on the line 40. Bars "cyclical phase" is painted in bright blue. Instant trendliniya is a straight line, drawn through 40, as in our theoretical example, the market is not a trend.
A few observations. Since we are in a "cyclical phase" indicator of harmonic oscillations gives the best signals. The intersection of an adaptive moving average half the dominant cycle with instant trendliniey gives false signals to the "cyclical phase." However, the fact that it indicates the amplitude of the cycle, is sufficient to conclude a successful transaction in the "cyclic phase."
The combination of cyclical indicators.
Trading strategy. In this section we look at the realities of trading in the September futures SP in 1998 (Figure 2). As the graph shows, futures trading in the "phase trend" from March to mid-April, mid-April to mid-May, the market was in a "cyclical phase." In mid-May, he returned to the "phase trend". In June there was a small gap, when the market has a cycle, but he quickly returned to the trending state. How do we define it? In March and early April, the dominant cycle length of the constantly changing (transient data) and the spectrum was out of focus. At the same time in the window phase, we constantly see that the graph is near to 180 degrees. Even though the schedule of prices only in that window, we can say that the market is in an uptrend.
picture 2
On-screen movement of the price bars, painted in blue to indicate "phase trend". Filter Klmana is in this phase of the instantaneous trendliniey. In "Phase trend" we are holding a long position in March to mid April. In mid-April of harmonic oscillations indicator generates a signal to open short positions. However, we do not use these signals because the amplitude of the cycle in the last half of the dominant period of the cycle (which is determined by the deviation from the moving average trend line) is small. Thus, when the market phase, we refrain from taking any action.
The next signal indicator forex harmonic vibrations generated for four bars before the end of April. When this signal, we go long, because the cyclical swing in the last half of the cycle was very significant. Similarly, we are working with other phase changes, based on signals indicator. In May, when the next change in the phase we are opening positions, since the amplitude is not sufficient to perform again for good deals. Once again, the best solution in this situation not to take action.
When the end of May the market reverts to the "trend phase" it is tempting to open a short position based on signals and Kalman filter trendlinii. Let's imagine that we have opened a short position. In the seventh month, the bar is big cyclical swing upward. While automatic analysis MESA2000 points to "cyclical phase of the" best hold a short position based on signals forex indicator of harmonic oscillations. Although the spectrum is not focused, the indicator should be considered. By mid-month indicator gives an excellent signal to go long in the "cyclic phase."
For the six bars before the end of June forex indicator generates a new signal to the shorts. However, the cyclical turning point is not clear. At the same time begins the "trend phase." In this situation it is better to turn to open Long and follow the trend further. In July, the phase is about 180 degrees, indicating that the upward trend. By the end of the month phase reaches 360 degrees - a measure of turning down.
So, on a real example, we have shown how to use the cycle theory in practice. I think that our little article is useful to you in the future. Successful bidding!